Relationalism

Women are not irrational; they are relational.

Archive for the month “August, 2012”

Goals

If you like what you read, please tell your friends.

If you don’t like what your read, tell me — but tell me why.

There are many reasons for posting this incomplete work on the Internet rather than keeping it with me:

First, I would like to benefit from the wisdom of the many, so I will welcome any suggestion for improvements.

Second, I believe that many readers will benefit from reading these posts even in their unfinished form.

Third, I need all the help you can give me…

August 15, 2012

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In philosophy

Original publication available at SSRN:

http://ssrn.com/abstract=2132969

From Rationalism to Relationalism:

As in the Transformation of a Line into a Sphere

Carmine Gorga

Somist Institute

2001

Abstract

Rationalism possesses enormous practical usefulness, yet it needs revision because it carries with it the seeds of being incorrect anthropologically, epistemologically, philosophically, geometrically, and theologically. Hence, it tends to fall prey to relativism. And relativism easily slides into vulgar absolutism, which states that “everything is relative to man.”

To climb out of this abyss, we must create new modes of thought and expression, which can be examined under the rubric of Relationalism.

Relationalism is an attempt to cure the shortcomings of Rationalism. In so doing, Relationalism makes a fuller use of the positive values of Rationalism. Relationalism maintains that linear thinking must be expanded into spherical thinking.

A New Beginning

We are witnessing the last throbs of Rationalism. The phenomenon is affecting not only philosophy but every other mental discipline, from literature to physics, from economics to art criticism.1 The existence of this vast web of relationships becomes incontrovertible if it is realized that whatever ails each discipline necessarily stems from the innate shortcomings of Rationalism.

This is the negative side of the coin. The positive one is that, if we cure what ails Rationalism, we will gradually be able to cure what at present ails all other mental disciplines. That is indeed the function of a dominant philosophical system. Whether the linkages are explicitly stated and recognized or not, the philosophy of the age provides the underlying structure for all mental disciplines of the age.

Intellectually, Rationalism has for the most part fallen prey to relativism.2 Coming down from incredible heights of certitude propounded over the last few centuries precisely with the assistance of Rationalism, again as at the end of the Renaissance, we are no longer certain of almost anything. Thus, we are back at the starting point of Rationalism. We must start again.

This time we can start not with a frontal thrust into the depths of agnosticism, but with a much easier task, the attempt to mend the structure of Rationalism. We will start from a reasoned analysis of the roots of Rationalism.

This paper is divided into four parts. Part I attempts to analyze some of the shortcomings of Rationalism. Part II outlines the major characteristics of Relationalism. Part III attempts to describe the methodology of Relationalism. Part IV gives an indication of some of the possible applications of this new methodology. In a few concluding comments, the paper makes some suggestions for speeding up the tempi of application of Relationalism.

Part I — Shortcomings of Rationalism 

Rationalism as Prey of Relativism

Rationalism has clearly fallen prey to relativism. If the existence of this phenomenon is granted, how did it happen? As we will see, the reason is because the structure of Rationalism carries with it the seeds of being incorrect anthropologically, epistemologically, philosophically, geometrically, and theologically. These weaknesses become manifest if for a moment we go back to the beginning of Rationalism and try to analyze its roots. If we do that, we realize that Rationalism was born as an incomplete response to what might be called naïve realism.

Rationalism as an Incomplete Response to Naive Realism

Rationalism is an incomplete response to a train of thought which started with the Greeks and was powerfully reinforced by the explicit acquiescence to it by St. Thomas Aquinas. This train of thought can be characterized as naive realism. Naive realism, in its attempt to extricate itself from the alluring vagaries of the mind, which have traditionally assumed a variety of forms from Platonic idealism to the rich array of nominalism and conceptualism, maintains that what exists is.3 Existence, then, becomes the basis of reality and the beginning of analysis.

This is a small error, which is formulated in a variety of expressions. But, as both Aristotle and St. Thomas Aquinas knew full well, a small error at the beginning becomes a great error at the end. The error is fundamental. Rationalism tried to heal it, and did not succeed. The significance of this error becomes most evident if we examine the failed effort of Rationalism to mend it.

With no epistemology supplanting the uncertainties into which the sophisticated agnosticism of the Renaissance had plunged us and logic evaporating into the syllogistic formalism of the Scholastics, all culminating in the abuse of casuistry, Descartes thought we could escape into certainty by shifting the ground of realism from the outside world of things to the internal world of the mind. Paraphrasing, so to bring the issues in greater evidence, he stated: I exist as a thinking human being, therefore I am.

With the benefit of hindsight, we now realize that this minimalism of Rationalism did not — and could not — let us escape the limitations of naive realism. It is now becoming increasingly clear that it only made matters worse. Here is a brief analysis of an otherwise well known territory.

Weaknesses of Naive Realism

The weaknesses of naive realism are many. They become most evident if they are analyzed as being part of the very structure of Rationalism. Naive realism is incorrect logically, epistemologically, philosophically, and theologically. These errors are put in higher relief when the linear structure of Rationalism is observed from an anthropological viewpoint. Anthropologically, when men and women are recognized only as a thinking entity, they are reduced to a minimalist abstraction, namely a thinking machine devoid of feelings and devoid of material needs. Logically, just as the principle of identity is impotent unless it is placed in relation to the principle of non-contradiction, so this thinking machine is reduced to impotence because it cannot get out of itself: there is no way for this A to become not-A; there is no way for this entity to deny itself. Epistemologically, this entity is given no objective tools that it might trust and use in its understanding and discovery of the world outside itself: from the given premise, outside itself, there is only itself. (These are points made most firmly, even though incompletely, by Benedetto Croce who taught us that men and women know only dialectically: we know white only in opposition to black; hence, men and women need something outside themselves to acquire certainty4). Philosophically, naive realism is incorrect at two levels: at the level of hidden premises, it does not distinguish being from existing (this is the small error at the foundation of the thinking of Aristotle, St. Thomas Aquinas, and Descartes) and, impossibly, it attributes to existing the qualities of being. Naïve realism assumes that existing is being; that existing is real. The error has self-evident theological implications that are better examined in a moment in a more appropriate context.

At first sight, this assessment seems highly implausible. It seems improbable that Aristotle, St. Thomas Aquinas, and Descartes should have committed such an elementary error as not to distinguish between existing and being. And, of course, they did not consciously commit such an error. The error was thrust upon them by an apparent lack of alternatives. If one does not start the analysis from what exists, where can one start?

Yet, there is an alternative. The alternative comes forward by standing on the shoulders of these giants. The alternative comes forward by going to the very depth of their line of reasoning. (At the end of this line of reasoning we shall find, not a line — clearly, an intellectual construction that has no correspondence in reality — but a sphere. Hence, Rationalism leaves something to e desired even from the point of view of geometry, the mental discipline on which it relied most to develop its methodology.5) The alternative is to consider not only being and existing, but also the relationships between these two entities. The alternative, in other words, springs forward if we transform Rationalism into Relationalism.

Part II — Bare Bones of Relationalism 

Being as the Absolute

Philosophically, among the whole set of attributes of being, the most important are these. What is — alone —dialectically includes the category of existing. (The small error at the beginning of naive realism, an error that is bodily carried over into Rationalism, consists in not realizing that the converse of this proposition is not valid: existing does not include being; existing can only be a part of being; therefore, existing is not being). What is — alone — exists in time and out of time; namely, it forever was, it is, and it will forever be. What is — alone — by reconciling within itself all opposites is the epitome of perfection: it is true, it is beautiful, it is good, and just. Indeed, it is absolutely true, absolutely beautiful, and absolutely good and just. It is the Absolute.

This is the foundation of Relationalism.

Two observations are in order here. It takes a moment’s notice to realize that human beings — making an effort of the will and with a sense of humility — can get outside of themselves and reach this conclusion on the strengths of Rationalism. It is because the “I” thinks, and relies on the conquests of a multitude of other thinkers, that the I can make such pronouncements about the Absolute. And that is not enough yet. The second observation is essential to the completion of this point. The I can accept such pronouncements only on the basis of the understanding of not-being. Thus the essential contribution of agnosticism to the thought process. It is only when the I can choose between being and not-being that the I can make an informed selection — and with the help of Pascal’s wager can opt for the existence of being.

These are some of the reasons why, to one’s great surprise since the error was ratified by a thinker no less theologically sophisticated than St. Thomas Aquinas, naive realism is incorrect theologically. It is not what exists that is. It is the Absolute that is. It is the Absolute, or theologically speaking, God that is.6

Indeed, philosophically speaking, only the Absolute is; or again theologically speaking, only God is.7

Partial Vindication and Major Fault Line of Relativism

If only the Absolute is, everything else must be relative. There is no alternative. Hence relativism is partially vindicated — and the great uncertainties of our age are validated. But this is neither the beginning nor the end of the discourse.

True, everything is relative. Yet, this is an empty proposition. One must still decide, relative to what?

The great error of relativism does not stem from a philosophically robust agnosticism or even solipsism, but from the abyss of vulgar absolutism. As a logical consequence of the Cartesian thinking machine’s general unwillingness to get out of itself, the answer most commonly given to the question, to what is everything relative, is this: Everything is relative to man. It is in this proposition that the self-destructive slippery slope of vulgar absolutism finds its origin. These are not words but deeds. The fanatical absolutism of the right, in its various forms from Dickensian to Nazi horrors, have given rise to the hallucinatory absolutism of the left, in its various forms from Robesperrean to Communist horrors. The center held until it gave in to a farcical absolutism that degenerated into the consumerism of the Me Generation. This is the consumerism that isolates people and reduces them to money-making-and-spending machines. This is the consumerism that celebrates death.

But consumerism by itself is a non-issue. There is also the consumerism that puts people in contact with each other, the consumerism in which things become extensions of one’s personality. This is the consumerism that celebrates life.

The Slow Climb out of the Abyss

Clearly, we must climb out of the abyss of vulgar absolutism and the climb cannot be but slow, yet not necessarily painful. We must heed Einstein’s warning that “The unleashed power of the atom has changed everything save our modes of thinking and thus we drift toward unparalleled catastrophe.”8 We must create a whole set of new modes of thinking. These modes of thinking might be examined under the rubric of Relationalism.

Relationalism as the Road to Recovery

Relationalism is not a denial of the values of Rationalism, which are many and well known, but an expansion of those values; thus Relationalism becomes an automatic potential escape from the limitations of Rationalism.

The fundamental question of relativism must be given a direct and satisfactory answer. If everything is relative, then there must be an absolute to which everything is related. Since the search for this absolute within the reality of man has led to the abyss of vulgar absolutism, it stands to reason that we must search for this absolute outside the reality of man.

Many have traditionally found the absolute outside man; they have capitalized this Absolute, and given it any of the names for God: Yahweh, Our Father, Allah, Brahma, Great Spirit. This conclusion is inescapable, and as such it is realistically accepted, but it is recognized only as a partial and preliminary conclusion reached within the train of thought pursued here.

From within the context of philosophy, we are impelled to ask: Have we inextricably fallen into the arms of religion?

From Traditional Analysis to a Third Road

So far, ours is very traditional and, from many points of view, inescapable analysis. Analysis however also suggests that, in order to climb out of the abyss of vulgar absolutism and avoid the danger of any repetition of falling into it ever (?) again, we must conclude not simply that the Absolute is. We must be firmer than that. We must conclude that only the Absolute is; everything else simply exists.

If we agree that only the Absolute is and that everything else exists, then it is easy to recognize that everything else, namely, the reality of men, women, and the cosmos exists only in relation to the Absolute — in relation to God.

It is at this juncture in our analysis, when we realize that we have fallen deeper into the bosom of religion, just as we resign to our destiny of being limited men and women, it is then that a great transformation occurs. Our consciousness impels us to remain faithful to our starting point in the analysis. Our concern was neither with being, nor with existing. Our concern was with reality. What is real? This is the cry that has been uttered for ever and, most insistently, for the last eight hundred years.

In answer to this cry, our consciousness, abruptly, makes us realize that the reality is relational — hence all philosophy must be relational. This is indeed a third road. It starts its analysis neither from being nor from existing, but from both being and existing — and from the interrelationships between being and existing. (Thus our consciousness is placed again at the center of the universe, as it was during the Renaissance. Indeed, does not contemporary cosmology suggest that the cosmos is infinite? If that is again a maintainable proposition, then the conclusion is evident: every particle is at the center of the cosmos. Man is again at the center of the universe.)

All Philosophy Is Relational

While the first proposition of Relationalism, the basic, preliminary proposition that “everything exists in relation to the Absolute,” can be taken as correct from the point of view of philosophy and, naturally, theology, it must be recognized that such a proposition is not and cannot be the end-all and cure-all for the ills afflicting our contemporary culture. In the end, many a nasty act has been justified on the basis of a blind belief in God. And the “fundamentalists” in any religion are not the only guilty party. Fundamentalists in many a secular train of thought have been equally, if not more, guilty of equally horrid effects. Clearly, much more needs to be done if we want to climb the long road out of the abyss of vulgar absolutism.

The fundamental proposition of Relationalism that one must explore from every angle and in every field of observation is that all that exists, exists in relations. Reality is relational. Being is. And since we are limited, we can see, touch, and understand being only in its existing. Thus existing also is — it has its reality as a part of being (thus the initial “error” of Aristotle, St. Thomas Aquinas, and Descartes becomes smaller and smaller the more closely it is observed). Yet, these statements are still very elementary. We graduate to another level of thinking when we analyze not only being and existing, but also the relationships between being and existing.

This conclusion is not a blind repetition of a statement that is almost commonplace today. That everything exists in relations is not an automatic conclusion of a facile relativism.9 It is a conclusion that Relationalism reaches, obtaining it not only from strict philosophical reasoning but also from the methodology of Relational Logic and the epistemology of Complementary Knowledge.

Let us briefly look into these two supporting pillars of Relationalism. Before proceeding, however, it might also be useful to point out that there is in Relationalism a third pillar which, often, sustains solid reasoning; this is the pillar of mathematics. For various reasons, the examination of this pillar is eschewed here. I have presented its geometry elsewhere.10 Indeed our program of research is more simply exposed geometrically than literally. It can thus firmly be said that we must transform the line (the linear mode of analysis) of Rationalism into a sphere. At every step, our analysis must be extended in all directions; hence, it becomes much more complete than the analysis of Rationalism.

Part III – The Methodology of Relationalism

Bare Bones of Relational Logic

Relational Logic is a new system of logic that I discovered and used while working on Concordian economics. For a long time in my research, I was faced with two models of the economic system.  They were both mathematically consistent. Hence mathematics became an impotent tool for choosing between the two models. I searched for other objective methodological tools and eventually I found them scattered in a variety of sources. All that I did was to put ancient principles of logic together into a new system, which I eventually called Relational Logic, and obtained the following results.

Unquestionably I accepted the validity of the Principle of Identity. Notwithstanding Hegelian reservations, I also accepted the validity of the Principle of Non-Contradiction. Then I observed that — whether consciously or unconsciously — logicians have constantly been in search of a third principle as a linkage to support the other two. Classical logicians formulated the Principle of Excluded Middle; Descartes developed the Principle of Indifference; Hegel conceived the Principle of Process; Eastern thinkers use the Principle of Contrast. Unable to profitably use any of these principles because of their excessive vagueness and lack of specificity, I adopted the Principle of Equivalence as the third principle of a complete system of logic. This is a principle with an impeccable pedigree. I found it used by thinkers much more ancient than the Greeks, and found the beginning of its codification in the thought of Boethius. The usefulness of this principle lies in its very detailed set of internal rules, which with the passage of time have become more and more exacting: the three entities that are subjected to analysis — and there must be three entities, otherwise there is no relation of equivalence — must each be reflexive, symmetric, and transitive. To establish a relation of equivalence, then, nine sets of proofs must be met.

To remain on the bare bones of the issues, we have to be aware that the principle of identity is an identity relation, that an identity relation is an equivalence relation looking inward, and that the principle of identity explains A by putting it in relation to not-A.

The conclusion of this analysis is that the rules of logic are all rules of relations. Hence Relational Logic. These rules come alive as they are used in conjunction with the epistemology of Complementary Knowledge.

Bare Bones of Complementary Knowledge

While our mind is finite, facts are infinite — and infinitely changing; therefore, facts cannot be understood directly. As soon as one makes peace with this basic proposition, one is also liberated from the alluring appeal of a whole set of theories of knowledge that range from inductivism to positivism. But one is not left free to fall into the arms of various forms of abstract deductivism either.

If one goes in search of a golden mean, one is likely to find it on the basis of the fundamental proposition that facts are understood through the mediation of tools of cognition, tools of epistemology that have been developed over the millennia through an ever larger level of abstraction. The most important such tools can be listed as names, ideas, concepts, theories, systems of thought, and lately computer models, so that we can instantaneously analyze the effects of a change in any assumption on the entire system. Eventually, through computer models we also ought to more easily implement the suggestions of each theory and system of thought, because some of their most evident pitfalls should be avoided through computer simulation, rather than crude experimentation.

Complementary Knowledge makes use of these tools, clearly distinguishing one from the other, and by using them all in a systematic and coordinated fashion.

All too briefly, based on work that I have done in economics, Complementary Knowledge suggests that in each mental discipline we verify the content of each one of the tools of cognition and accept it only after subjecting it to the scrutiny of the rules of Relational Logic. As a result, in its search for truth Complementary Knowledge proceeds most cautiously but most assuredly and resolves many a conflict by the use of the double conjunction “and also.”  For instance, it recognizes that color is made of white and also black, namely the complementarity of white and black in the theory of color; or the complementarity of good and evil in the theory of morality.

This method of proceeding leads to mature realism.

Part IV – Some Applications

Relational Modes of Thought and Expression in Political Science

The germ of Relationalism sprouted in the early sixties in the field of political science. This was the height of the Cold War. The world was polarized between two extremes. One group assumed that the political reality is grounded in the individual and the other that the reality is grounded in society. Neither faction was ready to consider that the individual does not exist without a society, namely that the individual alone is an abstraction, and that a much greater abstraction is society without individual human beings.

I assumed that the reality is composed of men and women living in society. Hence, I meshed individualism and collectivism into a new theory that I called Somism, namely the system of thought and practices of the social man, the civilized person.

The value of Somism, of course, lies in the fact that it allows us to make three separate investigations: one about the individual person, the other about society, and the third about the relationships between the two entities.

Relational Modes of Thought and Expression in Economics

In 1965, I changed one equation in Keynes’ model of the economic system and found myself plunged in a new intellectual world. To be credible to myself and to others, I developed the methodology of Relationalism and was able to gradually build a new structure, a structure that is composed of three levels —namely, economic theory, policy, and practice; a structure that, for its extraordinary degree of internal and external cohesion, I like to call Concordian economics.

Economic Theory. While Keynes’ model of the economic system yields the equality of Saving to Investment, whereby savers and investors are presumed to be the central economic actors, the new model yields the equality of Investment to Consumption. This relationship began to make sense to me and to other economists as soon as I used expressions well known to Classical economists and enlarged the equality into an equivalence. At that point, I was faced with the equivalence of Production to Distribution to Consumption. In the new system, the central actors are producers, consumers, and owners of wealth.

Classical economists conceived of those three phenomena as three separate and sequential events. Relationalism allowed me to see them as three instantaneous and intimately interconnected events. Everything happens at once. At a primordial stage, I produce, I apportion the ownership rights on what I produce to myself, and I consume my production in the very act of gathering the apple from the tree and eating it. The same chain reaction occurs in a modern industrial society, only time intervenes to separate those events from each other. It takes time for me to consume the steel that I produce. Analytically, of course, I need to keep those three major economic events separate from each other. While production conveys the understanding of a human effort to produce anything; distribution becomes the division of ownership rights among producers; and consumption expresses the separation of the real economy from the financial economy, whereby I can monetize the wealth I produce and have a more rational flow of its consumption by transforming the steel I produce first into money and then into bread.

I do not want to and I cannot belabor the point. But this is the essence of the economic process. This is the essence of economic theory. I only need to specify two points. Through a series of economic models, these literal expressions lead themselves to full translation into the language of mathematics and econometrics. Also, the primary importance of Concordian economics ultimately lies in the fact that it yields a new understanding of the possibilities of economic policy.11

Economic Policy. My central thrust in economic policy consists in an attempt to integrate the thought of Henry George, Louis D. Brandeis, and Louis O. Kelso into one coherent unit. Upon consideration, it becomes evident that these three thinkers were separately concerned with the three factors of production taken into account by Classical economists: land, capital, and labor. I have only proceeded to split the field of capital into physical and financial capital. The analysis of these three writers becomes clearer if their fields of study are presented not as a series of sequential events but as an organic set of policies and interrelationships that are concerned at once with the production, distribution, and consumption of wealth. Thus we can eventually have an enrichment of the field of economic policy, from the poverty of monetary and fiscal policy to which it has been reduced, to (a) a policy on land and natural resources, (b) an industrial policy that is concerned with the way we organize our modern societies, (c) a monetary policy that is built from the bottom up, and (d) an expansion of the current jobs-and-wage policy into an ownership policy.

It is in the writing of the present paper, however, that the key relationship inherent in my work in the area of economic policy has become manifest. The relationship between land, capital, and labor has a precise correspondence in three major ages of political economy: land capitalism, an age that prevailed up to the Renaissance; financial capitalism, an age that has been prevalent ever since the Renaissance; and human capitalism, an age still to come. In the future, the benefits of both land and financial capitalism have to be extended to one hundred percent of the people who are engaged in the production process. Land and financial capitalism have so far been five-percent-capitalism.

With human capitalism, people will gradually learn to develop a proper set of relationships with other human beings and with the world of goods and services. This is going to be the core of the transformation of Relationalism from an array of various theories to the practice of daily living. The transition might occur through the transmission belt of economic rights and responsibilities.

Economic practice. In the middle nineties, my work led me to explore the relationships that exist between politics, economics, and the law. Again, the equivalence of production to distribution to consumption guided me to discover that the theoretical work in economic justice had been arrested at the level reached by the Scholastic Doctors. They had analyzed all the nuances of the theory of Distributive Justice (principles used in the distribution of income and wealth) and Commutative Justice (principles used in the exchange or sale of wealth). What remains to be worked out are the principles of justice to be applied in the production of wealth — or Participative Justice.12 In this field I have proposed that the principles be a set of economic rights and responsibilities that apply to land, capital, and labor. The application of these principles, I like to predict, will result in human capitalism.

If people who produce wealth are entitled to a fair distribution of the ownership of the wealth they produce, a whole set of interrelated phenomena will occur. By integrating all costs of production into the production process, there will not longer be any disassociation, as at present, between needs and wants. People will be ready to cover the costs of satisfying needs and will keep wants under control. Stability will be added to the economic system and a relationship of stewardship will be developed with the world of nature.

Relational Modes of Thought and Expression in Physics

Einstein established the relationship between matter and energy and called it equivalence. Such is the separation of the mental disciplines from each other in the modern rational world that neither physicists nor logicians — nor, indeed, theologians — seem to have noticed that for an equivalence to be a proper logical relationship one needs to have three terms in a certain relationship to each other. What is the third term to which both matter and energy are related?

I was at forty thousand feet in the air over the Atlantic in 1997 when, coming back from Europe and reading Fritjof Capra’s The Tao of Physics (1984), I asked that question and the answer became incontrovertible to me. I established this equivalence relation:

Matter = Energy = Spirit.

This equivalence did not spur me to learn much more than I ever did about matter and energy. The very little I know in the fields of matter and energy keeps me very humble in front of those two constructions of our minds. But that equivalence empowered me to stick my nose under the tent of theologians. This dabbling has led to a couple of relationships that I find interesting in the field of the spirit.

Relational Modes of Thought and Expression in the Field of the Spirit

One of the first things I ever discovered in my study of theology is that all great religions are based on an equivalence relation:Brahma, Shiva, and Vishnu; Yahweh, the Messiah, and the Spirit; God, Jesus, and the Holy Spirit; Allah, Vali Asr, and the Spirit of Allah. Thus all theology is fully relational.

This discovery has led me to ask whether theologians will ever be able to establish this equivalence relation:

Yahweh = God (or Brahma or the Great Spirit) = Allah.

If they concentrate on what unites the human race, all the while reveling on the respective differences among these concepts, theologians will some day indeed be able to establish the above relationship of equivalence. If they make this great leap forward, they will also discover the immense possibilities of establishing the following equivalence relation:

Messiah = Jesus (the son of God, or nature) = Vali Asr.

If they offer this relationship for the deepest consideration of all human beings, they might discover that, no matter the essential defining formal differences of those three major concepts the last equivalence relation establishes an undeniable structural and formal identity between the three major monotheist religions (while opening up relationships with all polytheistic religions). Is Vali Asr, the revered Hidden Imam, whose appearance someday, Shiite Muslims believe, will establish the perfect Islamic political community any different from the Jewish Messiah? And are the Jewish Messiah and Vali Asr that different from the true Jesus? Quite apart from the historical Jesus, has the spiritual Jesus truly come yet in each one of his disciples?

Recommendations for Implementation

It is the deepest possible analysis of the full array of interrelationships posited above that might eventually lead to an appreciation of what unites us all as human beings. Truthful answers to those implicit or explicit questions might even yield peace on earth. Certainly, we will not perish in a sea of uniformity; rather, nourished by the same earth, we will all blossom in the infinity of individuality.

If such is the potential of the program of research outlined above, how can we speed up the tempi of much further analysis and eventual implementation of the discoveries of Relationalism?

In the past I have issued a slew of recommendations concerning economic theory, policy, and practice.13 The reality of these days impinges upon me to extend my recommendations to areas in which I am not an expert. They are more or less related to the imagination, the mind, and the heart.

Recommendations concerning the imagination. At one level, in our daily routines there is the struggle of the imagination vs. the mind. Somehow our Western civilization has been compelled to separate the two functions of a human being. Is it incorrigible optimism that makes me hope that we are on the verge of eliminating this dangerous dichotomy? Will Benoit Mandelbrot and his disciples be able to create new Arabesque figures with the power of fractals? If we are capable of doing that, by uniting mathematics and art we will eliminate a great source of friction created by those who believe that the work of the mind is separate from the work of the imagination.

Recommendations concerning the mind. If I were a University President, how would I immediately make some use of the inner workings of Relationalism? I think I would soon establish a Relational Department, entrust it to philosophers, and ask them to conduct seminars in which they would give the floor to members of each one of the other departments to present their thought to members of all other departments and keep notations about the relations that participants see emerging from the discussions. No paper would any longer be published by any member of the university without going through this type of true peer review process. Certainly, I would no longer tolerate a Divinity Department in which there were no theologians who strongly profess at least the three major monotheistic faiths. The only conditions for their remaining in the employ of the university would be that they spend all their lunch hours together.

Recommendations concerning the heart. If I were the Secretary of the United Nations, or even the head of any state, I would be struck by a simple observation. We have plenty of departments of defense and war, but no department of peace. How to fill this gap? I am firmly convinced that such a department should be established, be well endowed, and focus on the training of groups of young men and women who in the name of their respective religions would go, at least three by three, house by house attempting to pacify one home at a time in all the trouble spots of the world.

 

Notes

  1. For me, the epitome of the end of Rationalism in literature/art is Magritte’s statement/painting: ce nes pas une pipe. In physics, see Heinz Pagels, Cosmic Code: Quantum Physics as the Language of Nature (1982). In economics, follow the fault line of the discussion about rationality as the foundation of economic of decisions. In art criticism, see, e.g., Allan Bloom, Love and Friendship (1993).
  2. For the practical effects of relativism, see esp. Pope John Paul II, Veritatis Splendor (1993).
  3. The conflation of many meanings that makes naïve realism possible is perhaps best represented by this sentence by St. Thomas Aquinas, a sentence that he formulated to validate Aristotle’s teaching on the subject: “But ‘essence’ is used inasmuch as it designates that through which and in which a being has the act of existing” (On Being and Essence, chap. I, In Selected Writings of St. Thomas Aquinas, Robert P. Goodwin trans., NY: Macmillan, 1965). There and elsewhere, being is consistently defined as “that which is,” in any of its great variety of manifestations.
  4. The work to be consulted in this relation is his Logic as the Science of Pure Concept (1909).
  5. The essential work to be consulted in this relation is Descartes’ Discourse on the Method (1637).
  6. The analysis in the text seems to be confirmed by this statement by St. Thomas Aquinas: “It is evident, therefore, that an intelligence is a form and an act of existing and that it has its act of existing, from the First Being which is existence only; and this is the First Cause, God” (Loc. Cit., chap. IV).
  7. When speaking theologically, St. Thomas Aquinas of course knew that only God is. Not only did he often cite Exodus 3:13, 14, he also stated: “…God alone is Being by virtue of His own Essence…” (Summa Theologica, I, 104, 1).
  8. Quoted in Otto Nathan and Heinz Norden, eds. Einstein on Peace (New York: Avnet Books, 1981 ed, p. 376). From a pamphlet published by Beyond War in 1985 entitled A New Way of Thinking.
  9. Indeed, relativism is completely separate from Relationalism. The easiest proof is this. Relativism leads to the conclusion that all meaning is relative and therefore changing; Relationalism preserves the constancy of meaning within each system of thought.
  10. 10.In reduced form, take a segment of a line; spin it about its center at ever increasing speed, and you obtain the image of a circle; pull the center of the circle away from its shadow point on the back of the circle; inflate the construction until you obtain a sphere.
  11. 11.For details, see Carmine Gorga, The Economic Process (Lanham, MD: The University Press of America, forthcoming).
  12. 12.See Carmine Gorga, “Toward the Definition of Economic Rights,” Journal of Markets and Morality 2 (1999).
  13. 13.See esp. Carmine Gorga, “The Revised Keynes’ Model,” Atlantic Economic Journal 10 (September 1982); “Four Economic Rights: Social Renewal Through Economic Justice for All,” Social Justice Review 85 (January/February 1994); and, with Stuart B. Weeks, “Fisheries Renewal: A Renewal of the Soul of Business,” The Catholic Science Review 2 (1997).

In theology

The original of this publication is available at SSRN: http://ssrn.com/abstract=1695823 or http://dx.doi.org/10.2139/ssrn.1695823

THE EQUIVALENCE OF THE THREE PERSONS

 OF

THE TRIUNE GOD

Carmine  Gorga

The Somist Institute

December 2009

Abstract

The relationships among God the Father, the Son, and the Holy Spirit are logically explained though the relation of equivalence. The three terms are reflexive, symmetric, and transitive. This relation allows us to reach a better understanding of the mystery of the Triune God. A fuller understanding is reached through the mystical union with God. This union, which still does not pierce the mystery of God, is open to all human beings; and, with the help of the equivalence among Being, Becoming, and Existence, the paper clarifies that wanting to reach it is an entirely rational act.

Brief Bio

Carmine Gorga is a former Fulbright scholar and the recipient of a Council of Europe Scholarship for his dissertation on ”The Political Thought of Louis D. Brandeis” at the University of Naples, Italy. Using age-old principles of logic and epistemology, in a book and a series of papers Dr. Gorga has transformed the linear world of economic theory into a relational discipline in which everything is related to everything else—internally as well as externally. He was assisted in this endeavor by many people, notably for 27 years by Professor Franco Modigliani, a Nobel laureate in economics at MIT. The resulting work, The Economic Process: An Instantaneous Non-Newtonian Picture, was published in 2002 and is currently being republished in an expended version. For reviews, please see http://www.carmine-gorga.us/id18.htm. During the last few years, Mr. Gorga hasconcentrated his attention on matters of methodology for the reunification of the social and the physical sciences.

 

It is with some shock and much trepidation that this writer approaches the self-appointed task of presenting a paper on such an awe-inspiring topic as the equivalence of the three persons of the Triune God. Shock derives from the discovery that both Boethius, the philosopher who formalized the properties of the equivalence relation, and Thomas Aquinas, the supreme philosopher of the Middle Ages, left their treatises on the Trinity unfinished (1) and that neither they nor any other philosopher or theologian ever since has attempted to explain the Trinity with the help of the equivalence relation—a natural match, as we shall see. St. Augustine, of course, is fully exonerated from this lapse because he wrote before the equivalence relation was formally enunciated; and later philosophers and theologians can be excused only on the basis of Bernard Lonergan’s realization that the crises of modernity find their root in a crisis of “method”; what remains surprising, nevertheless, is that neither process philosophy nor process theology make use of the principle of equivalence. But all that only proves that it takes time for the continuing and persistent work of revelation to illuminate our thick grey matter. Trepidation derives from the knowledge of this writer’s limitations and inadequacy in the field of theology. And yet, writing on this subject is the fulfillment of a life’s dream for him. The intuition of the equivalence of the three persons of the Triune God has been the hidden source of his strength in applying the equivalence relation to a variety of fields during more than forty years of research. This effort, which has yielded a new methodology and a string of publications in economic justice,(2) economic theory,(3) economic policy,(4) and in physics,(5) has perhaps prepared him in a particular way for the present task. Thus, in the end, this is an attempt to express a miniscule measure of thankfulness to the Triune God for the strength, joy, and support that the construction of the equivalence relation has given him over the years as well as a request for forgiveness for taking so long to attend to this task. The hope, of course, is that if there is any scintilla of validity in the present work, it will eventually be perfected by more able minds.

When successfully completed, this paper humbly tries to suggest, this work will relate the Trinity to everything else. This is work that needs to be done. Ever since the Enlightenment, most intellectuals, with Newton and Hume at the head of the parade, have seen only a series of paradoxes in the theology of the Triune God. Casting theology into the format of the equivalence relation should reduce the dangers of seeing paradoxes in the relationships among the three persons of the Trinity. An implicit advantage in using this tool of analysis rests in the fact that the equivalence relation is well known to logicians and mathematicians and, once it is realized that the equivalence relation envelops also the structure of the syllogism, it becomes apparent that this relation is well-known to philosophers and all literati as well.

Of course, making the description of the Triune God a logically understandable set of relationships does not make the very existence of the Triune God a matter of logical necessity. Far from it. The existence of the Triune God remains—as it should—a mystery.

I. Plan of the Work

Since everyone, as we shall see, seems to use the equivalence relation mostly unawares of its characteristics, we shall first outline the canonical requirements for this relation to be logically valid as well as the fundamental advantages of casting our thought processes into this format. Only then we will use this relation to logically explicate the description of the Triune God. That analysis will lead us to mysticism. To curb the fear of lack of rationality in our search for the Triune God, we shall extend the use of the equivalence relation to briefly cover the field of metaphysics. It will then become evident that the search for God is a very rational act indeed. Such a conclusion leads to this core message: One should never abandon rationality; yet, one should always recognize the limits of rationality as inherent in the very structure and existence of human beings.

 

II. A New Method of Analysis

 The equivalence relation, this writer has discovered through long study, forms the foundation of a new “method” and, in turn, this method of analysis forms the seed a new philosophy that, when fully explored, will eventually transform rationalism into relationalism. It will then be seen that relationalism is the full bloom of rationalism. This is a new system of thought in which everything is logically related to everything else. As pointed out above, this method has already yielded substantial new insights into economic theory, economic policy, theory of economic justice, and physics. For the present purposes it is sufficient to remain on the foundation of the new methodology.

 

III. The Equivalence Relation

The canonical requirements of the equivalence relation are that there be three terms present in the discussion and that each term be reflexive (identical to itself throughout the discourse), symmetric (exchanging each term with the other, one observes the same entity from two points of view and thus obtains a deeper understanding of both terms), and transitive (each term must transition into the other in order that all terms be intimately related to each other; more specifically, as we shall see, a third term must exist to which both terms are equivalent in order to eschew the confines of circular reasoning, in order to observe the same entity from three points of view and thus have a triple check on our reasoning, as well as to make a complete analysis of the entity under observation). At the highest level of abstraction, the equivalence relation can be alternatively represented with these symbols: A ≡ B ≡ C; or A = B = C; or A ↔ B ↔ C.

There are various reasons why it is essential to cast any serious analysis in the format of the equivalence relation. The basic function of this relation becomes apparent as one realizes that the mind tends to avoid all singularities. There is a good reason for this practice. By definition, a single number, a single point, a single observation does not lead to an objective, replicable analysis or experiment: what is the meaning of “I”, what is the meaning of “am”? This type of investigation leads only to an abyss of words. Logical analysis begins with the observation of two terms, two events: “I am”; this is something worth investigating. Yet, the observation of two events necessarily leads to circularity of reasoning. Once we are faced with only two observations, we are obliged to observe all possible relationships linking the two terms. Hence, the mind is led back to the exploration of all potential outcomes of the position of Point B on the circumference in relation to Point A at the center of the circle. This is a process that, in extreme conditions, eventually leads to the reversal of one’s position (an 1800 turn): “am I (?)”; and then to a return to one’s original position—and no certainty is acquired in the meantime. Therefore, logic asks for a third term; one might as well start with the basics: “man” or “God.” The third term points the research in the right direction: “I am man”; “I am God.” And yet, if the third term is placed in a linear relation, position, or alignment the end result might be a dispersal of the thought process into the empty infinity of an enlarged circle, such as I → am → man, or I → am → God. Linearity leads to progressio ad infinitum. In any linear construction (such as, with their different levels of abstraction, A → B → C…; or, oranges → apples → tomatoes…; or, fish → apes → humans…), there is no logical beginning and no logical end to the analysis—except an arbitrary beginning and an arbitrary end. It is the equivalence relation that restrains the analysis from collapsing into an empty infinity by insisting that each end is a beginning and each beginning is an end, and by constraining the terms into a strictly interlocked relationship as in the standard configuration: A ↔ B ↔ C.

The equivalence of the three terms—“I,” “am,” and “man”—is indeed offered here at its highest level of generality, as A ↔ B ↔ C or as a positional equivalence. It is also offered as a conjecture of the possible equivalence of Subject, Predicate, and Object. How are the three essential ligaments of linguistics held together is a question that this writer has not had the opportunity to investigate yet. Their relation of equivalence is offered as a mere conjecture on the notion that those three elements tie words into a sentence and give them meaning.

Mathematics and logic are rather abstract and forbidding. Geometry is friendlier. Thus, in order to make them visually evident, one can recast the symbols of the equivalence relation into a geometric format. Using established protocols one obtains the following diagrammatic model, which can eventually be filled with any aspect of the reality that one wants to investigate:

Figure 1. The Equivalence Relation

Figure 1 reads as follows. A is equivalent to B and to C, if and only if A, B, and C are identical to themselves throughout the conversation; if and only if one progressively interchanges A with B, B with C, and C with A and obtains an always deeper understanding of the same reality; and, finally, if and only if one can reasonably conclude to have exhausted the analysis after having looked at the object under observation not only from the point of view of A and B, but also from the point of view of C. Thus, any assumed relation of equivalence has to pass these nine tests to be proved logically valid. As a result of these mental operations, as it can be seen, the equivalence relation uncovers (rather than establishes), not a linear or sequential, but an instantaneous, continuous, and organic set of relationships among the terms.

Substantively, in the equivalence relation each term forms a concrete world of its own, a condition that sheds lights of understanding on each one of the other two. The easiest method to realize that the three terms—while representing whole worlds of their own—are inextricably related to each other is to alternatively superimpose upon each other the three rectangles of Figure 1. Two rectangles are obstructed from view, but they remain stubbornly there. Indeed, it is then that we come to the full realization that only by distinguishing the three entities from each other can we hope to understand them all. Otherwise, we reduce the construction to a singularity such as A; or lock it into circular reasoning, if we were to deny either the reality of B or the reality of C.

The equivalence relation is well known and widely used. It starts in logic and is a constitutive element of all aspects of mathematics. It stands at the very foundation of the number system, in which three fingers of my hand (3 of base 10 number system) are equivalent to a word/number/symbol—namely, three, 3, or III—and to the three apples in front of my eyes. All algebraic relations are equivalence relations. A system of equations is based on the equivalence relation. A triangle is based on the equivalence relation. The whole of trigonometry is based on the equivalence relation. The equivalence relation has the widest possible range of application outside of mathematics as well. As noted, this writer has found it to be applicable to methodology, economic theory, economic justice, and physics. And since all forms of syllogism are based on the equivalence relation, it turns out that the equivalence relation is also well known to philosophers and the literati.

From the above it inexorably follows that the equivalence relation is ready-made for the study of Trinitarian theology. Indeed, as we shall briefly see, the equivalence relation is ready-made not only for the study of Christian theology, but for the study of all three monotheistic religions. And, mutatis mutandis, it appears to be appropriate for the study of all religions.

IV. The Equivalence of the Three Persons of the Triune God

The equivalence relation is a constitutive, axiomatic element of the theological conception of the Triune God. Its fundamental terms are reflexive, symmetric, and transitive. The identification of the three persons of Christian theology—God the Father, God the Son, and the Holy Spirit—and the relationships among them can be more easily studied if they are cast into the diagrammatic model outlined above, namely

Figure 2. Relational Theology

Figure 2 reads as follows. God the Father is posited as equivalent to God the Son and both are equivalent to the Holy Spirit. The tests of validity of this assumption are, at a minimum, as follows. Is God the Father identical to himself, is he ever confused with any other term of this equivalence or any other entity outside this equivalence, all through the theological discourse? The same question has to be asked of God the Son and the Holy Spirit. This test basically involves the application of the principle of identity. If there is any contradictory evidence throughout the discourse, then the posited equivalence is not valid. The second set of tests is this: Does one see God the Father through the Holy Spirit as well as through God the Son? Alternatively, does one see the Holy Spirit through God the Father and God the Son? Equally, does one see God the Son through the Hoy Spirit and God the Father?  The third set of tests asks us to ascertain whether observing God the Father one can at the same time see the Holy Spirit and God the Son. If and only if the analysis yields positive answers to these questions then one can rest assured that the relationship among the Father, the Son, and the Holy Spirit is a relation of equivalence. The three terms, in brief, have the same value and the same weight. These answers are indeed found in any Christian text of theology.

Figure 2 establishes that while each person of the Triune God occupies its own distinctive position, the three persons are in full relationship with each other. This complexity has been explained in theological texts innumerable times. Technically, it is better observed perhaps by rotating about its geometric center at ever increasing speed, not only the entire Figure 2, but also each rectangle inside Figure 2. One then obtains the image of four circles: one, the circle of God the Father; two, the circle of Holy Spirit; three, the circle of God the Son; four, the circle of the Divinity as a whole. And what is a circle, if not a two-dimensional image of a sphere? Ultimately, one is thus presented with a construction composed of four interpenetrating concentric spheres, one for each point of view from which the world of relational theology can be observed: the point of view of the Father, the Holy Spirit, the Son, and the point of view of the Trinity.

Figure 2 can be interpreted not only to mean that God the Father is a different manifestation of the Holy Spirit and God the Son is a different manifestation of the same Divinity, but also along these lines: The world of relational theology has to be observed first from the point of view of God the Father, then from the point of view of the Holy Spirit, and then from the point of view of God the Son. The essential prerequisite is to see these three aspects of the Trinity not in a linear fashion, but in a relational mode, namely as three separate and distinct viewpoints of the same Divinity. This description is nothing but standard Christian theology.

A) The Skeleton of Standard Christian Theology

God the Father remains the same through the entire Christian theological discussion, just as God the Son and the Holy Spirit do. One can exchange God the Father with God the Son and observe the same Divinity. The Spirit of God the Father and the Spirit of God the Son are together interpenetrated into the same Divinity that is called the Holy Spirit. No sooner does one take notice of such an invisible reality as the Holy Spirit, no sooner has one to recognize that the presence of the Holy Spirit is nothing but a third manifestation of the Divinity, an expression of the One God. The Holy Spirit is the relationship that links God the Father to God the Son to such an extent that, seeing the Holy Spirit, one sees God the Father as well as God the Son at the same time. Such a relationship is and cannot be other than a relationship of love, Love that represents both persons to such perfection as to become a distinct third entity. This person exudes not only love for the other two persons but also love for the created world and love for us human beings.

Think of love to the max, and you see God the Father in every speck of creation. Think of love to the max concretized in this world, and you see Jesus Christ. Think of both together and you see the Holy Spirit. Surely, there is ugliness and injustice in the world; but analyze ugliness and injustice profoundly and you discover that they are the effect of actions generated by human beings and tolerated by God because he does not want to take our freedom away. Surely, there were and there are other human beings who were crucified; but analyze the situation profoundly and you discover some essential differences: Jesus alone, being God, could have said “good bye” and slipped off the cross; Jesus alone, being God, knowingly consented to be crucified so that we might believe in God “our Father” who is Spirit; Jesus, perhaps first among all human beings, forgave those who crucified him, while they were crucifying him.

For a Christian this compenetration of the three persons in one is more easily recognized through the presence of God the Son. Jesus could perform the most impressive miracles such as only God the Father can perform; Christ could die and on the third day be resurrected because the spirit of God the Father that is in him could not die; Jesus could pass through the walls of the Sepulcher and the Cenacle—and he can be present in the consecrated Host—because he is pure Spirit; and, speaking personally, this writer has yet to discover any person on earth who has ever had such a comprehensive and penetrating knowledge of human beings combined with perfect knowledge of God the Father as Jesus. For this writer that is proof positive that Jesus is indeed God the Son: seeing the Son, one sees the Father;(6) seeing the relationship between the Father and the Son, one sees both persons together, and then one sees the Holy Spirit.

One can investigate all the characteristics of each one of the three persons, and be satisfied with the understanding of each person. However, reality suggests that by focusing exclusively on any one of the three persons, one loses the concept of the Divinity as a whole. One is not really in touch with the Divinity of the One God. Is not this the central message of Pope Benedict XVI in his Jesus of Nazareth?(7)

B) Does the Conception of the Triune God Exclude Judaism and Islam?

No, not al all. All monotheistic religions share the conception of the Triune God. Specific names might be different from religion to religion, but the various concepts reflect the same reality. Generalizing, it is possible to say that all monotheistic religions share the conception of God the Father, God the Son, and the Holy Spirit; indeed, they also share the conception of the structure that links these three entities to each other. Structurally, in fact, both Judaism and Islam are constructed as Trinitarian conceptions. To see this reality, it is necessary to recall that for Judaism the concept of the Son is manifested in the person of the Messiah; for Christianity the concept of the Son is manifested in the person of Jesus; and for Islam the concept of the Son is manifested in the person of Vali Asr, the revered Hidden Imam, whose appearance, someday, Shiite Muslims believe, will establish the perfect Islamic political community. The other major difference among the three religions is of course related to the timing of the coming of the Son on earth. This most contentious of all conceptions is elided here by recurring to a simple observation. If God the Father is eternal, it means that time does not exist for him; hence it does not exist for God the Son either: God the Son is, has been, and will be with us forever. A much more pedestrian but perhaps more convincing way of facing this burning issue is to admit that, while as Christians we believe in the presence of the historic Christ, nearly all of us have much work to do to reach the conception of the spiritual Christ in our hearts: this Christ is mostly still to come. Hence, Christians, Jews, and Muslims are on the same page. Much more pragmatically, to keep this distinction between the historic Christ and the spiritual Christ alive in the heart of humanity is perhaps the function of the Jewish people. (But ought the Jews to have paid and still pay such a heavy price for keeping the flame of the Spiritual Messiah alive?) Similarly, to keep the spirituality of Allah as a burning reality in our hearts is perhaps the function of the believers of Islam.

C) Does the Conception of the Triune God Exclude Other Religions?

The short answer again is: no, not at all. After granting all substantial differences, if one is in search of what unites—rather than what divides—humanity, one has to conclude that the conception of Brahma, Shiva, and Vishnu is structurally identical to the conception of the Triune God in monotheistic religions. The Indian theologian Raimon Panikkar has been developing the Trinitarian conception of Cosmotheandrism, namely the equivalence of Theos, anthropos, and cosmos; and another Indian philosopher and theologian, Joseph Kaipayil, points out(8) that the conception of Cosmotheandrism is akin to the Chinese idea of Heaven, Earth, and Man forming a trinity. And this conception, of course, is not far removed from the Native American conception of Man, Earth, and the Great Spirit.

To eschew the danger of embracing pantheism with or through any of these conceptions, it is sufficient to distinguish God from the Spirit of God. While the Spirit of God can be in any created entity(9) and, therefore, being infinite is everywhere, God can be conceived as an entity that stands outside time and outside space.

In such a conception, God is an absolute mystery to us.

V. The Mystery of God

Having said all that, having gained perhaps a better understanding of each person of the Triune God, and realizing that the whole of God can be understood only through the understanding of the divinity of the One God, we have to realize that having done all that still does not give us any better understanding of God. A good dose of realism combined with even a modicum of humility suggests that we will never understand God, we will never comprehend God. To comprehend God we would need to be at least, in every sense, as comprehensive as God.

Thus we must conclude that God is a mystery. And then we can sympathize with all Evolutionists who are in search of the explainable God and, since they cannot find him, they deny his existence. And, yet, ironies of ironies, why do Evolutionists not realize that, denying the mystery of God, they are compelled to believe in billions and billions of miracles occurring at every instant in order to keep creation together? (Is the suspicion totally unfounded that the late urge to solve these billions of mysteries with the aid of science is somehow related, in direct proportion, to the growth of the modern practice of public funding for this research? There seems to be a symbiosis there. If researchers had to put their money where their mouth is, it is questionable whether they would formulate as many questions as they do today.)

As soon as we admit to the awesome reality of the mystery of God, we open the door to the mystical union with God. If and when it pleases God, God reveals himself (herself? itself? God as spirit has no gender) to us. And indeed, he reveals himself to anyone who desires to be united with him. It is one of the strongest tenets of the Carmelite charism, one of the deepest and most democratic charisms on earth, to believe that the way to a mystical union with God is open to every human being.

Having said this much, is it tantamount to saying that the mystical union with God, that indeed any form of association with God, is an irrational act that demeans the superb reality of the rational individual human being?

Were we to stop our analysis at this juncture, that might indeed be the inexorable conclusion. But it would be a partial and basically wrong conclusion. We can recover the full degree of the dignity of our rationality as soon as we look at metaphysics through new eyes.

 

VI. A Hint of Metaphysics

Metaphysics is in such a sorry state these days that it has almost disappeared from the list of mental disciplines worthy of any attention. Yet, the sorry state in which metaphysics has fallen is not an indication of what metaphysics actually is. Metaphysics is the study of Being. And indeed, from Plato onward much thought has been spent on this concept as well as on the characteristics of Being. The reality is that Being is a dialectic concept;(10) hence one can begin to understand Being only as soon as one starts to pay serious attention to the concept of not-Being. It is not by chance perhaps that, through the intervention of Buddha, the concept of not-Being was born in the East at about the same time that the concept of Being was born in the West.

With or without knowledge of developments in the East, the world of thought has been polarized between these two concepts. Separate, they provide only confusion and dissension, just as any other dichotomy creates only confusion and dissention, because they lead to circular reasoning; hence, the need for the search for a third term in the analysis. It is together that Being and not-Being begin to offer some enlightenment. Formally, one can begin to understand Being by realizing that everything is included in it—even not-Being; alternatively, one can say that nothing is excluded from Being—not even not-Being.

Worse still than trying to keep Being separate from not-Being has been the attempt in the West to specify the reality of Being through the elaboration of two abstractions: essence and substance,(11) and the link between these concepts—and to us human beings—represented by the variegated meanings of the word “relation.”(12)  The philosophical discussion has gradually become so intractable that the entire investigation of the metaphysical project has been nearly completely abandoned in the modern world.

This is not an inescapable existential condition. Separate in-depth investigations by this writer have convinced him that the road to intellectual sanity lies first in the concentration on two additional forms of the metaphysical reality in which we are immersed: Becoming and Existence. And then by combining these three elements through the familiar diagram, in this fashion:

Figure 3. Relational Ontology

We thus have all the tools to reconstruct the bare bones of metaphysics. Here three sets of observations suffice. As the most impellent question, is this supreme, absolute, all-powerful, all-knowledgeable Being rational in becoming existence? We have no way of determining that—and if we were to determine it one way or the other we would be limiting this infinite Being: a clear impossibility. What can be determined for sure is that any form of Existence is entirely rational in wanting to return to Being. (This is more than a rational supposition. It is a fact. Simply exclude volition, and the return of Existence to Being becomes a sheer incontrovertible fact.) In the end, it is in this third entity, Existence, in its relation to Being, that we reach the deepest understanding of our life: While Being is, was, and will be forever, we as transient and transitory human beings exist in Being.

And it is within the realm of the equivalence relation that we Christians reach the deepest possible meaning of the Trinity: Christ at one moment in history (and the Spiritual Christ forever) joins us in our existence (we have absolutely no human indication, and we might never have any indication, of what was that relationship outside of time, outside the creation of the cosmos); he assumes our human characteristics; and at the same time we join him, because, as Scripture (Colossians 1:16) says “In him everything in heaven and on earth was created, things visible and invisible. All were created through him; all were created for him.” A father would do that for a son. (And are we not all sons of God? God did all that for us. God does all that for us all.)

(I never truly believed in the doctrine of the Original Sin, until I pondered upon the words I have just written. Somehow I thought it was a priestly fib, an invention to try to explain the mystery of our human nature to “the masses.” I was particularly incensed when this doctrine was reduced to the unholy misconception of equating sin with sex. With his splendiferous Theology of the Body, Pope John Paul disabused us of that misconception. And yet, unless mistaken, that misconception still taints the dogma of the Immaculate Conception of Mary. That is work still to be done. But what is the conception of original sin, then? The original sin, a sin that originally started with Adam and Eve, is a sin that is continued in us and is enveloped in the perpetuation of our willful separation from the Garden of Eden, from the full enjoyment of the fruits of Heaven, because of our mistaken belief—as an exercise of our pride—that we can ever separate ourselves from God.)

VII. Concluding Comments

Boethius, St. Thomas Aquinas, and all fervent religious persons have accepted the reality of the Trinity on the basis of faith and obedience to the Magisterium of the Church. In their arrogance, instead, the makers and the followers of the Enlightenment have discovered in the Trinity only a series of paradoxes, which they have resolved by separating church and state and by trying to exclude the power of God from human affairs.(13) The Enlightenment has resulted in the state religions of Nazism, Communism, and the Mixed Economy. Using the relation of equivalence, we have found no intellectual paradoxes in the Trinity—and we can also hint at the resolution of the church-state conflict by recovering the age-old economic justice project, which stubbornly aims to limit the power of the state to a few essential functions while attributing innate economic rights and responsibilities to each human being.(14) Using the relation of equivalence, we have confirmed the logical validity of the relationships among the three persons of the Trinity that were ever so gradually and painstakingly discovered by the “old time religion.” Using the relation of equivalence, we have reached a better intellectual understanding of the individuality of each person of the Trinity and the concept of the One Divinity as a whole, the Triune God. Yet, a better understanding is a far cry from a perfect understanding. To be thorough, all possible questions, if one begins to formulate them, and all possible answers, multiply in such a way as to make one’s head spin in a never-ending circular motion. It is the bosom of realism to surrender to the confounding power of the Divinity, accept that we are a very tiny part of this Absolute Immensity, and admit that it is wholly rational—wholly wise—to try to reach a mystical union with God.

In 1946 Einstein remarked: The unleashed power of the atom has changed everything save our modes of thinking.” (15) With the rational acceptance of the equivalence of three persons of the Triune God and the extension of this relation to envelop the unity of “Being Becoming Existence,” our modes of thinking about Existence change. And then potentially everything changes. From the linear world of Cartesian logic and rationalism, the seed is thrown to transform again everything into the organic world in which everything is indeed related to everything else. Above all, we discover that God is not dead. People ask, where is God? There is where the living God is: God is everywhere; God is with the just; God is with the unjustly afflicted; God is with the unjustly oppressed. There is where the living God is. If theologians cast their conception of the Triune God into the framework of the equivalence relation they get a step closer to logicians and mathematicians who consistently use this framework of analysis in their everyday operations, and then, with time, the warlike relation between the “two cultures”—with its multifarious manifestations of reductionism, materialism, and atheism, and, above all, mutual misunderstandings—will, through mutual adjustments, unavoidably come to a screeching halt. The hard sciences are not the fount of all certainty. If there is such a thing as certainty, it exists within the realm of theology and philosophy as well. After all, it was Einstein who said: “Science without religion is lame, religion without science is blind.”(16)

There are many indications that the world of linear, rational, Cartesian logic has come to an end—see, e.g., John Lukacs, At the End of an Age(17) or Morris Kline, Mathematics: The Loss of Certainty.(18) This is a world in which reality is reduced to isolated atoms. This is the world of punctilionism, the defense to the death of one’s small point isolated form the rest of the universe. To escape this abyss of linear, rational logic we have to get into the world of relationalism, a world in which everything is naturally related to everything else. The “old time religion” it turns out has room for improvement; yet, even as it was, it was much better than state and secular religion. This paper has used the principle of equivalence to present a rational explanation of the relationships that link the three persons of the Triune God among themselves to form One Divinity. In the process, we have ever so lightly touched upon metaphysics in order to link the existence of God the Son to the existence of us human beings. That is the seed for the eventual development of a full relational theology.

Unless this writer is totally conceited and totally misconceives history, in common language the search for relational theology is the search for the living God; in philosophical language, it is the search for Thomist realism.(19)

NOTES

__________________________________________________________________

  1. Douglas C. Hall, The Trinity: An Analysis of St. Thomas Aquinas’ Expositio of the De Trinitate of Boethius (Leiden, New York, Koln: E. J. Brill, 1992).
  1. Carmine Gorga, “Toward the Definition of Economic Rights,” Journal of Markets and Morality, 2:1, pp. 88-101, 1999. Md. and Oxford: University Press of America, 2002.
  1. Carmine Gorga, The Economic Process: An Instantaneous Non-Newtonian Picture (Lanham, Md. and Oxford: University Press of America, 2002). An expanded edition of this work is in press.
  1. Carmine Gorga, “Concordian Economics: Tools to Return Relevance to Economics,” Forum for Social Economics 38, 1, 53-69 (2009). Available online in cyber format at www.somist.org and in soft cover at www.createspace.com/3350635.
  1. Carmine Gorga, “On the Equivalence of Matter to Energy and to Spirit,” Transactions on Advanced Research 3, 2, 40-47 (2007).
  1. E.g., John 1:1; John 8:14-29; John 10:30.
  1. Pope Ratzinger, Joseph (Pope Benedict XVI), Jesus of Nazareth. New York: Doubleday, 2007.
  1. Joseph Kaipayil, personal communication, Mar 7, 2008.
  1. Cf. note 5 above.
  1. See esp. Benedetto Croce, Logic as the Science of the Pure Concept (London: Macmillan, 1917).
  1. See esp. Gilson, Etienne, Being and Some Philosophers. Toronto, Canada: Pontifical Institute of Medieval Studies; 2nd edition, 1952.
  1. See, e.g., LeRon F. Shults, Reforming Theological Anthropology: After the Philosophical Turn to Relationality (Grand Rapids: Eerdmans, 2003).
  1. Mark Lilla, The Stillborn God: Religion, Politics, and the Modern West (New York, NY: Knopf, 2007).
  1. See note 4 above.
  1. Albert Einstein. Quoted in Nathan O., and Norden, H. (eds), Einstein on Peace, p. 376 (New York: Avnet Books, 1981)and a pamphlet published by Beyond War in 1985 entitled A New Way of Thinking.
  1. Albert Einstein, ‘Science, Philosophy and Religion: a Symposium’ (1941). In The Quotation Page at http://www.quotationspage.com/quote/24949.html.
  1. John Lukacs, At the End of an Age (New Haven and London: YaleUniversity Press, 2002).
  1. Morris Kline, Mathematics: The Loss of Certainty (New York: Oxford University Press, 1980).
  1. The author wishes to acknowledge the technical assistance received from his long-standing collaborator, Louis J. Ronsivalli, an MIT food science technologist, and a most positive feedback from Dr. F. Hadi Madjid, a Harvard physicist. This presentation has greatly benefited from comments by Michael C. Jordan on an earlier draft of this paper.

In ontology

The original publication is available at SSRN: http://ssrn.com/abstract=1695809 or http://dx.doi.org/10.2139/ssrn.1695809 

Toward Relational Ontology:

From Matter to Spirit

Through Physics and Metaphysics

Carmine Gorga

President, The Somist Institute

December 2009

 

Abstract

On the basis of Alexander Marshack’s Roots of Civilization, the paper presents the essential steps in the development of a system of Relational Logic and a Theory of Complementary Knowledge as they have accrued from our early ancestors to the present. These methodologies help to transform Being, Becoming, and Existence into concepts of Relational Ontology. In the process, the paper discovers that the transition from matter to spirit is a logical necessity both in physics and in metaphysics.

 

Brief Bio

Carmine Gorga is a former Fulbright scholar and the recipient of a Council of Europe Scholarship for his dissertation on “The Political Thought of Louis D. Brandeis.” Using age-old principles of logic and epistemology, as well as mathematics employed by modern engineers and scientists, in a book and a series of papers Dr. Gorga has transformed the linear world of economic theory into a relational discipline in which everything is related to everything else—internally as well as externally. He was assisted in this endeavor by many minds, notably for twenty-seven years by Professor Franco Modigliani, a Nobel laureate in economics at MIT. The resulting work, The Economic Process: An Instantaneous Non-Newtonian Picture, was published by the University Press of America in 2002 and will be republished in an expanded edition in 2010. For reviews, see http://www.carmine-gorga.us/id18.htm. During the last few years Mr. Gorga hasconcentrated his attention on methodology and its application of to a variety of disciplines. The result is a new system of thought that he likes to identify as Relationalism.

In a culture in which Existence reigns, Dunash ben Labrat sings:

  Do not sleep! Drink old wine,

Amidst myrrh and lilies, henna and aloes,

      In an orchard of pomegranates, palms and vines,

          Full of pleasant plants and tamarisk;

      To the hum of fountains and the throb of lutes,

    To the sound of singers, flutes and lyres.

 

In a culture in which Being reigns, Dante sings:      

        fatti non foste a viver come bruti

 ma per seguir virtute e canoscenza.

                                                     (you were not made to live like brutes

      but to follow virtue and knowledge.)

 

  In a culture in which Agnosticism reigns, Lorenzo Il Magnifico sings:

     Chi vuol esser lieto sia

        Del doman non c’e’ certezza.

        (If you want to be happy, be happy

           Tomorrow is not certain.)

Metaphysics, with ontology at its core, has the ability to influence our lives in a pervasive and deep way. And yet, metaphysics is in disuse today. The focus of this paper is on the recognition that, without metaphysics, it is impossible to answer in an acceptable fashion three fundamental questions about knowledge: why do we know, how do we know, and what do we know.

The paper attempts to demonstrate that metaphysics is in disuse today, not because the modern philosophical mind finds something inherently objectionable in the subject, but because we have neither a widely accepted system of logic nor a widely accepted theory of knowledge on which to base the study of metaphysics. Traditional systems of logic and the tools of epistemology have been tacitly superseded by more adequate tools, which however have not yet been systematically gathered to form new and powerful tools of analysis. The paper therefore outlines a new system of logic, Relational Logic, and a new epistemology, the Theory of Complementary Knowledge in order to answer the question “How do we know.” It is on the basis of these two sets of tools of the human mind that the paper proceeds to outline a new understanding of ontology, which this writer likes to call Relational Ontology. This understanding is obtained from physics as well as from metaphysics.

The fundamental premise of the paper is that Relational Logic, Complementary Knowledge, and Relational Ontology are three essential pillars for the formation of a possible structure of modern philosophy, a philosophy that on the basis of experience and physics reaches the realm of metaphysics. Upon consideration, do not principles of logic and tools of knowledge by their very nature already belong to a world that automatically goes beyond pure physics? Since these three elements are so inextricably related to each other, and since ontology is a closely knit array of ultimate relationships, this writer proposes to call the resulting philosophical system Relationalism.

I. Why Do We Know

Metaphysics is used to be described as the knowledge of being.

The central reason why metaphysics currently is not a preeminent concern in philosophy is due to its traditional concentration on one entity: being. Were we to stop at the mere enunciation of it, we might attain the holistic wisdom of Eastern mystics, who concentrate on “OM” — and are happy to surround this symbol with the richness of sounds, smells, and colors. As opposed to mysticism, however, the intense tradition of both Eastern and Western philosophy impels us to break things (words and worlds) apart and analyze each component part one by one. Thus the dance of meanings starts.

Dissatisfied with symbols, thinkers who are called to go deep into the significance of things, write down “being” and maintain that being is a word. As soon as the human mind indicates that being is a word, this simple mental operation separates ourselves from being and being from us. We objectify both being and the word, and we run into all sorts of mental difficulties. We automatically become incapable of putting the two entities together again. In fact, rather than reducing the two to one, the number of entities involved in this objectification of being has, perhaps without our awareness, increased by at least one unit: being, the word, and me (us?). When, hoping to go to the bottom of the issues, we write “being is,” we compound the difficulties because, without having resolved the problems inherent to term logic, we pass into the realm of propositional logic. We thus enter the domain of logical positivism — and there we have remained prisoners for more than a century. Do parallel lines meet? The answer is negative, if we remain within the realm of Euclidean geometry. But as soon as we enter the realm of non-Euclidean geometry, parallel lines meet!

Clearly, there is no safety in individual propositions.1 No matter how complicated we make them, no matter how twisted or straightforward we make them, no matter indeed with which syllogistic figure we group them and analyze them, individual propositions do not lead to certain communication and understanding. Individual propositions cannot provide any guidance to our thought processes. Safety lies in the realization that propositions — tinted as they are with their rush to judgment — make any sense only in relation to systems of thought. This is not an assumption made only on the basis of the history of geometry and economics. It is equally valid in ontology. By writing “being is” without first developing ontology into a system of thought, the difficulties of understanding “being” become insurmountable, as demonstrated by the history of this search — which, strangely enough, was initiated both in the West and in the East at approximately the same time, about 2,500 years ago. The search has led to two major schools of thought: one, led by Parmenides and Plato, might be classified as Absolute Ontology; the other as Negative Ontology. The latter has been led by Buddha in the East and Plotinus in the West. (Placed in this context, Eastern and Western philosophy, rather than diverging, as too often assumed, can be seen as converging on the same path: the search for the meaning of being.)

Absolute Ontology

Being. No matter how hard the human mind has tried, centuries of effort by the keenest people on earth have so far come to naught. No sooner does one advance an explanation, a valid objection is raised against it. So the search starts anew. The basic problem is that the word “being,” even when extended into the proposition “being is,” is locked into a system of absolute ontology in which there is no room for anything else but “being.” Attempts to explain this word in terms of such other entities as essence, substance, or existence, by shifting the burden on to the meaning of these terms, have only compounded the difficulties — which are painstakingly described in the magisterial analysis of Etienne Gilson in his Being and Some Philosophers (1952).

In the proceeding we will examine why these efforts were destined to fail. At the moment, on the basis of such long and consistent history, we need only conclude that there is no way to escape the limitations of the metaphysical problem as construed at present, except by getting out of its closed system. If we do that, we extend the application of Gödel’s Incompleteness Theorem to metaphysics and we heed both its explicit and implicit message.

At first sight, this decision might appear to be a radical departure from traditional scholarship. Yet, it is a mere acceptance and explicit ratification of the reality that philosophy has abandoned the metaphysical project as construed in the past. This approach is also a recognition of the value of what — especially but not exclusively — Eastern philosophers have done.2 They have created a system of thought that might be classified as Negative Ontology.

 

Negative Ontology

Rather than saying what being is, some philosophers like to start the discourse from what being is not. Christmas Humphreys, the author of a comprehensive book entitled Buddhism (1964, pp. 127-128), explains that to understand being “Only a negative is possible, for we can conceive the Infinite only as the not-finite, as the word implies. All possible description is adding predicates to the All, which is either absurd for redundancy or, by exclusion, a limitation of the All.”

With that restraint, it appears that the discourse has advanced at least an inch and that the approach has added to our sum total of knowledge, but we still have no better understanding either of being or not-being. No sooner does one state that being is “not such and such,” another philosopher finds a logical contradiction in the proposition.Some deny the very existence of not-being.

And there we stand today: an impasse in the schools of thought that address metaphysics. The impasse is so deep and so vast that it has led to the abandonment of metaphysics. Yet, is it necessary to repeat that without an understanding of metaphysics it is doubtful we can ever have a proper understanding of the world. It seems appropriate, therefore, to assume that we need a new start.

 

A Fresh Start

This paper is an attempt to make metaphysics suitable to the modern mind through the creation of a new framework of analysis that might be described as Relational Ontology. To reach this aim, we will transfer the roots of the problem from philosophy to psychology and anthropology and we will start the discussion from the proposition that the fundamental problem of knowledge is a problem of consciousness. The assumption is that without understanding the problem of consciousness we cannot extricate ourselves from the sea of existence in which we are enmeshed.

Inspired by Colin McGinn (e.g., The Problem of Consciousness 1991; The Making of a Philosopher, 2002), this paper starts the analysis of the problem of knowledge from a basic word, namely the word “I” and suggests — as a working hypothesis — the following definition for this entity: I am consciousness.

This is a good start, provided we immediately take care of its inner weakness. By itself, it is a bombastic statement, which leads to solipsism, and there the discourse ends. To eliminate this pitfall, we have to purge the statement of its inherent structural weakness, namely, we have to open it up — from the start — to the outside world. Upon reflection, we realize that the solution of our problem thus ramifies into the need to surmount three difficulties: we have to define “I,” we have to define the meaning of “am,” and we also have to define the meaning of consciousness. We are back in the vineyard of philosophy.

Consciousness is the separation of a sensation from its memory. I become aware of a sensation as soon as something somehow affects me. But by the moment I notice that something, the sensation has already passed away. What I am left with is the memory of that particular sensation — even though some aspects of the same sensation may still continue. Pace Locke and Hume, it has to be specified both that the focus of our attention is on the memory of this sensation and that the particular sensation does not need to be based on something physical either: logic, love, a spirit, a dream, an angel, Pegasus, and Emma will also do it.3 They can all give us a “sensation” of something. Looking at the situation prospectively, we can also say that — paceBerkeley — consciousness is the integration of memory and sensation. Consciousness thus is neither memory nor sensation, but a third entity, the integration of the two — and it certainly is not a physical entity. This definition of consciousness does not distinguish us from the beasts, but that distinction is not essential at this stage of our discussion.

The fact that we are, and presumably we have always been conscious entities, namely that we have the innate ability to separate memory from sensation and manipulate memories, contains the reason why we know what we know — as distinguished from the reason why we are what we are. Granted, this is a low-level near-mechanical explanation. But eschewing a premature concern for the grandiosity of cosmology, eschatology, or teleology, we are free to proceed in our investigation. By further defining memory as a dematerialized sensation, we are confirmed that we have entered a field that is beyond physics.

The real difficulties in the statement “I am consciousness” lie in the definition of “I” and the definition of “am.” As soon as we reach this realization, we implicitly admit that without knowledge of metaphysics we cannot define even such apparently simple entities as “I” and “am.” Indeed, this realization is spur enough for the reconstruction of metaphysics. The best place to enter the argument is to place ourselves, not in the position of modern philosophers, but in the position of our earliest ancestors. How did they set things in motion? We will see that the immediate problem is one of how do we acquire knowledge rather than one of metaphysics.

The assumption that I hope to validate is that our ancestors gained their understanding of the world inch by inch on the strength of a system of logic and tools of epistemology that they developed as they went along. This is not work of fancy. The line of progress followed by our early ancestors can be rather confidently reconstructed by examining the brilliant investigation of Alexander Marshack, which he reported in The Roots of Civilization (1982).

It might be useful to specify immediately that what is here treated as an inevitable sequence of events might have occurred all at once — many times, perhaps, and undoubtedly through many trials and errors. In other words, the differentiation between logic and epistemology is something that we have to make for clarity of exposition. It might not have existed in the minds of the earliest practitioners of logic and epistemology, which of course does not mean that they did not distinguish between the various tools they were handling. The situation is akin to that of putting on a tie and, as Professor Paul A. Samuelson, a Nobel laureate in economics, once magically explained, describing the process by which one puts the tie on. Doing is an incredibly compressed unit of real life. It is also immaterial whether our ancestors used tools of epistemology before they used tools of logic — or vice versa. They might well have followed either approach.

II. How Do We Know

From a superficial reading of today’s stock of knowledge, it would appear that we cannot rely on anything we know, that knowledge at best forms random globs, and that there are no rules in the process of its acquisition. The certainty that Descartes gave us with his Discourse on the Method (1637) has disappeared. Induction turned out to be too complex a method of analysis. We are indeed, as John Lukacs points out, At the End of an Age (2002). It seems that we no longer have any reliable method to assist us in our thinking process. Indeed, as soon as someone has come forward brave enough to propose a method — even simply a paradigm or framework of analysis — not much time has elapsed before someone else has found a hole in the reasoning.  At the moment, the last word seems to belong to Feyerabend, the cat that chased and ate its tail, who in a telling title declared himself “Against Method” (1975). It would appear that Lewis Carroll’s Master of Words is indeed in charge. From much of what is said, especially but not exclusively for and against deconstructionism, it would appear that anything goes.

Not so. An analysis of systems of logic and tools of epistemology reveals that there are stringent rules that guide our reasoning. Let us quickly review them.

The Theory of Knowledge

We identify each item within the sea of existence, and we acquire knowledge about it, only on the strength of a theory of knowledge. Since the topic is that important, the field is replete with controversy. We shall try to eschew the controversies by being concerned primarily with a system of tools, which compose the outline of a theory of Complementary Knowledge.

The Tools of Epistemology

To simplify to the extreme, it is possible to suggest that while officially, so to speak, we still pay outward respect to the ten Aristotelian categories of thought, in practice we have abandoned them as useful tools of epistemology. It is sufficient to read any writer on methodology today — from Mises to Popper, from Samuelson to Friedman, from Kuhn to Lakatos — to realize that the transition to the use of different tools of analysis has indeed occurred silently. It is further possible to suggest that, while this literature (which, tellingly, is mostly gathered under the heading of philosophy of science) is involved in enormous controversies of its own as to the meaning and functionality of each theory, in practice, with minor differentiations, we all know and use a few basic tools that the theory of knowledge has created over the millennia.

Following a progressive level of abstraction, without paying any attention to their own subtle subdivisions these tools are: names, ideas, concepts, theories, and systems of thought — and, for some technical intrinsic advantages of their own, today we might want to add computer models to this list. Any “thing” that comes under our observation — be it a specific baby, a specific tree, or a specific subatomic particle — enters the field of our knowledge as soon as we give “it” a name. The “word” is indeed the alpha and the omega in the process through which we acquire knowledge of anything. This process is complex, but its outline is well known and it does not need to be highlighted here. It is the next stage that bears a moment of our attention: how are names gathered into ideas. It would be cumbersome to carry in our brain the myriad of names that correspond to the myriad of individual “things.”  Thus, following a large variety of factors, we group them into a more abstract container that we call ideas: with the sum of all particular babies, we acquire the idea of baby. And since ideas are equally immensely numerous, we group them into concepts, and concepts into theories, and theories into systems of thought.

One specific example might be useful. In economics, we pass from the name of this oak to the idea of oak tree, to the concept of investment (in wood), to the complementary theory of hoarding and investment, and — tolerating many non-essential elisions — we end up with a system of economic thought. An important caveat much open to discussion is in order: Contrary to the entire train of thought pursued in the last few centuries in which empiricism has dominated our thought processes, facts are not tools of epistemology. Facts are infinite; and they are outside our consciousness. They enter our consciousness as soon as we give them a name and we gradually construe a theory about them. Facts are not tools, but products. Thus facts are not the beginning, but the end of epistemology. Facts are what the theory of knowledge attempts to understand and to explain. Outside of a theory, there have been cases of “facts” that turned out to be nonexistent: see phlogiston; and conversely, there are facts such as hoarding that are not taken into account by mainstream economics because they do not enter its mathematical models. To insist on the point: There are no facts, until we give them a name. And then, as if to prove that we do not create the world, there is no certainty about the existence of these facts until we have proved their existence through a theory. And then, of course, the theory may be proved wrong in the course of time. Thus the dance of meaning continues forever and ever, until man is alive.

Once we recognize the existence of these tools of epistemology, we can integrate them into a theory of knowledge whose bare outline is as follows.

 

The Bare Outline of a Theory of Complementary Knowledge

If all true knowledge is not linear but can ultimately be reduced to a complex array of systems of thought, it means that we can set each one unit of knowledge as equal to the number one. The sum of the component parts of that unit then must be equal to one. When possible, to simplify to the extreme the number of components can be reduced to two.

At that point in the reasoning, it might be possible to determine that the two components, rather than being in opposition to each other — as most often they appear to be when they are analyzed in isolation from each other; and, indeed, thanks to Benedetto Croce’s Logic as the Science of Pure Concept (1909), even when they are in clear opposition to each other — the two components are instead revealed to be essential parts of the same unit of knowledge. They are complementary to each other.

At that instant, much controversy might be avoided simply by the use of the double conjunction: and also. There are innumerable such cases in our intellectual life. We will have occasion to observe some of those that occur in the field of metaphysics: the most evident is being and not-being. As pointed out above, before reaching that point we need to equip ourselves with a manageable theory of logic.

To insist on the point, systems of logic and theories of knowledge are so interlaced that one cannot speak of one without the assistance of the other. Nor does one come before the other. And yet, for clarity of analysis they need to be kept separate from each other.

A System of Relational Logic

The theory of knowledge, as we have seen, allows us to identify items (such as trees) and acquire (economic) knowledge about them; principles of logic allow us to isolate items from the sea of existence, and to keep them separate from each other.

Even though the system of classical logic, the earliest system of logic about which we have a written record, was codified by Aristotle, we have to realize that our Cro-Magnon ancestors — living some forty-thousand years ago, if not earlier — investigated the world around them through a full-fledged system of logic.

The evidence is overwhelming. This is what they did. As Alexander Marshack points out, they put notations on bones and other objects of durable material that today are collected in innumerable museums throughout the world. Clearly, our ancestors were counting something. Counting, no less — an act which, upon consideration, is so complex because it turns out to be filled with memory (or fear of losing it), imagination, and hope. Let us suppose that they were counting the number of salmon going upstream. And let us not even ask why they would spend their time doing a thing like that. One salmon, one notch, on one bone. The operation is so familiar to us today that we do not stop to think of the many issues involved in it. Let us reflect on that central discovery made by Marshack.

Whether by trial and error or by one stroke of genius (repeated anew many times by many minds over many millennia?), before counting anything our ancestors took firm decisions regarding three fundamental matters of methodology. First, they made sure that “this” bone contained information related to salmon — and salmon only. Our ancestors thus discovered, and perhaps in the same breath made use of, the principle of identity: a term must be identical to itself throughout the discourse.

Clearly, this principle — and the other principles observed below, just as much as the very name salmon — did not exist in anything or anyone outside the innate creativity of our ancestors. And however described, especially in its oral version, it certainly was not a physical element. Strictly speaking, we can therefore classify this principle as a metaphysical element. Unavoidably. (What was the hard wiring in their brain and the programming that allowed our ancestors to make such decisions — and the similarity of the hard wiring and programming in the brain of their interlocutors — are fascinating investigations that go beyond the scope of this paper. Also, how did, mechanically, our ancestors create this principle? Were they aware that they were creating such a principle? Were they aware of its importance? All neural, genetic, psychological, hermeneutical, sociological, teleological, or philosophical issues involved in the discovery of this principle are interesting to analyze and to discuss. But they do not change three simple facts. The principle of identity was discovered in the very ancient past, it is still used today by us all, and it belongs to a world that is not physical in any sense of the word physical.)

And how were our ancestors sure that such a notation was related to the salmon — and the salmon only? They were so sure because they used a different bone for notations concerning the appearance of the moon. By stating that this bone related to the salmon, they were implicitly or explicitly saying: “This bone does not relate to the moon.” They were therefore applying the principle of non-contradiction. They could be sure that this bone belonged to notations regarding the salmon, because it did not relate to notations regarding the moon — or any other object under the sun. (Pace Hegel, unless we want to fall into the abyss of his “inverted world,” we must recover the use of the principle of non-contradiction. If we do not, we enter the night in which, as he said, “all cows are black.” And much worse than that. We enter a totalitarian world in which the speaker has the final say. Why? Because without the principle of non-contradiction one cannot prove anything — hence one cannot disprove anything.)

This is basic complementary knowledge (of salmon and moon).

Our ancestors also did something of even deeper value. In the process of setting their method of gathering, recording, and manipulating knowledge, they implicitly or explicitly discovered and gave expression to the following tight relationship:

This Notation = The Word Salmon = The Fish I See Swimming.

And they had great faith in this relationship, which would eventually be called the relation of, or principle of, equivalence. Decoding what our ancestors did, they used a complete system of logic to help them gain their understanding of the world. Let us call it Organic Logic, or perhaps better, Relational Logic. The principle of equivalence was inextricably flanked by the principle of identity on one side and the principle of non-contradiction on the other. To note the fertility of this system of logic, let us quickly see how it led our early ancestors to the discovery of the power of syllogisms, mathematics, and geometry. On a cold winter night, by the light of a roaring fire, they took two tablets and they said:

If tablet A contains knowledge about salmon,

And if tablet B contains knowledge about salmon,

Tablet C that summarizes A and B contains knowledge about salmon. (This is the first time this writer has noticed the root of summarize.) This reasoning allowed them to store one tablet, rather than two; it expressed perhaps the first syllogism; and it also led to the invention of mathematics. In this fashion: If (Five fingers = Five digits/notations = Five salmon) and/plus (Five fingers = Five digits/notations = Five salmon) then Ten fingers = Ten digits/notations = Ten salmon.

Following the same reasoning, they put two bones/tablets together and they began to observe the relationship of lines and angles they formed. Thus they invented geometry.4

***

A Reassuring Vignette. Before proceeding, it might be good to take a moment to reassure ourselves of the need to distinguish between the tools necessary to gain knowledge and the content of our knowledge. Without the inherent participation of such metaphysical tools as the principles of identity, non-contradiction, and equivalence, in our process of acquiring knowledge we would not be able to separate “reality” from its description/name; we would not be able to separate one item from another in the sea of existence; we would not be able to see ourselves as separate entities from the sea of existence. Instead, we would only accumulate such powerless verbiage as this: The moon is the salmon; the salmon is the moon; last August I saw 130 moons going up river; there was only one moon per month going upstream last year; perhaps, there were 130 + 12 = 142 salmon going up river; no, perhaps, there were 142 moons going up river. Without the assistance of names, without the assistance of the principles of identity, non-contradiction, and equivalence, we would only be able to acquire jumbled verbiage — if that at all. (Of course, as this silly vignette points out, to acquire any knowledge we need an understanding of time, let alone space — but in the large scheme of things, and away from the strictures of Aristotelian logic, these are inherent subtleties.)

Conclusively, the very process of discovery of the world is inextricably linked to a (metaphysical) methodology for the understanding of the world: the two proceed hand in hand. It is only for purposes of analysis that we might need or want to separate the two entities, the tools of understanding from the content of the understanding. Indeed, at a deeper level still it is impossible to separate those two elements from a third one: one’s own consciousness. It is the unity of these three elements that yields what we so casually call knowledge.

III. What Do We Know?

On the surface of things, we know a tremendous amount and we are outwardly quite boastful of our accomplishments. Verbal correspondences, prophesy, and experimentation have solved many problems concerning the “reality” of our observations.2 Digging deeper, however, we realize that our knowledge is partial and above all incomplete. Indeed, it is so partial and incomplete that we are experiencing a deep crisis, one of the deepest in the history of gnoseology.

A Set of Issues at a Glance

The discussion that occurred from the high Middle Ages to the end of the Renaissance captures many of the issues at a glance — and directly affects us today. The great minds of the Middle Ages began to doubt everything. Having the Greeks misapplied the principle of equivalence by relegating it to syllogistic logic, and having medieval thinkers so enriched the field as to lose their way in the rich complexity of syllogistic figures (a condition akin to that experienced today by the practitioners of econometrics), philosophers began to doubt that behind each word there was anything at all to understand. The discussion became locked between the position of the realists who said that there was something real behind the word “salmon,” and the position of the nominalists who could not find anything more than a name there. Later, with Kant, the search was completely forestalled. Kant declared that the “noumenon,” whatever entity existed behind each “name,” was unknowable. This is the quandary we are in today. But why?

 

A Quick Explanation and a Superficial Solution

As we have briefly seen, tired of pointing to this, and that, and that, our earliest ancestors began to name “this” bread and “that,” let us say, pasta. Using the principles of identity and non-contradiction, the realists up until the late Renaissance could prove that bread was indeed bread… because it was not pasta. Yet, charged by the nominalists who wanted to know what were the distinguishing features that kept bread separate from pasta, some realists began to talk of a certain something (a quiddity) that was the essence — or perhaps the substance — of bread and pasta. The more they tried to explain the constituent elements of reality, the deeper in trouble they got. Clearly, “the essence of bread” was an invention of our mind. Not only that. Such categories of thought as essence (actually a transcendental) and substance were not at all helpful in determining the identity of items in between. Aristotle had “excluded” all terms in between, and Descartes was to say he was indifferent to them. Yet the nominalists continued to press: “What is a wafer?” Clearly, a wafer contains characteristics of bread and characteristics of pasta. How can one distinguish any of the three items from the other two — and the zillions of other items in our sea of existence?

Beginning at what is characteristically called the modern age, trying to eschew such disquisitions altogether, rationalists, empiricists, and later positivists came down with the conclusion that what united bread, pasta, and wafers was something that we all could comfortably call “matter” and they remained at peace with that solution. Some thinkers even called themselves materialists. In fact, most thinkers — with Galileo at the head of the parade — were so satisfied with that solution that they began to measure matter, and weigh matter, and squeeze matter, and push matter around. Empiricists and positivists — aided by such powerful intellectual tools as calculus provided by rationalists — made great strides. They have given us knowledge of the world around us, and the world above us, and the world below us. All the laws of physics and chemistry and biology known to us — together with their wondrous technological applications — have all gradually been discovered on the strength of that great simplification: the humble word matter.

The Peace Breaks Down

Some rationalists, materialists, empiricists, and positivists eventually became so overly confident with their solution to the problem of epistemology that, neglecting the additions brought forward by their own minds, they admitted of no other knowledge than the knowledge of matter. Practical men and women that they were, they unavoidably made some assumptions about the metaphysics of matter; and some of them concluded that it was controlled by an inner force that they called evolution. Since the word had no other function than to dispel the emptiness in which the study of metaphysics had fallen, no one really objected too strongly to the entire construction of evolution.

All remained at relative peace and in relative order, until — on the force of gigantic developments especially in electricity and electromagnetism — Einstein established a close relationship between matter and energy, which he called an equivalence. Then the world began to fall prey to doubt again. Was matter, matter; or was it energy? In the vacuum created by the absence of a firm theory of knowledge, uncertainty spread like a wildfire to envelop one after the other all the disciplines that studied matter first and all other mental disciplines soon thereafter, from physics to cosmology and from psychology to political science to economics to art criticism and even art. Not only the outsiders to the various disciplines held doubts, but especially the insiders. Post-modernist deconstructionists eventually held the day. Nothing is certain, they said.

Had they stopped there, their effects might have been circumscribed to the content of the disciplines they studied. But they went further, much further, and affected our culture as a whole. First, they encroached upon metaphysics and asserted that nothing has any meaning at all (“nothing” is a term that makes sense only in the context of metaphysics).

Metaphysics fell in disuse.

Then, abruptly passing from metaphysics to sociology, they asserted that all meaning is an expression of sheer power. The power of the one who holds the pen. The power to dominate others.

In short-hand, this is the contemporary crisis in which epistemology has fallen. Nothing is clear. And all values have been reduced to one: power. (Obviously, the full inner force of these movements of thought is revealed with hindsight; with foresight, they are quite murky. Neither do they occur linearly in a logical sequence.)

Some Implications of the Current Crisis in Epistemology

These are not merely theoretical issues. Our entire way of life is affected by the crisis in epistemology — and, of course, metaphysics. In the microcosm of the life of too many human beings, the result is loneliness, meaninglessness, disassociation from other people and communities. Keep in mind that the predominant feeling for the majority of people is powerlessness. This is the feeling which, used and abused by one and all, functions as the transmission belt from the microcosm of the individual person to the macrocosm of the world of politics. The crisis in the theory of knowledge, through very circuitous and not-so-circuitous routes, routes that inevitably pass through the mind of the leading intellectuals of the age,5 has had one fatal result: it has left free reign to a bloodthirsty string of Fascists, Nazis, and Communists to dominate others.

When the ideologies of these sordid characters fell under the weight of the horrors they thrust upon men, women, and children, even the hope of ever changing the world — the hope which was the inner strength that those ideologies shamelessly exploited — was taken away from the dispossessed. In the wasteland left by the vacuities of consumerism6 and self-adulation of Western democracies, a strange combination of religious fundamentalism and humanistic nihilism has gradually taken over: we have ultimately been presented with the final solution, the horrors of terrorism — endogenous and exogenous terrorism.

Is There a Way Out of the Crisis?

The current crisis in politics will have to be solved within the realm of politics. The hope is that the democracies will work for the transformation of the rhetoric into the reality of freedom and economic justice for all. Thus will democracies uncover the lie of the deconstructionists. Democracies have to work for this goal, first for all their citizens, and then for all the citizens of the world. That is the only road to peace. There are no short-cuts. As Pope Paul VI well knew, “If you want Peace, work for Justice.”

Since the deepest roots of the crisis in politics lie in metaphysics, rather than pursuing issues of political science, we had better confine our attention to issues that are central to the theory of knowledge and to metaphysics. There is an extraordinary dictum by Einstein. It contains a deep analysis and the glimmer of a solution to our crisis. This is what Einstein said: “The unleashed power of the atom [which became possible because of the equivalence he established between matter and energy] has changed everything save our modes of thinking and thus we drift toward unparalleled catastrophe.”7 Einstein made this statement in 1946. The beginning of the new millennium might be an appropriate time to act upon Einstein’s warning. Let us continue with our efforts to reconstruct our modes of thinking, focusing now on the very heart of the crisis.

Not yet an Equivalence

Einstein said that matter and energy are bound together by an equivalence relation. The rules of equivalence are well established. In any equivalence, there must be three terms. And each term must be reflexive, symmetric, and transitive. Judged against these standards, it becomes clear that the relation between matter and energy is not yet an equivalence.

Since the terms have to be reflexive, it is necessary that both matter and energy be identical to themselves throughout the discourse. The relationship between them, in other words, can be organic but it cannot be linear. This relationship does not suggest that matter ends and energy begins; rather, it suggests that matter organically transforms itself into energy. Stated in different terms, there are two ways in which the cosmos can be seen: namely, from the point of view of matter and from the point of view of energy; one point of view at a time. This is one of the meanings of Heisenberg’s Principle of Indeterminacy. One cannot add these viewpoints to each other, because they represent the same thing observed from two different points of view.

That the terms must be symmetric means that it is possible to exchange one term with the other and one obtains the same result. In physics, only one way of this relationship has been investigated for the time being. Perhaps a new field of study is hidden in the converse relationship, the possibility of transforming energy into matter. Are experiments with antimatter straddling the field?

And then the terms have to be transitive. This characteristic implies that there must be a third term to which both matter and energy are organically related. The world of physics has not yet asked this question; therefore, it has not provided any answer. Yet, the question must be asked and an answer must be found. Otherwise, this field of study does not rest on a solid logical foundation.

From Matter to Spirit in Physics

Once this writer asked the question, as Bill Gates would say, the answer came at the speed of thought. The third term to which both matter and energy are related is spirit. We are now in the presence of a complete equivalence.

A group of physicists has analyzed these propositions, accepted its validity, and published a paper by the writer on the topic.8

Of course, the writer does not even dream of exploring the deep cultural meanings of this formulation. It seems to offer a rich potential. Personally, he accepts it mainly as a logical necessity. And he likes to consider that, if this equivalence is not simply a logical consequence of the dictates of abstract principles but contains true concepts, by relating it to the outside concrete reality, as Kant might say, it should lead to a variety of conclusions, some true and some false. Let us quickly observe some of these issues.

A False Conclusion

If the equivalence of matter to energy to spirit is studied as a rational sequence, it can lead to any such construction as depicted in the following geometric figure:

Figure 1. A Sequential Pattern

In this type of construction the three entities — namely, matter (M), energy (E), and spirit (S) — remain separate from each other. Two consequences ensue: Physically, no amount of rationalization can set the three entities in an organic relationship with each other; and, metaphysically, one is led to define spirit as being. As seen at the outset of this paper, history proves that this is a wrong starting point of the metaphysical discourse. There is one more reason why we should not jump from spirit to being. True, spirit is something that is beyond physics; but without the explicit assistance of ontology one would only fall within the embrace of either physics or religion — and not settle any doubt that the human mind might have.

 

A More Fruitful Conclusion

The mature realism of Relationalism suggests these nonlinear links:

 

Figure 2. An Organic Pattern

Whatever the consequences of this structure for physics, as far as metaphysics is concerned it helps us reach two tenable conclusions. First, it is now possible to define spirit as the relation between matter and energy, as the glue that holds the two entities together. A relation is an immaterial and therefore directly unmeasurable entity, but it does exist and it is advisable that it be taken into consideration. Indirectly, with time, we often become quite proficient at finding quantitative measurements for at least some of the effects of such entities. Indeed, it might well be that physicists will simply have to accustom themselves to calling spirit what they now call gravity and their search for the definition of gravity might finally be over. Second, it is now possible to pass from matter to spirit and, once that is done it is possible to conceive of spirit as an integral part of the physical world. Many lay people have done that from time immemorial, and many scientists have also done it — no matter the biases to the contrary held by the modern secular environment. It appears that the reality of the world can indeed be studied as the integration of matter, energy, and spirit. This understanding is yielded by the mature realism of Relationalism. From this platform, the discourse is better carried forward with the tools of metaphysics. But, first, let us go back on one issue left pending: We now have more tools to define the “I” in our original statement: “I am consciousness.”

A Valid, Still Partial Conclusion

Our newly acquired knowledge of the world outside us lets us be certain of who the I is. The I is an integration of body, mind, and spirit — or, to remain within the field of knowledge we have just reached, the I is an integration of matter, energy, and spirit.

However, this is a statement of fact. It is not a definition. It is not a universal definition. A stone is also an integration of matter, energy, and spirit. Hence we can now say that the I is a conscious integration of body, mind, and spirit.

Clearly, the characteristic that distinguishes human beings from all other beings is consciousness, that entity, in other words, that has allowed us to carry the discourse along thus far. It is in fact the consciousness of our ability to receive, to hold, and to manipulate sensations that distinguishes human beings from all other entities in the universe — at least until we find another such conscious entity with whom we can exchange views. And, as to the possibility that either a stone or a monkey has consciousness, the writer has a curt question: And so? (If there are people who care about this possibility, they are free to care, of course. And clearly this is not an invitation to mistreat either a stone or a monkey.) More. Implicitly, it is consciousness that lets us extricate ourselves from the world of existence. We now have a better understanding of ourselves and the world around us. What we still need to understand is the most difficult component of all: that “am” we have left in abeyance so far. To understand this entity we need to have a clear and unobjectionable understanding of metaphysics.

 

The Current Status of Metaphysics

As noted, metaphysics is in disuse today. How to remedy this situation, since as have seen even the understanding of such an apparently simple word as “am” depends on metaphysics? Thanks to wide experimentation, it seems that we can advance toward our goal only if we reach a firm grasp of the fundamental causes of the present condition of metaphysics. A few observations might set us on the right path. First, we have to admit that the field is not simply in disuse; it is in ruin — an ideal condition because, rather than starting from scratch, it is possible to use building blocks belonging to earlier constructions. Second, we have to recognize that the root cause of the current inability of the structure to stand on its own lies in the conflation of two entities: being and existence. Naive realism maintains that what exists is. This is an assumption that, without examination, was held true even by such a profound mind as Saint Thomas Aquinas.9 Mature realism, instead, maintains that we are presented with two entities: existence (from the action “to exist”) and being (from the action “to be”). Indeed, the hypothesis of this paper is that in order to understand “to be” we need to distinguish it from “to exist” and that this operation can be performed. Third, we need to realize that those two entities are held together by Aristotle’s logic and categories of thought, tools that have been superseded by research carried out during the last two millennia. Let us therefore openly abandon those tools of analysis in favor of Relational Logic and the Theory of Complementary Knowledge and see whether they can guide us in our endeavor.

Let us pick up our discourse where we left it, namely at the integration of matter, energy, and spirit. How do we pass from the Relationalism of mature realism to metaphysics? The route for this transition starts with the traditional question: What is that each and every aspect of reality shares in common? As far as we know, it seems that, starting most systematically and extensively with Plato and Buddha, philosophers have asked this question and they almost to one person have given the same answer: the ultimate reality is the world of being — or not-being.

This is a hurried answer given to an improper question that has led philosophy to the conflation of existence and being. The proper question is: What is the ultimate reality of existence? Yet, philosophers did not and could not ask this question because, give or take a few centuries, it took another thousand years before existence was taken into serious consideration at all as a possible separate entity. The obvious is always and everywhere most difficult to discover. With the benefit of hindsight, however, it is easy to notice all sorts of contradictions, all sorts of anomalies inherent in the conflation of existence and being. For instance, it is impossible to reconcile the caducity of existence/reality (of which we are certain) with the eternity of being — or at least its ability (possibility? necessity?) to be out of time; it is impossible to reconcile the lack of consciousness of existence (in the world outside me) with the previously encountered self-consciousness of (at least my) being; it is impossible to reconcile the evident lack of self-generation of existence (grazie, mamma e papá!) with the inner creativity of being — is not evolution a form of inner creativity, after all? But is that the inner creativity of birds, for instance? To accept this hypothesis we have to assume that one day “birds” set at a drawing board and designed their feathers.

To distinguish existence from being we need to perform three mental operations: First, we need to define existence; second, we need to transform being, from such a categorical entity as a universal, into an independent concept; third, we need to see the relationships between them. Only then will we obtain a clear understanding of both existence and being.

Existence

Even tough, with roots in the sixth century AD, the word “existence” was introduced into the philosophical discourse by Avicenna, an Arab philosopher of the tenth century AD, its meaning is still elusive and needs to be integrated into the structure of metaphysics.

To establish this need, it ought to be sufficient to point out first that existence is not a quality of matter and therefore solely related to matter and physics; and second that existence by itself can be made to appear as a static and inert entity. That clearly is the way to deprive existence of all its vitality and validity. To avoid both pitfalls, the word existence has to be transformed into a concept, namely an independent entity. This aim can be achieved by defining existence as the active work of integration of matter, energy, and spirit, not in the abstract, but in the here and now, into one concrete unit. We can now verify the reality and rationality of existence by applying to it Kant’s criteria for the validity of a concept. They are: “qualitative unity,” “truth,” and “completeness.”

Does existence manifest a qualitative unity? It seems to be indisputable to say that the characteristic shared by the world inside and outside us is existence. Existing is what I do: I constantly integrate matter, energy, and spirit — just as a stone does. And since I am consciousness, I am able to separate myself from the world outside me. There I distinguish three major entities: You, I, and the Physical World. Since You confirm the reality of my sensations of the physical world, and since You verbally confirm to me that what You do is to exist also, You and I should quickly agree that You, I, and the World exist. There. Everyone might be satisfied — except the philosopher. Using Descartes technique, however, we beg philosophers to wait until we finish our argument before passing their ultimate judgment.

Does existence manifest completeness? Existing is something done by everything that is here and now; was in the past; and is reasonably expected to be in the future. Existing is done by all such units variously defined as: Carmine; man; woman; Pegasus; table; earth; star; cosmos, the idea of beauty, and so on. Even the idea of Pegasus requires air and vocal chords, let alone pen and ink, for its creation and transmittal. Existence now appears to be an indisputable, a very firm concept. Or, is it?

Does existence manifest truth? A minor question of the philosopher can be easily addressed. The question what is the world of existence, is quickly answered again in this fashion: Existence is an activity performed in the integration of all the matter, all the energy, all the spirit — including all the You(s) and I(s) — that have ever existed and will ever exist (as they manifest themselves to our senses and our mind). The major objection that remains is the very existence of existence. So far we have the same understanding of existence as we had reached observing the physical world. What we have added is only a name, but not a deeper understanding of this reality. (If the issue were that easy, it would have been settled long time ago). The issue is deep. Let us suggest that the core of the difficulty lies in the fact that Existence is a complete system of its own. And, as Gödel taught us, we cannot analyze the validity of a closed system of thought while remaining inside it. Hence the solution might be found, with guidance from Benedetto Croce, in observing our concept from an opposite point of view: the point of view of being. If we get a thorough understanding of being, we will automatically obtain a good understanding of existence.

If this approach is conjectural and abstract, there is another more direct route to discover the inherent link between existence and being. We know that all existence is relative.Existing is not forever: we know that this world started at some point in time. Existing is partial: the entire cosmos occupies only a part of time, if not a part of space also. Existing is not true forever: our knowledge has often drastically changed in the past and is clearly destined to change in the future. Existing is not always real: Pegasus is not real, and still it has existence in our mind. But why do we have such an understanding at all of existence? The answer is rather simple. We have such an understanding of existence because we relate all these characteristics to an absolute. A partial and relative activity requires the whole and the eternal — an entity that metaphysicians call being — to be fully understood.

Being

Let us try to defuse the explosive charge that this word has always carried with it. We know nothing of being. Personally, with my mind alone, I know nothing of being. I intellectually conceive of it as Fullness; yet, if you insist that being is Emptiness, I will have to agree that you might be right — even though I would prefer we both agreed that being is Fullness and also Emptiness. If you insist that being is Nothingness, I will also agree with you — but I will ask you to define Nothingness. And I will beg you to consider whether by this route we do not involve the discussion in the biggest mystery of them all: how can not-being create being, or at least existence? Miracles are disallowed in metaphysics.

More. I am convinced that, intellectually, I will never be able to understand being, because to comprehend being I should (almost physically) be as large (or as small) as being. It is with my experience and with my heart that I know being. But once I say that, you and I agree that I have abandoned the terrain of philosophy and entered that of religion. And we both might want to stay a little longer in the field on which we have labored so hard.

We begin to have a better understanding of being if we agree to conceive of being as something like the limit in calculus — a guiding star, something toward which we must go, something we can never quite reach and beyond which we certainly cannot go. In philosophy this entity has traditionally been called the absolute. Philosophically, then, we can list these as the most important attributes of being. What is — alone — dialectically includes the concept of not-being (an empty set). What is — alone — exists in time and out of time; namely, it forever was, it is, and it will forever be. What is — alone — by reconciling within itself all opposites is the epitome of perfection: it is true, it is beautiful, it is good, and just. Indeed, it is absolutely true, absolutely beautiful, and absolutely good and just. It is the absolute.

Complementary Knowledge confirms us in the validity of the most fundamental conclusion. In Complementary Knowledge all contradictions are resolved: Being is being and it is also not-being. (Complementary Knowledge can achieve this much because it sees the reality, not as a linear, but as an organic and dynamic set of relationships.)

More. The “I” can accept such pronouncements only on the basis of the understanding of not-being. Thus the essential contribution of agnosticism to the thought process. It is only when the “I” is allowed to choose between being and not-being that the “I” can make an informed selection. This process can then be aided by Kant’s criteria for the validity of a concept — preferably asked in a different order.

Is there truth in being? If “to be” is what being does, then the truth of being is unquestionable. It manifests itself to me in the entire order of existence: all that exists is a (partial) manifestation of being. It manifests itself to me in the entire order of rationality: there is nothing rational I can say about anything, unless I complete the thought or observation by first asserting its being.

Is there completeness in being? If “to be” is everything and everywhere, then there is utter completeness in being. Being is absolute — a renewed conclusion, from which we can now draw a novel observation. Since existence is unavoidably limited, it is not what exists that is. It is the absolute that is. Indeed, philosophically speaking, only the absolute is. Everything else simply exists — and because of the completeness of being, everything exists only in relation to being.

Is there qualitative unity in being? If being is absolute, then it has the ability to resolve in itself all seeming contradictions. The truest knowledge of being is indeed acquired through complementary knowledge. In being, there is no truth or falsity; no beauty or ugliness; no caducity or eternity. In being there is everything — and nothing. In being, there is beauty and also ugliness; truth and also falsity; goodness and also badness. (At times it seems we are surrounded by ugliness and falsity and badness — hence, they exist in these particular manifestations of being; when they are in being, given the existence of free will, they are not necessarily created by being.)  In being, there is even not-being. All rationalistic limitations that one attempts to impose upon being stem, not from the reality of being, but from the smallness of our mind. If we start from the assumption that being is absolute freedom and absolute power, all rational limitations vanish. (And let us definitely eschew the problem of the existence of evil.)

Absolute freedom and absolute power, to be operative in the world that we know, must be reduced to spirit. Only spirit can be everything and everywhere. The law of impenetrability of bodies does not apply to being. Hence one can say that being is spirit.

If this conclusion is ambiguous, contradictory, inscrutable — well it is.  And it is as it should be. Otherwise, we would be equal or even superior to the absolute. This is not an admission of defeat. Rather, it is a realistic recognition of our human limitations. If we accept our limitations, we realize that we have made tremendous strides. We have acquired a rather in-depth knowledge of two essential, complementary concepts: existence and being. As far as we are concerned, one cannot be without the other, and each completes the other. Indeed, instead of wallowing in our limitations, let us see how we can go forward from here.

Not yet an Equivalence

It is now appropriate to call upon Relational Logic to verify the validity of our work. Let us remember that the equivalence relation requires a third term to be valid. Thus having acquired two concepts we need to find a third one to which both concepts are equivalent. If we fail in this enterprise we have once again failed to build a solid structure of metaphysics. As Buckminster Fuller taught us, a two-legged stool does not stand: It is the triangle that is the basic stable construction.

We have to find a new concept that shares some of the features of being and existence. The term “essence” comes to the rescue. The link between existence and being is essence.

We might thus have the equivalence of existence to essence to being. Let us see whether there is indeed truth in this assumption, namely the possibility that Essence is the relation of existing to being.

 

The Problem of Essence

To be a concept, essence has to have a reality of its own. Tested against this need, we realize why the word essence has created so many great difficulties in metaphysics. The problem is that by itself the word has no meaning. “Essence is” has no content; hence, it means nothing. The phrase has to be completed in such a fashion as “the essence of” is. Then it behooves us to inquire, not what is essence, but what is the essence of both being and existence.

For the essence of being one turns to metaphysics and discovers all the attributes that the human mind has been able to conceive as pertaining to being. For the essence of existence, we have to turn to physics and all other hard sciences. If we do that, we discover that these two concepts share a characteristic of fundamental importance: The essence of both being and existence is continuous transformation: try to catch being and you will be lost. Philosophy has identified this continuous change by the word becoming.

We have thus found the third entity that might be a concept to which both being and existence are equivalent.

Becoming

The essence of being is becoming, just as the essence of existence is becoming. A traditional metaphysician would not flinch at the statement that the essence of being is becoming. Yet, undoubtedly a modern metaphysician will. Let us try to allay possible concerns, then.

One qualification. While it is indubitable that the essence of existence is becoming, the definition of the essence of being also as becoming can be accepted only on the basis that being, being an absolute concept, includes also the concept of becoming.

The important realization is that we now have three concepts, and potentially a fully valid equivalence. As far as the dictates of logic and epistemology are concerned, we are now on solid ground. It only remains to be seen whether we are also on fertile ground; whether the three concepts indeed form a system of thought. If they do, we have the basis for a reconstruction of metaphysics that might become acceptable to the modern mind. On the basis of our three concepts, an entirely new ontology opens up to analysis: relational ontology.

Relational Ontology

There are many ways in which Being, Becoming, and Existence are related to each other or, more modestly, can be assumed to be related to each other. They can be partially meshed as in a Venn diagram; or they can be placed along a spatial and temporal straight line; or the line can be assumed to perform all sorts of erratic movements. Having gotten good results from various other applications of Relationalism, however, let us get the benefits of that experience. Let us assume that our three concepts are in an organic relationship with each other, as in this typical construct:

 

Figure 3. The Metaphysical Process

This is a construction that allows us to relate the “full story” of metaphysics: the metaphysical process in its entirety. For some reasons that we do not know, being one day (or, if time does not ontologically exist, forever) decided to become existence. Being, being pure spirit, being the absolute, was free to do that and had the power to do that. Once being reached the state of becoming, out of the billion and zillion possibilities, he/she/it chose (was forced? cajoled?) to become existence.

Existing, a term that presented a series of insurmountable difficulties either by itself or in relation to essence, when put in relation to being acquires its full meaning. Existing is true and real and here and there and everywhere and at every moment — not by itself — but in relation to being. Existing assumes all those characteristics not as a creator of all those qualities but as a participant in the essence of all the qualities of being.

We have thus reached the sanctum sanctorum of metaphysics: Being is the essence of existence — just as existence is the essence of being. Being has the existence of pure spirit. Hence, what is — alone — dialectically includes the category of existing. (Existing does not include being; existing can only be a part of being; therefore, existing is not being).

Indeed, the full story of where we are intellectually at present can be related only by realizing that the metaphysical process can also be logically interpreted starting from existence and leading to being. We would then say that existence tends to become being or even that existence creates — “invents” — being.

In this context, this writer has no comment to make in relation to this second logical possibility — except to specify his conviction that he can understand the world, not because he makes it up, but because we are made of the very same essential constitutive elements: matter, energy, and spirit. The noumenon of salmon is a chunk of existence, just as my noumenon is a chunk of existence.

The concern is to point out that, once we understand existence, being, and the link between the two entities, we can also understand the meaning of “am.” To be is what being does. Rather than keeping this discussion in the abstract, however, it might be better to relate it to human beings, specifically by inquiring whether I am indeed consciousness.

Am I Consciousness?

If I were part of being, I would indeed “be” consciousness. Instead, I am a part of existence. Therefore I have to conclude that I am not consciousness. I only exist as consciousness.

These differences can be clarified as follows. Since what exists seems to be so real, it is natural to believe that what exists is. Yet, it is not. It is not a portion of being but of existence. The table in front of me is not; it exists. Because of the lack of truth in it, the expression “what exists is” has led to jargon and gibberish that cannot be tolerated by philosophers —hence it has led to the abandonment of the metaphysical project.

To put it in sharper tones, what exists is not ontologically real. By itself, it is a figment of our imagination. By itself it could not last one second. The nominalists were and are right. What exists, exists only in relation to being. Everything, namely the reality of men, women, and the cosmos exists only in relation to being. Only being is.

However we construe the story of creation, as things stand, reduce the entire human race to one person and you realize that the human race will soon be extinct, because the individual person is not; it only exists. More precisely still, the individual person exists only because of society. It would not even exist without society, without the rest of the human race. (And society, of course, can even less exist without individual human beings.)

Rather than expounding much more on things that we do not know, on things which we do not fully understand with our mind and our powers of reasoning, let us draw the outline of a much more certain theory, the Theory of the Little I.

Toward a Theory of the Little I

If we now fully examine our opening statement, namely ”I am consciousness,” we have to conclude that the statement is false: “am” does not apply to me. The correct statement is “I exist as consciousness.”

Then the linguistic compulsion to add the preposition “as” makes me reflect that such a statement would be limiting in the extreme. Yes, I am not, I was not, and I will not be. Yes, I do exist only for a brief moment in time. But I exist much more than as consciousness alone.

Let me, therefore, give you a capsule description of a theory that I like to call the Theory of the Little I.

“I” came into this world as a Little Big Bang on December 8, 1935, at 12:00 am, the day of the Immaculate Conception, son to Luisa Capuano in Gorga and Ulisse Gorga…

Concluding Comments

Being is.

Everything else exists.

Everything exists in relation to being.

If this paper has established these three statements firmly in the mind of the reader, it has accomplished its aim: The seed of metaphysics is firmly implanted into the modern mind. The seed will grow to shed light on the past and to illuminate the future.

 

NOTES 

  1. The writer is also familiar with another such case. Is saving equal to investment? In mainstream economics, it is; in Concordian economics, it is not.
  1. Vide Jean-Paul Sartre, Being and Nothingness [1943 (1956)].
  1. Perhaps it is worth spending a few words on the “reality” of sensations. This morning I woke up and heard a crackling noise. I paid no attention to it, got up and peaked though the window curtains to discover a beautiful Santa Fe morning. Obviously I went back to bed. My wife woke up and asked: “Is it raining out?” I firmly assured her that it was not raining out, whereby we both began to focus on the source of the crackling noise and we assuredly decided that it was a defect in the air conditioner. To make a long and complex story short, we established the following equivalence: sensation/I = word/noise = rain. We tested the validity of this assumption as soon as we shut the air conditioner and the noise disappeared. As to the reality of Pegasus, we hit the books and we find it there.
  1. To realize the full import of what our early ancestors accomplished in the field of methodology, we need to remember that by the time of Aristotle, while the principles of identity and non-contradiction were codified into a set of rules governing them — and, apart from Hegel’s challenge to the principle of non-contradiction, they have been accepted with minor variations by all subsequent systems of logic — the principle of equivalence disappeared from sight. Aristotle talked of the principle of excluded medium as the third essential principle constituting what we call the system of classical logic.

And the substitution of the principle of equivalence with the principle of excluded middle did not prove to be a permanent solution either. It served as a practical expedient for eliminating from the discourse terms that were in between such extremes as “black” and “white” These were easy choices. When the terms of distinction became rather more subtle than that, the mind could not remain satisfied with this short-cut. Thus the Renaissance mind gradually lapsed into the unbearable uncertainties of agnosticism.

When Descartes tried to reestablish a logical basis for certitude in our reasoning, he substituted the principle of excluded middle with the principle of indifference. No one seems to know when or by whom the principle of indifference was formulated. But it was well-known in the Sixteenth and Seventeenth Century. In fact, it was formally incorporated into a new system of logic by Descartes, rational logic, with these words:  “If some of the matters… should offend at first sight, because I… seem indifferent about giving proof of them, I request a patient and attentive reading of the whole… for it appears to me that the reasonings are so mutually connected… that, as the last are demonstrated by the first which are their causes, the first are in their turn demonstrated by the last which are their effects” [Discourse on the Method (1637) l938, p. 60]. In live discourse, this Cartesian method is translated as: “Please, let me finish.”

Evidently dissatisfied with Descartes’ solution, Hegel substituted the principle of indifference with the principle of process — because a third principle must exist to form a system of logic. He obtained dialectic logic. And forms of dialectic logic existed already at the time of Plato. As is well known, Alfred North Whitehead did say: “The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.”

  1. Paul Johnson’s Intellectuals (1989) is a must read.
  1. But consumerism by itself is a non-issue. There is also the consumerism that puts people in contact with each other, the consumerism in which things become extensions of one’s personality. This is the consumerism that celebrates life.
  1. Quoted in Otto Nathan and Heinz Norden, eds. Einstein on Peace (New York: Avnet Books, 1981 ed, p. 376). From a pamphlet published by Beyond War in 1985 entitled A New Way of Thinking.
  1. See, Carmine Gorga “On the Equivalence of Matter to Energy and to Spirit,” Transactions on Advanced Research, July 2007 | Volume 3 | Number 2 | ISSN 1820 – 4511: 40-45 and is available at http://internetjournals.net/journals/tar/TAR2007july.pdf.
  1. The conflation of many meanings that makes naïve realism possible is perhaps best represented by this sentence by St. Thomas Aquinas, a sentence that he formulated to validate Aristotle’s teaching on the subject: “But ‘essence’ is used inasmuch as it designates that through which and in which a being has the act of existing” (On Being and Essence, chap. I, In Selected Writings of St. Thomas Aquinas, Robert P. Goodwin trans., NY: Macmillan, 1965). There and elsewhere, being is consistently defined as “that which is,” in any of its great variety of manifestations.

Acknowledgments

This paper is uniquely due to suggestions and comments by Msgr. George P. Graham on an earlier paper. Near total agreement with the analysis of Professor John Lukacs, At the End of an Age (2002) has been a source of inspiration and comfort in writing this paper. I would also like to acknowledge the moral and intellectual support provided over the years by Professor Franco Modigliani, a Nobel laureate in economics at MIT, in the application of the tools of analysis presented here in the difficult field of economic theory.

In sociology/political science

 The original publication is available at SSRN: http://ssrn.com/abstract=1696013 or http://dx.doi.org/10.2139/ssrn.1696013

SOMISM

BEYOND INDIVIDUALISM AND COLLECTIVISM

 TOWARD A WORLD OF PEACE AND JUSTICE

Carmine Gorga

President, The Somist Institute

October 2010

  

Abstract 

Somism attempts to discover some of the interrelationships that exist among politics, economics, law, philosophy, and spirituality. These interrelationships tend to transform our understanding of each discipline treated. They will eventually become safe guides to action.

 

Short Bio

Carmine Gorga is a former Fulbright scholar and the recipient of a Council of Europe Scholarship for his dissertation on ”The Political Thought of Louis D. Brandeis.” Using age-old principles of logic and epistemology, in a book and a series of papers Dr. Gorga has transformed the linear world of economic theory into a relational discipline in which everything is related to everything else—internally as well as externally. He was assisted in this endeavor by many people, notably for twenty-seven years by Professor Franco Modigliani, a Nobel laureate in economics at MIT. The resulting work, The Economic Process: An Instantaneous Non-Newtonian Picture, was published in 2002 and reissued in an expanded edition in 2010.. For reviews, see http://www.carmine-gorga.us/id18.htm. During the last few years, Mr. Gorga hasconcentrated his attention on the requirements for the unification of economic theory and policy.

Communism, as one of the extreme forms of Collectivism, is dead. And Individualism is not too well off. Even though guided by ideologies oscillating between these two extreme categories of thought, the social, economic, and political conditions that once gave rise to Communism are rampant again the world over.

It is clearly time to look for an alternative theory of political science. Somism might just be what we are searching for. Somism stands for the theory and practice of the Social Man and Woman, the Civilized Person; it is a contraction of “men and women in the social context.”

The roots of Somism are very old in substance and rather new in form. Just as Individualism and Collectivism find their roots in rationalism—whose death throes we are now witnessing; 1 so Somism is rooted in relationalism, an expansion of rationalism; and relationalism, in turn, is rooted in relational logic.2

The Fundamental Structure of Somism

Somism is an intellectual attempt to fuse the aspirations of Individualism with those of Collectivism. This is not a search for the “third way”; rather, it is a search for the right way. The historical roots of Somism lie, in equal parts, in Individualism and in Collectivism. The full display of Somism is contained in the following figure:

 

Figure 1. The Somist Synthesis

This construction allows us to make a fundamental adjustment in our understanding of the world of political science. It allows us to see that Individualism and Collectivism, rather than being opposed to each other, are two complementary conceptions of the social and political reality. One moves the observation from society to the individual person, the other from the individual person to society. The two visions, if and when complete, are perfectly symmetrical.

The dialogue, and often the lack of dialogue, between adherents to Individualism and Collectivism primarily stems from their insistence on giving primacy either to society or the individual person. Underneath this choice there are terribly complex philosophical issues, 3 which are eschewed here just because Somism is an attempt to escape the circularity of argumentation that is unavoidable in any symmetrical visions of reality. To achieve this feat, rather than two, Somism posits the existence of three objective entities: Man, Society, and Man in Society. The difference between the Individualist, the Collective, and the Somist understanding of society can be put this simply: for Individualists, society does not exist; 4 for Collectivists, society is composed of the numerical addition of Self plus The Other; for Somists, society is composed of the relation between Self and The Other. Somism is best approached through an analysis of its content.

The Content of Somism

Somism accepts the existence of both Man and Society, not as separate elements but as an integration of the two. Hence, the Social Man and Woman, the Civilized Person: the individual person observed into the context of the civilized society. And, with the goal of building or rebuilding the civilized society, rather than spending much time on the analysis of these general characteristics, Somism prefers to deal with the specifics. Specifically, Somism makes twelve concrete and three abstract recommendations. The first four relate to politics; one relates to sociology; and four relate to economics; some of these suggestions are then fused into three additional recommendations to be applied in international relations. These suggested practices are unified by the word “Concordian,” hence we will be looking at four recommended practices of Concordian politics, one practice of Concordian sociology, four practices of Concordian economics, and three practices of Concordian international relations—as well as three intellectual recommendations about Concordian financing, Concordian ontology, and Concordian spirituality.

Concordian Politics

Four recommended practices of Concordian politics are: Unity in Diversity; Popular Sovereignty, Democratic Equality, and the Rule of Law. These four core ideals have been discovered by this writer’s colleague, William R. Collier, Jr., who synthesizes them in United People’s Democratic Republic, from which the acronyms Upadaria and Upadarianism spring forth.5 The four ideals are an integrated set: it is not possible to achieve any one of them without achieving all four of them as a pervasive and lasting state. Also, while these four core ideals are well understood individually, they have only by Collier been proposed together as an integrated system of politics.

Unity in Diversity. As the Biblical insight states, “A house divided against itself cannot stand.” Unity is essential to the preservation, indeed to the very dynamic existence, of any political state. Without unity nothing can be achieved; and whatever was ever achieved at great cost in the past is put in jeopardy by protracted disunity. If so, how can unity be achieved? The answer is only apparently contradictory, which means that it hides a deep verity. In a state like the United States unity can be achieved only if the infinite diversity of “the other” is deeply respected. This truth is self-evident and has mostly been practiced in the United States; yet, it is valid for every other country in the world as well. There is no state that is so homogeneous as to not require respect for diversity; and even if one could produce a country homogenous in one respect, it would not take long to discover elements of deep diversity in its population—whether in relation to distribution of incomes or distribution of talents.

In the face of such ineradicable differences among human beings, how can one achieve unity? The magic solution—and the solution is indeed magic, because it is not reducible to the constraints of mechanical reproduction—is to reduce the search for unity to the area of essentials. The greater the respect for diversity, the higher the chances of achieving unity. The search always starts anew. The solution is never achieved forever.

The respect for diversity is rooted in the acknowledgment that everyone has something to bring to the table of life. Not only that. The respect for diversity is rooted in the acknowledgment that diversity is the source of life—whether biological or intellectual life.

Essential are matters that relate to preservation of existence and morality.

The first duty of a state is to preserve its existence; the second is to preserve the conditions of morality. And morality cannot be reduced to sex. Morality is the condition that allows for a maximum space of love and the restriction of the sources of hate among human beings. Thus morality, properly interpreted, fosters the life of other human beings and automatically the life of all human beings. Hence morality is the precondition for the preservation of the state. In matters of preservation of existence and morality there can be no compromise; in all other cases compromise ought to reign—especially if, as Louis D. Brandeis pointed out, the other fellow insists on wanting something I want to get rid of.

Popular Sovereignty. In a non-theocratic state, the sovereign is neither the king nor the mob. In the United Sates, it is clear who reigns. The sovereign is We the People. We are all singly and jointly sovereign. We govern ourselves; we have self-government; we have government of the self. Which means that we, the ideal citizens, are those who have fully integrated into our existence the principle of Unity in Diversity—as well as those who are fully conversant with the principle of Democratic Equality.

Democratic Equality. Equality has become an ideology capable of destroying the infinite individuality of each human being. What is equality then? While in the present we are all unique, we are all potentially equal: we all have the same potential of becoming saints and/or sinners. We are all equal only to the extent that we are all different from one another. Equality does not destroy all differences. True equality tends to elevate each one of us to the standards of those who have pursued and achieved the highest virtues in life. This is a topic whose most important characteristics are best addressed within the concrete context of economic policy.

Rule of Law. We can achieve and preserve unity only if we live by and in the law. We will respect the law, because we made it. After much considered opinion, we can even change the law. We can change the law because we made it. We all contributed to the extent of our potential to the creation of the law. We make the law because we govern ourselves. And the best laws we make are those that respect each and every one of us in our awesome diversity.

If we pursue these four core ideals, we achieve Concordia. So far, Concordia is the private Utopia of a few Concordians. If, as John Kenneth Galbraith put it to this writer, our thrust is in the right direction, we will get there: we will live with multitudes in Concordia. In any case the journey, as Robert Louis Stevenson put it in “El Dorado,” is more important than the destination. The important decision is to start walking together now.

Come to think of it, do not these four core ideals constitute the spirit of the United States Constitution? Do they not form our spiritual constitution? If we aim to preserve our Constitution, as stressed by Benjamin Franklin, we had better observe these four core ideals in our daily lives. We had better walk in our forefathers’ shoes. The walk is tested and true. It is the tempting detours that are leading us astray.

Concordian Sociology

From Sun Tzu to von Clausewitz and their followers, the world has spent an inordinate amount of time devising ways to create relations of subjugation and dependence among people. The genius of the American Revolution and the United States Constitution was to create structures of Political Independence. It is now time for everyone to learn socio-economics, a task which is much simplified in the classic, “I, Pencil: My Family Tree as told to Leonard E. Read”. It is available at http://www.fee.org. The lesson learned by Leonard Read is that economics is ruled by relations of interdependence. Hence, the core of Concordian sociology is composed of only one recommendation that can best be put in the following terms:

Fully appreciative of the many blessings of the Declaration of Independence

 it might now be an appropriate time to draft a

 A DECLARATION OF ECONOMIC INTERDEPENDENCE

 

Whereas the Declaration of (Political) Independence has, without open discussion, been

mostly transformed into a Declaration of Personal Independence;

Whereas this ideology has given rise to the Age of Entitlements, an age dominated by the conception that there can be rights without responsibilities;

Whereas the lack of personal and civic responsibility has generated the conception of Life as

One-Against-All;

Whereas this emphasis on our own welfare—independent of, if not at the expense of, the welfare of our fellow citizens—has created economic insecurity

for everyone, rich and poor alike,

we affirm that our greatest social need

is

to build a society

in which

the reality of

 

Economic Interdependence

 

is fully acknowledged.

 

In this society, we declare, the fundamental conception of Life is

One-With-All

and we trust that the effect will be economic jubilation for all.

In order to build such a society

we are called upon to realize the political ideals of

Liberty, Justice, and Goodwill toward one and all,

specifically, we are called upon to realize the four core ideals of Concordian politics:

Unity in Diversity

Popular Sovereignty

Democratic Equality

Rule of Law.

                                                           In order to build such a society

                                                                                    our challenge is

to deny

all

      structures of individual and societal selfishness

and

to affirm

A Bill of Economic Rights and Responsibilities.

Concordian Economics

The core of Concordian economics is composed of the following integrated set, a bill, of economic rights and economic responsibilities.6 This bill is constructed on the basis of the needs of the three factors of production that were identified by Classical economists as land, labor, and capital—enlarged to four factors so to clearly distinguish between modern forms of financial and physical capital.

First Set: We all have a right to access natural resources and a responsibility to compensate the community for the exclusive use of such resources; 

Second Set: We all have a right to enjoy the fruits of our labor and a responsibility to work to the best of our ability; 

Third Set: We all have a right to access national credit for the purpose of creating new wealth while spreading its ownership among all those who create it and a responsibility to repay any such loans; 

Fourth Set: We all have a right to protect our wealth and a responsibility to respect the wealth of others.

As it can be seen, this set of economic rights is rooted into its own correspondent set of economic responsibilities. Indeed, as pointed out by this writer in the Spring 1999 issue of the Journal of Markets and Morality, economic rights can be legally and morally acquired only through the exercise of their correspondent economic responsibilities.7 This is a construction that does not only allow us to receive economic justice from everyone, but also to grant economic justice to everyone else.

Since this bill of economic rights and responsibilities is an expression of true interdependence, its implementation will do wanders; especially if implemented at home and abroad. Hence we need to advocate for Concordian international relations; we need to build a world of peace and justice.

Concordian International Relations: Toward a World of Peace and Justice

We all talk peace. From the United Nations to City Halls to family parlors, we all talk peace. But, harsh as the expression might sound at first hearing, we do not do peace. We seem to labor under the spell of The Great Rationalistic Illusion that it is enough to utter the word in order to perform the deed. There are three actions we have to pursue, if we really want peace. We have to create three sets of teams for peace and justice.

First Set of Teams Experts in Foreign Affairs Within A Department of Peace. We have to stop thinking that we have to destroy the town in order to save the town; that we have to destroy the country in order to make it safe for democracy. The Department of Defense can save us from attack, but it cannot bring peace to lands where there is no peace. It is only a Department of Peace that can bring peace abroad—and in the long run it is the only instrument for mankind to win the war against terrorism.

As advocated by US Representative Dennis Kucinich, let us establish a Department of Peace right here in the United States. If we do that, it is reasonable to expect that Europe, and perhaps even Russia and China and Iran and Venezuela, will follow suit. Duplication of effort, redoubling of effort throughout the world should be welcomed.

Let us assist Palestinians to establish their own Department of Peace immediately thereafter. And of course, the other country that should be encouraged to establish a Department of Peace is Israel. And then there are all other countries from Iraq to Sudan. We know the list.

The most important element in the chain of needs is that the Department of Peace, without resources, would be a mockery. But where do we find the resources, especially at a time of substantial deficits and budget cuts? Well, the first candidate is a voluntary—free and willing—transfer of, say, ten percent of resources from the current budget of the Department of Defense. The experts in this department will candidly tell you that it is impossible—with their means—to stop terrorism. What the voter has to see is that, given the proper means, it is possible to stop terrorism. We cannot give in to pessimism and despair. We must indeed stop terrorism.

Only a Department of Peace can plan for peace, by intimately knowing the geography, the history, and the culture of each county in which the USA is involved, by creating SWAT Teams for peace and justice for each country, then by training local people to carry out their mission of peace and justice, and finally endowing them with satisfactory intellectual and material means to achieve their goal. These then are the next two sets of teams that we have to create: Teams for Peace; Teams for Justice—teams that no longer talk and plan about peace and justice, but teams that actually carry out the tasks of peace and justice on location.

Second Set of Teams SWAT Teams for Peace. The second suggestion is for the Department of Peace to create an appropriate number of SWAT teams for peace. (Would not ten percent of the people currently within the Department of Defense give an eyetooth for the transfer of their energies toward such a function?) Call them Circles of Love. I prefer to call them Mary’s Messengers of Mercy, because Mary is the only person who is highly respected in all three monotheistic religions. If we monotheists truly honor her, she will be more easily honored by other religions as well.

The Circles of Love should do precisely what their name implies: They should create circles of love around hamlets, and villages, and cities, and nations where hate prevails today. Depending on the number of teams available and the specific mission to be carried out, the pacification program should proceed house by house, starting from the outermost ring of the area of trouble and proceeding toward the center. The ideal is to build “circles of love” around every trouble spot of the world.

Each team should be composed of at least two or three volunteers—one volunteer from each of the major faiths that prevail in the areas to be pacified. There should be no discrimination as to age or sex. The specific formation of the teams will depend on the particular needs to be addressed. Indeed, one need not even go abroad. With perhaps only minor modifications, the entire approach might also be used to help solve many problems of “downtown” areas in all major cities of the world. In each nation there seem to be areas in which peace does not reign.

The prerequisite should be a simple willingness to pray together with the victims of violence. The teams should implore for the shooting to stop—and for the vicious circle of revenge to stop. No sane politics issues from the barrel of a gun.

A More Specific Definition of Means. Governments use force trying to achieve peace. And they rarely succeed. The churches, the mosques, the synagogues, and most other religious affiliations know this reality quite well. They have always preached that peace can be achieved only through love. The time perhaps has come to transform preaching into teaching and enacting.

Training the Teams. Perhaps the most important tool to be given to each member of the team is the ability to pray together with people of a different faith. Each team should be trained to speak local language(s), and should be familiar with the history and the culture of the place to be pacified. But development of leadership skills and negotiating techniques such as “getting to yes” should also be part of the curriculum. Above all, members should not only teach but practice the four core ideals of Concordian politics.

Participation of Civil Authorities. The various religions might want to start the effort on their own. But, if the formation of such teams should involve large number of trainees, financial support from various Departments of Peace might be a necessity. To a very minimum, overall support from governments might be requested from the start for a variety of purposes: for instance, to obtain current intelligence data, and at least detailed information about the geography, demographics, and economics of the area. But since the “circles of love” should be conceived as an army of love, advice as to strategic deployment of the teams should also be obtained from military experts of the various nations that might want to participate in the effort.

Risk to Life and Limb. Undoubtedly, there would be risk to life and limb involved in the deployment of such teams. The rationale for accepting this risk is simply stated. If the various Departments of Peace and the various religions do not take the initiative to obtain peace, the military sooner or later will intervene. Through the military, risk to life and limb is increased many times over for all contestants—not excluding extant civilian populations.

Third Set of Teams SWAT Teams for Justice. The third suggestion is for all religions and the Department of Peace to create SWAT teams for justice. Specifically, SWAT teams for economic justice. It is easy to conceive of teams of farmers and plumbers, carpenters and electricians working together with local populations building projects that are essential to the sustenance of life—all the while using the four sets of economic rights and economic responsibilities concerning land, financial capital, physical capital, and labor. They would indeed do peace; they would indeed do justice.

 

Upadaria or Concordia, the New Utopia

The health of all past Utopias has not been too strong or long lasting. No sooner was their intellectual structure erected that it was destroyed by mad men and not a few mad women in authority. Indeed, if the world appears to be touching the bottom of despair these days, it is because we are no longer able to do much better than construct Negative Utopias—and with Communism and Fascism we came too close to realizing them. What is the hope then of ever building Upadaria or Concordia, to use words coined by Bill Collier, as the New Utopia?

The hope stems from the realization that all past Utopias were going into the future blind. Concordia is instead led by Somism in its tripartite division of Concordian politics, Concordian sociology, and Concordian economics—to be implemented both at home and abroad. And, if this is not enough reassurance yet, Somism has in its quiver three additional recommendations that can also be deployed: Concordian financing; Concordian ontology; and Concordian spirituality. These are constructs that, even without our awareness, enter deeply into every aspect of out lives.

Concordian Financing. So far, this writer has not dared to utter the word “capitalism,” not so much because it is one of those ultimate words that arrest the conversation, but because we did not yet have the proper framework of ideas to deal with it. We do now. The inner spirit of Capitalism is such a mysterious and powerful force that it was transmogrified into State Capitalism, rather than being destroyed by its presumed mortal enemy, Communism. (Communism is State Capitalism-minus-political-freedom.) Such an adaptable institution as Capitalism must be a peculiar variety, a stunted variety, of true Capitalism. (By the same token, State Communism can also be construed as a transmogrified form of true Communism.)

The Capitalism of our daily experience can in fact be identified as 5% Capitalism—or Capitalism that favors only about 5% of the population.

These transformations can be clarified when placed into our familiar framework:

 

Figure 2. Three Forms of Financing

The middle rectangle of this construction presents a new entity, Concordianism, not as a form of abstract Concordian economics but as a specific form of financing: Concordian financing. (Concordianism is not as a “third way” between Capitalism and Communism, but the right way.) The task is to build a system of financing that benefits 100% of the population 100% of the time. Other possible names are: 100% Capitalist, or Upadarian, or Somist, or Relational financing. For such concrete alternatives, the reader might look into some of the financial institutions designed by this writer over the years: A Mutual Assurance Fund, A Financial Interdependence Fund, and A Bottom-Up Monetary Policy.8 Next recommendation.

Concordian Ontology. It was a healthy shock to this writer’s being a few years ago to discover that at the same time Plato—circa 500 BC—set the intellectual world of the West ablaze with his conception of Being, Buddha set the intellectual world in the East ablaze with his conception of Not-Being. The world has not stopped intellectualizing about the meaning of these two entities ever since. In the process, both the East and the West have—though apparently unawares—agreed that both conceptions cannot be static. They must be dynamic. Hence both the East and the West have invented the conception of Becoming. Yet, the West has lost its sense in the totally abstract conception of Essence—without ever asking the simple question: essence of what? The East, instead, has been much more advanced and concrete in its intellectualization of Becoming. The East has deeply investigated it through the amazingly complex and fertile apparatus of Ying/Yang. Strangely enough, but quite naturally enough, the Middle East—or more specifically, the Muslim World—came up with a middle ground conception beyond Being and Becoming: At its very birth during the VII Century AD, Islam discovered the conception of Existence. Western ontology has fought the acceptance of this conception ever since, preferring the unavoidable death of metaphysics.

Relational methodology allows us to rebuild ontology along the following lines:

Figure 3. Relational Ontology

Figure 3 reads as follows: Being, an entity which we know not, hence might equally appropriately be called Not-Being, becomes Existence. And Existence constantly attempts to return to the state of Being.

Concordian Spirituality. We will not achieve peace—and concord, or Concordia—in the world, until we achieve intellectual peace. Relational ontology offers us a chance to create peace horizontally, so to speak, across the vast geographic confines of the world. Yet deep—or vertical peace, so to speak—peace and concord will not be achieved until we obtain pace internally within each one of us. Relational spirituality might grant us that much. Again, the world of spirituality is replete with strife. We have even given a name to this state of affairs: we call it the war of the “two cultures.” It all starts with, well, the Cartesian and rationalistic conception of the world; namely, the split between matter and mind. Starting from this dualistic, hence totally symmetric—and yet still presented in a linear fashion—conception of the world, our familiar relational methodology offers us the opportunity to construct a tripartite and organic understanding of the world.

When Einstein revolutionized the world of physics, he announced his discovery as the equivalence of matter to energy. Yet, neither he nor any other physicist has asked this question: if the relation between matter and energy is one of equivalence, where is the third term? This writer discovered the third term one day while reading Fritjof Capra’s The Tao of Physics (1980). He was then up up up in the sky over the Atlantic. Did this position help him along? Whatever the case, this is the answer he found that day: Spirit. Spirit is the third term that logically and indissolubly links matter to energy. He then built this equivalence:

Matter ↔ Spirit ↔ Energy.

Later, these relationships were analyzed in greater technical detail, presented together in our familiar geometric format, and published in a peer-reviewed journal run by a group of physicists.9 As pointed out there, the simplest way to read this construction is this: One enters into the stone with a hammer; into the energy of the stone with a cyclotron; and into its spirit with prayer.

In 1946 Einstein remarked: “The unleashed power of the atom has changed everything save our modes of thinking.10 With the establishment of the equivalence of matter to spirit and to energy, everything changes. The war between the two cultures will eventually come to a screeching halt, because, as Einstein also said: “Science without religion is lame, religion without science is blind”.11 We will then be on the road to acquire internal peace.

In fact, even the wars among the various religions might come to a screeching halt. This is the last aspiration of Somism; the last aspiration of the Social Man and Woman, the Civilized person. It might take some doing and some time. Yet, if we think hard about it, this goal is fully within our grasp. Certainly, adherents to Hinduism will recognize themselves in the fundamental equivalence proposed above; and adherents to Americanism, the religion of the American Indians, will do the same. But what of the three monotheistic religions? It seems that the conception of the Messiah is the stumbling block. Yet, a true understanding of the Messiah reveals an astonishing similarity in the inner structure of the three religions: Christians and Jews will no longer disagree, if we Christians are humble enough to ask this question: sure I hold in my spirit the precious body of the historic Christ at Communion, but do I also hold the Spiritual Christ? That is the Jewish Messiah, indeed.

The followers of Allah will have the most difficult task of all. Their conception of the Messiah is written very deep into the Koran. Vali Asr is the revered Hidden Imam, whose appearance someday, Shiite Muslims believe, will establish the perfect Islamic political community. Is Vali Asr any different from the Jewish Messiah?

It is then up to Christians to reveal to the world that Jesus came to unify the world, not to divide it. It is up to the Christians to live up to their tripartite commandment to love God, love neighbor, and love oneself. It is up to Christians to reveal that Jesus did not ask to be revered but to revere “our father,” namely to revere Yahweh just as much as to revere Allah!

If we do believe that Jesus is God, then Jesus is Yahweh; Jesus is Allah.

Concluding Comments

This is certainly not the place to defend the validity of any one of the proposed recommendations included above. Each one of them will have to stand on its own. They can be seen as a series of spheres within spheres. There is plenty of room for improvement; there is plenty of room for detail to be added on each point.

There is no separation among the worlds of politics, economics, law, philosophy, and spirituality. Our innermost being is deeply rooted in each one of these worlds. We do not achieve a world of peace unless we integrate all those worlds within ourselves first and in relation to other fellow human beings thereafter. There was a time when all we had to care for was the neighbor next cave over. Then we started taking care of the neighbor within our village. With the development of the megalopolis, we have lost all ability to recognize our neighbor. Strangely though, the neighbor is now clamoring to be recognized across national boundaries as well as across spiritual boundaries. We had better listen to that person.

Chaos theory, after all, has proven that the flap of a butterfly in China might lead to a hurricane in the Untied States.12 How much more true is this theory in human relations! How much more true it is in international relations.

Notes

 1 See, e.g., John Lukacs, At the End of an Age (2002)

2 Relational logic results from the integration of the principle of identity, the principle of non-contradiction, and the principle of equivalence into one system of logic. All logicians and mathematicians understand, indeed, work with, and apply all three principles. Yet, they are dealt with as if they were independent of each other. They are not. They are fully dependent on each other. They are fully interdependent. The following figure offers a synthetic, geometric, and visual representation of the organic, rather than linear, relationship among these three principles:

Figure A. Relational Logic

3 Some of these theoretical complexities have been recollected in Vol. 4, No 1 issue of The Aquinas Review (1997).

4 Most famously, Margaret Thatcher, now Lady Thatcher, falls into this category of thinkers. Interestingly, it must be remembered that, as Alasdair MacIntyre emphasized in After Virtue (1981), the conception of “the individual” has come into existence only during the last four to five hundred years, with Pico della Mirandola as a standard bearer leading the parade. Prior to that only the community was considered “real.”

5 See www.upadaria.com.

6 The word “bill” was added by Stuart-Sinclair Weeks.

7 Carmine Gorga, “Toward the Definition of Economic Rights,” Journal of Markets and Morality2 (1999): 88-101. See also “The Productivity Standard: A True Golden Standard” (with Norman G. Kurland), in Dawn M. Kurland (ed.), Every Worker an Owner: A Revolutionary Free Enterprise Challenge to Marxism, Washington, D.C.: Center for Economic and Social Justice, 1987, pp. 83-86; “Bold New Directions in Politics and Economics”, The Human Economy Newsletter, March 1991, 12 (1) 3-6, 12; Four Economic Rights:Social Renewal Through Economic Justice for All,” Social Justice Review, January-February 1994, 85 (1-2) 3-6; “Fisheries Renewal: A Renewal of the Soul of Business” (with Stuart B. Weeks),       The Catholic Social Science Review, Vol. II, 1997, pp. 145-161; “Concordian Economics: Tools to Return Relevance to Economics,” Forum for Social Economics, 2009, vol. 38, issue 1, pages 53-69. See also chs. 1, 11, and 12 in in Albert Tavidze, ed. Progress in Economics Research, Vol. 19, Hauppauge, NY: Nova Science Publishers, 2010

Ideas scattered among these writings and others can perhaps best be synthesized in two diagrams representing respectively the economic process (Figure B) and the theory of economic justice (Figure C):

Figure B                                                                Figure C

The advantage of presenting these two diagrams back to back is to reveal the inner relationship between them: economic justice is the mirror image of the economic process. One can just as soon separate one from the other as one can separate people from their shadows.

8 See www.polis-tics.com and www.somist.org.

9 “On the Equivalence of Matter to Energy and to Spirit,” Transactions on Advanced Research, July 2007 | Volume 3 | Number 2 | ISSN 1820 – 4511: 40-45.  Available at http://internetjournals.net/journals/tar/TAR2007july.pdf

10As quoted in O. Nathan, H. Norden, eds. Einstein on Peace (Avnet Books, New York, 1981 ed,): 376, from a pamphlet published by Beyond War in 1985 entitled A New Way of Thinking.

11 Albert Einstein, “Science, Philosophy and Religion: a Symposium”(1941). From The Quotation Page at http://www.quotationspage.com/quote/24949.html.

12 See, e.g., J. M. T. Thompson, Nonlinear Dynamics and Chaos, Geometric Methods for Engineers and Scientists. (New York: Wiley, 1986).

In economics

The original publication is available at Forum for Social Economics (http://www.springerlink.com/content/1w885686112kt7r7/), May 2008.

For Soc Econ (2009) 38:53-69

Concordian Economics

 Tools to Return Relevance to Economics

 

Abstract    With the help of planes and solids, this paper presents an enlargement of the field of observation of economic theory. Through this transformation, the distribution of ownership rights to money and wealth assumes a central position in economic analysis. Thus social relevance is returned to economics. The validity of this operation is confirmed by the return of the millenarian field of economic justice to its traditional function as guidance to economic policy. The paper then presents four sets of economic rights and responsibilities that offer the potential of translating principles of economic justice into the complexities of the modern world.

 

Keywords   economic theory, economic policy, economic practice, economic justice, economic rights and economic responsibilities, social relevance.

 

As problems of human and natural ecology mount up, there is growing in mainstream economics the conception of economics for economics sake. The tendency is to see economics as an autonomous discipline isolated from other sciences, and yet dominating all other social sciences. No matter what concerned people within and without the economics profession maintain, the tendency is to neglect those concerns because mainstream economics has an unstoppable inner force of its own that makes it impossible to change course. This paper assumes that this tendency is due not to the will of any individual economist but to the sheer power of their tools of economic analysis. The action is involuntary. The process is mechanical (cf PAER).

The process is not without consequences. Economic theory has lost control of itself. Perhaps no one has made the case stronger than Alan Blinder (1999), who has said: “…too much of what young scholars write these days is ‘theoretical drivel, mathematically elegant but not about anything real.'” As a direct consequence, economic theory has become splintered into various schools, which vie for their own preferred policies. Because of the current disarray, monetary policy has largely been left to the bankers; fiscal policy to the politicians; and hardly anyone speaks of labor or land or industrial policy any longer. In a word, by becoming detached from reality, both economic theory and policy risk becoming socially ineffective—which does not mean that economic practices are not causing social consequences of their own.

This paper offers a set of new tools that is capable of changing this course of action. Through these tools social relevance reveals itself as an integral part of the constitution of economic theory, policy, and practice. To be specified at the outset, the new tools do not reject but incorporate the old tools of analysis. Using planes and solids in space, in addition to points and lines, economic theory automatically encompasses a larger social reality and returns to the fold of socially relevant sciences with authority to suggest desirable policies and practices.

While the proposed tools in economic theory are the result of forty years of analysis published in Gorga (1982, 2002), desirable policies and practices are distilled from a program of action presented in Gorga (1959, 1964, 1987, 1991a, 1994, 1997, 1999, 2002, and 2007). More extensive treatments can be found in the writings of Benjamin Franklin, Henry George, Louis D. Brandeis, and Louis O. Kelso—with their works, necessarily all their works, read in rapid succession and not any of them as a stand-alone effort. Standing alone, these works are open to debilitating objections. Together, they become an impregnable fortress.

 

TOOLS TO CONTROL ECONOMIC THEORY

Mainstream economic theory is an impressive intellectual construction with its own internal logic. Its structure is a bastion impervious to any external influence; it has become a mathematical science, and as such it is autonomous of any influence that does not enter into its logical structure. The intellectual apparatus of mainstream economic theory, once deconstructed, revolves around the following tool kit, which we propose to preserve and to build upon.

Existing Tool Kit

As everyone knows, economics is built on the theory of supply and demand. The demand of most everything increases as its price decreases; and the supply of everything increases as its price increases. This is the bare structure of most theories in economics, from the theory of growth to the theory of money. To appreciate the full force of this method of analysis one needs to realize that the lines of supply and demand represent sets of numbers—in turn derived from functions of two variables, prices and costs—and then one must see those schedules in movement. As they move up or down, right or left, they meet each other at different points on the Cartesian grid and determine a specific equilibrium of prices and quantities offered and accepted of any item of wealth in the market, from bread to gold. The basic characteristics of this framework of analysis become evident upon reflection. The focus of attention is on the market exchange; all that goes on before or after the exchange lies outside the purview of the analyst. The mainstream economist qua economist can only analyze, forecast, and report on present or likely future tendencies toward equilibrium of items of wealth that are offered in the market in exchange for other items of wealth, be they currency or pet rocks. The consequences that follow from market exchanges lie mostly outside the purview this framework of analysis. Is the production of items being exchanged in the market causing physical damage, or moral depravation?  Is the distribution of ownership rights over items being exchanged causing a concentration of wealth into too few hands? Is the consumption of items being exchanged causing ecological disaster? These are all familiar questions that are at the heart of the economist’s concern. Yet, they can at best be acknowledged by the economist, but they will unavoidably be dismissed as belonging to other fields of analysis such as politics, ecology, morality, and the law, fields that lie outside the expertise and control of the economist.

The analysis becomes more complex daily by the sheer weight of accumulated data; hence equations multiply, econometric applications become more sophisticated, and theorems concerning the characteristics of economic relationships become more and more subtle; indeed, there now seems to be a model for every economic activity—and, lately, for many non-economic activities as well; and if the information is missing or it does not quite fit the case, there is the stand-by option of “as if” assumptions. Impressive as these techniques are, beyond all refinements in the state of the art of mainstream economic analysis, most economists admit to its basic limitations; not only that, they also admit that economic theory has been in a state of crisis at least since the publication of Keynes’ General Theory in 1936. (What did Keynes say is a question that has plagued the profession ever since.) Three of the most recent recognitions of the crisis span the arc from acknowledgment of the limits of mainstream economics (Mankiw 2006) to criticism about the relevance of mainstream economic theory (Manicas 2007) to the belief that economic theory has improved and that it is expected to improve over time (Warsh 2006).

As the history of minor and major theoretical revolutions and counterrevolutions proves, economists are ready to try nearly any stop-gap measure to resolve the crisis—provided the proposed measure does not affect the structure of the theory. This position is non-negotiable; and it is not the purpose of this paper to negotiate it. What is presented for discussion is a far simpler proposition: if we want more comprehensive and more accurate results, we need different tools of analysis. In addition to points and lines, we shall be using planes and solids in space: at first, only rectangles and spheres.

The consequences of this transformation are far-reaching. Rather than attempting to create an improved mainstream theory, we shall incorporate its vital and functioning core into a new framework of analysis which, for a number of consilient reasons, this writer likes to call Concordian economics: as we will see below, the structure makes room for the perspective of each one of the various schools dominating today’s economic analysis; it opens its doors to inputs from various other intellectual disciplines; and it extends itself in a seamless web to cover economic policies and economic practices. 

New Tools in Economic Theory

Through laborious logico-mathematical steps (Gorga 2002: 41-158), one obtains a restructure of mainstream economic theory (Gorga 1982) and its gradual transformation into Concordian economics. While the book presents a description of that transformation with its resultant new mathematical models (Gorga 2002: 25, 38, 71, 74-6, 121-25, 129-37, 153-58, 168-70, 264, 303-20), the present paper reproduces the core of that ground with primary assistance from geometry; thereafter, it extends the analysis to cover economic policy as well as economic practices for implementation of selected economic policies.

The key results of Concordian economic analysis are these. In order to eliminate a set of innate logical contradictions at the very foundation of economic analysis, the nexus between saving and investment is broken and it is replaced by the complementary relation between Investment defined as all productive wealth and Saving defined as all nonproductive wealth—a term that is better replaced with Hoarding.1 The analysis starts anew on the basis of the proposition that Investment is Income minus Hoarding. Furthermore, since money and financial instruments are not wealth, but only represent wealth, in macro, as distinguished from microeconomics, one cannot add money to real wealth.2 The two entities have to be kept separate. And then the question arises: What is the relationship between the two? From Aristotle to the Doctors of the Church there was no doubt as to the answer to this question. During this long stretch of time, much economic analysis was built on the equivalence of money and goods in the exchange. It was the distinction between the two and their linkage in the relation of equivalence that provided the objective base for the determination of conditions of justice in the exchange of wealth. If we accept this answer, to satisfy well-known requirements of the principle of equivalence, we search for a third element to link monetary and real wealth together and we find it in the set of rules and regulations that in every society governs the distribution of ownership rights over real and monetary wealth—and we do not stray away from pure economic theory, because we are presented with the monetary value of those rights. The following diagram (Gorga 2002: 36, 163, 314) incorporates these results; it represents the integration of these values on one plane, in this fashion:

Figure 1. The Economic Process

In this figure, the values of “production”, namely the values of all real wealth produced over a specified unit of time are assembled into one category of thought that is recognized as aggregate supply. (It is to be noticed that this unit is “pure” because it contains only stocks of real wealth and no monetary wealth. It is also to be noted that in a more complete treatment this value ought to be observed from the point of view of demand as well as supply: thus we ought to have an analysis of the demand and supply of the production of all real wealth.) We follow the same procedure for the values of monetary wealth, thus firmly separating real wealth from monetary wealth, and we call the result “consumption” or aggregate demand. (Ditto for the treatment of all monetary values, which here are not observed from the point of view of supply: The question of the quantity of monetary values created lies outside the scope of this presentation.) We finally repeat the procedure for the aggregate values of ownership rights over real and monetary wealth, and we call the result “distribution” of ownership rights. (At this juncture we assume that the values of ownership rights over real wealth are identical to the values over monetary wealth). In sum, we have enlarged our field of observation from points and lines to planes and interactions among planes; and, rather than leaving the question of the interaction between demand and supply open (cf. Klein 1970: 143), we have continuously specified—and distinguished one from the other—the demand and supply of (a) real goods, (b) monetary instruments, and (c) values of ownership rights over real and monetary wealth.

Figure 1 reads as follows. When real goods and services pass from producers to consumers, monetary instruments of a corresponding value pass from consumers to producers. Then one cycle of the economic process is completed—and it is accompanied by the silent exchange of values of ownership rights over monetary and real wealth. Both money and goods change hands. The unit of account can be the economy of one person, one nation, or the world. In macroeconomics, the exchange occurs neither between two insignificant commodities (cf. Schumpeter 1936) as in microeconomics nor between any two forms of financial instruments as in the economics of Wall Street. In macroeconomics, fully respecting the laws of supply and demand the total production of real wealth is exchanged for the total availability of financial resources—as in Keynes’ principle of effective demand (see Brady 1996). Finally, in this figure the exchange visibly occurs under a regimen of social and legal relationships: ownership is apportioned at the moment of creation of wealth; and only owners can legally exchange wealth.

An effective way to analyze the instantaneous relationships captured by Figure 1 is to reduce it all to the economics of only one person. A person who snaps the apple from a tree, vs. gathering seeds, for instance, while respecting as always the rules of supply and demand commits an act of production. This person automatically apportions the ownership of the apple to the self, which means that this person is legally empowered, as it were, to sell the apple to the self. Thereafter, this person is free to eat the apple—or sell it to others. One of the merits of Figure 1 is that it describes the economic process as a whole. Everything is instantaneously related to everything else. Thus we run away from the shattered world of the schools and go back to the world of Classical economists who knew that economics is composed of the integration of Production, Distribution, and Consumption of wealth. This integration can be made more specific by a more extensive and updated reading of the terms, along these lines: The Theory of Production—namely a pure and robust production function—is concerned with the production of real goods and services (as might be studied by Supply-Side economists); the Theory of Distribution is concerned with the distribution of the value of ownership rights over real and monetary wealth (as might be studied by Institutionalists); and the Theory of Consumption is concerned with the consumption—or expenditure—of monetary, i.e., financial instruments (as might be studied by Demand-Side economists). More importantly, by recognizing that Figure 1 is the flat image of a sphere we bring the mathematics and geometry of economics up to the standards that prevail among modern engineers and scientists (see, e.g., Thompson 1986: 36), namely:

Synthetic Model of the Economic System as a Whole

(From Gorga 1991b)

 

p· = fp(p,d,c)

d· = fd(p,d,c)

c· = fc(p,d,c)

where

p· stands for rate of change in total production

d· for rate of change in the values of distribution of ownership rights

c· for rate of change in total expenditure.

 

And, most important for our immediate purposes, we can see that the theory of distribution of income and wealth now occupies a very central position in economics. All that relates to the distribution of ownership of income and wealth becomes an immediate and integral concern of economic theory—no longer an afterthought or an issue placed at the margins of economic science. Related issues of social relevance of economics can no longer be shunned aside by the economist on the assumption that they are external to economic theory. These are indeed issues that lie at the very core of economic theory; and one does not stray away from mathematical and quantifiable theory either. What is to be measured and evaluated is the economic value of ownership rights over income and wealth—and the different economic effects of different patterns of distribution of income and wealth. Decisions relative to these issues are taken during the very process of production and exchange of wealth; they are not something to be concerned with only after the more impellent problems of production and exchange are resolved, as assumed in Keynesian economics and, mutatis mutandis, in mainstream economics, see, e.g., Klein ([1947] 1968: 187). The concern about the social relevance of economics—as all Institutionalists have devoutly wished—is now brought within the purview of the economist.

Issues of distribution of economic values of income and wealth are not givens; they lie at the very core of the economic process and are determined by the inner workings of this process. On Mars the situation might be different; on earth, people create not only real or physical wealth—they also assign values to this wealth. Indeed, it is economists (and accountants) who, assisted by the laws of supply and demand, assign these values as best they can. Lawyers only validate these statements by transforming them in negotiable legal instruments that are called ownership rights. These rights might belong to an individual person, to a corporation, or to the state; but they legally belong to someone. And an exchange of real wealth for monetary wealth involves at the same time an exchange of the value of ownership rights over real and monetary wealth. It is thus that, no matter the disclaimer by many economists, economic values are created and are created at the very core of the economic process.

 

(c0nt’d)

In economic justice (cont’d)

The original publication is available in

Forum for Social Economics (http://www.springerlink.com/content/1w885686112kt7r7/), May 2008.

PART II

Concordian Economics

 Tools to Return Relevance to Economics

 

TOOLS TO CONTROL ECONOMIC POLICY

Having discovered that the distribution of ownership rights over income and wealth is an integral part of economic theory, the question becomes: What are the tools to obtain the desired pattern of distribution of income and wealth? This is the eminent question of economic policy. Economic theory tells us that, once this pattern is set, most other questions of economic policy are automatically settled. The answer to the question is well known.

 

Existing Tool Kit

 

Even though the historic roots of economics lie in moral philosophy, economists have lately assumed that they have nothing to contribute to the discussion concerning the selection of patterns of distribution of income and wealth. They have left the field to lawyers, ethicists, philosophers, sociologists, and political scientists. Mainstream economists believe that they do not have—and, what is more important, they ought not to have—any tools to control the pattern of distribution of income and wealth. Mainstream economists assume that this is a given, namely a determination that is and ought to be left to society as a whole. Economics, as pure science, as an autonomous mathematical science, is supposed to analyze the effects of various societal decisions, but not to intervene in those decisions. It is a direct consequence of this assumption that economic theory is fast becoming socially irrelevant.

Under these conditions, the discussion on economic policy falls into a trap. The discussion becomes the property of various schools of economics, each purporting the benefits of its own dictates and none being able to convince the other schools of the validity of its positions.

We do not need to put a step on this slippery slope. Once it is established that the pattern of distribution of income and wealth is an integral part of economic theory, the analysis is restricted to this question: How can we translate economic theory into economic policy? In the paragraphs below we will offer a set of new/old tools for consideration. This set calls for the construction of the theory of economic justice, and therefore economists will discover that they have much to contribute to it. This is the high road to re-establish social relevance to economics.

 

Proposed Tools to Control Economic Policy

 A mere glance at the history of economic thought makes us glean this proposition: The transmission belt that for millennia carried economic theory into economic policy is the doctrine of economic justice. While remaining astonishingly constant from Aristotle to the Doctors of the Church (see, e.g., Wood 2002: 83), this understanding allowed for continuous adaptations to the circumstances of the moment. The doctrine of economic justice was divided into two planks: distributive and commutative justice. Distributive justice guided rules and regulations that govern the division of wealth as it is created; commutative justice guided rules and regulations that govern the transferal of wealth between buyers and sellers at the moment of the exchange. While the Doctors of the Church left much room for discretion in the determination of distributive justice to the parties involved in the economic process, they reached a firm and revolutionary conclusion about the dictates of commutative justice. The commutation of wealth, namely the exchange, occurs in accordance with principles of justice, they discovered, only if it reflects a free market price: a price determined in a market that is not dominated by either governmental or private monopolistic forces (see, e.g., Schumpeter 1954: 98-99).

While this formula appears simple, it envelops great complexities. With it, the Doctors of the Church unified the social requirements of freedom with those of morality in economics; and it was the exercise of morality that yielded freedom. The application of this formula created the essential conditions for the enterprise system to be as free as it could be at the time.

Over time, this ordered set of priorities was twisted around and its power dissolved. Through insistence on unfettered economic freedom, the unity of freedom and morality—with its inherent social relevance—was shattered and the doctrine of economic justice was lost in the fog of time.

Truth to tell, the dissolution of the doctrine of economic justice was facilitated by the fact that it was never presented with a visible head. People with direct or indirect access to land and natural resources participated in the economic process as a matter of fact through well-established privileges and as a consequence of unspoken sets of rights (indirectly, access to land and natural resources was secured through the commons: for millennia the safety valve to preserve the dignity of the poor). Hence, it never occurred to Aristotle or any of the Doctors of the Church to make explicit the requirements of a third plank that might be called participative justice (Gorga 1999, 2007). For a great variety of reasons, those conditions are no longer in existence. Today, one has to beg in order to participate in the economic process. And if one does not take part in it, one is marginalized; one is shunted to the margins of society. Hence the plank of participative justice, as it is increasingly recognized from many quarters, must be explicitly formulated. When participative justice is added to the other two planks, the doctrine is completed and transformed into the theory of economic justice. Once that is done, one is presented with a framework of analysis that can be represented in this fashion:

Figure 2. Economic Justice

Figure 2 reads as follows. Participation in the economic process is a matter of justice, because only men and women who participate in the production of wealth are entitled to the distribution of ownership of a share of the wealth created through their participation.3 A just commutation of wealth, a just exchange, is implicit in the very distribution of wealth in accordance with one’s participation; but, of course, the principle of commutative justice extends itself to cover the exchange of wealth just created for other wealth existing on the market.  It is in accordance with these objective principles that the pattern of distribution of current income and wealth is and ought to be determined. Economists can render these calculations very precise.

But economists have much broader tasks than these. Figure 2 is a mirror image of Figure 1. If the distribution of ownership rights is an inherent part of the economic process, as we have seen in the previous section, economic justice becomes a natural extension of economic theory. Indeed, one can just as soon separate economic theory from economic justice as one can separate a person from her shadow. (The forced separation of these two entities has ineluctable consequences of its own that ought to be of great interest to the investigative powers of the economist.) Given this condition, a minimum set of questions to be asked by economists in the formulation and evaluation of any economic policy might be: Does the proposed policy favor participation in the creation of wealth? Does it allow for a fair distribution of the wealth thus created? Does it allow for a fair transfer of wealth from one person or group to another? Much could be said on these issues, but since much is already well known, we shall shun away from broad and elaborate discussions of these issues.

The wisdom of staying away from broad and elaborate discussions, however, does not necessarily require staying away from the specifics of the case. The specific question is: How can we transfer the principles of economic justice into the complexities of the modern economy?

Needless to say, this is a question that is not formally and comprehensively raised in mainstream theory. This is a question that arises naturally and forcefully within the context of the structure of Concordian economics.

  

TOOLS TO CONTROL ECONOMIC PRACTICES

In the section on economic theory we have seen how does the economic system create wealth, how its value is determined by economists and accountants, and how its value is then transformed in ownership rights by lawyers. In the section on economic policy we have observed how economic justice determines the apportionment of those ownership rights. In this section we shall observe how the economic system operates in practice.

 

Lack of an Existing Tool Kit

“High” mainstream theory is silent on the practices of economics. This neglect is not due to chance; rather, it is due to the assumption that, since economic practices are determined by society at large and are supposedly controlled by allied social disciplines, they lie outside the economist’s field of expertise. Indeed, having abandoned the field to lawyers, and ethicists, and philosophers, and sociologists, and political scientists, mainstream economists have become passive takers of a proposition that lies at the very core of the issue. This is the proposition that present ownership rights provide practical rules for the distribution of future ownership rights. The proposition has long legs, because it determines the pattern of future distribution of income and wealth. Economists observe every day the manifold negative consequences of this belief, but feel powerless to even address the issues. This is another juncture at which, by taking themselves out of the discussion, economists are threatening to make economics a socially irrelevant discipline.

To regain their power, economists have only to look at it as an economic, rather than a legal, political, or moral issue. If they do that, they discover that their assumptions are faulty. The error is elementary. The reasoning is circular. In order to enter and to break this circular form of argumentation, namely that present property rights determine future property rights, economists need to remember that property rights are pieces of paper: a piece of paper does not—and cannot—create real wealth. It is not even the exercise of property rights that creates real wealth. Property rights are a bundle of rights that link human beings to things. Their current owners may wish as hard as they can, it is not in the nature of property rights to create wealth.

It is not the use of property rights, but the use of property—namely, the use of real goods and services—that creates new wealth. The distinction is fundamental. The discussion is shifted away from the abstract legal field on to a concrete field. The discussion is focused on the observation of the economic reality. The use of real goods and services to create new wealth is infused, not by property rights, but by the exercise of economic power. To an economic power corresponds an economic right. As specified below, temporally, logically, economically, and legally, economic rights precede property rights. Economic rights are the generators, the fathers and the mothers, of property rights. The nature of economic rights becomes clear when the two rights, economic rights and property rights, are observed as separate and distinct entities, and then both rights are placed in contraposition with entitlements. The three terms are often used as synonyms. They are not. As specified in Gorga (1999),

First, the content of these three entities is different. The object of property rights are marketable things, tangible or intangible things such as material goods and services. The object of entitlements are human needs, from food to shelter to health. The object of economic rights are economic needs. Second, the legal form of these three entities is different. Property rights are concrete legal titles over existing wealth; economic rights are abstract legal claims over future wealth; and entitlements are moral claims on wealth that legally belong to others. Finally, the quantity that they measure is variable. While both property rights and entitlements relate to existing wealth, and therefore a necessarily finite quantity, economic rights relate to future wealth, an unknown and elastic—if not a potentially infinite—quantity.

Economically, and consequently legally, real wealth is created by the exercise of economic rights—indeed, economic rights and economic responsibilities, as we shall see. Hence economists are fully entitled to extend their competence to the field of economic rights and economic responsibilities. Economists will discover that the field is wholly within their range of expertise and responsibility. At the end of this journey, economists shall be able to offer to lawyers, ethicists, and philosophers, as well as political scientists and politicians, this proposition: Future ownership rights are determined, not by property rights, but by economic rights—indeed, they are determined by economic rights and economic responsibilities. Thus the closed circuit that at present imprisons economic theory, the proposition that property rights beget property rights, is broken. Economists are in charge of economic issues.

New Tools to Control Economic Practices

The transmission belt that carries principles of economic justice into the complexity of modern economic life, and shapes objective guidelines for the formulation and evaluation of just economic policies is the presence of economic rights and economic responsibilities (ERs&ERs), both lodged in the same person at the same time. These two conditions need to be clarified. Economic rights and responsibilities need to be lodged into the same person, otherwise one does not follow an economic discourse in which everything is strictly related to everything else; rather, one follows escapism: if my father, my uncle, or the state is responsible for my welfare, we are lost, as Keynes used to say, “in a haze where nothing is clear and everything is possible” (Keynes 1936: 292). The second condition is equally important. Economic rights are rooted, not in abstract morality, but in our own concrete economic responsibilities (cf. Gorga 1999).

ERs&ERs come forward in response to the well-known requirements of the factors of production identified by Classical economists as land, capital, and labor—with the addition of a modern distinction between financial and physical capital. Guided by these economic needs, our focus of attention is on the satisfaction of the plank of participative justice; successive iterations that are mostly skipped in this presentation would reveal that the same rights and responsibilities satisfy also the requirements of the planks of distributive justice and commutative justice. A minimal set of economic rights and corresponding responsibilities is as follows:

1. We all have the right of access to land and natural resources. This is a natural right. It belongs to us just in virtue of our humanness. Land and natural resources are our original commons. They belong to us all. This is an essential right, because without the possibility of exercising it, we are deprived of the possibility of participating in the economic process. And without this participation, we are marginalized; we are made dependent on the good will of others. The most direct way of securing this right in the complexity of the modern world is neither through squatting nor through expropriation; rather, it is through the exercise of the responsibility to pay taxes for the exclusive use of those resources that are under our command—with a corresponding reduction of taxes on buildings and man-made improvements on the land. The exercise of the responsibility to pay taxes on land has a double function: It secures our right to the use of the resources that are under our command and it also makes room for others to access land and natural resources that they need. Land taxation is the economic bridge between hoarding, namely the accumulation of idle land, and the right of access to that land with its natural resources. Paying taxes on the value of land and natural resources gradually encourages dis-hoarding, hence it lowers the price of the land, and correspondingly opens up the resources of that land to all those who need them and can make use of them. Worrisome hoarding is especially that which occurs both downtown and in the belt surrounding major cities and towns. It is to leapfrog over this belt that people go to the suburbs in search for affordable land, thus creating overstretched lines of communication and protection and overlong commuting lines—with consequent waste of fuel that overtaxes nonrenewable resources, the ozone layer, the pocketbook, and the nervous system. Paying taxes on land value is a most fair form of taxation, because it implies returning to the community part of the value that is created, not by the individual owner, but by the community. Land that sits idle does not produce income, true; yet, it produces capital appreciation over time: Rare is the case of capital loss; and even when that occurs, the relative loss tends to be smaller than the loss on other assets. (To see how this pair of ERs&ERs meets also the requirements of distributive and commutative justice, let us simply consider that, if one avoids taxes, the total tax load is not going to be distributed fairly among the population. And if one avoids taxes, one obtains something—i.e., private control over a quantity of resources—for which one does not offer proportionate compensation to the rest of the community.)

2. We all have the right of access to national credit. Since national credit is the power of a nation to create money, and since the value of money is given by the value of wealth left over by past generations and the creativity of every person in a nation, national credit is the last frontier, the last commons. Without access to credit today one is made economically impotent. Worse, since this advantage is granted to the privileged few, it is automatically denied to the majority of the population who are henceforth condemned to pay a higher rate of interest, if they obtain credit at all. Of course, such a loan should be extended only on the basis of the responsibility to repay the loan. And these loans will have a high chance of being repaid because they ought to be issued at cost and issued exclusively to individually owned enterprises, Employee Stock Ownership Plans (ESOPs), and cooperatives, as well as states and municipalities, and issued exclusively for capital formation, namely for the creation of new wealth—not to buy financial paper, consumer goods or goods to be hoarded or to cover administrative expenses of states and municipalities. Capital credit liberates people, while consumer credit enslaves them.

3. We all have the right to the fruits of our labor. This right should not be limited to the right to obtain only a wage. It should be extended to cover the other major fruit of economic growth over time: capital appreciation—as well as being subject to capital loss, of course. The only justification for reserving capital appreciation for stockholders, the owners of a corporation, and excluding workers from it, can be found in the fact that loans are given only to owners of past wealth (the Catch-22 of today’s economic reasoning: “save and invest and you too can become rich”—as if this proposition were either economically feasible or ecologically sustainable.) But from now on this right can be extended to people who do not have prior wealth through the right of access to national credit—especially by legally transforming workers into owners through individually owned enterprises, Employee Stock Ownership Plans (ESOPs), and cooperatives. Of course, this full right should be extended only in correspondence with the responsibility to offer services of valueequivalent to projected compensation. And there will be an outpouring of such services because, while in a command and control economy workers are requested to check their brain at the factory gates, in a socially responsible economy—an economy in which rights are exercised on the basis of responsibilities—workers/owners are legally, socially, and psychologically empowered to exercise their brain fully at their work post.

4. We all have the right to protect our wealth. This right seems to be universally accepted, except in one case that matters most: in the case of the trustification process, the process used especially after the Civil War in the United States to create corporate trusts and repeated in a hundred subtle variations ever since. (People feel free, not only to acquire shares of the stock of one corporation, but free to use that stock to acquire another whole corporation by all forms of trusts, mergers, and acquisition. The very idea of the corporation, forever a public entity, has thus been privatized and monetized.) There are two ways in which corporations grow: One is through internal growth, and this approach ought to be protected in no uncertain terms; the other is through external purchase and, with limits, this manifestation ought to be prohibited in no uncertain terms. Why? Because this prohibition is the only certain way to protect the wealth of present owners. And if it is assumed that most stockholders of the modern corporation are happy to have their shares bought and sold on the market, it must be granted that growth-by-purchase takes wealth away from workers who have contributed to create that value—and many times, in the trustification process, lose their work site as well. All in the name of efficiency—a misnomer that stands for private financial gain generated at the expense of shifting costs onto the shoulders of the community at large. Of course, this right ought to be purchased only at the cost of the responsibility to respect the wealth of others. These are two-way streets. We cannot even attempt to restrain the Pac-Man economy, while we use Pac-Man instruments.

These economic rights and responsibilities can be exercised by anyone who does not only want to receive economic justice, but also wants to grant economic justice to others. Indeed, these are the essential conditions for the establishment of economic justice, as well as the establishment of a free enterprise system, in the modern world. As a consequence of the dynamics of the implementation of these four marginal changes in our current practices, economic freedom will be expanded to embrace all who want to subject themselves to the rigors of the economic process—and then the few remaining hard cases can be easily taken care of by charity. No. There is no compulsion in any of the above suggestions. The landowner can pay more taxes and control more land or can escape the tax levy altogether by reducing land ownership to zero; the applicant for a national loan can escape the constraints suggested for access to national credit by tapping into private capital markets; the worker can escape the responsibilities of ownership by vying for a job rather than an equity position; and the owner of physical capital can escape the constraints implicit in the proposed anti-trust policy by remaining below the trigger of an agreed-upon threshold for growth-by-purchase prohibition. This prohibition should apply to the largest corporations first and be gradually expanded to include eventually all except, let us say, corporations engaged in intrastate or regional commerce.

Intellectually, the proposed economic rights and economic responsibilities perform functions outlined in the conception of “general abstract rules” by Hayek (1960: 153), the “original position” by Rawls (1971: 12, 72, 136, 538), the “reverse theory” by Nozick (1974: 238), and the “Principle of Generic Consistency” by Gewirth (1985: 19); practically, they will function as Gladwell’s (2000) “tipping points”. Ultimately, it was a poet, Vincent Ferrini (2002), who caught the essence of economic rights and economic responsibilities by identifying their ability to provide “the answers to universal poverty and the anxieties of the affluent.”

Operating as tipping points in our modus vivendi, ERs&ERs will set in motion a process of interdependence that respects the reality of economic affairs, and the reality of human relationships. Recognizing that most people and most businesses always act morally, the increasing number of “bad apples” that at times seem to receive all the attention (and envious support) of a superficial intellectual world will be recognized as dangerous exceptions, perhaps ostracized, but certainly no longer applauded. Once the tendencies of these people are kept in check, all wealth will be distributed, not equally—that is meaningless utopianism—but fairly. The assurance for this result resides in the transformation of the current social contract into a legal contract: when landowners pay their share of land taxes, they will sell their hoards and access to land and natural resources will automatically be opened up for most people; when people will get access to national credit, many will become independent entrepreneurs; when workers are transformed into owners, they will have the legal tools to demand a fair distribution of income; when growth-by-purchase will mostly become a forbidden activity, most corporations and most employee/owners will preserve their independence. These measures, by consistently curbing the excesses of the few for a period of at least ten years, will cumulatively lead to a fair distribution of income and wealth. To reassure ourselves of this outcome, let us comprehensively look at the issues from another point of view. If land owners were to use their possessions of land and natural resources efficiently (with efficiency measured through lower private capitalization and higher effective demand), would there be such wanting in the world? If national credit were made available to all entrepreneurs at cost, would we not translate the immanent reservoir of creative powers into economically profitable ventures? If workers were transformed into worker/owners, would we not increase our extant productive capacity incommensurably? If corporate growth-by-purchase—with accompanying translation of that economic power into corruption of our political system—were curbed, would we not obtain less concentration of economic power into a few hands?

All four ERs&ERs naturally lead to a fairer distribution of income than prevails today. Eventually, with a fair distribution of income and wealth, there will no longer be any need for redistributive programs, which are an expression of double utopianism (first, people as if living in la-la land are allowed to accumulate much, no matter how; and then they are expected to peacefully discharge their ill-gotten wealth). Preserving their current wealth, the rich will grow richer at a steady but slower pace; and the poor will no longer be poor, because they will have all they need. Lacking fuel at both ends, violent oscillations in the business cycle will be abated.

We will thus recover the essential truth of economics. This is the truth that there are two conditions of growth: economic freedom and economic justice, as concrete expressions of freedom and morality. Both are essential. The relationship between the two is quite clear: While freedom does not necessarily bring justice with it, justice unavoidably brings freedom. One can abuse freedom by denying freedom to others, one can never abuse justice. Hence, the initial condition of freedom for all is proof positive of the existence of economic justice in the land. This is economics that is socially relevant. And the relevance is not an afterthought. The relevance is implicit. The social import of economic theory is realized when the distribution of ownership rights is seen as an integral part of its constitution; and the social import of economic justice and economic rights and responsibilities is simply stated: We must prevent all foreseeable injustices from occurring. Once an injustice has occurred, there is nothing that can be done to undo the dastard deed. This is the bosom of realism.

One last question: Is the proposed program of action the latest expression of utopianism? The curt answer is: No. Utopianism has consistently been based on the wishful thinking of a single person. The proposed program of action results from filling in the gaps of a millenarian train of thought that, in a seamless web, extends itself at least from morality to economic theory and from there—through economic justice—to economic policy and practice. Utopianism promises immediate results, as if by magic. This proposed program of action asks for concerted, protracted effort. Whatever life Utopianism has, it is based on the fanatical following of a small group of people who try to force it upon the will of the multitudes. The proposed program of action is expected to be readily understood and spontaneously implemented by the multitudes.

CONCLUSION

The lament that economics lacks social relevance assumes many forms, but these are mostly centered on the treatment of issues of distribution of income and wealth. We have found that these issues are not even investigated by economists today because they assume that they lie beyond the field of economics. Hence, by placing this issue at the very core of economics, we have given back social relevance first to economic theory, then to economic policy, and finally to economic practices. Without ever abandoning the field of economics, we have established a continuity of discourse between three stepping stones in economic analysis. We have followed this line of reasoning. Since money and financial instruments are not wealth, but only represent wealth, in macroeconomics one cannot add money to real wealth. The two have to be kept separate. This condition raises the question about the relation between money and real wealth. As in the economics tradition from Aristotle to the Doctors of the Church, we have recognized that money and real wealth must be equivalent in value. But equivalence is a formal relation among three terms. What is the third term? The third term that links money to real wealth is the economic value of ownership rights; hence, we have presented a restructure of economic theory that reflects the need to study not only the monetary economy but also the real and the legal economy at the same time. From this new framework of analysis, novel answers are given to the question: How is the distribution of ownership rights achieved today, and how “should” it be achieved? An investigation of the economic, rather than the legal, moral, or philosophical aspects of this question leads to the transformation of an age-old doctrine into the theory of economic justice and to the discovery that the creation of wealth is achieved, not through the exercise of property rights, which are static, but through the exercise of well-defined economic rights and economic responsibilities, which take care of the dynamic needs of the economic world.

 FOOTNOTES

Every step of the way in Concordian economics, decisions are taken following relentlessly the dictates of fundamental rules of logic. For instance, analysis reveals that since current definitions of saving and investment contain items that are productive (farmed land) and items that are nonproductive (fallow land) of further wealth, both saving and investment respect neither the principle of identity nor the principle of non-contradiction and therefore they cannot be equivalent to each other, as they ought to be for their relation of equality to be formally valid (see, e.g., Allen 1970: 748).

  1. The separation of real wealth from monetary wealth is an integral part of the transformation of Keynes’ model into the series of mathematical models that provide structure to Concordian economics. This is a procedure that, outlined with the help of geometry (Gorga 2002: 32-37), starts with the enlargement of the definition of consumption from expenditure on consumer goods to spending in all its manifestations (ibid., 139-50), passes through the definition of money (ibid., 222) and the monetary formulation of the Flows Model (ibid., 309-12), and ends with the establishment of the equivalence of the processes of production, distribution, and consumption (ibid., 312-19). The description of these three processes and the economic process as a whole form the substance of Concordian economic theory (ibid., 159-234).
  1. What to do with the widow, the orphan, and the handicapped is a moral issue. Economics does not do anything for them. Indeed, as proved by the history of the world, even in the richest of the communities at the height of the business cycle, economics cannot do anything for them. Their number can become so overwhelming, their needs so vast, that even charity becomes powerless. Economics cannot do anything for the widow, the orphan, and the handicapped—unless, of course, they own stocks and bonds. But then they are not poor; they do not need any assistance through morality. They are capitalists and by the virtue of being capitalists, by the virtue of owning the machines, they participate—through remote control of the machines—by right in the economic process.

Acknowledgments   This paper is uniquely due to several maieutic interventions, truly beyond the call of duty, by Dr. Wilfred Dolfsma. I also would like to acknowledge a clarification brought to this paper by Godfrey Dunkley. If this paper has become a cogent presentation less exposed to potential debilitating criticism of single points, it is due to innumerable constructive suggestions by two referees of Forum.  A more detailed background for this paper is contained in “The Economics of Jubilation”, an unpublished monograph that has been well received by such a diverse audience as Dr. Michael E. Brady, Dr. John C. Rao, Professor William J. Baumol, and Professor Roger H. Gordon. That work, in turn, is based on a framework of analysis which was greatly assisted for 27 years by Professor Franco Modigliani and 21 years by Professor Meyer L. Burstein, among others.

 

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In physics

The original publication is available in

Transactions on Advanced Research

On the Equivalence of Matter

to Energy and to Spirit

Gorga, Carmine

 Abstract

A basic assumption in logic is that the principle of equivalence formulates a relation among three terms. Yet, there is no recognized third term in physics that completes the established relation of equivalence between matter and energy. This paper suggests that the third term to which both matter and energy are equivalent can be posited to be spirit. Spirit is defined both as the link—as glue—that holds matter and energy together and as Spirit, a notion that is akin to the spirit of God, which is by definition everywhere. All three terms might eventually be measured by a calorimeter. If this application of the principle of equivalence is accepted, physics is transformed from a linear into a relational discipline. And then everything will change in the “two cultures”, namely in both the physical and the social sciences.

Index Terms Equivalence, equivalence of matter to energy, equivalence of matter to energy and to spirit, linear rationalism, relationalism

 C. Gorga is with Concordians.org Inc. (email: cgorga@jhu.edu)

1. Introduction

Einstein established a relation of equivalence between matter and energy [1]. An equivalence relation is composed of three distinct and separate terms. To the knowledge of this writer, so far there is no identified third term to which both matter and energy are equivalent. Hence the relationship is not formally valid yet.  This paper proposes that the third term of the equivalence be posited to be spirit.

After observing some of the canonical requirements of the equivalence relation and the fundamental advantages of casting our thought processes into this format for the force it brings to our reasoning, we shall first note the shortcomings of some potential solutions to the lack of formal validity of the equivalence of matter to energy and then we shall try to obtain an operational definition for the word spirit. Only then shall we observe some of the consequences of accepting the proposal of making spirit the third term of the equivalence.

If the proposal stands to all the tests of validity, this solution will eventually yield two considerable benefits. It will transform physics from a linear into a relational discipline. It will also tend toward the reunification of the physical with the social sciences.

2. Problem Statement

Matter and energy are two terms. E = mc2 is not an equivalence relation; cis not a third term: cis a unit of measure (of speed). As logicians know, to be valid, an equivalence relation must be composed of three terms. The three terms have to be reflexive (namely identical to themselves throughout the discourse), symmetric (one observes the same entity from two points of view in order to obtain a deeper understanding of both entities), and transitive (a third term must exist to which both terms are equivalent in order to eschew the confines of circular reasoning and to complete the analysis). With the assistance of the equivalence relation the analysis does not start from an arbitrary point nor does it end at an arbitrary point, but is rigorously interlocked.

These observations can be made more evident by specifying the progress of our thought processes and by casting them into a set of figures. Science eschews all singularities. There is a good reason for this practice. A single point, a single observation does not lead to an objective, replicable analysis or experiment. Analysis begins with the observation of two events. Yet, the observation of two events necessarily leads to circularity of reasoning.

 Once we are faced with only two observations, we are obliged to observe all possibilities. Hence the mind is led back to the exploration of all potential outcomes of the position of Point B on the circumference of the circle in relation to Point A at the center of the circle. This is a process that eventually leads to a reversal of one’s position and then to a return to the original position—and no certainty is necessarily acquired in the process. Therefore, science asks for a third term. The third term points the research in the right direction. However, if the third term is placed in a linear position, the end result might be a dispersal of the thought process into the empty infinity of an enlarged circle. Linearity leads to progressio ad infinitum.

It is the equivalence relation that restrains the analysis from collapsing into infinity by constraining the terms into an interlocked relationship as in its standard configuration: A ↔ B ↔ C. The equivalence relation starts in logic and has the widest possible range of applications. All forms of syllogism are based on the equivalence relation. Hence the relation of equivalence is well known to the literati. The equivalence relation is also part and parcel of all mathematics textbooks. It stands at the very foundation of mathematics, in which three fingers of my hand (3 of base 10 number system) are equivalent to the word/number/symbol (three, 3, or III) and to the three apples in front of my eyes. A triangle is based on the equivalence relation. The whole of trigonometry is based on the equivalence relation. Indeed, as R. G. D. Allen pointed out, the rules of equivalence “hold” also for the relation of “equality (=)” [2].

In brief, there are many reasons why it is essential to cast any scientific analysis in the format proposed by the rules of logic in general, and the principle of equivalence in particular. A few of them, not necessarily in their order of importance, are as follows. Logic, as a whole, provides objective criteria for the evaluation of any proposition; most disagreement, as is well known, disappears as soon as the magic words are pronounced: “But that is not logically tenable.” Logic provides guidance to our analysis; without it, we are rudderless. Guided by rules of logic, we know whether or not we have completed our analysis. Logic makes it possible to replicate the reasoning or the experiment.

From the above it inexorably follows that the fundamental relationship that Einstein established between matter and energy is yet incomplete. Two terms do not make an equivalence relation. The relationship between matter and energy is completed only when a third element is found to which both matter and energy are equivalent.

3. Inadequacy of Some Possible Solutions

There are no explicit formulations of a third term to which both matter and energy are equivalent. As pointed out above, cis not a third term, but a unit of measurement of speed that has nearly nothing to do with light. It happens to be the speed of light; hence, at best, it is an attribute of light. By extension, it might be assumed that mc2 contains in it, not just the meaning of matter, but also—implicitly—the meaning of light. Even if cstood for light, it cannot be the third term because light is a form of energy (clearly in the wave conception of light; or a form of matter in the particle conception of light). Thus, whether light is an intrinsic component of E or m, it cannot at the same time be an extrinsic term to which either E or mcmight be equivalent. It cannot appear as an addition to either side of the equation, without creating double counting and without violating the first requirement that each term of the equivalence must be reflexive, namely identical to itself throughout the observation. The addition of the term light does not make the construction symmetric; one cannot change the term light with the term energy (or matter) and obtain positive results: one does not gain a better understanding of either matter or energy. Neither does that addition make the terms of the construction transitive: from light one necessarily goes back to either matter or energy—not to both. These considerations can also be put in common language: a part cannot be confused with the whole. If light is part of energy or part of matter, light cannot be equivalent either to energy or to matter, because this definition would run into the impossibility of equating a part with the whole. Since matter and energy, to be equivalent to each other, must be whole units, namely units or entities all complete in themselves, the third term must also be a whole unit, a whole entity. It cannot be a part of a whole.

The same considerations apply if the term third is assumed to be derived from the equation E = hν, where E is energy, h is Planck’s constant (which is equal to 1 and thus disappears from the equations of physics), and ν is the measure of the frequency of energy radiation emitted as photons, rather than the speed of light.

A more abstract set of considerations are necessary to dispel the notion that space (like the old ether and the futuristic “higher order”) might be the third element of the equivalence. The third element has to have an existence of its own. Take away matter and/or energy and space disappears from our field of observation. Hence it cannot be the third element that would make the equivalence of matter to energy a valid relationship.

We must search for a third term to which both matter and energy are equivalent.

3. Findings

This paper proposes that the search for the third term to complete the equivalence of matter to energy is exhausted with the introduction of spirit into the relationship. This is the answer that Fritjof Capra [3] inspired. One then obtains the following equivalence: matter ↔ spirit ↔ energy. This is a relationship that reads: matter is equivalent to spirit and spirit is equivalent to energy. This is a complete relationship of equivalence, which can be defined as the Relational Reality, and it can be diagrammed using these established protocols:

 

Figure 1. The Relational Reality

Figure 1 can be interpreted not only to mean that matter transforms itself into energy and energy into matter, but—at the very least—especially along these lines: The physical world in which we live has to be observed first from the point of view of matter and then from the point of view of energy. The essential prerequisite is to see these two aspects of reality not in linear fashion, but in a relational mode, namely as two separate and distinct viewpoints of the same reality. When that is done, one can also see that the total reality in which our daily existence is immersed can be grasped only if it is observed, not only from the viewpoint of matter and energy, but also from the viewpoint of spirit. One enters into the stone with a hammer; into the energy of the stone with a cyclotron; and into its spirit with prayer.

Thus we come back to the very roots of our civilization. Our ancestral ancestors—not unlike many brothers and sisters in many civilizations of today—started their analysis of the world neither from matter nor, certainly, from energy. It is fairly certain that they started their analysis of the world form the point of view of spirit.

But what is spirit? Can we obtain a precise definition of this term? Can we obtain an operational definition of this term?

4. On the Definition of Spirit

Spirit is incommensurable. Therefore, it is difficult to define. Once it is realized, as we shall more clearly see below, that mathematics, the most precise of all sciences proceeds on the basis of two incommensurable entities, namely zero and infinity, this inherent difficulty that is presented by the word spirit ought not to be of much concern to a physicist. That said, we shall try to identify some of the characteristics of spirit. As used in this paper, spirit is a relation, the relation that binds matter to energy. It keeps them both factually together and intellectually separate from each other. With the word spirit, we can stop thinking of the universe as a linear relationship in which matter somehow passes into energy, and we can start conceiving of the universe of matter being in organic relationship with the world of energy. We can study the objective reality first as a world of matter and then as a world of energy. These are all enclosed worlds of their own. If we conceive of both matter and energy as two entities, indeed as two worlds, in their own, without their individual link to spirit, they would both be in fatal conflict with each other. Instead, we notice near perfect and continuous harmony between the two entities. This we might say is an attempted definition of spirit in the small, as in “the spirit of this stone”: spirit is the link, the glue that holds matter and energy together.

By trying to define spirit in the large, as an infinite entity into which both matter and energy are encompassed, and indeed as an infinite entity in which we—observers—are all encompassed, we might gain a greater control over the forces of this world by regaining the sense of what used to be called the “sacred”. Only if the earth is seen as sacred again will we feel obliged to respect its inner existence. It is through the word spirit that we reach a better understanding of both matter and energy. Through that word, we enter deeply into their essence and we get in close contact with each of them. In an age in which we are discovering the essential importance of a sound ecological management of the planets, the word spirit will incite us to gain a greater respect for the world of matter as well as the world of energy than we have at present.

Thus the word spirit has a theoretical as well as an operational validity. And then it can inexorably be observed that the infinity of spirit manifests itself to us most clearly as both matter and energy. Hence, the preeminence of the study of physics in today’s culture is no longer surprising.

5. An Extension of the Word Spirit

But spirit does not manifest itself only as matter and energy. It also manifests itself, indeed, as spirit. Man’s mind has forever been engaged in the attempt to define “spirit”. We must admit that the task has eluded us. And there is a very good reason why the task is destined to elude us forever. Spirit is not an intellectual affair, hence it can never be caught by the intellect. Since it is an intensely personal relation, indeed an intensely personal affair, the essence of the word spirit can only be caught by our feelings. This is the fundamental reason why approximation to the understanding and explanation of spirit have been in the past the prerogative of mystics, theologians, philosophers, literati, and musicians. As the practitioners of these disciplines have forever made an attempt to convey their understanding of spirit to all other people who may be interested in the topic, so physicists in the future—as they have indeed done in the past (see, e.g., Aristotle and Thomas Aquinas)—have to try to convey to the practitioners of the spirit the goodness, the truth, and the beauty that they discover in both matter and energy.

6. Some Limitations of the Meaning of Spirit

One could define spirit as Spirit, namely as God. However, this definition might be misleading; it might lead into the old pitfalls of pantheism. To avoid such dangers, it is necessary to distinguish God from God’s spirit; it might be necessary to say that God is also spirit; and then one must be careful to limit God’s presence in matter and energy by saying that the spirit of God is also in matter and energy, also in the stone and its energy. If God is by definition everywhere, then—given the above qualifications—it is possible to say that God is also in the stone and in its energy. And then one surprising result ensues: a very practical consequence indeed. It appears that all three entities, namely matter, energy, and spirit might share the same unit of measure: degrees of heat. One of God’s characteristics is to be in essence love, Love par excellence. And is not warmth and heat one of the most endearing physical manifestations of love?

7. Some Implications for Physics

Not being a physicist, this writer can suggest some of the implications for physics of establishing a true equivalence between matter, energy, and spirit only at a very broad level of generality. When one multiplies the mass by the square of the speed of light, when one spins matter at the squared speed of light, one no longer observes matter but energy. One is no longer in the world of matter, but in the world of energy. One has made such a definite break between the two worlds that, in order to achieve clarity of mind and expression, one must accordingly design a new nomenclature. Using words from one world and applying them to the other leads to analogical thought, but not to innovative and incisive thought.

The second consequence that this writer can envisage is the need to jettison the old attachment to absolute quantification. Quantification in physics has always taken place within sharply defined limits. One has simply to resign to the nature of things that this is the only type of quantification that might forever be viable in physics. In order to reduce the level of apprehension about this condition, physicists will want to notice that mathematics too has always been subjected to this condition. If one does not see the number system as a linear but a relational organization of numbers, it becomes clear that mathematics is based on the following foundational equivalence: 0 ↔ 1 ↔ ∞. The first impression is that mathematics has been able always to proceed with the quantification of only one of its terms: namely, the number 1. Mathematics does not, and cannot quantify either zero or infinity. And it does not matter. Indeed, on second thought, mathematics does not quantify the third of its foundational terms either; mathematics does not present us with an absolute quantification of one, but a relative quantification of one. Numbers proceed from (plus or minus) one to infinity, but they never touch infinity; the conception of the limit is there to recognize this deficiency and to allow us to work within the limits offered by reality. Thus, taking a leaf from the transition from Galileo and Newton to Einstein through Hume in relation to space and time [4], we shall not be concerned with absolute but with relative quantification.

Hence, we can safely maintain that

If the universe is infinite, we shall never weigh its mass;

If the universe is infinite, we shall never measure its length;

What we measure is its mass and its length in relation to man.

Then, man—indeed, every man and woman—is again positioned at the center of the universe.

8. Some Conceptual Consequences

In 1946 Einstein remarked: The unleashed power of the atom has changed everything save our modes of thinking [5]. With the establishment of the equivalence of matter to spirit and to energy, everything changes. Technically, Figure 1 establishes that while any element of reality occupies its own distinctive position, everything is in full relationship with everything else. Hence, as proved by the Internet, everything is indeed directly related to everything else. This complexity is better observed by rotating at ever increasing speed, not only the entire Figure 1, but also each rectangle inside Figure 1 about its geometric center. One then obtains the image of four circles: one, the circle of matter; two, the circle of spirit; three, the circle of energy; four, the circle of the relational reality as a whole. This is a Venn diagram delimited by a circle. And what is a circle, if not a two-dimensional image of a sphere? Ultimately, one is thus presented with a construction composed of four interpenetrating concentric spheres, one for each point of view from which reality can be observed: the point of view of matter, spirit, energy, and the system as a whole. An analysis of this type of construction can be followed in detail in the humbler reality of the world of economic justice [6] and the world of economics [7]. The mathematics of this construction is well-known [8] and it might be useful to reproduce it here in a very abstract form as follows:

 = fa(a,b,c)

 = fb(a,b,c)

c· = fc(a,b,c),

where a· = rate of change in the first element of the relationship, b· = rate of change in the second element of the relationship, and c· = rate of change in the third element of the relationship.

From the linear world of rationalism, thus everything is transformed into the organic world of relationalism. Above all, beyond changes of perspective in physics, if this construction of reality is accepted, the warlike relation between the “two cultures” is expected to change and eventually to come to a screeching halt; with time, this war—with its multifarious manifestations of reductionism, materialism, and atheism, and, above all, mutual misunderstandings—will unavoidably come to a screeching halt.

While waiting for a response to these observations from the people of science, we already know the response from the people of spirit. Poetry and philosophy have spoken forcefully about the evident relationship between matters of the earth and matters of the spirit [9]. Since this writer is more familiar with the Catholic tradition, he will limit himself to one quotation from within this belief system. But many other expressions come easily to mind. “Every culture,” Christopher Dawson wrote, “is like a plant. It must have its roots in the earth, and for sunlight it needs to be open to the spiritual. At the present moment we are busy cutting its roots and shutting out all light from above” [10].

If mathematicians and physicists, following strict rules of logic that they already obey in all steps of their reasoning, can be convinced that their own fields—as moral theologians insist—are all immersed into the world of spirit, all other scientists, especially social scientists, will not take long to follow suit. After all, it was Einstein who said: “Science without religion is lame, religion without science is blind” [11].

9.  CONCLUSION

There are many indications that the world of linear, rational, Cartesian logic has come to an end—see, e.g., John Lukacs, At the End of an Age [12]. This is a world in which reality is reduced to isolated atoms. The principle of equivalence is a ready-made tool that allows us to escape the strictures of Cartesian logic and leads us into the world of relational logic, a world in which everything is naturally related to everything else. This paper has used this principle and reached some novel conclusions in relation to physics and mathematics. In the process, it has laid the groundwork for healing the ongoing schism between the “two cultures”.

A POSTSCRIPT

The reader might be interested to know that this paper was not written with the Shroud of Turin in mind. Yet, at one point it became apparent to this writer that the paper makes the Shroud a logical and “natural” necessity. Even the Transfiguration and the appearance of Jesus in the Cenacle become understandable, because—if this reasoning is right—Jesus is, was, and will forever be the perfect union of matter and energy and spirit. And, of course, accepting this reasoning one can see that the consecrated communion host is real.

If this reasoning is accepted to be theologically and logically valid, it leads to a further observation. The study of singularities is not concluded by the study of matter alone, or energy alone, or spirit alone. It is the integration of the three worlds that might yield a better understanding of singularities as well as a better understanding of the world as a whole.

The study of singularities cannot be eschewed by science. Science cannot thus limit itself. Indeed, as various technical studies of the Shroud of Turin prove, science has an essential role to play in the analysis and the distinction of true from false singularities.

ACKNOWLEDGMENTS

The author wishes to acknowledge the technical assistance received from his long-standing collaborator, Louis J. Ronsivalli, an MIT food science technologist, and a most positive feedback from Dr. F. Hadi Madjid, a Harvard physicist. The paper has greatly benefited from comments and recommendations from six referees on an earlier draft. Thanks also go to Jonathan F. Gorga for invaluable editorial assistance.

REFERENCES

[1]          Einstein, A. (1905). “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?” (Does the Inertia of a Body Depend upon its Energy-Content?). Annalen der Physik. Ser. 4, Vol. 18, pp. 639-641. See also, [1935 (1971)]. “Elementary Derivation of the Equivalence of Mass and Energy”. American Mathematical Society, Bulletin. Vol. 41, pp. 223-30. In R. W. Clark. Einstein—The Life and Times. New York and Cleveland: World Publishing, p. 538; see also pp. 98-103, 115-120, 126, 141, 144, 268, 537, and 587.

[2]          Allen, R.G. D. (1970). Mathematical Economics, 2nd edn. London and New York: Macmillan, St. Martin’s, p. 748.

[3]          Capra, F. (1980). The Tao of PhysicsNew York: Bantam Books.

[4]          Cf. Feinstein, J. S. (2006). The Nature of Creative Development. Stanford: Stanford Business Books, esp. pp. 303-315 and 322-328.

[5]          Einstein, A. (1946). In Nathan O., and Norden, H. eds., Einstein on Peace. New York: Avnet Books, 1981 ed, p. 376, from a pamphlet published by Beyond War in 1985 entitled A New Way of Thinking.

[6]          Gorga, C. (1999). “Toward the Definition of Economic Rights”, Journal of Markets and Morality Vol. 2, No. 1, pp. 88-101.

[7]          Gorga, C. (2002). The Economic Process: An Instantaneous Non-Newtonian Picture. University Press of America, Lanham, Md., and Oxford.

[8]          Thompson, J. M. T. (1986). Nonlinear Dynamics and Chaos, Geometric Methods for Engineers and Scientists. New York: Wiley.

[9]          For poetry, Walt Whitman’s work should suffice. For philosophy, see. e.g., Hegel, G. W. (1807). The Phenomenology of Spirit and Emerson, R. W. The Natural History of the Intellect (or The Natural History of the Spirit) unpublished.

[10]       Dawson, C. In Catholic Educator’s Resource Center (CERC), Bi-Weekly Update, November 5, 2004. At www.catholiceducation.org.

[11]       Einstein, A. (1941). “Science, Philosophy and Religion: a Symposium”. From The Quotation Page at http://www.quotationspage.com/quote/24949.html.

[12]       Lukacs, J. (2002): At the End of an Age. New Haven and London: Yale University Press.

Brief Biographical Sketch of the Author

Carmine Gorga is a former Fulbright scholar and the recipient of a Council of Europe Scholarship for his dissertation on ”The Political Thought of Louis D. Brandeis.” Using age-old principles of logic and epistemology, in a book and a series of papers Dr. Gorga has transformed the linear world of economic theory into a relational discipline in which everything is related to everything else—internally as well as externally. He was assisted in this endeavor by many people, notably for twenty-seven years by Professor Franco Modigliani, a Nobel laureate in economics at MIT. The resulting work, The Economic Process: An Instantaneous Non-Newtonian Picture, was published in 2002. For reviews, see http://www.carmine-gorga.us/id18.htm. During the last few years, Mr. Gorga has concentrated his attention on matters of methodology for the reunification of the sciences.

In mathematics

The original publication is available at
International Journal of Mathematics, Game Theory and Algebra, 2010, vol. 19, issue 4, pp. 235-244.

ON THE TRANSFORMATION OF MATHEMATICS
FROM A
LINEAR TO A RELATIONAL DISCIPLINE

Toward the Reunification of the Physical and the Social Sciences

Carmine Gorga

Abstract

While the structure of mathematics is built on an uninterrupted series of equivalence relations, the number system forms a linear progression. To eliminate this dichotomy, while leaving the functionality of the number system intact, the present paper proposes to transform the relation between zero, one, and infinity into a relation of equivalence. This relation breaks the empty linear progressio ad infinitum of the number system; selects zero, one, and infinity as the most important elements in the series; and locks them into a position of mutual relationships. The terms turn out to be reflexive, symmetric, and transitive. It is thus possible to see that each element represents a concrete world of its own, a condition that sheds lights of understanding on each one of the other two and yields the derivation and the definition of each term in relation to the others. If this application of the principle of equivalence is accepted as valid, mathematics is transformed into a relational discipline. Then everything changes in the spirit of both the physical and the social sciences. Mutual adjustments will eventually facilitate the re-unification of the physical with the social sciences and abate the warlike relation between the “two cultures.”

Keywords: number system; linearity; equivalence; rationalism; relationalism

 

Brief Bio

Carmine Gorga is a former Fulbright scholar and the recipient of a Council of Europe Scholarship for his dissertation on ”The Political Thought of Louis D. Brandeis.” Using age-old principles of logic and epistemology, in a book and a series of papers Dr. Gorga has transformed the linear world of economic theory into a relational discipline in which everything is related to everything else—internally as well as externally. He was assisted in this endeavor by many people, notably for twenty-seven years by Professor Franco Modigliani, a Nobel laureate in economics at MIT. The resulting work, The Economic Process: An Instantaneous Non-Newtonian Picture, was published in 2002 and it is currently being reissued in an expanded version. For reviews, see http://www.carmine-gorga.us/id18.htm. During the last few years, Mr. Gorga has concentrated his attention on matters of methodology for the reunification of the sciences.

 

Introduction

While the structure of mathematics is built on an uninterrupted series of equivalence relations, the number system is constructed as a linear progression. To eliminate this dichotomy, the present paper, without affecting the inner workings of the number system, attempts to consider zero, one, and infinity as three distinct entities, unlike the numbers 2, 3, or 4, and ties them together into an equivalence relation. This pivotal operation transforms mathematics from a linear to a relational discipline: Each foundational element is related to the rest of mathematics and to the outside world.

After observing some of the canonical requirements of the equivalence relation and the fundamental advantages of casting thought processes into this format, the paper calls attention to some of the major links in the series of equivalence relations on which mathematics is built. Equivalence is not composed of a mechanical addition of one element to another, as in the linear relation of 0, 1, 2, 3… ∞: 0 + 1 + ∞ is meaningless. Rather, it searches for the most important elements in a set and interlocks them. This approach transforms a linear mode of thinking into a relational one. Hence the paper proposes that the most fundamental relation in mathematics is the equivalence of Zero to One to Infinity; in traditional notation, 0 ≡ 1 ≡ ∞; or, 0 = 1 = ∞; and, in different notation, 0 ↔ 1 ↔ ∞. As can be seen, nothing changes but our mode of thinking about the number system: The system is all there, but changed from a linear to a relational apparatus.

If the present proposal stands all the tests of validity, this solution will eventually yield two considerable benefits. This internal transformation (1) reveals some inner characteristics of mathematics that are shielded from plain view and (2) tends to facilitate the eventual re-unification of the physical with the social sciences.

 

Problem Statement

The number system is conceived as proceeding from zero to one to infinity. This is a progression that leaves the three fundamental entities of mathematics—namely zero, one, and infinity—unrecognized and unrelated to each other or related to each other in a linear mode of thought. This linear linkage leads the mind to an empty progressio ad infinitum. This condition leaves mathematics serving, yet conceptually isolated from, all other mental disciplines. The proof is that each one of the three terms, namely zero, one, and infinity are conceived as being identical in form to the number two, three, and all other numbers (the ever incomplete listing of which yields one of the approaches to the meaning of infinity). As such, zero, one, and infinity are left unidentified as in the Hegelian night in which all cows are black. In reality, all numbers are not equal. As will be seen, those entities are three fundamentally distinct building blocks of mathematics.

While the relationship tying zero to one and to infinity is conceived as being linear, the equivalence relation stands as part and parcel of all of mathematics. It stands at the very foundation of the number system, in which three fingers of the hand (3 of base 10 number system) are equivalent to a word/number/symbol—namely, three, 3, or III—and to the three apples in front of our eyes. All algebraic relations are equivalence relations. A system of equations is based on the equivalence relation. A triangle is based on the equivalence relation. The whole of trigonometry is based on the equivalence relation. Indeed, as R. G. D. Allen points out, the rules of equivalence “hold” also for the relation of “equality (=)”.1 Hence, 1 = 1 is an equivalence relation, because its validity stands on the proof that 1 = (6 – 5) or any other such relation. Hence, in extenso, 1 = 1 ought to be written 1 = (6 – 5) = 1 or 1 = (6 – 5) = (7 – 6).

The equivalence relation starts in logic and has the widest possible range of application outside of mathematics as well. All forms of syllogism are based on an equivalence relation; most religions are based on an equivalence relation. Hence the relation of equivalence is well known to theologians, philosophers, and the literati. As logicians—and mathematicians—know, to be valid an equivalence relation must be composed of three terms. The three terms have to be reflexive (identical to themselves throughout the discourse), symmetric (one observes the same entity from two points of view in order to obtain a deeper understanding of both entities), and transitive (a third term must exist to which both terms are equivalent in order to eschew the confines of circular reasoning, to observe the same entity from three points of view or have a triple check on our reasoning, and to complete the analysis). With the assistance of the equivalence relation the terms of the analysis do not start from an arbitrary point and end at an arbitrary point, but are strictly interlocked.

These observations can be made more certain by specifying why science eschews all singularities. There is a good reason for this practice. Punctilionism, the defense to the death of a single point unrelated to the rest of the universe, is not analysis. A single event does not lead to an objective, replicable analysis or experiment. Analysis begins with the observation of two events. Yet, the observation of two events necessarily leads to circularity of reasoning. Faced with two observations, one is obliged to observe all possible relationships between them. Hence, the mind is led back to the exploration of all potential outcomes of the position of Point B on the circumference in relation to Point A at the center of the circle. This is a process that eventually leads to the reversal of one’s position (an 1800 turn) and then to a return to one’s original position—and no certainty is acquired in the meantime. Therefore, science asks for a third term. The third term points the research in the right direction. If the third term is placed in a linear relation-position-alignment, however, the end result might be a dispersal of the thought process into the empty infinity of an enlarged circle. Again, linearity leads to progressio ad infinitum.

It is the equivalence relation that restrains the analysis from collapsing into infinity by constraining the terms into an interlocked relationship as in its standard configuration: A ↔ B ↔ C. In brief, there are many reasons why it is essential to cast any scientific analysis in the format proposed by the rules of logic in general, and the principle of equivalence in particular. A few of them, not necessarily in their order of importance, are as follows. Logic, as a whole, provides objective criteria for the evaluation of any proposition; most disagreement, as is well known, disappears as soon as the magic words are pronounced: “But that is not logically tenable.” Logic provides guidance to the analyst; without it, the analyst is rudderless. Thanks to the rules of logic, it becomes apparent whether or not the analysis is complete. Logic makes it possible to replicate the reasoning or the experiment.

From the above it inexorably follows that, in the number system is commonly conceived, the relationship that exists between zero, one, and infinity is linear and unspecified; namely, it is 0 → 1 → ∞. The terms do not make an equivalence relation. The terms are thoroughly specified when it is recognized that the relationship linking them is a relation of equivalence, namely when they are linked in this form: 0 ↔ 1 ↔ ∞.

 

Inadequacy of Present Conception

There are various reasons why the present linear conception of the number system is inadequate. The most important one perhaps is that placing zero, one, and infinity in a linear relationship to each other condemns the number system, and by extension the whole of mathematics, to remain a closed entity separate from all other forms of thought. Where is the relationship between mathematics and poetry? Or philosophy? Or religion? Also, by placing the three terms in linear succession with each other, they become an indistinct part of the number system: 0 is a number just as 1 is a number; and 0 occupies a position just as 1 occupies a position on the number list. Thus they lose their distinct identity, and cannot be defined: More specifically, they cannot be defined in a manner that, ideally, might satisfy everyone once and for all. In addition, it will be seen that the closed world of mathematics provides a faulty and misguided sense of certainty to the rest of the intellectual community; instead, by ascertaining and affirming the truth about its own modus operandi, mathematics could indeed offer much useful guidance.

 

Findings

This paper proposes that the search for the relationship among Zero, One, and Infinity is completed when it is realized that what links the three terms to each other is a relationship of equivalence. One then obtains this equivalence: Zero ↔ One ↔ Infinity. This is a relationship that allows the number system and by extension the whole of mathematics to be classified as Relational Mathematics. The relationship can be diagrammed interchangeably using these established protocols:

 

Figure 1. Relational Mathematics

Figure 1 can be interpreted not only to mean that Zero is a different aspect of One and One is a different aspect of Infinity, but also along these lines: The mathematical world which controls so much of our lives has to be observed first from the point of view of Zero, then from the point of view of One, and then from the point of view of Infinity. The essential prerequisite is to see these three elements of the number system not in a linear fashion, but in a relational mode, namely as three separate and distinct viewpoints of the same system. The easiest method to realize that the three entities are inextricably related to each other is to superimpose the three rectangles forming Figure 1 upon each other at once, alternatively by separately placing each one of the three rectangles on top of the other two. Two rectangles then are obstructed from view, but they remain stubbornly there. Indeed, it is then that we come to the full realization that only by distinguishing the three entities from each other can we hope to understand all three of them. Otherwise, we reduce the construction to a singularity; or lock it into circular reasoning, if we were to deny either the reality of Infinity or the reality of Zero.

Technically, Figure 1 establishes that while any element of the mathematical reality occupies its own distinctive position, everything is in full relationship with everything else. This complexity is better observed by rotating about its geometric center at ever increasing speed, not only the entire Figure 1, but also each rectangle inside Figure 1. One then obtains the image of four circles: one, the circle of Zero (A); two, the circle of One (B); three, the circle of Infinity (C); four, the circle of the mathematical relational reality as a whole (M). This is a Venn diagram of sets A, B, C, and M delimiting four circles. And what is a circle, if not a two-dimensional image of a sphere? Ultimately, one is thus presented with a construction composed of four interpenetrating concentric spheres, one for each point of view from which the mathematical world can be observed: the point of view of Zero, One, Infinity, and the system as a whole. An analysis of this type of construction can be followed in detail in the humbler reality of the world of economic justice2, economic theory3, and economic policy4—as well as, in outline, in the parallel world of physics.5 The mathematics of this construction is well-known6 and it might be useful to reproduce it here in a more abstract form as follows:

A· = fA(A,B,C)
B· = fB(A,B,C)
C· = fC(A,B,C),

where A· = rate of change in the first element of the relationship, B· = rate of change in the second element of the relationship, and C· = rate of change in the third element of the relationship. (M is there to suggest that the equivalence relation is and will always be open to form the next equivalence and to understand the rest of the world.)

When the analysis is completed, it is possible to see that the total reality in which the number system is immersed can be grasped only if it is observed, not only from the viewpoint of One, but also from the viewpoint of Zero and Infinity. Through a set of equivalence relations, in the night of time we built the number system. We posited 1 + 1 = 2. This last entity, 2, is a convention. The magic—or creative synthesis, as Benedetto Croce pointed out—is in the sum of 1 plus 1; and then another magic is in the universal acceptance of the convention that 2 equals the sum of 1 plus 1.

Following the same reasoning, we built the entire number system. On the positive side. The negative side is not a new chain, but a symmetric reversed chain: -1, -2, etc. The proof can be constructed by following this evidence: 1 – 1 = 0, just as (-1) – (-1) = 0.

The number system forms a well recognized unit of thought. The seed of this system is all contained in the entity that we call One. And from One, as briefly seen above, we gradually pass to the initial understanding of Infinity through both the positive and the negative chain of numbers. A fuller understanding of Infinity is contained in the realization that, just like One, the entity that we call Infinity is a whole unit in itself; it is a complete system: it is a “full” set—a set whose understanding is approached by the inclusion in it of the entire number system. Similarly, the entity that we call Zero is the “empty” set—a set whose understanding is approached by subtracting one number at a time from the number system until we are left with no more numbers. This empty set, this null set, is a whole entity in itself. The briefest possible proof that Zero is not “another” number is contained in the realization that Zero is not the half point between all positive and all negative integers: Since both chains are infinite, every point on them is the half point. Furthermore, Zero is not another number because we are not able to distinguish whether it is derived from 1 – 1 or from (-1) – (-1). Were it necessary, the practical function of Zero as indicating position could be replaced by any other symbol, such as a forward slash, without altering the structure or the integrity of the number system.

In other words, we reach a fuller understanding of the set we call One by putting it in relation with the set we call Infinity as well as the set we call Zero. We enter into the world of One precisely as we have done ever since the dawn of civilization, by observing things and counting them with the help of our fingers. Once we begin to recognize that there is no end to the number system we enter the world of Infinity. Thus we come back to the very roots of our civilization. Our ancestral ancestors—not unlike many brothers and sisters in many civilizations of today—started their analysis of the world with the understanding of the number One. Then they jumped off to the understanding of such an esoteric concept as the world of Infinity. Only relatively recently in the history of civilization have we discovered the need to understand the world of Zero.

How do we define these entities?

 

On the Definition of Zero, One, and Infinity

One is incommensurable. Therefore, it is difficult to define. Indeed, by itself we might never be able to define it. One represents a whole world of its own. And we can be sure of its existence, not only because we have created it, but especially because it functions as the seed of the entire number system. The number/word “two” would be a complete abstraction if it were not possible to say that it results from the addition of One plus One or, in standard notation, 2 = 1 + 1. (And we can be sure that this equality is valid, because the two sides of the equation are equivalent to each other: they have the same meaning, the same value, the same weight.)

Indeed, it might be forever impossible to define One if it were not for the concept of Infinity. Thus, calling for assistance on the principle of non-contradiction, it can be said that One is not-Infinity. Yet, both One and Infinity would forever remain locked into a circular relationship if both concepts were not anchored in the reality of Zero. With the inclusion of this third element, we can now distinguish One from Infinity, not simply by saying that One is not-Infinity, but by specifying that One is the beginning of a set that separates itself from Zero and tends to Infinity.

Similarly, it might be forever impossible to define Infinity if it were not for the concept of Zero. Thus, calling again for assistance on the principle of non-contradiction, it can be said that Infinity is not-Zero. By extension, we can now say that Infinity is a full set, while Zero is an empty set. Yet, both Infinity and Zero would forever remain locked into a circular relationship if both concepts were not anchored in the reality of One. With the inclusion of this third element, we can now distinguish Infinity from Zero, not simply by saying that Infinity is not-Zero, but by specifying that Infinity is the end/beginning of a set that starts with One.

In turn, since Zero is not-One, Zero is also not-Infinity. It is by subtracting, one by one, all the content of Infinity—one by one all the numbers from the number system—that we reach the concept of Zero. Zero then is the symmetric, but negative, image of Infinity. It is only by understanding Zero that we can conceive of Infinity; and only by understanding Infinity that we can conceive of Zero—and indeed One.

Zero, One, and Infinity can be understood only in relation to each other. Zero is the other face of Infinity; One is the other face of Zero; Zero is the emptiness of Infinity; One is the fullness of Infinity; Infinity is the fullness of One and the emptiness of Zero; One is the limit between Zero and Infinity or, conversely, One is the separation of Zero from Infinity. The terms are reflexive, symmetric, and transitive.

As used in this paper, One is a relation, the relation that binds Zero to Infinity. One is the link, the glue that holds the world of Zero and the world of Infinity together. It keeps both Zero and Infinity factually together and intellectually separate from each other. With the word One, we stop thinking of the universe of mathematics as a linear relationship in which Zero loses its distinction and its existence when it inexplicably passes into One and eventually into Infinity, and we start conceiving the three terms of the universe of mathematics as being three whole entities—complete in themselves and in organic relationships with each other. We can then study the objective reality of the number system first as the world of One, then as the world of Zero, and then as the world of Infinity. Each term is an enclosed world of its own.

 

Some Implications for Mathematics

Observed at a very broad level of generality, some of the implications for mathematics of locking Zero, One, and Infinity into a relation of equivalence are as follows. The number system is no longer composed of an infinite series of elements; it is composed of a comprehensible series of three elements, the world of One, the world of Zero, and the world of Infinity. These three elements are no longer independent of each other but are strictly interconnected. It is through the word One that we reach a better understanding of both Zero and Infinity. Through the concept of One, we enter deeply into the essence of both Zero and Infinity and we extend our intellectual grasp to encompass both of these totally abstract entities.

More importantly perhaps, by trying to define One as an infinite entity into which both Zero and Infinity are encompassed, and indeed are One, we realize that this is an infinite world in which we—observers—are all encompassed. Conversely, we can look at the world of Zero or the world of Infinity by realizing that they also encompass the world of One. Thus the utmost hope is that, having reached this level of understanding of the number system, we might gain greater control over the forces of this world by regaining the sense of interconnectedness that links everything to everything else.

The most evident and practical consequence of transforming mathematics into a relational discipline is the need to jettison the old attachment to absolute quantification. Quantification in mathematics has always taken place within sharply defined limits. Thus, taking a leaf from the transition from Galileo and Newton to Einstein through Hume in relation to space and time,7 we shall not be concerned with absolute but with relative quantification. We shall conclude that quantification is never absolute; it is always relative. And it might forever remain relative. In order to reduce a possible level of apprehension about this condition, we might notice that mathematics has always been subject to this condition. Mathematics, the most precise of all sciences, proceeds on the basis of two incommensurable entities, namely Zero and Infinity. Indeed, on second thought, mathematics presents us, not with an absolute but with a relative quantification of its third foundational term as well: One, One as symbolic representation of the number system as a whole. The number system is infinite; hence, it is incommensurable. One is incommensurable.

Of course, we must not confuse the instrument of measurement with the object being measured. Yet, reference to the object of measurement confirms the validity of the observation that quantification is never absolute. We can number the apples in front of our eyes as being three because they are in a relative relationship with us. But can we dream of measuring all the apples that ever existed and all the apples that will ever exist? Did not Mandelbrot conclude that even the coastline of Britain is infinite?8

Needless to say, this is not an advocacy of not measuring things that can be measured.

From these considerations there ensues a surprising and interesting consequence. Blind believers in the powers of mathematics have imparted a wrong sense of security to the world. From every corner it is heard: Measure things, quantify them, number them—and you shall acquire certainty. Through the equivalence relation of Zero to One and Infinity, it becomes utterly clear that mathematics does not impart any sense of certainty to the world. None of its three foundational terms can ultimately be numbered or transformed into a measurable or quantifiable entity. What is invaluable is that mathematicians do know it and have learned how to cope with their world of uncertainty. They have invented the instrument of the limit—whereby numbers, proceeding from (plus or minus) One, approach Zero and Infinity, but never quite reach them. Thus mathematicians, from being the most abstract of all people, turn out to be the most concrete and practical ones indeed.

 

Some Conceptual Consequences for Other Disciplines

In 1946 Einstein remarked: “The unleashed power of the atom has changed everything save our modes of thinking”.9 With the establishment of the equivalence of Zero to One and to Infinity, while the number system remains as intact as before, our modes of thinking about mathematics change and transform this discipline from a linear to a relational entity. And then (potentially) everything changes.

From the linear world of Cartesian logic and rationalism, everything is transformed into the organic world of relationalism in which—as proved by the Internet—everything is indeed related to everything else. Above all, beyond changes of perspective in mathematics, if the proposed construction of the number system is accepted as valid, with time, the warlike relation between the “two cultures”—with its multifarious manifestations of reductionism, materialism, and atheism, and, above all, mutual misunderstandings—will, through mutual adjustments, unavoidably come to a screeching halt. Mathematics is no longer the fount of all certainty; if neither Zero, nor One, nor Infinity is a measurable entity, mathematics is as imponderable as all other mental disciplines. This is a verity that is well-known to insiders (Kline 1980);10 yet, it does not seem to have yet percolated among non-mathematicians. If there is such a thing as certainty, it exists outside the realm of mathematics.

While waiting for a response to these observations from the people of science, we already know the response from the people of the spirit. Poetry11 and philosophy12 have spoken forcefully about the evident relationship between matters of this earth, including man’s mind, and matters of the spirit; between ponderable and imponderable entities. Since this writer is more familiar with the Catholic tradition, he will limit himself to one quotation from within this belief system. But many other expressions come easily to mind. “Every culture,” Christopher Dawson wrote, “is like a plant. It must have its roots in the earth, and for sunlight it needs to be open to the spiritual. At the present moment we are busy cutting its roots and shutting out all light from above”.13

If mathematicians, following strict rules of logic that they already obey in all steps of their reasoning, can be convinced that their own fields—as moral theologians insist—are all immersed into the unmeasurable world of the spirit, all other scientists, especially social scientists, will not take long to follow suit. After all, it was Einstein who said: “Science without religion is lame, religion without science is blind.”14

 

Conclusion

There are many indications that the world of linear, rational, Cartesian logic has come to an end—see, e.g., John Lukacs, At the End of an Age15 or Morris Kline, Mathematics: The Loss of Certainty.16 That was a world in which reality was reduced to isolated atoms. The principle of equivalence is a ready-made tool that allows us to escape the strictures of linear, rational logic and leads us into the world of relationalism, a world in which everything is naturally related to everything else. This paper has used this principle to link Zero to One and to Infinity. In the process, it has reached conclusions in relation to the world of mathematics that lay the groundwork for eventually healing the ongoing schism between the “two cultures.”

 

ACKNOWLEDGMENTS

The author wishes to acknowledge the technical assistance received from his long-standing collaborator, Louis J. Ronsivalli, an MIT food science technologist, and a most positive feedback from Dr. F. Hadi Madjid, a Harvard physicist. This presentation has greatly benefited from comments and recommendations from six referees on an earlier draft of this paper. Thanks also go to Jonathan F. Gorga for his invaluable editorial assistance.

 

NOTES

1. R.G. D. Allen, Mathematical Economics, 2nd edn, p. 748 (London and New York: Macmillan, St. Martin’s, 1970).

2. C. Gorga, ‘Toward the Definition of Economic Rights’, Journal of Markets and Morality 2, 88-101 (1999).

3. C. Gorga, The Economic Process: An Instantaneous Non-Newtonian Picture (Lanham, Md., and Oxford: University Press of America, 2002). An expanded edition is in press.

4. C. Gorga, “Concordian economics: tools to return relevance to economics”, Forum for Social Economics (forthcoming).

5. C. Gorga, “On the Equivalence of Matter to Energy and to Spirit”, Transactions on Advanced Research 3, 2, 40-47 (2007).

6. J. M. T. Thompson, Nonlinear Dynamics and Chaos, Geometric Methods for Engineers and Scientists (New York: Wiley, 1986).

7. Cf. J. S. Feinstein, The Nature of Creative Development, esp. pp. 303-315 and 322-328 (Stanford: Stanford Business Books, 2006).

8. B. B. Mandelbrot, The Fractal Geometry of Nature, p. 25 (New York: W. H. Freeman and Company, 1982).

9. A. Einstein. In Nathan O., and Norden, H. (eds), Einstein on Peace, p. 376 (New York: Avnet Books, 1981) and a pamphlet published by Beyond War in 1985 titled A New Way of Thinking.

10. M. Kline, Mathematics: The Loss of Certainty (New York: Oxford University Press, 1980).

11. For poetry, W. Whitman’s work should suffice.

12. For philosophy, see. e.g., G. W. Hegel, The Phenomenology of Spirit (1807) and R. W. Emerson, The Natural History of the Intellect (or The Natural History of the Spirit) unpublished.

13. C. Dawson. In Catholic Educator’s ResourceCenter (CERC), Bi-Weekly Update, November 5, 2004. At http://www.catholiceducation.org.

14. A. Einstein, ‘Science, Philosophy and Religion: a Symposium’ (1941). In The Quotation Page at http://www.quotationspage.com/quote/24949.html.

15. J. Lukacs, At the End of an Age (New Haven and London: Yale University Press, 2002).

16. Kline, op. cit. (note 8) p.7.

Short title: Mathematics as a Relational Discipline

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