Godel’s Incompleteness Theorem-Reciprocal Movement

Between Syntax And Arithmetic-Godel’s Incompleteness Theorem-Reciprocal Movement (RM)

Foundational Crisis In Mathematics


Divergencies, convergencies and, at times, insurmountable paradox, has marked the history of mathematics. A major discontinuity in the history of mathematics occurred in the l880’s when Georg Cantor developed his theory of sets. Cantor developed a diagonal method from which he worked out the mathematics of infinities. The essence of this method is, according to Douglas Hofstadter, “the fact of using one integer in two different ways--or, one could say, using one integer on two different levels--thanks to which one can construct an item which is outside of some predetermined list.” [Douglas R. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid, 1979, p. 423]

The diagonal method developed by Cantor was not the problem, rather, the controversy sprang from what Cantor was able to prove with this method. For instance, in his investigations into non-denumerable sets Cantor was able to prove:

“Any line segment, no matter how small, contains as many points as an infinite straight line. Further, the segment, contains as many points as there are in an entire plane, or in the whole of space of n dimensions (where n is any integer greater than zero) or finally in a space of denumerable infinite number of dimensions.” [E.T. Bell, Men Of Mathematics, 1937, p571]

By bringing into question fundamental axioms such as: every magnitude is equal to itself; the part is less than the whole; two magnitudes, equal separately to a third, are equal to each other; etc., Cantor’s transfinite mathematics brought the very foundation of mathematics into question.

Three foundational schools of mathematics arose in response to Cantor’s transfinite mathematics. Each produced their own point of view concerning the nature of number. Bertrand Russell advocated that mathematics could be reduced to a system of logic while the school of thought representing intuitionalism accepted number as a “given”. Kronecker, a spokesperson for the intuitionalist school, is reported to have said, “The whole numbers were made by the good Lord, everything else is the work of man.” [A.S. Luchins and E.H. Luchins, Logical Foundations Of Mathematics For Behavioral Scientists, 1965, p.56] Not surprisingly the intuitionalists took exception to many of the concepts associated with the mathematics of infinitesimals.

In an attempt to end the controversy over number, the third foundational school, the formalists (Hilbert), set themselves the task of creating an axiomatic language (using methods acceptable to both logists and intuitionalists) that would define a formal number-theoretic system (a system inclusive of the natural numbers, analysis and calculus). If successful, this axiomatic language would have been both consistent and complete and it would have eliminated the paradoxes and antinomies that were found in set theory and classical mathematics. For better or worse, the formalist school of thought did not achieve their goal. What was achieved however was a 1931 paper by Kurt Godel which determined the goals of the formalist approach to mathematics to be unattainable. In his paper, entitled, On Formally Undecidable Propositions of TNT (typographical number theory) and Related Systems, Godel offered a proof which demonstrated that given any sufficiently powerful formal system, it is not possible for it to be complete and, while it may be consistent, its consistency is not provable within the system.


When The Foundation Of Mathematics Is Based On Indeterminate Numbers

Between Content And Form, Between Assimilation And Accommodation Are The Polar Phases Of The Total Life Process—And Reciprocal Movement (RM)


There are a number of important consequences that follow from Godel’s proof but the one that is most significant in respect to Piaget’s constructionist structuralism, it seems to me, is the one that implies the existence of supernatural numbers. The derivation of a true theorem in number theory, which is its own negation, may be interpreted as the requisite condition for the existence of supernatural numbers. These numbers are peculiar in that they have the property of being infinitely large while possessing no numeral representation. But, everything that can be proven for natural numbers can be proven for supernatural numbers, with the exception that natural numbers are determinate while supernatural numbers are indeterminate.

When the foundation of mathematics is considered in this light, Piaget becomes easier to comprehend. For instance, when Piaget describes the nature of knowledge as being like a pyramid of knowledge that “no longer rests on foundations but hangs by its vertex, an ideal point never reached and, more curious, constantly rising,” he is being very consistent with the latest developments in number theory. Piaget continues:

“In short, rather than envisaging human knowledge as a pyramid or building of some sort, we should think of it as a spiral the radius of whose turns increases as the spiral rises…This means, in effect, that the idea of structure as a system of transformations becomes continuous with that of construction as continual formation.” [Jean Piaget, Structuralism, 1970, p. 34]

The concept of “knowledge as structure” and structure as a “double movement” e.g., the “completeness proof” for natural numbers requiring supernatural numbers and the “consistency proof” for supernatural numbers requiring natural numbers, becomes generalized in the thought of Piaget as the relationship of interdependence that exists between content and form. It is in this interdependent relationship that we find the basis for Piaget’s constructionist theory. Piaget puts this conclusion in his own words:

“Since Godel,...the idea of a formal system of abstract structures is thereby transformed into that of the construction of a never completed whole, the limits of formalization constituting the grounds for incompleteness, or, as we put it earlier, incompleteness being a necessary consequence of the fact that there is no “terminal” or “absolute” form because any content is form relative to some inferior content and any form the content for some higher form.” [Piaget, Structuralism, 1970 p. 140]

With the knowledge of the interdependence of content and form firmly established, Piaget turns to the subject of Biology in order to give his theory a concrete elaboration.

Piaget was deeply influenced by Darwinian evolution. In Piaget’s understanding of processes and states, in terms of developmental stages, we see the depth of this influence. However, Piaget went further than Darwin in his elaboration on the effects of the environment on the development of the individual. In addition to natural selection, Piaget believed something more was going on in an organisms adaptation to its environment. For Piaget an active restructuring and accommodation of an organism to its environment also influenced the development of the organism. Piaget described this new level of accommodation in terms of the interplay of accommodation and assimilation that occurs in the normal life processes. Martindale explains:

“Basic to all Piaget’s explanations is a conception of the individual life process. This has two major aspects or phases: the assimilation of objects to individual activity, on the one hand, and the accommodation of activity to the object world on the other. The two processes of assimilation and accommodation are polar phases of the total life process. They are not always in equilibrium and may even operate in partial autonomy from one another. One of the fundamental facts of the life process is the establishment of an equilibrium between assimilation and accommodation.” [Don Martindale, 1981, p. 342]

Our Experience Is Structured Along Subject And Object Poles

The Logic Of The Spontaneous Organization Of Activity In The Thought Of Piaget


“There seems to be little evidence that Cassirer, Mead, and Piaget ever had much direct influence on one another. This makes all the more interesting their convergence on a common point of view.” [Don Martindale, 1981, p.339] Indeed, whereas Cassirer found the origin and evolution of symbolic meaning to reside in the “work” of man, Piaget, in a like manner, put the origin of structure and the symbolic content that it generates, in the organisms capacity for action. Howard Gardner has this to say regarding the priority of the act in Piaget’s psychology:

“Piaget reached a crucial insight: the activity of an organism can be described or treated logically, and logic itself stems from a sort of spontaneous organization of activity. At this time he also formulated the notion that all organisms consist of structures--i.e., of parts related within a whole--and that all knowledge is an assimilation of a given external into the structures of the subject.” [Howard Gardner, The Quest for Mind, Piaget, Levi-Strauss, and the Structuralist Movement, 1973, p.54]


In addition to the similarity that occurs in Cassirer’s and Piaget’s concepts of “work” and “action” the thought of these two men converge in another respect also. Both men believed that the subject and object poles of experience are not simply “given.” Rather, for Cassirer and Piaget, the subject and object poles of experience are “products” of experience. As we have already seen, Cassirer came to this conclusion, at least in part, based on his studies of Pre-modern man’s mythology. Piaget, on the other hand, arrived at this conclusion as a result of his investigations into the language acquisition of young children. In a study of early two-word utterances (1951) Piaget “was able to show how the subject pole and object pole of a child’s experience remains undissociated in the early stages of language development.” [Edited by B.Z. Presseisen, Topics in Cognitive Development, 1978, p.7]


For Piaget, the long and active process that results in what we take to be the knowledge of our objective and subjective experience begins in the recognition and coordination of sensorimotor activity. By locating the source of cognitive structure in the sensorimotor activity of babies, Piaget opened up the possibility that “structure” was grounded in “nature” and not in “mind”. In his investigations Piaget inquired into the source of this structure. He asked the question, “Did structure lie in man, nature, or both? In an attempt to answer this question Piaget offers us his own “constructionist” structuralist method.


Structure Constitutes Something More Than Its Elements

Structure’s Boundary Conditions—Wholeness, Transformation And Self-Regulation


Piaget began his inquiries into structuralism by first isolating what was common to all structuralist thought. Number one on his list was the “affirmative ideal”; that is, the ideal of intelligibility aspired after by all structuralists. In addition to the definitions that are proffered by the various structuralists as part of the “affirmative ideal,” Piaget characterized three other attributes of structuralism. Structure, in its very inception, constitutes wholeness. In this sense structure may be understood as formed of elements but within the sum total of its elements structure constitutes something more than its elements.

Structuralism is also characterized by transformations e.g. 2=1+1, the synchronic/diachronic distinction, not, not A = A etc., and by self-regulation processes that tend to maintain and perpetuate the continued existence of structures. In so far as structuralism is characterized by transformations the laws that constitute structure must themselves be structuring. Piaget clarifies:

“Indeed, all known structures--from mathematical groups to kinship systems--are, without exception, systems of transformation. But transformation need not be a temporal process: 1+1 “make” 2; 3 “follows hard on” 2; clearly, the “making” and “following” here meant are not temporal processes. On the other hand, transformation can be a temporal process: getting married “takes time.” Were it not for the idea of transformation, structures would lose all explanatory import, since they would collapse into static forms.” [Jean Piaget, Structuralism, 1970, p.12]

In the characterization of the self-regulation aspect of structuralism, structuralism may be considered from a logical or mathematical point of view i.e. the rules defining structure, or, in the self-maintenance systems that define a healthy organism. Within the diverse range of the structuralist movement Piaget has located the boundary conditions for structuralism in the attributes -- wholeness, transformation, and self-regulation.

Piaget places a great deal of emphasis on mathematical structure. In fact, to the extent that structure can be formalized, Piaget believes that it should be formalized. “To the extent that structure can be formalized” is a very important concept for Piaget for, I believe, the basis of his constructionist method rests on the notion of “the limits of structural formalization.” Because the significance of this concept is so important, I would like to digress into a brief account of this concept’s history.

Tapping Into The Panhuman Mainstream Of Objective Thought

Society Is The Determining Agent For Levi-Strauss




Using the concept of binary opposition, Levi-Strauss analyzes the Greek Oedipus myth into its constituent parts. For Levi-Strauss, the problem of the relationship of these parts becomes resolved in the third level of semiological analysis, i.e., the continuum of successive and related oppositions. For instance, he tells us that, in order to analyze a myth, we should isolate and identify its constituent units, and that we should write down these units, in the form of sentences, on multiple small cards. These sentences should describe a certain function as it relates to a subject at a particular time, as in the case of “Kadmos kills the dragon” in the Oedipus myth. When we group these cards according to common relationships we not only get the myths diachronic meaning (a record of events as they occur in the story), we also get the myths synchronic meaning (the “langue” side of myth-- its structure frozen in time). By using this technique (Strauss compares this technique to reading an orchestra score sheet the harmony part of which is read vertically while the melody is read horizontally) the synchronic and diachronic levels of mythological meaning come into view, thus Levi-Strauss tells us: “There-from comes a new hypothesis which constitutes the very core of our argument: the true constituent units of a myth are not the isolated relations but bundles of such relations and it is only as bundles that these relations can be put to use and combined so as to produce a meaning.”[Ibid. p. 293]

In his essay on myth, Levi-Strauss, goes on to identify the bundles of relations that define the Oedipus myth and he comes up with an interpretation of the myth that is supposed to show how man, through his mythology, copes with the enigmas and inconsistencies which occur in nature e.g., birth/death, the cultural answer to origins as opposed to biological answers, etc. To sum up, Levi-Strauss’s analysis of myth plays one group of binary opposites over and against another group of binary opposites in the belief that, on some level, conflicting opposites tend to neutralize one another, or, at the very least, make myth and myth making a lively, productive and ongoing utilitarian experience. But, after all is said and done, the question, “Who fathered the first mother?” still persists.

For Levi-Strauss, man is engaged in a society that is not just a simple reflection of the mind’s universal internal categories, man is engaged in a society which is a determining agent in itself, a determining agent arising out of the unconscious laws of semiological systems. The mind, according to this view, is a thing among things, arising from the same laws that produce culture and societal relationships. This idea becomes more clear if you consider a famous passage from the introduction to The Raw and the Cooked, (where Levi-Strauss... defended himself against the criticism that his interpretations of South American myth may tell more about the interpreter’s thinking than about that of the Indians):

“For, if the final goal of anthropology is to contribute to a better knowledge of objective thought and its mechanisms, it comes to the same thing in the end if, in this book, the thought of South American Indians takes shape under the action of mine, or mine under the action of theirs.

“Here Levi-Strauss assumes that it is possible to by-pass the problems of social and cultural analysis that are central to anthropology and to tap directly into the panhuman mainstream of objective thought.” [David Maybury-Lewis, Wilson Quarterly, 12:82-95]

Is it any wonder that critics of structuralism respond that structuralism in not humanism because it takes away, or refuses to grant, man any status in the world? Levi-Strauss’s anthropology and philosophy cannot, in my opinion, escape the bite of this criticism. In the psychology of Jean Piaget we encounter another variety of structuralism which attempts to analyze the structural origins of mind from a less fixed point of view. It is now to Piaget’s structuralism that we turn.

The Illusive Code Waiting To Be Discovered

Levi-Strauss’s Search For The Illusive Code-Fixed In Time And Waiting To Be Discovered

The Kinship System As A Form Of Language

Although one could argue that Levi-Strauss is as Kantian in outlook, as is Chomsky, it quickly becomes apparent after reading some of Levi-Strauss’s anthropology that there will be no attempt on his part, to populate his mansions with real, freedom loving people. Whereas, as I have already pointed out, Kant makes an attempt to personalize his transcendental subject, Paul Ricoeur tells us “Levi-Strauss’s philosophy is a Kantianism without a transcendental subject.” [Philip Pettit, p. 78] Levi-Strauss’s zealous attempt to capture the categories of mind in his structural analysis of myth, kinship, and totemism turns the subject into the object produced by his structural analysis.

Levi-Strauss’s 1949 study on kinship systems came at the beginning of his career before he had fully developed his structuralist method. But, in his approach to kinship, his object method was already apparent. Levi-Strauss brought to this study a collectivist, functionalist perspective. He was following the line of study already documented in the works of Durkheim and Mauss. In his emphasis on using women as objects for gift giving, he was simply extending Mauss’s thesis that gift giving promotes social solidarity within one’s own culture as well as promoting a cross culture solidarity when gifts are cross culturally exchanged. Like Mauss, Levi-Strauss believed that these reciprocal relationships were established for integrative rather than for economic purposes.

Kinship relationships are varied and perplexing. All societies have to have social arrangements which allow men and women to get together for the purpose of having children. For Levi-Strauss the incest taboo became the distinguishing characteristic which sets man apart from other animals. This rule, that one had to marry outside of the family, became the first principle in his kinship system. The second and more controversial principle could be found in his explanation concerning who gets to marry who. “In early human societies,” Lewis informs us, “kinship was too important a matter to be left to chance or to individual whim. Systems of regular intermarriage among groups were therefore set up, and Levi-Strauss demonstrated ingeniously how they could have resulted from the idea of marrying out, but not too far out i.e., marriage between certain kinds of first cousins.” [David Maybury-Lewis, Claude Levi-Strauss and the Search for Structure, Wilson Quarterly, 12:82-95] This cross culture marriage and exchange of cousins (usually on the maternal side but not always) became the key, according to Levi-Strauss, that unlocked the perplexing nature of kinship systems.

Another suggestive and more structuralist feature of Levi-Strauss’s analysis of kinship systems is found in his claim that marriage regulations and kinship systems are a kind of language. He says:

“(Marriage regulations and kinship systems are)...a set of processes permitting the establishment, between individual and groups, of a certain kind of communication. That the mediating factor, in this case, should be the women of the group, who are circulated, between clans, lineages, or families, in place of the words of the group, which are circulated between individuals, does not at all change the fact that the essential aspect of the phenomenon is identical in both cases.” [Philip Pettit, p.70]


Understanding kinship systems in this way moves us, once again, in search of that illusive “code,” fixed in time and waiting to be discovered, that, ultimately, Levi-Strauss believes to be at the core of his investigations. In his structural analysis of myth we get a better understanding of this idea.



The Code-When The Brain Acquired The Ability To Make Plus/Minus Distinctions

Things Can Be At The Same Time Both Similar And Different



A major influence on Levi-Strauss’s anthropology came by way of Marx and Freud. Both of these men tended to place extreme emphasis on the concealed aspect of the motivational force behind human behavior. For Marx this motivational aspect was a natural consequence following from the social fabric of social structure and economic realities, while for Freud these motivational aspects were repressed deep within a person’s psychological experience of the unconsciousness. Following in the path of the thought of these men Levi-Strauss identified gift giving (as the integrative function promoting social solidarity) and the incest taboo to be part of the hidden matrix holding together kinship systems. But, for Levi-Strauss, the hidden agenda behind a person’s motivational consciousness is nowhere more revealing than can be found in the mythology of any given culture.

Levi-Strauss began his investigations of myth with the publication of The Structural Study of Myth (1955). He believed myth to contain the “universal code” that if properly understood would unlock the door to the unconscious as well as the conscious mind. For Levi-Strauss, mind
represented an objective component of the brain and, like any other object, the principles underlying its constitution could be investigated and discovered. With this end as his goal, he investigated the structural nature of myth. In his book The Savage Mind, he sought to disclose in his description of the “concrete logic” of Pre-modern man that “...there is no such thing as ‘The Primitive Mind’; or, for that matter, ‘Modern Mind’; there is only ‘Mind-As-Such.’” [Hayes and Hayes, editors, Claude Levi-Strauss: The Anthropologist As Hero, 1970, p.224]

One cannot read very far into the works of Levi-Strauss without concluding that he believed he had found the mind’s code, however subtle, variable, and kaleidoscopically shifting it was, in the elementary logic of Pre-modern man. According to Bottomore and Nisbet, this universal logic becomes identifiable in the significance Levi-Strauss places in the concept of binary opposition:

“Levi-Strauss argues that man, by the very nature of his mind, views the world with binary concepts--for example, odd and even numbers. ...(M)an’s capacity to symbolize with his fellows requires that in the course of evolution the brain acquired the ability to make “plus/minus distinctions for treating the binary pairs thus formed as related couples, and for manipulating these relations as in a matrix algebra.” [Tom Bottomore and Robert Nisbet, A History of Sociological Analysis, 1979, p.584]

It was precisely in the significance Levi-Strauss attributed to binary opposition that lead him to believe “the mythical value of myth remains preserved, even through the worst translation.” [W. A. Lessa and E.Z. Vogt, Claude Levi-Strauss, The Structural Study Of Myth, p. 292] Using the framework of binary opposition, Levi-Strauss has given us a description of how to structurally analyze myth. Accordingly, myths are more susceptible to a semiological analysis then were kinship systems and he wastes no time in making that analogy. Acknowledging the Saussurean principle of the arbitrary character of linguistic signs, he says:

“In order to preserve its (Myth) specificity we should thus put ourselves in a position to show that it is both the same thing as language, and also something different from it. Here, too, the past experience of linguists may help us. For language itself can be analyzed into things which are at the same time similar and different. This is precisely what is expressed in Saussure’s distinction between langue and parole...If those two levels already exist in language, then a third one can conceivably be isolated.” [Ibid. p. 291]

God—The Topic Of Conversation

Okay, the other day I found myself mulling over whether or not I wanted to go to my next High School class reunion and almost immediately I was overcome with this feeling of dread; after all, do I, a life long janitor, really want to throw myself into that mix of story telling, story telling that on one level amounts to real communication, while, on a different level, offers up the evenings real entertainment of pinning the tail on the people who made it as opposed to the under achievers. Well, I didn’t have to think very hard before I came up with my “no answer” to that question. The problem was, though, that I couldn’t help but keep thinking about what it would be like if I did go to that class of ‘66 reunion. It was a slow Friday at work, so I proceeded to follow my imaginings until I had enough content to proceed with this writing project, which I now offer up as a light hearted “time out” from my structuralism posts. I guess I should point out that it’s been twenty years since I last attended my high school reunion. I do not feel bad about that, but I do feel a bit guilty about not attending the last scheduled reunion because a high school friend telephoned to encourage me to attend that reunion and begged off. Anyway, what follows is a bit of what I imagined I would say to my friends if indeed I ever do attend a future class reunion, but first some context details.

In high school I grouped with the smart kids (I was kind of an outlier, but my curiosity and enthusiasm for learning always garnered approval). All my friends were on the fast track to success. I came from a small school in a small town, so the kind of success I’m talking about is mostly the kind that keeps society moving along on an even keel-- middle class success, but there were/are always exceptions. For instance, after I googled the name of the friend that telephoned me (let’s call him Paul), I stopped clicking the computer mouse after page seven. The list of his accomplishments continued, however.

So, to begin this imagined conversation: after a few beers and the friendly chit chat out of the way, and after hearing the life stories of everybody sitting at the table, it was my turn to contribute to the conversation. After verbally celebrating my wife, two children, pets, and my never ending love for music, I had run out of things to say; that is, until the conversation had turned away from health issues and the topic of religion came up. After listening to my friends religious views which ranged from non-belief to Christian belief to a belief in a kind of pantheism, I surprised everyone by giving a different point of view. I said, “I’ve been searching for God most of my life, but after about 40 years of searching I found something to believe in.” Well, as you might imagine, everyone wanted to know which God I had found. So I told them—“God, the God of all religions, even the God that is purported not to exit, is alive and well and doing just fine.” And again, as you might expect, this assertion was quickly challenged and even became the object of some ridicule. Paul, however, came to my rescue when he asked me to expand on what the God of all religions means.

“For me,” I said, “God is not only one with nature, God is also one with the learning process that both asks and answers questions, questions pertaining to God, nature, and everything else. And because of this, God has many names; in fact there is no one name that can fully express God’s divinity. The expression of ‘difference, no difference,’ since that expression encompasses all distinctions, all identities, all differences, all that ‘is’ and ‘is not,’ seems to me to be the best description of the God that I believe in. So, basically, my search for God ended when I found that I could express God, the functionality of God, in the linguistic expression ‘difference, no difference.’”

“And what pray tell is the functionality of God?” asked Paul.

“The short answer to your question,” I replied, “is that there isn’t a short answer to your question, but I’ll give it a go anyhow. We encounter the manifestation of ‘difference, no difference’ in the physical nature of ‘quantum strangeness,’ and again in the terminal state of death in the biological sciences, and yet again in the maintenance of our own ‘conscious identity,’ the identity that demonstrates a degree of permanence in the midst of constant change. All of this and more is the functionality of God. In other words, everything—our physical environment, life, identity, analysis, truth, justice, and religious meaning, are attributes of the functionality of God.”

“So how is your vision of God different from pantheism,” replied Paul.

“As functionality,” I responded, “God manifests ‘difference,’ but as Divinity, God manifests ‘no difference.’ In other words, God is both immanent in nature, while being transcendent to nature. Also, God’s functionality, as it evolves, evolves qualitative differences, differences that emerge in the human being as the quest for truth, justice, and religious meaning. Functional differences, all of them, are made whole through Divinity, but in human consciousness, the qualitative difference of free will emerges. Free will separates and divides Divinity, but even this divided Divinity is made whole in the God of transcendence, and that is why the concept of pantheism is really not adequate when it comes to expressing my vision of God.”

“Christians understand ‘judgment day,’” responded Paul, “as a balance to free will. How does this God of yours handle unnecessary suffering, rewards and punishments?”

“Even though I am expressing my own personal vision of God,” I replied, “others have expressed concepts of Divinity similar to mine. In Whitehead’s process reality, for instance, the judgmental God of Christianity does not exist, but Divinity exists, and within this Divinity judgment, rewards and punishments also exist. God is ‘eternal presence,’ for Whitehead, and as such God bears witness to all past and present occasions. The future, however, is like an unused role of film. Being exposed, it is always in the process of being developed. God works through the transition from the eternal to the actual, and from the actual back to the eternal and in this respect, the entire physical universe is processing its way back to God. God is the reason for all becoming, and nothing exists that is separate from God. So how does Whitehead deal with unnecessary pain, cruelty, and injustice? He combines freedom with feelings and that unique combination changes everything because if a retributive justice is called for here, then one has to look no farther then the first mirror to pinpoint the guilty. Insofar as occasions conform to their environment, insofar as the ‘self-aim’ conforms to its immediate past, there is determinism, but insofar as any entity modifies its response through the subjective element of feeling, there is freedom. Feeling and freedom are codependent for Whitehead, and God is in touch with all feelings. God is there, inside agonizing screams, and God is there in suffering, especially suffering caused by injustice. God is there also, however, in all hopes, joys, and happiness, in addition to fears, regrets, and sorrows. Good feelings move the world forward to a better place. It is feeling that gives subjective aim to occasions. We encounter, in good feelings, the ‘allure of realization.’ It is possible to create a more humane, peaceful, and loving world. Whitehead said as much, and Gandhi told us how to proceed, ‘You must be the change you want to see in the world’—both in life and love.' This is the Divine dynamic that shouts out for change in the world and if no action is taken to prevent unnecessary pain, cruelty and injustice then we only have ourselves to blame. In my vision of God, feelings and freedom are necessarily connected also. Ultimately then, all that is meant by spirit and the spiritual— all intuitive sensitivity and religiously felt compassion—is there in the whole of Divinity, embracing human nature and nature’s creatures, up through the many levels and transformations of freedom until it finally becomes manifest in the life long pursuit of love, caring, happiness and reverence. And, all of this too, represents the functionality of God."

Searching For The Hidden Code

The Hidden Code At The Heart Of Language, Myth, Literature, History, Etc.

The Diachronic Axis Of Language




The concept of “irreducibility” is a universal concern of all structuralist thought. In Kant we witnessed his desire to identify the defining “universals” of all human experience. In Saussure this desire becomes fulfilled in his systematic and holistic interpretation of language. Shortly, we will be talking about how Levi-Strauss, Piaget, and Foucault express this same idea. The credibility of structuralism rests, I believe, on making the synchronic aspect of nature intelligible and accountable to some form of empirical verification. Saussure’s synchronic nature of language, at least in the form of linguistic theory, moves us in that direction. Sensitive to this issue, Saussure believed he was removing the mystery of language and placing it in the material world with his concept of language’s synchronic aspect. And, indeed, this idea that language can be understood synchronically, frozen in time, has inspired many structural investigations into the “hidden code” that the proponents of structuralism believe lies at the heart of language, myths, literature, history, etc.. At the very least, after Saussure, there arose a new skepticism for any investigation of language that had as its goal the disclosure of the “essence” of language.

In addition to its synchronic component, language may also be characterized, in the terminology of Saussure, along its diachronic axis. Language evolves as the expression of a collectivity moving through time. Language is not invulnerable to societal or cultural pressures. The institution of language, over time, becomes violated by dialects and slang. Language changes, but it does so according to its own inertia. According to Michael Lane, this evolution takes place as a result of societal pressures and influences. He says:

“This is apparent from the way in which language evolves. Nothing could be more complex. As it is a product of both the social force and time, no one can change anything in it, and, on the other hand, the arbitrariness of its signs theoretically entails the freedom of establishing just any relationship between phonetic substance and ideas. The result is that each of the two elements united in the sign maintains its own life to a degree unknown elsewhere, and that language changes, or rather evolves, under the influence of all the forces which can affect either sounds or meanings. The evolution is inevitable; there is no example of a single language that resists it. After a certain period of time, some obvious shifts can always be recorded.” [Michael Lane, Introduction to Structuralism, 1970, p.51]


Language, at any given moment in time, may be investigated along its synchronic or diachronic axis. Structuralism, for the most part, prefers to study language in its synchronic aspect. It is for precisely this reason that structuralism opens itself up to attack by those schools of thought which deny the possibility of studying anything whatsoever independent of its social context e.g., Marxism. In general, structuralism, and Saussure’s structural linguistics in particular, have also been criticized for its disregard for human creativity. Noam Chomsky, a leading advocate of structural linguistics in today’s academic environment, has responded to the latter criticism with his discovery and development of transformational grammar.



Chomsky-Deep Structure Is Common To All Sentence Meaning


The Free And Spontaneous Acts Of Inquiry Through Self-Expression


Whereas Saussure dealt with language in terms of a holistic system of differentiation, Chomsky extends this system into the realm of transformational or generative grammar. Saussure’s structuralism did not build bridges between itself and Kantian philosophy. It might even be argued, in fact, that Saussure tried to burn a few of these bridges. Except for his use of certain essential Kantian categories, e.g., identity (memory), plurality, differentiation etc., Saussure’s structuralism restricts itself to organizing and orientating the methodological study of language. Chomsky, on the other hand, developed a differentiating, holistic theory of language that allows for novelty and creativity. Saussure’s langue and parole, in Chomsky’s linguistics, became language competence and performance. With the performance attribute of language, Chomsky took a syntagmatic approach to language which essentially means that Chomsky added to Saussure’s theory a recursive body of rules for the purpose of generating syntax or sentences in the performance of speech. This generative syntax became one component of the two-component aspect of Chomsky’s linguistic theory.

Chomsky believed language to be a product of both a deep and surface structure of mind. In this respect, he split language syntax into two levels, one to describe the deep structure of language and one to show how this deep structure transforms into surface structure.

[Footnote. Chomsky illustrates: To take a simple case, consider the sentences “John appealed to Bill to like himself” and “John appeared to Bill to like himself.” The two sentences are virtually identical in surface form, but obviously quite different in interpretation. Thus when I say “John appealed to Bill to like himself,” I mean that Bill is to like himself; but when I say “John appeared to Bill to like himself,” it is John who likes himself. It is only at what I would call the level of “deep structure” that the semantically significant grammatical relations are directly expressed in this case. Noam Chomsky, Problems of Knowledge and Freedom, 1971, p.24]

In this regard Chomsky is giving language analysis a more Kantian perspective. Chomsky was not shy about his belief in innate structures of the mind. Kant’s influence becomes apparent when he says:

“There are, then, certain language universals that set limits to the variety of human language. The study of the universal conditions that prescribe the form of any human language is “grammaire generale.” Such universal conditions are not learned; rather, they provide the organizing principles that make language learning possible, that must exist if data is to lead to knowledge. By attributing such principles to the mind, as an innate property, it becomes possible to account for the quite obvious fact that the speaker of a language knows a great deal that he has not learned.” [Noam Chomsky, Cartesian Linguistics, 1966, p.59]


Chomsky’s concept of “innate qualities of mind” must itself be understood as a form of the creative aspect of mind for, in his analysis of deep structure and surface structure, he describes a system of rules for generating sentences and the sorts of words that may replace any given word in a sentence, in the context of a creative process. He says: (Human language)...”is free to serve as an instrument of free thought and self-expression. The limitless possibilities of expression constrained only by rules of concept formation and sentence formation, these being in part particular and idiosyncratic but in part universal, a common human endowment.”[Ibid. p. 29]

For Chomsky, the deep structure that expresses the meaning of the sentence is common to all languages. It is the transformation rules that rearrange, replace, or delete items of a sentence that differ from one language to the next. In conjunction with language’s deep and surface structures these transformation rules come together in the form of the “organic” nature of language in which, according to Chomsky, all the parts are interconnected and the role of each element is determined by the generative processes that constitute language’s underlying form. Language, from Chomsky’s point of view, even though it is conditioned upon maturational processes, and interaction with the social and physical environment, is understood to be free from stimulus control as it permits the spontaneous activity of inquiry and self-expression. Chomsky, in this sense, if not totally successful, at least attempts to secure in his structuralist interpretation of language, a place for the free and spontaneous acts of the human spirit.

Reciprocal Movement In Structuralism

Reciprocal Movement (RM) Is What Saussure Identifies As The “Structure” Of The Word

The Structure Of Language



With his analysis of language, the Swiss linguist Ferdinand de Saussure contributed greatly to the modern structuralist school of thought. Saussure instituted into language analysis the working concept of wholeness. Prior to Saussure, language was studied as an independent phenomena arising out of the individual circumstances of various cultural groups. Using wholeness as a working concept was a new idea for language theory but it was not a new idea for the already well established tradition of organic sociology as it was expressed in the works of Comte and Durkheim. This organic connection became evident in what Saussure took to be the linguistic principles at work in all languages. The purpose of language study was in fact to reveal these principles.

Saussure argued that language was a collective, orderly, and coherent phenomenon. Language, therefore, could be studied as if it were a social system that was susceptible to understanding and explanation as a whole. Saussure thought of individual linguistic units as a patterned wholeness. Words, he argued, were devoid of content when studied in isolation. Their meaningful content arose only when they were studied in relation to one another. He based his conception of the linguistic unit on the assumption that where there was meaning - in a word or sentence - there would also be structure. This idea was in conflict with the nominalist view of language that took words to be mere “names” of things. For instance:

“Some people regard language, when reduced to its elements, as a naming-process only - a list of words, each corresponding to the thing that it names. This conception is open to criticism at several points. It assumes that ready-made ideas exist before words; it does not tell us whether a name is vocal or psychological in nature (arbor, for instance, can be considered from either viewpoint); finally, it lets us assume that the linking of a name and a thing is a very simple operation - an assumption that is anything but true. But this rather naive approach can bring us near the truth by showing us that the linguistic unit is a double entity, one formed by the associating of two terms.” [Michael Lane, Introduction to Structuralism, 1970, p.43]


Saussure goes on to explain how this “double entity” must be conceived. The word, according to Saussure, unites a concept and a sound-image and not a thing and a name. In this sense, the sound-aspect of a word becomes inseparable from the meaning content of the word and the reverse also holds true. This double movement, sound acquiring conceptual meaning as conceptual meaning becomes differentiated by sound, is what Saussure identifies as the “structure” of the word. Saussure, in the following diagrams illustrates this idea.

In the diagram below imagine three circles, one around each of the joined identifiers. Then imagine an up and down arrow on each side of each circle—that’s six arrows, three pointing up, three down-- and you will have a mental image of Saussure’s diagram.



concept “tree” picture of tree
Sound-image arbor arbor



[Ferdinand De Saussure, Course In General Linguistics, Translated by Wade Baskin, 1959, p. 66-67.]

In these diagrams we see a representation of the working concept of wholeness as it becomes operationally defined in the linguistic structure of the word. Here the two elements of sound and word become intimately united, as each refers to the other. Saussure, by calling the sound-image of a word the signifier, differentiates the meaning of the word into its two components, the signifier and signified. Together, the signifier and the signified combine to form the sign i.e., the whole as differentiated from its opposing elements.


Language Depends On The Word For Its Field Of Signification-The Word Depends On Language For Its Meaning-Reciprocal Movement


The “Fixed Nature Of Wholes” Along The Synchronic Axis Of Language



Once Saussure had delineated the structure of the word, he also delineated the structure of language. For Saussure, the sign relates to language in the same way as the signifier relates to the signified. In the same way that the signifier is arbitrarily connected to the signified (any sound may be used to designate a particular meaning), the sign is arbitrarily connected to language. The word, as opposed to being a name for an object, is a differentiation in the set of linguistic units that, when taken as a whole, constitute a language. A word acquires its meaning, according to Saussure, in the way it differentiates itself from the whole, the whole being the collective expression of an entire language. We find here the same double movement constituting the meaning of the sign, as it relates to language, as we did in the relationship of signifier to signified. In this way we see how the word becomes dependent on language for its meaning and language becomes dependent on the word for its “field of signification.” Thus the arbitrary character of the sign, in Saussure’s conception of language as a rule driven and self contained system, is what permits order and meaning to arise in the world. John Sturrock, in his book Structuralism and Since, underscores this distinction when he says:

“The extremely important consequence which Saussure draws from this twofold arbitrariness is that language is a system not of fixed, unalterable essences but of labile forms. It is a system of relations between its constituent units, and those units are themselves constituted by the differences that mark them off from other, related units. They cannot be said to have any existence within themselves, they are dependent for their identity on their fellows. It is the place which a particular unit, be it phonetic or semantic, occupies in the linguistic system which alone determines its value. Those values shift because there is nothing to hold them steady; the system is fundamentally arbitrary in respect of nature and what is arbitrary may be changed.” [John Sturrock, Structuralism From Levi-Strauss to Derrida, 1979, p.10]

It is in this characterization of language that Saussure bases his distinction between langue and parole. For Saussure, parole becomes the particular acts of linguistic expression in speech while langue becomes the component aspect of language that generates meaning through the internal play of differences. In this respect language forms a system of contrasts, distinctions, and oppositions that come together in the form of pure values which, as Sturrock points out, are solely determined by how they differ from each other as they are produced in the system of language. Language, for Saussure, becomes a theoretical system operating according to linguistic rules which speakers of language must obey if they are to communicate. It becomes the job of linguistics to discover the mechanisms which make language possible.

Language, Saussure informs us, is always inherited. Language forms a corpus of linguistic rules arising out of ahistorical conditions that allow a person to understand and be understood. To the extent that language succeeds in this endeavor, it is collectively determined and not susceptible to arbitrary change. This aspect of language is what Saussure calls the synchronic nature of language and it is in this synchronic nature of language where we encounter for the first time the idea of the “fixed nature of wholes.”

For many reason's I've decided to post my paper on structuralism. Following that paper, I will post a new way to understand the observer/observed relationship. Eventually, though, I will get back to posting my answers to YA questions.


Begin Structuralism Paper --preliminary remarks in Children Pain post below.

Reality Is Revealed Through The Active Construction In Which We Participate

Introductory Remarks On Structuralism And On Kant’s Philosophy



“Whatever we call reality, it is revealed to us only through the active construction in which we participate.” Ilya Prigogine, Order Out Of Chaos

Structuralism emerges from the elementaristic side of the holism/elementarism debate as an extension of the neo-Kantian position. Form, within this tradition, takes precedence over content, but in so far as structure itself is a holistic concept, the actual locus of structuralism in relation to the holism/ elementarism debate is somewhat ambiguous. I believe that within this ambiguity will be found a resolution to the holism/ elementarism debate. In order to bring this debate to a resolution, however, we must first look at the various structural models that have been described in linguistics (Saussure and Chomsky,) anthropology (Levi-Strauss,) psychology (Piaget,) and philosophy (Foucault.) My description of those various forms of structuralism will concentrate in the areas that have a direct bearing on bringing this debate to a satisfactory conclusion. With that end in mind, I would like to begin by taking a look at the philosophy of Immanual Kant.

Kant, in his attempt to synthesize the rationalist thought of Descartes and Leibnitz with the empirical thought of Locke, Berkeley, and Hume, understood sense experience to be manipulated within the inherent structure of mental categories. In his analysis of this structure he concluded that there is more than one kind of knowing (Critique of-- Pure Reason, 1781, Practical reason, 1788, and Judgment, 1790) but the major importance of Kant’s analysis is found in his understanding of the logical consistency and necessity of both sensed space and time and mathematical space and time. This aspect of Kant’s philosophy, although it represented a major success for Kant, in retrospect, is not so well received.

Just as Locke was driven to his theory of ideas by the consequences of Newton’s deterministic universe, Kant had to face a similar determinism. It was not with atoms and forces which his determinism had to contend, rather, it was with the determined nature of knowledge itself. Kant’s transcendental ego, when pursued to its logical conclusion, did not allow for individual freedom. He accounted for man as a knower of the universe, but he did not account for man as a free moral agent within the universe. Kant used the presuppositional method to solve this problem: “It is impossible to conceive anything at all in the world, or even out of it, which can be taken as good without qualification, except a good will.” [Immanual Kant, The Moral Law, 1948, p.59]

In other words, he presupposes free will to allow for moral action i.e. Kant’s practical ego. This is a key concept because upon reading Kant the German champion of freedom, Fichte, was able to show that it was not the categories of understanding which allowed a person to know the universe, it was the person’s own individual will that will’s knowledge of the universe through the categories.

This statement is more than an arbitrary assessment by Fichte on Kant’s presupposed ego. The science of Einstein, Bohr, Schrodinger and Heisenberg has demonstrated the error in Kant’s constitutive and hence necessary relationship between the categories of understanding and reality. Thus, science has taught us that mental categories, if indeed there are such things, are only interpretive for the measurable observable events that we identify with reality. Within the context of the scientific method, these events are hypothetically postulated and aposteriorily (to use Kant’s terminology) verified. Consequently, it is not the facts that imply the theory; rather, it is the theory that implies the facts.

The breakdown of the necessary relationship between Kant’s categories and sensed experience does not invalidate Kant’s distinction of sensed space and time and mathematical space and time. Kant’s philosophy, not withstanding its assumption of necessity, is still a major force in the world today.1


It is unfortunate, however, that Fichte’s identification of the will with Kant’s practical ego helped to supplement the deterministic portions of Hegel’s idealism and in no small way contributed to the totalitarian ideologies of Nazi Germany and the U.S.S.R. In a nutshell, an ego free from the constraints of reason, motivated purely through the expression of the will, identifies the is of society with the ought for society. This, in turn, became the determinism by which Hegel’s “world spirit” and Marx’s “dialectical materialism” swallowed up the individual. What began in Kant as an attempt to restore and secure the notion of a person’s free will, ended up contributing to in the brutal consequences of fascist and communist dictatorships. Here we once again see the irony of the political animal called man. But, moving in the other direction, that is, remaining under the umbrella of Kant’s transcendental ego, the more modern movement of structuralism has come to the fore.

[1. In his ontological structuralism, W.V. Quine, a person of major significance in the defining aspects of today’s philosophy of science, establishes a Kantian position when he takes structure (mathematical form) and events of confirmation to be the ultimate ground for knowledge. Quine informs us that the structural aspect (the categorical aspect) of this knowledge as it relates to verification is, in addition to being Kantian, is also uncertain. He says, “Science ventures its tentative answers in man-made concepts, perforce, couched in man-made language, but we can ask no better. The very notion of object, or of one and many, is indeed as parochially human as the parts of speech; to ask what reality is really like, however, apart from human categories, is self-stultifying. .....We saw that reference (structure) could be wildly interpreted without violence to evidence. We see now that that is just part of a wider picture. Presumably yet more extravagant departures, resistant even to sentence-by-sentence interpretation into our own science, could conform equally well to all possible observations.” W.V. Quine, The Journal Of Philosophy, Volume LXXXIX, NO. 1, January l992]


Structuralism Extracts Meaning From Phenomena

Conflicting Opinions




Metaphorically speaking, it has been said that the structuralists have built incredible mansions for people to live in and, indeed, the mansions have been built and the lights are on, but, we might want to ask the question: Is anybody living in these mansions? Out of the five structuralists I will discuss only Chomsky and Piaget appear to be actively seeking the mansion’s inhabitants. As our lesson on Kant warns, finding these inhabitants takes extraordinary care.

Structuralists understand experience on two levels. Phenomena is first encountered by a given, arbitrary level of experience, and second, phenomena is then integrated (transformed) into communicable levels of experience. There is little disagreement by structuralists concerning this point. Structuralism prescribes a method for understanding how to extract meaning from phenomena. However, that may be the only assertion they agree too since, on the whole, structuralism constitutes a diverse agenda of pursuits. By way of an introduction De George gives us the following perspective on structuralism:

“Structuralism has been described as a method, a movement, an intellectual fad, and an ideology. Each of these characterizations is in part valid. For structuralism is a loose, amorphous, many-faceted phenomenon with no clear lines of demarcation, no tightly knit group spearheading it, no specific set of doctrines held by all those whom one usually thinks of as being associated with it. It cuts across many disciplines--linguistics, anthropology, literary criticism, psychology, and philosophy. For some it gives hope of uncovering or developing a common basic approach to the social sciences, literature, and art which would unify them and put them on a scientific footing, much as the “scientific method” grounds and unifies the physical sciences.” [ De George and De George, The Structuralist: From Marx To Levi-Strauss, 1972, p. xi]


In a l986 lecture delivered at the University of Melbourne, Australia, the renown sociologist Anthony Giddens had the following to say about structuralism:

“Structuralism, and post-structuralism also, are dead traditions of thought. Notwithstanding the promise they held in the fresh bloom of youth, they have ultimately failed to generate the revolution in philosophical understanding and social theory which once was their pledge.” [ Anthony Giddens, Social Theory and Modern Sociology, 1987, p. 74]

I disagree with Giddens!

Reconciliation Post 3rd of 3

The Living Logos

Obviously, life is the precondition for speech, but what are the preconditions for life? In Cosmology we know that we are connected to a friendly universe (at least from the point of view of the observer asking why). Why are the parameters of the universe –the relative strengths of gravity and electromagnetism etc. (so far, three dozen and counting)—so fine-tuned to the existence and survival of life? This connection to a friendly universe is just one of the “connectivity problems” that must be dealt with. In quantum mechanics we know that our knowledge of the collapse of the wave function, Bohr’s complementarity theory, the measurement problems in quantum mechanics, etc. are all interconnected with our participation in the event—as the “agencies of observation.” But here’s the connectivity stumper, we also know that our participation in an event (at the quantum level) instantaneously connects us to an event (theoretically) at the other side of our space/time continuum. That connection presupposes a whole different kind of connection. Many people are working to solve that problem. Bohm’s implicate order, just to mention one theory, addresses the complexity of that problem. I, on the other hand, recognize that in “this whole different kind of connection” there may be no answer to this problem. Rather, if you want to call it an answer, this answer will come in the form of recognition of the precondition for any answer whatsoever. In brief, here is the rest of my theory:

After much consideration, I ended up using the negation of not-being-- a double negation-- for the precondition of life. In a double negation an affirmation is implied. What is being affirmed? At minimum, it’s simply the logical space of implication. I can’t really talk about the significance of this space until I fill in more of the theory (that will come with more posts). It’s what occurs on the other side of this space, however, that I want to talk about now.

The easiest way to describe my theory is to take a structuralist approach. This approach tends to emphasize “wholes” and “totalities” –ultimately the ground for everything. The double negation becomes, in this respect, the innate structuring capacity of all structures, and as such, characterizes the synchronic axis of all phenomena. This axis may be thought of as unconstructed, but even so, it circumscribes all phenomena (content) by its form. In other words, everything that we know about the universe takes place between the two Nots.

For the most part, I take a systems view of phenomena. Things change as they move away from equilibrium and, over time, become more complex. Structurally, this is called diachronic movement. Personally, I call this movement liberating. I call it liberating because, once a sufficient level of complexity is reached, and a shift in structure occurs, life gets liberated. At conditions far from equilibrium, life progresses within a different structure—the structure of continuity and discontinuity (death). Freedom and complexity expand within this new structure, and, on a level of sufficient complexity, once again, the structure of life shifts. The “space of the implicative-affirmative” gets liberated in this new shift of structure. The implicative-affirmative space, the auto-catalytic attribute of the double negation that circumscribes all phenomena, in this second structural shift, gets birthed in the phenomenal world. This phenomenal space of affirmation has become the “workhorse” that builds civilizations. Anthropologically speaking, at the time when animals refused to passively accept the environment and instead began to actively transform it,--that was also the time when animals acquired the mental space of the implicative-affirmative’s symbol-generating capacity—the birthright of inquiry, analysis, conscience and imagination.


Relativity Theory And Quantum Phenomena Reconciled

Let the following quote from David Bohm provide the underlying context for what I am about to suggest:

“Relativity and quantum physics agree in suggesting unbroken wholeness, although they disagree on everything else. That is, relativity requires strict continuity, strict determinism, and strict locality, while quantum mechanics requires just the opposite—discontinuity, indeterminism, and non-locality. The two basic theories of physics have entirely contradictory concepts which have not been brought together; this is one of the problems that remains. They both agree, however, on the unbroken wholeness of the universe, although in different ways.” (The Reenchantment of Science, p, 65)


“Relativity did away with space and time as the backdrop of deterministic motion of mass points,” says Laszlo (p.80, 2004), “but it preserved the unambiguous description of the basic entities of the physical universe.” By basic entities of the physical universe, I assume here that he means those entities that do not show signs of discontinuity, indeterminism, and non-locality. Opposites are necessary in order to preserve “wholeness” in my theory, so discontinuity, indeterminism, and non-locality become just as essential for a description of the real world as determinism, continuity, and locality. Looking specifically at the different levels of negation in my theory may shed some light on the contradictory aspects that separate Relativity from quantum physics.

Since it’s all about implicative space, we begin with double negation—the ground level. An affirmation is implied on this level. Double negation connects, not only to affirmation, it connects to other levels of more complex affirmations by way of the negative space of those same affirmations—their own unique negations. Life is embedded in one of these negations and self-consciousness is embedded in another one of these negations. In other words, the negative space that separates here also permits its opposite while being simultaneously connected to the “ground state of double negation”. So now we may ask: What are the pre-conditions for this state of affairs?

Enter Relativity with its conditions of strict continuity, strict determinism and strict locality. In life’s negative condition, the environment, locality is certainly necessary. In self-consciousness, continuity and determinism—the conditions necessary for a physical event-- become its negative condition. Thus, determinism and continuity allow for the reductionist methods of science to work; that is, until science penetrates deep into that area where the integrity of the physical universe breaks down, where the deterministic motions of mass points no longer exist!

At the depths of the “material world” there exists a fuzzy world that exhibits behavior only when we observe it. There we find a physical reality with no uniquely determinable location, a physical reality that exists in several states at the same time, a physical reality structured by a mathematical equation. Do we find there also the “ground negation” that connects all subsequent levels of negation and affirmation to---the affirmation that connects everything? If we do then the connectivity problems found in our experience at the quantum level begins to make sense. In the theory of dialectical freedom’s structural form, two “forms” stand out as a way to better understand the contradictory concepts that have not been brought together in Relativity and quantum physics.

The same physical attributes (discontinuity, indeterminism, and non-locality) that characterize self-consciousness characterize also the “ground negation.” At “ground” implication remains open, while in self-consciousness, implication opens up the world-historical-process. In other words, the negation that lies at the center of self-consciousness, the negation that permits our capacity to solve mathematical equations, lies also at the “ground level” of our experience with quantum physics. Because observation (affirmation) takes place in the space of continuity, determinism and locality-- self-consciousness’s negative space— there is an unavoidable clash of worlds—the world of continuity, determinism and locality (Relativity) clashes with the world of discontinuity, indeterminism, and non-locality (quantum physics). Bottom line—Relativity accurately describes natural phenomena. Einstein’s equations, when applied to the world of physical events, provide accurate information concerning our status as participating agents in the physical universe. Likewise, quantum mechanics accurately describes natural phenomena. Only the phenomena being described are “fuzzy” because, as it is throughout freedom’s dialectic, the space that separates also embeds and connects. In other words, on the quantum level, self-consciousness confronts its own ground condition in the form of the “phenomenal strangeness” of quantum physics.

Ultimately, from its most holistic perspective, dialectical freedom’s structural form tells us: Were it not for the negative space/condition of determinism, continuity, and locality, the human consciousness of discontinuity, non-locality, and indeterminism (opposites are necessary to conserve wholeness) would not be free in a world of our own experience (by degrees, experience of our own choosing), seeking truth, justice, and religious meaning!