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Early Inroads in Philosophy[]

The skeptics of the Greek period are poorly presented today. And Greek knowledge has been transformed into several bodies of ideology, one being religion, and another being science.

The Divergence Between Logical and Rhetorical Formalism[]

The inherent formality of mathematics, and the related desire to mathematicize all logical methods, such as permutation, hierarchy, and delineation, along with the seeming logical obsession with the provability of rhetorical arguments, marked by the invention of the reductio ad absurdium, led to a schism between logical systems ('entities', 'quantities') and rhetorical arguments ('causes', 'conditionals').

The divide increased as each of the two areas experienced a certain marked degree of specialization, each form of student or researcher being obsessed with his or her own traditional arguments and familiar terrain.

Aristotelian logic, itself more rational than scientific, became absconded in the problem of reducibility which became evident at the time of Godel, Tarski, and Russell (the three paradoxes of incompleteness and incoherency, which amount to one idea: the incomprehensiveness of mathematics).

Developing from Aristotle and Wittgenstein's logical positivism, the Modal Realists such as David Lewis became caught on a double-horned dilemma, that experience provided proof, while only abstraction could provide a theory.

Now arguments could be divided between the empirical and the theoretical, just as logical formalism could be divided into theories and facts. However, neither theories nor facts automatically constitute arguments. Indeed, not every theory of fact might qualify as rhetorical validity. The uniqueness of Aristotle's deductive reasoning was proven again and again, as hundreds of less successful forms of argument were discovered.

However, the modal realists were caught on the subject of the old relation between entities and conditionals. The new rhetoric, it seemed, needed to relate with either the world of universal language, or the world of atomical facts. But Modal Realism was neither a theory of language, nor a method for deriving psychic evidence of the ordinary.

Psychological and Objective Theories[]

After the conflicts of the early period of the 20th Century, considerable turmoil was thrown up over the nature of the human condition, and the need for human definition, a definition subject to flux and fractionalization, as expressed by the Dadaist movement and the artwork of Picasso, Chagall, and in England, Vorticism, and in Russia, Futurism.

Although Freud concluded that the human condition was miserable and conflicted, Jung, who was the other major psychologist at the time, developed a theory that some individuals could 'individuate' and realize the universal properties of their own collective unconscious, a process which he saw to be present in dreams.

Overall, the conflict between the difficult, transcendent impulse ('how to dream?', 'how to make a work of art?'), and the fractionalization of belonging to a collective 'mass society' brought about a new consciousness of qualities which had been absent from human significance.

Existentialism began to be seen as a generic catch-all for the struggle for human significance, a movement that was not a movement. Writers began to apply existential vituperances selfishly, within their own writing.

The world underwent a period of prodigious intellectual stagnation, and simultaneous economic and technological advance. The human genome was discovered, and for a period, major systems seemed to be only computer applications, or scientific achievements. The best writers turned to the exceptional qualities of their own condition.

A Technological Opportunity[]

The emergence of technological awareness and futurism, the prospect of artificially extending human life, the possibility of android or cybernetic bodies, artificial intelligences, and other advances offered the prospect of considerable scientific achievement. Many of these aspects had yet to emerge, although they had been floating in the human mind for some decades, perhaps centuries. But in another sense, technology was an opportunity to advance the working tools of philosophy, mathematics, and other disciplines. Although in some ways, this virtue seemed only like a crutch, computer programming offered a new metaphor for logic and rhetoric, which included now the concepts of recursivity and processing.

Whitehead's early work Process and Reality introduced the philosophical principle of process before the programming age. But philosophers tended to believe that the applications of logic to process involved a large number of conditionals, and therefore was not a universal application.

An exception to this was found by Coppedge, who in The Dimensional Philosopher's Toolkit revealed that the Cartesian coordinate system could be used for the comparison of opposite qualities. While the comparison of qualities was due to the existentialists, the use of Cartesian coordinates was due to mathematical formalism. However, the result was a middle path, an exponential system with deductive validity.

What Will the Future Hold?[]

As new tools as important as computer programming and logical deduction emerge, there will be new opportunities to expand the metaphor of philosophical formalism. Although some suspect that these methods will involve an inherent complexity, it is clear that computational methods will clear space for that possibility. Further, it is possible that new advances in logic and the theory of meaning will reveal new systems and nodes of reference which will in turn create new important systems and methods of computation. Some of the new systems are bound to be complex, while others may be as condensed as a logical syllogism.


Coppedge, Nathan. The Dimensional Philosopher's Toolkit. AuthorHouse 2013, CSIP, 2014, 2015.