Friday, October 3, 2014

Chapter 23 - Strange Footprints: Part 3 - Qualitative Mathematics

Korzybski: A Biography (Free Online Edition)
Copyright © 2014 (2011) by Bruce I. Kodish 
All rights reserved. Copyright material may be quoted verbatim without need for permission from or payment to the copyright holder, provided that attribution is clearly given and that the material quoted is reasonably brief in extent.

The theory of types represented one result of the general approach of the Principia which formed, in Whyte’s words, “the culmination of two centuries of mathematical research, mostly in the direction of increasing abstract generality, formal definition of axioms, analysis of the basic relationships implicit in mathematical systems, and the discovery of appropriate mathematical symbolisms.”
All this work can be summarized in the concept of mathematical structure, which means a pattern of relationships with certain formal properties. By ‘formal properties’ one means properties like equivalence and non-equivalence, symmetry and asymmetry, and so on, which now are seen to underlie the primitive ideas of number and geometrical form. (3)

Korzybski had had the unconscious feel of this approach before he knew anything about mathematical logic. He had already accepted what Willard Gibbs, one of his intellectual heroes, had noted—“Mathematics is a language.”(4) It had gradually become clear to him: in many ways, mathematics served more effectively than our everyday language at depicting the complex relations of nature. After George Boole, others had pursued the notion of mathematizing logic (language), i.e., putting it into mathematical form. In doing so they had shown that formal mathematics was not limited to the study of quantity but could deal with quality as well. Thus had grown the field of symbolic or mathematical logic, which had led to research into the foundations of mathematics such as the Principia, elaborated into more and more exotic symbolism—highly abstract and more and more inaccessible to the layman.

By the time he got to La Jolla, Alfred—though following the field of mathematical (“symbolic”) logic with great interest—was beginning to realize this was not his project, although he was still explaining his work in terms of ‘logic’. He began to realize that from Boole’s starting point he was following a path different from the one the mathematical logicians had taken: he had begun to consider everyday language as a kind of mathematics.

Rather than mathematizing language, he was going to find out to what extent he could “linguistisize mathematics” (a phrase he would use later in letters). At this point, Korzybski was beginning to talk about what he was trying to do as a kind of “qualitative mathematics”. Viewing every man and woman as a mathematician did not mean he wanted them to end up speaking in algebra. Not at all. Rather, as he eventually framed it, he was seeking ways “to impart mathematical structure to language without technicalities.”(5) In other words, as he was starting to see in this early phase of his researches, he was looking for ways (as he would put it later) “to bring ordinary language closer to mathematics”. (6) What did this strange-sounding reversal of the program of mathematical logic—Korzybski’s reformulation of Leibniz’s dream—entail in practice?

You may download a pdf of all of the book's reference notes (including a note on primary source material and abbreviations used) from the link labeled Notes on the Contents page. The pdf of the Bibliography, linked on the Contents page contains full information on referenced books and articles. 
3. Ibid., p. 46. 

4. Rukeyser, p. 279-280. 

5. Korzybski 1994 (1933), p. 50. 

6. Ibid., p. 69. 

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