Monday, October 20, 2014

Chapter 25 - "The Brotherhood Of Doctrines": Part 2 - Mathematical Philosophy

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.

At the end of February, Dutton published Keyser’s book Mathematical Philosophy: A Study of Fate and Freedom. Keyser sent a copy to Korzybski at once. Despite being especially busy—with speaking engagements in Los Angeles and with whatever he had to do to help Mira set up a painting exhibit at the Hotel del Coronado in San Diego—Alfred had nearly completed his first reading and marking of it by March 10. (1)

He had already seen the manuscript and table of contents, having quoted from it in Manhood. Nonetheless, reading the completed work seemed like a revelation. The force of his response was not only a function of his gratitude to Keyser for devoting the next-to-last chapter of the book to a discussion of “Korzybski’s Concept of Man”. Keyser—in his discussion of “logical fate”—had revealed to Alfred an essential aspect of the foundation of time-binding. The formulation would help Alfred begin to unify the numerous influences he had been absorbing over the past year. The notion of “logical fate” (logical destiny) formed the nucleus of two articles he would write over the following year, and would continue to guide the development of his work thereafter.

Mathematical philosophy, as Keyser indicated in the subtitle of his book, could be viewed as “the study of Fate and Freedom—logical fate and intellectual freedom.” What did this logical ‘fate’ or ‘destiny’ and the corresponding intellectual freedom consist of? As Keyser had described it:
…[I]t is in the world of ideas and only there that human beings as human may find principles or bases for rational theories and rational conduct of life,...; choices differ but some choice of principles we must make if we are to be really human—if, that is, we are to be rational—and when we have made it, we are at once bound by a destiny of consequences beyond the power of passion or will to control or modify; another choice of principles is but the election of another destiny. The world of ideas is, you see, the empire of Fate. (2) 

As his discussion in his chapter on Korzybski indicated, Keyser seemed particularly impressed by Korzybski’s notion of time-binding. In Manhood of Humanity—without having formulated it clearly himself—Korzybski had shown the mechanism of ‘logical fate’ at work in his discussion of the pernicious effects of specific false principles about humans and of the need to choose a new, more accurate base—time-binding—for the rational conduct of human life. What we humans think, and think about ourselves, makes a difference in how we behave. Manhood of Humanity provided a particularly significant example of such fate and freedom in human affairs.

In his book, Keyser—who had studied the history of mathematics for some time and had an interest in the thought processes of mathematicians—discussed various basic formulations in mathematics (postulates and postulational systems, doctrinal functions, transformation, invariance, groups, variables and limits, infinity, hyperspaces, non-euclidean geometries, etc.). Keyser demonstrated how mathematics—as the exemplar of logical fate—involved a consummate effort to make conscious and to work out the implications of particular starting principles or postulates. His chapter on “Non-Euclidean Geometry” seemed particularly clear about this.

For more than two thousand years, Euclid’s geometry had been considered ‘the’geometry of this world. Euclid’s axioms, viewed as ‘self-evident’, included this postulate: through any point outside of a line, only one other parallel line can be drawn. The absolutistic nature of this assumption was finally challenged in the 19th Century by several mathematicians such as Bolyai, Lobachevski, and Riemann. These men found they could create equally consistent and valid non-euclidean geometries by postulating either no parallel lines or an indefinite number of them. The resultant revolution in mathematics entailed a greater recognition of the freedom of humans in creating their starting postulates or assumptions. The propositions of Euclid represented not ‘the’ geometry of this world but rather a geometry, one among many. Indeed, relativity-oriented physicists had found the non-euclidean geometries to more closely approximate some features of the world than the euclidean did.

Korzybski could see quite clearly: logical fate and the time-binding shift from euclidean to non-euclidean geometry exemplified a general process in human life. Man was a doctrinal creature. From our postulates, i.e., our assumptions, premises, presuppositions, expectations, etc.—often unconscious —conclusions follow. We can, however, become conscious of and revise our assumptions. In his book, Keyser had discussed mathematical thinking as a consummate effort to make conscious and to work out the implications of assumptions. It served as the prototype of rigorous thinking in any field.

Of all the mathematicians he’d encountered and read, Alfred had not found anyone other than Keyser who emphasized this application of the mathematical ‘spirit’ to human life—in other words to all sorts of thinking not normally viewed as mathematical. In his chapter on “Truth and the Critic’s Art”, Keyser had even suggested how to go about examining non-mathematical doctrines—from the Sermon on the Mount to Darwin’s Origin of Species to “all manner of doctrinistic contentions of wise men, knaves, fanatics and fools”(3)—in terms of logical fate, i.e., postulational analysis. Interested as he was in human behavior in general, and problem-solving and trouble-shooting in all fields, Korzybski was going to pick up Keyser’s ‘ball’ and ‘run’ with it. He began talking and writing in letters about “logical fate” almost immediately after his first reading of Keyser’s book.

The label “logical fate” might lead the unwary astray here. At this time, Korzybski rather regularly harped on mathematical logic and talked of his developing work in terms of it. For example, he had just mailed a copy of Manhood to Eddington, writing, “My work is a trial of application of mathematical logic to life problems.”(4) But as Korzybski would come to realize over the next few years, ‘logical fate’ was not primarily a matter of formal logic. Even now, what Keyser called ‘logical fate’ seemed to Alfred primarily an assertion about human psychology: to a large extent, what a human does gets ‘driven’ internally by his doctrines or attitudes which involve, among other things, his choice of assumptions and his willingness to analyze and revise them when needed. Formal logical follow-through has a genuine but limited part to play in this process. In seeing mathematics in such a psychological light, Keyser did not seem like a typical mathematician or mathematical logician. (5) But this was exactly the kind of illumination Alfred was seeking.

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. 
1. AK to C.J. Keyser, 3/10/1922. AKDA 8.460. 

2. Keyser 1922, p. 5. 

3. Ibid., p. 151 

 4. AK to A. S. Eddington, 4/5/1922. AKDA 8.361. 

5. See Keyser’s chapter on “The Psychology of Mathematics” where he wrote that:
…It is indeed obvious that the whole literature of mathematics may be read and interpreted as a commentary upon the nature of the human mind...A normal human mind is such that, if it begin with such-and-such principles or premises and with such-and-such ideas and if it combine them in such-and-such ways, moving from step to step in such-and-such order, it will find that it has thus passed from darkness to light,—from doubt to conviction. Obviously such a proposition is not mathematical; it is psychological—it states a fact respecting the nature of a normal human mind. Such interpretations of mathematical literature are psychologically very illuminating; the possibility of making them is so evident, once it is pointed out, that I should have refrained from mentioning it except for the fact of its being commonly overlooked and neglected. [Keyser 2001 (1922), pp. 412-413]

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