THE PLACE OF ARISTOTELIAN LOGIC IN NON-ARISTOTELIAN EVALUATING : EINSTEIN, KORZYBSKI AND POPPER Stuart A . Mayper (After hearing Bob Pula's paper yesterday on only mathematical formula I was able to get into this Korzybski's origins, I realized there was a lot more paper.) I had to do on my paper . I had to Polish it .) In contrast, the empirical side of science, the There is a subtitle to this paper : EINSTEIN, observations, the low-level abstractions, have to be KORZYBSKI, AND POPPER . But there must be a expressed in existential propositions, whose form is : fourth person in this cast of characters, to act as "There exists an x such that x is C and x is D ." Devil's Advocate . I start with him : Walter Stuer- "There exists an x called Mars, such that Mars is mann, who was Professor of Philosophy at the Uni- a planet and Mars has an elliptical orbit ." Or "There versity of Tulsa, and also an Associate Editor of exists an x, such that x is a swan and x is white ." ETC. In 1962 he laid down a challenge to general Now that's quite different from saying "All swans are semanticists : to reassess our theoretic foundations, white . " The universal proposition can be refuted or particularly our claim to have a non-Aristotelian falsified very easily, if you can assert "There exists system . That claim, he said, is an oversimplifica- a swan which is black . " (And there does ; I've seen tion; what we need is to go back to formal logic . black swans .) We have only to see one black swan, Hence the title of his article in ETC . was : "Science, and we have refuted the universal proposition. But Logic, and Sanity . "1 it's much harder to refute a low-level existential proposition. If we have : "There exists a jabberwock He did not think that our usual attack on a two- which is white," how do we show that nowhere in the valued orientation should be turned into an argument universe there exists a jabberwock which happens to against a two-valued logic, because he believed that be white? Refuting existential propositions is extreme- logic is "the indispensable tool by which the meaning ly difficult . and power of a scientific system is brought to bear upon human behavior and the world," a tool which is Well, this is the structure of science, accord- necessary to join the two aspects of science, the ing to Walter Stuermann : the universal propositions, rational and the empirical . By the rational we mean the theories, lead to deductions : we can deduce from theoretical, high-level abstractions, which have to "All swans are white" that if there exist any swans be expressed in universal propositions, of the type : at all, they have to be white . As soon as someone "For all x, if x is A, then x is B . " "For all x, says "There's a swan," we know it must be white, if x is a planet, then x has an elliptical orbit . " according to our theory. But the existential proposi- The important thing about this is that it states some- tions are tested against the facts ; if we find there thing for all x's . exists a swan which is black, then we know there's something wrong with the theory ; it is refuted. That's Take an example that philosophers of science the structure of science, which requires this two- seem to feel much more comfortable with: "For valued logic . all x, if x is a swan, then x is white ." Philosophers of science : somehow I get the feeling they wish that Now Stuermann said that general semanticists' scientists would just restrict themselves to white intense concern with phenomenal data, indexing, re- swans and black swans to make the whole philosophy ports, etc ., is a quite proper insistence on the neces- much simpler . sity of existential propositions . It is a battle against the universals that are unrelated to existentials, But you might respond that the most advanced against "abstractions uninformed by phenomenal con- science these days is highly mathematical . Even tent, " as he put it ; or against intension without ex- so, the mathematical formulas can be regarded ass tension . But it can not be a battle against all univer- elaborations of this universal proposition form . For sal propositions, and it certainly can not be a battle example, we can say "For all x, y, and r, if x and against all high-level abstractions -- if we undertook y represent the masses of two bodies, and r repre- that battle, that would quickly reduce this whole meet- sents the distance between their centers, then there ing to silence . Even the fight against universal pro- is a gravitational force which equals x .y/r2 times positions, is, according to Stuermann, "a venture a universal constant, G ." This may be considered in the direction of scientific suicide. " a universal proposition, as saying something about all bodies at all distances. This of course is New- Sometimes we might have to rule out a two-valued ton's gravitational formula . G represents a number logic, as inadequate for certain purposes, because of which depends on what particular system of units the "either-or" exclusion of a third possibility . Then we're using, but it is the same over the universe : -11 all we can use a three-valued logic . But if we do that, 6.67 • 10 nt•m2/kg2. (That, by the way, is the then we have an excluded fourth possibility. As 10 7 Stuermann followed this up, he asked : "Are there I think he would agree with Korzybski that non-aristotelian systems, in the sense in which many first, we do not see what 'is' ; we are much more general semanticists have been asking for them ? No; likely to see what we expect to see ; and second, our for any n-valued logic will, as an ideal structure, definitions and classifications do not inhere in Nature ; fail to model precisely the phenomenal domain" -- we put them there. Let me give a quote from Korzyb- that's an elegant way of putting it -- "and there will ski at this point : "No 'facts' are ever free from always be an excluded (n + 1)th . Any adequate doctrines : so whoever fancies he can free himself scientific system requires the use of some precisely from 'doctrines', as expressed in the structure of structured formal language in order to make deduc- the language he uses ., simply cherishes a delusion, tions and predictions . " Therefore his title, "Science, usually with strong affective components . "S Logic, and Sanity . " A so-called 'simple proposition', like "There Walter Stuermann died an untimely death three exists a swan which is white, " loses its simpli-y years later, in 1965, without having received any city when we try to decide whether some large bird answer to his challenge . I'm taking it up now very should or should not be called a swan, or whether belatedly . But this is an appropriate time, because that bird is still white if we hear it trumpeting in a to answer him I have to draw on the work of the two pitch-black cave . Being white is not just a predicate great men whose centennial we're celebrating this for a swan, but it's a relation between the swan, the year: Albert Einstein, Alfred Korzybski ; and the light, and our eyes . So let me pronounce what I'll third man, a comparative youngster, Karl Popper, modestly call Mayper's Dictum : "No fact is simple ." who is still productive at 77 . We live in a complicated world of infinitely interre- lated processes, not just existential propositions . First, let's consider this idea of existential propositions that express the "facts ." Popper puts Well, we try to make the world understandable, the matter beautifully, in a paper delivered to the with our theories, our high-level statements, the Aristotelian Society in 1946 answering the question : universal propositions of logic and mathematics . "Why are the Calculi of Logic and Arithmetic appli- Bertrand Russell (his centennial was seven years cable to Reality?" What Popper says is : ago), who has certainly done his part to advance these high-level propositions, said at one point : "The same philosophers who oppose " . the Law of Excluded Middle" (the law that a naive realism with regard to things are establishes a two-valued logic) "is true when precise often naive realists with regard to facts . symbols are employed, but it is not true when sym- While perhaps believing that things are bols are vague, as, in fact, all symbols are ." And logical constructs (which, I am satisfied, a little further on he said: "All traditional logic is a mistaken view) they believe that facts habitually assumes that precise symbols are being are part of the world in a sense similar to employed. It is therefore not applicable to this that in which processes or things may be terrestrial life, but only to an imagined celestial said to be part of the world ; that the world existence . " (Good thought for a Sunday morning . )4 consists of facts in a sense in which it may be said to consist of (four dimensional) Einstein, in his famous essay on "Geometry processes or of (three dimensional) things . and Experience," made the pronouncement: "Insofar . And they sometimes even believe that as the statements of mathematics apply to reality, sentences are something like pictures of they are not certain, and insofar as they are certain, facts, or that they are projections of facts . they do not apply to reality.