Aristotle's Logic

General semanticists often advocate a "non-Aristotelian" perspective without themselves having any familiarity with Aristotle's actual works.  The best discussion I have encountered, which should be required reading for all would-be general semanticists, can be found at the Stanford Encyclopedia of Philosophy article Aristotle's Logic

A premise of the form "All A are A" is one of the common statements that general semantics object to as a paradigm case example of what they call the so-called Aristotelian law of identity that is to be eschewed. Those that might understand this, counter with Heraclitus and the Doctrine of Flux and the Unity of Opposites.  Heraclitus may have been the first to recognize levels of abstraction, because he actually holds to the view of "change thinging", as as one general semantics wag put it. That which is "thinging" is the higher, more abstract, level of abstraction while that which is changing is the lower, more objective, level of abstraction. The water (higher level) changes from cold to hot (lower level).  New waters (lower level) are ever rushing onward at any point in the river (higher level).  That Heraclitus often spoke in riddles and apparent contradictions bespeaks his Zen-like approach seeking to awaken awareness in his listeners.  Aristotle's law of identity applies to the higher level of abstraction.  Heraclitus's doctrine of flux applies to the lower level of abstraction. General semanticists who insist on only one point of view are confusing levels of abstraction..

This is a working draft in progress.

 

 

Aristotle explicitly says that what results of necessity must be different from what is supposed. This would rule out arguments in which the conclusion is identical to one of the premises. Modern notions of validity regard such arguments as valid, though trivially so. (Aristotle's Logic)

 

Aristotle's statement of the law of the excluded middle.

It is impossible for the same thing to belong and not belong simultaneously to the same thing in the same respect (Met. ) (ibid)

Aristotle makes exceptions to this "law".

A contradiction (antiphasis) is a pair of propositions one of which asserts what the other denies. A major goal of On Interpretation is to discuss the thesis that, of every such contradiction, one member must be true and the other false. In the course of his discussion, Aristotle allows for some exceptions. One case is what he calls indefinite propositions such as "A man is walking": nothing prevents both this proposition and "A man is not walking" being simultaneously true. This exception can be explained on relatively simple grounds. (ibid)

Aristotle also considered "three-valued" logic in his discussion of logic related to future propositions.

It has been proposed, for instance, that Aristotle adopted, or at least flirted with, a three-valued logic for future propositions, or that he countenanced truth-value gaps, or that his solution includes still more abstruse reasoning. The literature is much too complex to summarize: see Anscombe, Hintikka, D. Frede, Whitaker, Waterlow. (ibid)


Annotated bibliography of general semantics papers
General Semantics and Related Topics

This page was updated by Ralph Kenyon on 2009/11/16 at 00:27 and has been accessed 723 times at 0 hits per month.