Max Black, in an essay criticizing general semantics, credits Aristotle with "pioneering modern discoveries in multivalued logics" (Ref. Max Black, Language and Philosophy, Cornell University Press 1949, p228-229).
Can anyone direct me to passages in Aristotle's writings that substantiate this claim, or to any relevant on-line articles or discussions?
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jpg: Max Black, in an essay criticizing general semantics, credits Aristotle with "pioneering modern discoveries in multivalued logics" (Ref. Max Black, Language and Philosophy, Cornell University Press 1949, p228-229). Can anyone direct me to passages in Aristotle's writings that substantiate this claim, or to any relevant on-line articles or discussions? jpg
Aristotle didn't pioneer multivalued logics in any strict sense. Aristotelian logic is strictly two-valued, adhering to the laws of identity, contradiction and excluded middle.
According to Wikipedia though a remark concerning future events served as the catalyst for others to develop multivalued logic.
The first known classical logician who didn't fully accept the law of the excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of logic"[1]), who admitted that his laws did not all apply to future events (De Interpretatione, ch. IX). But he didn't create a system of multi-valued logic to explain this isolated remark. The later logicians until the coming of the 20th century followed Aristotelian logic, which includes or implies the law of the excluded middle. The 20th century brought the idea of multi-valued logic back. The Polish logician and philosopher Jan Łukasiewicz began to create systems of many-valued logic in 1920, using a third value "possible" to deal with Aristotle's paradox of the sea battle. Meanwhile, the American mathematician Emil L. Post (1921) also introduced the formulation of additional truth degrees with n>=2,where n are the truth values. Later Jan Łukasiewicz and Alfred Tarski together formulated a logic on n truth values where n>=2 and in 1932 Hans Reichenbach formulated a logic of many truth values where n→infinity. Kurt Gödel in 1932 showed that intuitionistic logic is not a finitely-many valued logic, and defined a system of Gödel logics intermediate between classical and intuitionistic logic; such logics are known as intermediate logics.
The first known classical logician who didn't fully accept the law of the excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of logic"[1]), who admitted that his laws did not all apply to future events (De Interpretatione, ch. IX). But he didn't create a system of multi-valued logic to explain this isolated remark. The later logicians until the coming of the 20th century followed Aristotelian logic, which includes or implies the law of the excluded middle.
The 20th century brought the idea of multi-valued logic back. The Polish logician and philosopher Jan Łukasiewicz began to create systems of many-valued logic in 1920, using a third value "possible" to deal with Aristotle's paradox of the sea battle. Meanwhile, the American mathematician Emil L. Post (1921) also introduced the formulation of additional truth degrees with n>=2,where n are the truth values. Later Jan Łukasiewicz and Alfred Tarski together formulated a logic on n truth values where n>=2 and in 1932 Hans Reichenbach formulated a logic of many truth values where n→infinity. Kurt Gödel in 1932 showed that intuitionistic logic is not a finitely-many valued logic, and defined a system of Gödel logics intermediate between classical and intuitionistic logic; such logics are known as intermediate logics.
I think it was a mistake to conclude a need for multivalued logic from Aristotle's remark though. Roderick Long has a working paper that reconciles Leibniz's Law with "Aristotle's Fantasy" and also, in my opinion, incidentally serves to show multivalued logic to be unnecessary for resolving the alleged paradox.
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Roderick T. Long, "Future Truth and Leibniz’s Law: An Aristotelean Sea Battle in a Heracleitean River "
Contact me by email and I can send you the Word doc.
Yours in liberty,Geoffrey Allan Plauche, Ph.D.Political ScienceLouisiana State University
"Quis custodiet ipsos custodes?"(Who watches the watchmen?)-Juvenal, Satires VI.347
Geoffrey Allan Plauche: I think it was a mistake to conclude a need for multivalued logic from Aristotle's remark though. Roderick Long has a working paper that reconciles Leibniz's Law with "Aristotle's Fantasy" and also, in my opinion, incidentally serves to show multivalued logic to be unnecessary for resolving the alleged paradox. Roderick T. Long, "Future Truth and Leibniz’s Law: An Aristotelean Sea Battle in a Heracleitean River " Contact me by email and I can send you the Word doc. Geoffrey, I will send you an email. I look forward to reading Long's paper. Thank you for your reply. jpg
Geoffrey,
I will send you an email. I look forward to reading Long's paper.
Thank you for your reply.
What was his concern with excluded middle? I cannot see the problem with the sea battle.
scineram,
For me, the excluded middle holds, even in cases for which it is not be possible to establish which statement of a contradictory pair holds. However, some people have argued that holding the view that one or the other of a contradictory pair of statements about future events is true commits one to the idea that future events are predetermined. And since Aristotle believed in free will, he considered making an exception that allows a third value: “not yet determined”. Here is that argument: http://www2.drury.edu/cpanza/aristotleseabattle.html.
In the paper Geoffrey refers to, Roderick T. Long gives a reasoned interpretation of Aristotle that avoids paradox.
It is not clear to me that Aristotle really thought that the Sea Battle was a problem for excluded middle. From what I have read, that view is conjectural.
(Ref: http://plato.stanford.edu/entries/aristotle-logic/ (Scroll to 12. Time and Necessity: The Sea Battle, later paragraphs.)
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