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Gluts and Gaps

a topic in Logic & Mathematics, a part of the RPG forum.

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Let's talk about formal logics, mathematical models, and theoretical constructs.

Gluts and Gaps

Tips: 0.50 INK Postby dealing with it on Thu Nov 04, 2021 8:51 pm

I can't think of any law deeper than the Law of Non-contradiction; I consider questioning it to be more fundamental than the question of God's existence.

Does rationality (any and all rationality) /presuppose/ that the Law of Non-Contradiction is always going to be there? Can there, alternatively, be "true contradictions"?: I'm referring to logic gluts (a proposition that is both true and false) and gaps (a proposition that is neither true nor false) -- or ought we consider the consideration of these nothing more than the fanciful experimentation of an unrestrained imagination?

(n.b. The common strategy to attack the Law of Non-Contradiction is via. a challenge to The Law of the Excluded Middle, which states that a proposition is either "a" or "not-a", but not "both" nor "neither".)

It's hard to think of many good examples (paraconsistent/non-Classical logic is a very new development, so is not yet furnished with a wealth of palatable metaphors), but self-referential sentences may serve:

"This sentence is a lie" might be an example of a gappy proposition. How legitimate of a challenge is the Liar's Paradox to Classical (Aristotelian) logic? Does it break the shiny, perfect toy that we call the Law of Non-Contradiction? Are we left only with tautologies like "A=A"?

If you want more context, please refer to:

https://plato.stanford.edu/entries/dialetheism/


(I've mentioned this in earlier threads ("Paraconsistency" and "Fuzzy Logic"), but I think the phraseology of this OP is different enough to warrant another treatment.)

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Re: Gluts and Gaps

Tips: 0.00 INK Postby Remæus on Fri Nov 05, 2021 12:07 am

Logic is fundamentally flawed! Gödel proved that any logical system necessarily includes inconsistencies, but the thrust of your argument is correct — "logical gluts" exist in the void of inconsistency that Gödel posits.

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Re: Gluts and Gaps

Tips: 0.00 INK Postby dealing with it on Sat Nov 06, 2021 1:49 pm

Have you read “Gödel, Escher, Bach” by Hofstadter?

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