Questions tagged [principle-of-non-contradiction]

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Transconsistency operators and degrees of logical explosivity?

So I noticed in an article I was reading that they talked about consistency and/or inconsistency or otherwise transconsistency operators. I don't recall the details, but they sound like propositional ...
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Can the law of contradiction be applied to prove that *something cannot possibly exist? [closed]

This question is primarily concerned with Aristotle's law of contradiction. Please elaborate on how it can be proven that something cannot possibly exist by using Aristotle's law of contradiction. ...
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Does Aristotle's defense of the LNC involve the "argument from explosion"?

Aristotle purportedly had a rather exalted view of the law of noncontradiction: Aristotle explains that, given its peculiar status as the firmest first principle, PNC is not susceptible to ...
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Do there exist ideas which are true beyond axiom systems?

I find that sometimes there are many systems in which one could prove/ describe a single idea given in Mathematics. This made me wonder, is the thing we are proving actually true beyond the proof ...
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What could be some general unifying principles to guide what a philosophical reflection/enquiry might look like?

The notions of logical consistency, pertinence and possibly relevance seem important for a philosophical inquiry on some matter to be fruitful and interesting. Other notions once considered important, ...
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Transconsistency and Diaconescu's theorem

Let T be some set theory. Now there is at least one constructivist T such that T(AOC) ⊨ LEM, that is, via the axiom of choice in T, the law of the excluded middle becomes a theorem (Diaconescu's). So ...
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How to understand a proof by contradiction in minute detail?

I am following the course "Language, Proof, and Logic" from Stanford on EdX. I am trying to understand proof by contradiction specifically. I understand the gist of this type of proof, and I ...
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Can a category of non-difference exist in Western logic?

Indian philosophy has a logical category of non-difference (related somewhat to abheda) in which something is different from something else but identical to it as well. An example is that of the the ...
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Relationship between Principle of sufficient reason and Law of identity [closed]

I have an intuition that one can derive the principle of sufficient reason from the law of identity or non-contradiction but i don't know how. If someone knows I'd like some help.
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Why is it that the statement "All goblins are yellow" does not contradict the statement "All goblins are pink?"

From what I know, I think it has something to do with vacuous truths, but my understanding is not quite there yet.
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Why law of identity is formulated in terms of "things" and not statements?

The law of non-contradiction (LNC) and law of excluded middle (LEM) are both formulated in terms of statements. That is "A and not A" is always false and "A or not A" is always ...
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Can we know that law of non contradiction is true a priori?

I have seen some arguments for why should we accept law of non contradiction, and it seems to works in almost all areas. But some argument for it is like an argument for principle "nothing comes from ...
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Where did Suárez say the principle of non-contradiction does not apply to the Trinity?

Fr. Réginald Garrigou-Lagrange, O.P., says, in Le Sens du Mystère et le Clair-Obscur Intellectuel: Nature et Surnaturel p. 128 fn. 1 (Engl. transl. p. 142 fn. 41): St. Thomas never would have ...
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How do Thomists prove that: "Everything that exists must exist by something."?

One variation of principle of sufficient reason that Thomists use is: Everything that exists must exist by something. How do they prove such a statement? In particular, why can not something just ...
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