Philosophy Stack Exchange
Philosophy Stack Exchange

Questions tagged [principle-of-non-contradiction]

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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.
loopzoop
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What is ⊥ called in paraconsistent logic?

I am building a weakened version of the intuitionistic logic. It wouldn't satisfy (p∧¬p)→⊥ as a tautology, but rather, (⊤→(p∧¬p))→⊥. In plain English, contradictions admit no proof, but there might still be true contradictions anyway. (Of course,…
Dannyu NDos
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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 admitted like Suarez that the principle of contradiction…
Geremia
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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 drop of ocean water to the ocean. So the concept…
Amala
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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 exist (de facto) and not by anything else? Edit. I…
Thom
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Everything must have a cause?

In a possible reality, if something came into existence without something giving rise to it, the fact would be that , there was nothing stopping something from coming into existence without anything giving rise to it, and if this was the existing…
loopit
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"Impredicative" definitions in mathematics

In this blog post, the following definition of an "impredicative definition" is offered: A definition is said to be impredicative if it defines an object E by means of a quantification over a domain of entities which includes E itself. An example: the…
Frank
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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 nothing", such as if we don't accept principle…
Hare Krishna
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A resolution to liar's paradox

Let's consider the famous liar paradox's statement: This statement is false Now, in classical logic, principle of bivalence could be stated as "All statements can either be assigned a value of true or false", if we assume principle of bivalence to…
Siddharth Chakravarty
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Would a universal (tran)set violate the law of identity?

At least, here's the argument that opened the question for me: The anticlass-theory principle: there are no discrete proper classes. There are intensional elementhood parameters such that if some set X satisfies those parameters in all such cases,…
Kristian Berry
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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, such as the notion of causality, are possibly…
Davius
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Does Artistole's principle of non-contradiction imply/concede/allow there are contradictions, we just can't learn much via them?

From Graham Priest and the SEP it seems like the world doesn't have to be a certain way with the PNC being necessary for "scientific inquiry, reasoning and communication" (SEP). The world could be any which way, but to engage in one of the above…
J Kusin
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Kant's remarks about the concept of time and the principle of noncontradiction

In the Transcendental Aesthetic he notes: ... I shall add that the conception of change, and with it the conception of motion, as change of place, is possible only through and in the representation of time; that if this representation were not an…
Kristian Berry
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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 operators, though presumably on conjunctions? Let…
Kristian Berry
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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 have done many proofs using this method in math. But when…
evianpring
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