Questions tagged [principle-of-non-contradiction]
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The absolute truth paradox
Read before answering:
I don't want to edit the whole question because it has some interesting answers to it the way it is written now. So I will just add this as a tip before answering since many ...
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Is there a stable derivation of the LNC from "Aristotle's thesis" and using a logical "instead of" operation?
This was my reasoning:
Assume that ¬(A → ¬A) (the corollary of Aristotle's thesis AT). Expand this to ¬(A → ¬A) → (A → ¬¬A). DNI is legitimate even in intuitionistic logic (as far as I know), so this ...
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Why do some claim that the law of non-contradiction is non-trivially unprovable?
By non-trivially unprovable, I mean that unprovable unless proven by virtue of being an axiom or an inference rule. If a logic has an inference rule or an axiom that is not stated as ¬(A ∧ ¬A), but it ...
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Can logical inference be based on non-contradiction?
In philosophy it was once common to claim that logical truths are based on the law of non-contradiction. Today it is more common to refer to modality, as in: an inference is deductive if the ...
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Do religious people actually believe all that stuff, or is it some kind of adult make-believe? [closed]
[Letter of Thomas Jefferson to James Smith][1], 1822:
"We find in the writings of His biographers [the Gospels] a groundwork of vulgar ignorance, of things impossible, of superstitions, ...
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Object language, Self Contradictory and Syntax
Following a previous question I asked about Falsum as primitive Symbol of the Object Language of the Propositional Calculus and its Semantic Interpretation, a similar question arises regarding its ...
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Is saying "Both A and not-A can do B" contradictory? [duplicate]
Take this example:
(1) Both blondes and non-blondes can do logic. (Premiss)
(2) If someone is blonde, then they can do logic (Derived from 1)
(3) If someone is not blonde, then they can do logic (...
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Trivialism "inside" a paraconsistent logic?
Trivialism is the view that every contradiction is true and accepts the principle of explosion of inconsistencies
Paraconsistency in turn is an attempt to study contradictions in a controlled way. ...
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What does "contradictions trivialize truth" mean?
I hope there's no regulations against posting a series of consecutive questions.
In the past decade or so I've read around 3-4 books on logic; they were 101's (introductory books) so more about ...
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How many kinds of contradictions are there?
I'm familiar with contradictions as the compound/molecular statement p ∧ ¬p. There's no truth-value combination of p (and ¬p) that can make p ∧ ¬p true. Stated differently, no possible world (as ...
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Why isn't the Liar's Paradox just accepted to be complete nonsense?
I can understand that some self-referential sentences can be sensible and have truth/false values (e.g. "This sentence is written in English." is true, "This sentence has 1,000 words.&...
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Is truth-in-a-model understood as consistency-of-discharged-antecedents?
I was trying to understand the thing about connexive logic, the fundamental ideas that ~(A then ~A) and ~(~A then A), or Boethius' playing of the theme, and so on. (One case I couldn't accept: "...
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Why "guilty" or "not guilty" but not "guilty" or "innocent"?
Why do some courts (like those in America) decide through the dictum "guilty"(g) or "not guilty"(~g) instead of using the term "innocent"(i) for "not guilty"(~g)...
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does Hegel's Dialectical Materialism needs justification when we re-examine the notion of "opposite" and whether that's a fact of the world?
Hegel basically says thesis-antithesis-synthesis, and this works because there are opposition of ideas or there are contradictions
Derrida also uses concepts like "binary oppositions"
he ...
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Why should I not believe there are true contradictions?
Kane Baker has a YouTube video in which he introduces the word 'wulture'. 'Wulture' applies to all things that are vultures, and excludes all things which are white. Delia is a white vulture. He asks: ...
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Law of non-contradiction violated [closed]
Can we consider these three examples as a violation of the law of non-contradiction?
The photon (and also some other particles) is mathematically its own particle AND anti-particle
The Moebius strip ...
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Is "may exist" and "may not exist" a negation that isn't a contradiction?
As usually happens, a statement (p) and its negation (~p) contradict each other. So, e.g. God does not exist, the negation of, God exists, together form a contradictory pair. A statement (p) and its ...
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How does one differentiate between the logically possible and the impossible?
The term “married bachelor” seems to be an obvious contradiction. The very definition of bachelor and unmarried are with respect to each other and so it seems nonsensical to talk about a married ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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