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When intuitionists and classicists use the word "infinity," do they even mean the same thing?
Before the actual/potential distinction, even, then, when intuitionist negation is not the same as classicist negation, so that "not finite" has a different meaning for the intuitionist vs. ...
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Is p→p a theorem in intuitionistic logic?
In 'normal' propositional logic, the formulae p→q and ?p∨q are interchangeable. The rule of excluded middle, namely ?p∨p, is replaced to p→p. Since intuitionistic logic rejects law of excluded middle, ...
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Some questions about the material conditional and entailment in intuitionist math
In an excellent answer to a question about the history of material implication, @Bumble notes:
Unfortunately, the word ‘implies’ is ambiguous between these meanings. In particular, mathematicians are ...
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Does Not(A and not-A) = Not(A nand A) in intuitionistic logic?
I guess this comes out to: in intuitionistic logic, is the positioning of the negation relative to conjunction nontrivial? Is not-and different from and-not, here?
Motivation: I was trying out a ...
user40843
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Theory build on the top of a Logic
Could somebody elaborate the meaning of following statement from wikipedia concerning intrinsical differences between set theory and type theory:
Unlike set theories, type theories are not built on ...
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Do intutionists think the law of the excluded middle is universally, metaphysically false?
The law of the excluded middle (LEM) is that every well-formed formula of a sound logical system is either true or false. In systems that do not reject the law of the excluded middle, there can be ...
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What is the Normal Form of Proofs in Intuitionist Logic?
I came across the concept of a normal form of proofs in Neil Tennant's A New Unified Account of Truth and Paradox (2015). I did a quick scan on SEP, and it seems to be a concept specific to his ...
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Why do constructive mathematicians claim that mathematical truth is temporal?
(crossposted here, wasn't sure where it belongs...)
It seems to me (and correct me if this is a misconception) that the traditional divide in the interpretation and practice of mathematics is between ...
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Is there a modal modification of the law of excluded middle that may render constructive?
Intuitionistic logic rejects the law of excluded middle, and paraconsistent logic rejects the law of non-contradiction. I wondered whether the rejected laws can still be incorporated, if they're ...
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Is disjunction pointless in intuitionistic logic?
Sec. 5.3 of the SEP article on constructive and intuitionistic set theories makes note of a property meant for theories that compromise on the LEM:
A theory T has the disjunction property (DP) if ...
user40843
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Continuum and Choice sequence
I am reading a paper on Brouwer's intuitionism. It mentions that according to Brouwer, the concept of continuum is perceived as a whole by intuition. However, it also mentions setting up choice ...
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Is there a version of intuitionistic logic, or at least some sort of logic, where ¬¬𝘈 → 𝘈 is kept but LEM is not?
The Wikipedia article on double negation in logic says that intuitionistic logic does happen to keep ???A → ?A, as well as A → ??A. I'm pretty confused by this, but I'll take it for granted for now. ...
user40843
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Intuitionism, the law of excluded middle and mental construct
I don't get why LEM is rejected in intuitionistic logic. The basic idea behind intuitionism is that math is a mental construct. But how does this make LEM not acceptable? I've seen some similar posts ...
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Why was intuitionist logic abandoned?
I have seen many questions discussing intuitionist logic (Brouwer, Weyl etc.) on the site.
However, this whole area of logic seems to be dead, and it also looks like philosophers / mathematicians / ...
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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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