Questions tagged [intuitionistic-logic]
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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, this gives people a kind of feeling that p→p is…
fantasie
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If you used intuitionistic logic in real life, would you not sound absurd?
Intuitionistic logic does not include the law of the excluded middle and double-negation elimination.
I imagine a real-life conversation with an intuitionist might go like this:
Amy said you didn't go to school yesterday.
She was wrong about it…
MWB
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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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What is the relationship between intuitionistic logic and 3-value logic?
Intuitionistic logic is a form of logic that doesn't have the law of the excluded middle, or LEM. The LEM says basically that a proposition that is not true is false, and a proposition that is not false is true. Classical logic has LEM but…
David Gudeman
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Was Kant an Intuitionist about mathematical objects?
In regards to the ontology of mathematics, as far as I can understand, Kant believed that Mathematical objects existed only as features of our perception that influenced how we viewed things-in-themselves, saying that, for example, geometry was the…
J.M.W Turner
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What is the difference in logic between strong and weak negation?
My main concern is to separate different forms of logic. I am hoping to use negation as a way to do that.
In the abstract to "Web Rules Need Two Kinds of Negation", Gerd Wagner writes
... there are two kinds of negation: a weak negation expressing…
Frank Hubeny
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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 often taught to call the material conditional…
mudskipper
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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 platonists, who believe that mathematical objects…
user9812063
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Does intuitionistic negation of A mean that there does not exist a proof of A?
Section 13 of Kleene's Intoduction to Metamathematics introduces briefly Brouwer's informal intuitionistic school of thought. There he writes that the interpretation of not A is meant to be taken as A implies a contradiction.
From this…
BENG
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What it the relationship between (intuitionist) type theory and logic?
I am aware that a similar question was asked about the type theory in the principia, but I'm more interested in what the relationship between, say Martin-Lof Type theory, and intuitionistic logic is.
Carlo Lori
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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 intuitionist logic, Core Logic, although I'm not sure…
confusedcius
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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 / logicians don't even take it seriously (or am I…
Dennis Kozevnikoff
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Is there a reference list of classic tautologies that are not intuitionistic tautologies for propositional logic?
An example of a classic tautology would be ¬¬A ↔ A. Since double negative elimination is not intuitionistically valid, this classic tautology would not be an intuitionisitic tautology since ¬¬A → A is not intuitionistically valid.
I am particularly…
Frank Hubeny
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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. the classicist? But then I'm not sure how to take…
Kristian Berry
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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 semiotics for logic where negating an atomic sentence…
user40843