Questions tagged [intuitionistic-logic]
21 questions
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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 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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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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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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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 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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What's the constructivist's view to the S4 modal logic?
Intuitionistic logic can be translated to S4 modal logic by parsing intuitionistic P→Q to classical □(P→Q). There is no other way round, for there is no intuitionistic equivalent to ◊P. To analyze more, ◊P is equivalent to classical ¬□¬P, and that…
Dannyu NDos
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How do proponents of finitism respond to the claim that their position is "dubiously coherent"?
Michael Dummett writes (page 349)
Since primality is decidable, the statement that any particular natural number is prime must be determinately either true or false, since the decision procedure, if applied to that number, would have a determinate…
Frank Hubeny
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Instinct driven decisions
I know there are many factors when making decisions such as emotion, logic and reason etc ... But my question is how significant is instinct or intuition driven decision making important when human beings make decisions on a daily basis? Like I…
Aurora Borealis
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Reference Request for an introduction to constructive mathematics and intuitionistic logic
I have become deeply interested in intuitionist and constructivist logics after reading the well phrased answer of joberkmark here:
Nondisprovable Claims
And some of the works of Brouwer. I am looking for an introduction to these ideas, possibly…
user26166
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understanding intuitionistic logic
Just started a chapter on Intuitionism, and already I'm kinda confused on how to structure a proof in favor of intuitionistic logic. Here are the following definitions I am supposed to use:
Intuitionistic logic definitions:
And so I made an attempt…
M.Alexander
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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 modified with modal aspects.
I see an easy…
Dannyu NDos
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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 sequences. If "continuum" is indeed perceived…
Irene
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Is there a version of intuitionistic logic, or at least some sort of logic, where ¬¬ → 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. Still, by whatever means are used to preserve…
Kristian Berry
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