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Questions tagged [intuitionistic-logic]

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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 ...
user267839's user avatar
2 votes
4 answers
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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 ...
Julius Hamilton's user avatar
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1 answer
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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 ...
confusedcius's user avatar
5 votes
2 answers
349 views

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 ...
user9812063's user avatar
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1 answer
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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 ...
Dannyu NDos's user avatar
2 votes
2 answers
98 views

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 ...
Kristian Berry's user avatar
1 vote
1 answer
109 views

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 ...
Irene's user avatar
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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. ...
Kristian Berry's user avatar
1 vote
0 answers
88 views

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 ...
Irene's user avatar
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5 votes
3 answers
3k views

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 / ...
Dennis Kozevnikoff's user avatar
6 votes
1 answer
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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 ...
Dannyu NDos's user avatar
2 votes
1 answer
98 views

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 ...
Dannyu NDos's user avatar
6 votes
3 answers
471 views

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 ...
David Gudeman's user avatar
1 vote
0 answers
64 views

Moral constructivism and intuitionistic logic

What with all the times Rawls uses mathematics examples in AToJ, such as the guy who counts blades of grass for fun and survives by solving math problems for a fee, or π being transcendental, or the ...
Kristian Berry's user avatar
12 votes
8 answers
5k views

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 ...
MWB's user avatar
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1 answer
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Intuitionistic derivation of ~~~A --> ~A

I need to give an intuitionistic derivation of ~~~A --> ~A by using natural deduction. I know that in intuitionistic terms ~~~A --> ~A converts to ~~~A → ~A i.e ⊦ ((A → ⊥)→ ⊥→ ⊥) → (A → ⊥). These ...
Fiona717's user avatar
5 votes
1 answer
122 views

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 ...
BENG's user avatar
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4 votes
2 answers
1k views

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 ...
Frank Hubeny's user avatar
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1 vote
1 answer
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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 ...
Frank Hubeny's user avatar
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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, ...
Frank Hubeny's user avatar
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2 votes
1 answer
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Instinct driven decisions [closed]

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 ...
Aurora Borealis's user avatar
6 votes
1 answer
649 views

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-...
J.M.W Turner's user avatar
2 votes
1 answer
160 views

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 ...
user avatar
1 vote
1 answer
237 views

Intuitionism and physics

Is there a conflict between Brouwer's intuitionism and the claim that the free will must not exist because nature is deterministic ? It seems to me that the act of mental construction of mathematical ...
dbrane's user avatar
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2 votes
1 answer
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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: ...
M.Alexander's user avatar