Questions tagged [intuitionistic-logic]

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11
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7answers
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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 ...
0
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1answer
33 views

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 ...
5
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1answer
73 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 ...
2
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1answer
193 views

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: ...
3
votes
1answer
236 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 ...
1
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1answer
162 views

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 ...
2
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1answer
130 views

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, ...
2
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1answer
114 views

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 ...
6
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1answer
421 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-...
2
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1answer
134 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 ...
1
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1answer
164 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 ...