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Intuitionism is a philosophy of mathematics that was introduced by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881–1966): he developed a very personal philosophy of mathematics that founds mathematics (partially following Kant; see Kant's Philosophy of Mathematics) on a pure intuition of time. You can see his Intuitionism and formalism (1912) : ...


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No, you did not contradict LNC. In your program (( A == A ) and (A != A)) is true, but you also changed the function of '==' and '!=' so that '!=' is not longer a negation of '==': Your '==' function always returns True: def __eq__(self, other): self.last = True return self.last But your '!=' function no longer behaves as the negation of '==': ...


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It does bring in more than (ephemeral) security of foundations, but what it is more of is different for different people. The early intuitionists like Brouwer and Weyl saw mathematics as free play of a Kantian creative subject, and to them "excesses" of classical mathematics were simply unfaithful to the mathematical intuition of that subject and his other ...


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So far considerations based on computational resources are consequential only to a small group of philosophers known as radical anti-realists, who extend strict finitism to epistemology. Unlike constructivists and moderate anti-realists (intuitionists) like Dummett, who are usually satisfied with computability in principle radical anti-realists insist on ...


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I do not think that Searle will agree on labelling with "Social constructivism" his theory about Social relaity. According to Ian Hacking, Searle's book The Construction of Social Reality (1995), is not a social construction book at all. For sure, Searle is not a relativist. You can see: Barry Smith (editor), John Searle, Cambridge UP (2003), page 18: ...


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The second sentence of the SEP's article on mathematical intuitionism gives a pretty good explanation of why it is named as it is: Intuitionism is based on the idea that mathematics is a creation of the mind. As Mauro points out in his comment to your question, Brouwer based a lot of his ideas on Kant's views of mathematics. Central to Kant's views is ...


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Maybe you would understand @Logikal comments if you think about it like this: A physical machine (computer) takes a set of input conditions, then evaluates/operate according to a predetermined logic to produce a new set, then repeat... Time is intrinsic to the operation. (Your program works by exploiting the time aspect.) However formal logic has no time ...


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Yes there is. Maddy takes this position in Perception and Mathematical Intuition, and so do recent mathematical Aristotelians. The alternative of believing it all real usually comes with full blown Platonism (forms in a separate realm), and is not very popular, see however Brown's Platonism, Naturalism, and Mathematical Knowledge for a modern defense. Let me ...


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There are myriad answers to this question and all of them, informed by their own experience, and thus, different. Ultimately, constructions (like mathematics) point to a universal experience. Therefore, there are things outside of constructions that can be shared, or at the very least, pointed to. I mean no malice here, but the question is rather vague and ...


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I would say YES regarding the NP problem. See the Fundamental Theorem of Arithmetics. It is a theorem, so it is knowable as being true and demonstrable. However, if you can factorize a number in NP time then you're a god and you screwed the whole Internet. Studying propositions as being a valid reasoning has nothing to do with the involved time or number of ...


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The Wikipedia article on constructivist epistemology may provide the key references and overview you are looking for. Regarding philosophy of science and constructivism they write: Thomas Kuhn argued that changes in scientists' views of reality not only contain subjective elements, but result from group dynamics, "revolutions" in scientific practice and ...


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