Questions tagged [philosophy]
Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.
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What mathematical questions or areas have philosophical implications outside of mathematics?
Please list both the problem/area and justify why it is important philosophically. This question doesn't cover questions that are only important within the philosophy of mathematics itself.
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Why do statements which appear elementary have complicated proofs?
The motivation for this question is : Rationals of the form $\frac{p}{q}$ where $p,q$ are primes in $[a,b]$ and some other problems in Mathematics which looks as if they are elementary but their ...
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Are the computable reals finitary?
In the comment thread of an answer, I said:
The computable numbers are based on the intuitionistic continuum, and are not finitary.
To which T.. replied:
Computable numbers are not based on ...
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What is "ultrafinitism" and why do people believe it?
I know there's something called "ultrafinitism" which is a very radical form of constructivism that I've heard said means people don't believe that really large integers actually exist. Could someone ...
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If all sets were finite, how could the real numbers be defined?
An extreme form of constructivism is called finitisim. In this form, unlike the standard axiom system, infinite sets are not allowed. There are important mathematicians, such as Kronecker, who ...
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Do complex numbers really exist?
Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious ...