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Questions tagged [philosophy]

Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.

The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.

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On the existence of sets

It is an important question whether mathematical objects in fact exist. Certainly, we can't locate them in the physical world. I want to know whether sets exist. If they in fact do not exist, then all the axioms of ZFC are either false or vacuous.…
user107952
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Maybe it is not necessary to define set membership?

I guess it is a normal reaction to be a bit surprised by the usual statement in books that the set membership relationship is "undefined". But I have had this idea: a typical definition of the natural numbers, by von Neumann, is that the number zero…
BlackSwan
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Are there any mathematical discoveries that are considered trivial or useless?

Are there any mathematical discoveries that are considered trivial or useless? And if that's the case, how do you know if they are trivial or useless? I am asking this question, because I am wondering if imaginary numbers were considered useless for…
Sayaman
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Is it possible to generalize without abstracting?

According to Wikipedia, Abstraction: Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and…
csp2018
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Are there examples of theorems incompatible with ZF that have proven useful in the sciences?

I was thinking about "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" and I realized all the mathematics I know about in science are compatible with ZF (even if they sometimes take additional axioms). So if I'm correctly…
zenten
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Why and how Mathematicians define unity?

I hope this one (pun intended) post won't get ripped by the community. I wondered what are the most abstract ways to define unity element? Why is there a need for unity element in general? Is it just to define reciprocal elements in algebraic…
0x90
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Are all questions solvable?

This is math/philosophical question. Are all problems solvable? By solution, I also mean that if a problem has no solution, then that is still a solution. What I mean is that for every problem, is there always a solution? I was inspired to think…
Brothersquid
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How is it possible for something to be less then nothing?

What is the ontological state of negative numbers? Is it a human invention or a does it live with reality?
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