Questions tagged [foundations-of-mathematics]

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6
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1answer
307 views

What's so bad about giving up the Axiom of Choice?

The Axiom of Choice (AoC) in set theory famously gives rise to controversial and counterintuitive theorems. (Examples: Banach-Tarski paradox and existence of non-measurable sets.) I'm aware of some ...
5
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1answer
2k views

What are the main issues on which the schools of Intuitionism, Formalism, and Logicism disagree?

What is the difference between Intuitionism, Formalism, and Logicism? Namely - on which issues do they disagree? And what is the relation of those schools of thought to Platonism, Nominalism, and ...
3
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3answers
159 views

Do picture proofs of the Pythagorean theorem make it empirical?

As I understand it, the Pythagorean Theorem, which defines the metric for Euclidean space, is said to be strictly mathematical in the sense that it is derived from a set of purely theoretical axioms (...
2
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0answers
126 views

Relation of Mathematical Propositions to Natural Language

Treating Natural Language as a language game, what role does it play in our understanding of mathematics? Does natural language provide meaning to mathematics? Does a proof of a conjecture, say FLT,...
1
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2answers
198 views

Can zero be defined without some definition of one? Can one be defined without some definition of zero?

I would prefer to ask this in the math community, but that crowd is hostile toward anything hinting of philosophy. It is my contention that a construction of the real number system which begins with ...
1
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0answers
67 views

The nature of Nominalist Formalism

In this entry in the stanford encyclopedia of philosophy, it is stated that the theory of nominalist formalism deals with the metatheory problem of formalism as follows: Commendably, Goodman and ...
0
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1answer
174 views

Where to start with the philosophy of mathematics?

This may be a duplicate question. What is the best way to get started with the philosophy of mathematics? Given that I know (from university) the basics that are discussed (Set theory, Russell's ...
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2answers
110 views

Argument against Platonism

Platonic view of mathematics states that numbers have abstract reality. One way to test what this really means is to do a thought experiment of extinction of humanity. Also suppose after all evidence ...
0
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0answers
24 views

Discovery VS Invention in Mathematics [duplicate]

Asking specifically in the context of philosophy of Mathematics, on what basis do we classify or should classify a new expression as a Creation of Mind (Invention) OR a Discovery?