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Results tagged with mathematical-philosophy
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user 1610
Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.
2
votes
Are all mathematical theorems necessarily true?
Charles wrote:
Robert Hanna (Kant's Theory of Judgment, SEP 2009, sect. 2.2.2) interprets Kant as saying that "logically possible worlds are nothing but maximal logically consistent sets of concep …
- 9,201
6
votes
Badiou and Mathematics
There's an interesting review of Badiou's "Number and Numbers" at the Notre Dame Philosophical Review by John Kadvany.
- 9,201
5
votes
Accepted
Defining variable, symbol, indeterminate and parameter
Regarding the status of variables, you probably want to look at Chung-Kil Hur's PhD thesis "Categorical equational systems: algebraic models and equational reasoning". Roughly speaking, he extends the …
- 9,201
31
votes
Accepted
How do they verify a verifier of formalized proofs?
Is there such a "dumb" system around? If yes, do formalization projects use it? If not, do they recognize the need and put the effort into developing it? Or do they have other means to make their s …
- 9,201
10
votes
Were Bourbaki committed to set-theoretical reductionism?
The difficulties in formalizing categorical reasoning in set theory are actually pretty simple to understand -- it's just an annoying incompatibility in how the notion of size is used in practice in c …
- 9,201
65
votes
Accepted
Is there any formal foundation to ultrafinitism?
Wikipedia also says that Troelstra said in 1988 that there were no satisfactory foundations for ultrafinitism. Is this still true? Even if so, are there any aspects of ultrafinitism that you can get …
- 9,201
31
votes
What is Realistic Mathematics?
At the other side, existence of large cardinals, non-measurable subsets of the reals, etc. are not (immediately) useful for such a study.
I don't know about non-measurable subsets, but large card …
- 9,201
16
votes
Logic in mathematics and philosophy
I agree with Timothy and Andrej's answers, and will complement them by suggesting a few books by philosophers and philosophically-inclined logicians which I have found very interesting. I am sure the …
- 9,201