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Results tagged with mathematical-philosophy
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user 2273
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.
29
votes
Abstract thought vs calculation
A toy example, using the Yoneda lemma:
Claim: There are two canonical bialgebra structures (the “additive” and “multiplicative” structures) on $k[x]$, and one of them (the additive one) in fact makes …
10
votes
Accepted
In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that $\mathsf{PA}$ i...
The PA sentence “$\newcommand{\Con}{\text{Con}}\Con(\newcommand{\PA}{\text{PA}}\PA)$” says that PA is consistent in exactly the same ways that the PA sentences representing, say, the fundamental theor …
- 21.3k
63
votes
Accepted
Why should we believe in the axiom of regularity?
Regularity (aka Foundation) can be seen philosophically as an axiom of restriction. It is not necessarily saying “all the things you consider as sets must be well-founded”. It can be read saying “fo …
- 21.3k