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Results tagged with mathematical-philosophy
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user 2733
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.
17
votes
(Fictive) story of a time where people reasoned only up to isomorphism
As Todd has already written an answer for me, maybe I can claim it as an Answer:
Exercise 1.1 in my book Practical Foundations of Mathematics
(CUP 1999) reads,
When Bo Peep got too many sheep to see …
- 8,481
0
votes
Extensionality in HoTT versus extensionality in internal language of a category
No, sorry, but you haven't got the point of HoTT.
$x \equiv y$ means "$x$ is the same as $y$", so they are terms such that one can be transformed into the other by "rewrite rules" such as expanding o …
- 8,481
4
votes
Is rigour just a ritual that most mathematicians wish to get rid of if they could?
Please would somebody better qualified than me to do so write accounts here of Reallisability and Proof Mining.
17
votes
Intuitionistic logic as quantization of classical logic?
MathOverflow is a valuable resource because it is interdisciplinary. Some of the people who have written about this question come from a traditional pure mathematical background where classical logic …
- 8,481
24
votes
Categorical foundations without set theory
Since Tom Leinster queries my reference to actual/completed versus
potential/incomplete infinities, maybe we should ask a philosopher
whether I am using these terms in the standard way.
In any case, …
- 8,481
46
votes
Accepted
Categorical foundations without set theory
On the subject of categorical versus set-theoretic foundations there
is too much complicated discussion about structure that misses the
essential point about whether "collections" are necessary.
It d …
- 8,481