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If you want to hear of Friedman in real debate there is great discussion in the foundations of mathematics mailing list archives that are public. There there is

If you want to hear of Friedman in real debate there is great discussion in the foundations of mathematics mailing list archives that are public. There there is real lively yet high-standards scholar figth of first rate experts from all viewpoints. I liked for instance the 'myth of second order logic' theme initiated by S. Simpson. It seems to me that the article is wrong when it says that the spheres recompounded bigger are a problem of large cardinal axioms. I think it derives from Choice, the C in ZFC instead.

golergka 10y ago
> I liked for instance the 'myth of second order logic' theme initiated by S. Simpson. Can you link to the thread? The archives seem gigantic
- wfn 10y ago
  Possibly http://www.personal.psu.edu/t20/fom/postings/9903/msg00069.html http://www.personal.psu.edu/t20/fom/postings/9903/msg00069.h... (and Simpson's replies downthread, e.g. http://www.personal.psu.edu/t20/fom/postings/9903/msg00151.html http://www.personal.psu.edu/t20/fom/postings/9903/msg00151.h...)
- jesuslop 10y ago
  I made this version for me of the relevant posts, too big for pastebin, hope permissions are ok: https://app.box.com/s/l36rfge3stx6go34or6l64m2eexijd26 https://app.box.com/s/l36rfge3stx6go34or6l64m2eexijd26 Some initial posts are warmup.
Chinjut 10y ago
I find Harvey Friedman has made the FOM mailing list completely unreadable. AND incredibly hostile to anyone with any sympathy to category theory, type theory, or the like. See https://plus.google.com/+CodyRoux/posts/6TiKLxjSCnu https://plus.google.com/+CodyRoux/posts/6TiKLxjSCnu (not by me, but expressing many of the same thoughts I've had; I particularly agree with many of the comments made by John Baez).
- jesuslop 10y ago
  That's true that categories are not going to find any special love there and that's sad. Much of the foundational tradition has been made in Set Theoretic language and its value cannot be ignored (think say on Gödel on CH), but it's sad that there is such community divide forbidding any osmosis. Categorical thinking leads to natural costless abstractions with practical unifying power and transversal applicability, and while that's not a FOM, it's an indicative that there may be something there. Also by comparison, as user fmap said, there is much coding in Set Theory. Just look at an ordered pair. In set theory it is the Kuratowski pair, and that a violent encoding. It a hack. We're not nearer to answer what they really are by that. Categorically they are a limit, which perhaps it's also not metaphysical chant, but we can feel it however less hacky.
  - catnaroek 10y ago
    Categorically, what's a limit is an object of ordered pairs (assuming you define them negatively, by their projections), not individual ordered pairs, right? If I recall correctly, categorical thinking doesn't emphasize elements of objects much, but in certain categories (perhaps pretoposes? I forget), morphisms from the terminal object to X can be considered the “global elements” of X.
    - jesuslop 10y ago
      yep I should have made the distinciton cartesian product and pair of elements, thanks.
  - deleted 10y ago
    [deleted]

golergka 10y ago

> I liked for instance the 'myth of second order logic' theme initiated by S. Simpson. Can you link to the thread? The archives seem gigantic

wfn 10y ago
Possibly http://www.personal.psu.edu/t20/fom/postings/9903/msg00069.html http://www.personal.psu.edu/t20/fom/postings/9903/msg00069.h... (and Simpson's replies downthread, e.g. http://www.personal.psu.edu/t20/fom/postings/9903/msg00151.html http://www.personal.psu.edu/t20/fom/postings/9903/msg00151.h...)
jesuslop 10y ago
I made this version for me of the relevant posts, too big for pastebin, hope permissions are ok: https://app.box.com/s/l36rfge3stx6go34or6l64m2eexijd26 https://app.box.com/s/l36rfge3stx6go34or6l64m2eexijd26 Some initial posts are warmup.

Chinjut 10y ago

I find Harvey Friedman has made the FOM mailing list completely unreadable. AND incredibly hostile to anyone with any sympathy to category theory, type theory, or the like. See https://plus.google.com/+CodyRoux/posts/6TiKLxjSCnu https://plus.google.com/+CodyRoux/posts/6TiKLxjSCnu (not by me, but expressing many of the same thoughts I've had; I particularly agree with many of the comments made by John Baez).

jesuslop 10y ago
That's true that categories are not going to find any special love there and that's sad. Much of the foundational tradition has been made in Set Theoretic language and its value cannot be ignored (think say on Gödel on CH), but it's sad that there is such community divide forbidding any osmosis. Categorical thinking leads to natural costless abstractions with practical unifying power and transversal applicability, and while that's not a FOM, it's an indicative that there may be something there. Also by comparison, as user fmap said, there is much coding in Set Theory. Just look at an ordered pair. In set theory it is the Kuratowski pair, and that a violent encoding. It a hack. We're not nearer to answer what they really are by that. Categorically they are a limit, which perhaps it's also not metaphysical chant, but we can feel it however less hacky.
- catnaroek 10y ago
  Categorically, what's a limit is an object of ordered pairs (assuming you define them negatively, by their projections), not individual ordered pairs, right? If I recall correctly, categorical thinking doesn't emphasize elements of objects much, but in certain categories (perhaps pretoposes? I forget), morphisms from the terminal object to X can be considered the “global elements” of X.
  - jesuslop 10y ago
    yep I should have made the distinciton cartesian product and pair of elements, thanks.
- deleted 10y ago
  [deleted]