Post #1816034

2026-04-29 19:06 UTC

I am going to repeat something I believe I have already said here: there is only one mathematics, which includes both classical and constructive mathematics, and all possible mathematics that we haven&#39;t seen yet. Mathematics is something that people do. The philosophy of mathematics should not be about what kind of mathematics is &quot;the right one&quot;. It instead should be about understanding what people do, in all directions. To some extent it is. But the philosophy of *foundations of mathematics* seems to imply that &quot;the right foundations should be found&quot;. I don&#39;t think there is a right foundation, but I do think that a foundation that incorporates all kinds of mathematics we do *today* is possible (and exists). In any case, the reason I started this post is that I feel that whenever I state something like the above, I upset both my &quot;constructivist&quot; friends and my &quot;classist&quot; friends at the same time. Can I say, without being criticized, that I do constructive mathematics simply because I love it, and that this doesn&#39;t stop me loving classical mathematics, too (sorry, I love you much less, but I still love you a lot).

Replies (4)

@MartinEscardo@mathstodon.xyz 2026-04-29 21:02

In other words, I am a self-declared panmathematician. The good thing about this terminology is that, unlike "constructivist" or "classisist", definitely "panist" doesn't make sense at all. I particularly dislike "constructivist", especially when applied to myself by other people.

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@dlakelan@mastodon.sdf.org 2026-04-29 19:56

@MartinEscardo@mathstodon.xyz As a fan of nonstandard analysis, I am right there with you. It drives me crazy when people act like limits are the one true way to think about analysis and that any other way is an affront to the one true path! But that response is essentially the single most common one I get when I discuss anything about NSA.

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@mjd@mathstodon.xyz 2026-04-29 20:20

@MartinEscardo@mathstodon.xyz This reminds me of something J-Y. Girard wrote, about it being a mistake to think of “intuitionistic logic” or “linear logic”, because there is only one Logic.

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@nilesjohnson@mathstodon.xyz 2026-04-30 13:45

@MartinEscardo@mathstodon.xyz This popped back into my mind this morning because I was thinking about a discussion with another friend about some art. There's a long history of people trying to exclude certain styles, or media, or themes, or etc., by calling them non-art, or (even worse) not *true* art. Those kinds of separations always seem to be more about the motivations of the people calling for them, rather than something intrinsic about the nature of art. I'm not enough of an art historian to say more about that, but the parallels between the questions "what is art?" and "what is math?" are interesting, and maybe useful. The answer you started with---"It's something that people do." is one I like a lot, both for what it says, and what it doesn't say.

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