There are a number of anecdotes in circulation among mathematicians
about how dumb philosophers are about mathematics. Not all of these
are deserved.

The story that Hegel claimed (in 1801) that it was a priori
impossible that there be more than seven planets is one of these. The
reality is definitely rather more interesting, and I think that to
get the full picture I would have to read and understand Hegel's
argument, which I have not yet done. I have not yet found the full
text, and the original was in Latin. (“Quadratum est lex naturae,”
says Hegel, “triangulum, mentis.” That's “the square is the law of
nature; the triangle, of the mind.” Ummmm, okay.)

Another story tells that Kant claimed (1781) that Euclidean geometry
was a priori correct and that a non-Euclidean geometry was not
merely impossible but inconceivable. The claim of course is false,
but I wonder how much of Kant's claim is really recognizable in there,
and also how many mathematicians might have made similar claims in
1781.

Philosophy can be really tricky. Philosopher X seems to be saying
Y, but then it turns out that you have misunderstood Y and it
really means Z. Here's what the Stanford Encyclopedia of Philosophy
says:

Kant introduced the notion of a priori knowledge in contrast to a
posteriori, and synthetic knowledge in contrast to analytical
knowledge to allow for the existence of knowledge that did not rely on
experience (and was thus a priori) but was not tautological in
character (and therefore synthetic and not analytic). Analytic
statements are a priori, the contentious class of a priori
non-analytic statements contains those that could not be otherwise and
so provide certain knowledge. Among them are the statements of
Euclidean geometry; Kant ascribed synthetic a priori status to the
knowledge of space. He also ascribed certainty to Euclidean
geometry.

(Gray, Jeremy, "Epistemology of
Geometry",
The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward
N. Zalta (ed.))

Okay, maybe? Gray continues:

But, wrote Kant, it is not the philosopher who knows that
the angle sum of a triangle is two right angles, it is the
mathematician, because the mathematician makes a particular
construction that makes the truth of the claim demonstrable.

Now I wonder if, where the whole situation explained to him, Kant
would want to classify this theorem not as synthetic and a priori but
as tautological, since the mathematician can only prove it by assuming
that the triangle is in a Euclidean space.

I am willing to give Kant and Hegel the benefit of the doubt here.
But if anyone is looking for a really good example of an indefensible
mathematical fuckup by a first-class philosoper, check out this
article I wrote about Thomas Hobbes a
while back.

Subject: Hegel and the Seven Planets Path: you!your-host!wintermute!wikipedia!uunet!asr33!skynet!m5!plovergw!plovervax!shitpost!mjd Date: 2018-04-29T16:50:17 Newsgroup: misc.hegel Message-ID: <84a7130edbc4f8eb@shitpost.plover.com> Content-Type: text/shitpost

Right now I'm reading this paper titled
"Hegel and the
Seven
Planets".
The tabs at the bottom of my screen look like this:

Every time I see that one about Hegel I think “Hegel and the Seven
Dwarfs”.