Why Is Physics Important? To Refute Arguments such as these:

I suggest that we do not use the oxymoron "speculative math". It is an obsolete term for pure math. The way I learned math from mathematicians, math is essentially built on logic, is not a science as often falsely stated and does not make any claim on reality although whole branches of math are inspired by the success of modelling reality with the assistance of math.

What you probably mean is "speculative physics", e.g. creating physical theories for which we have not yet any empirical base.

Yes, geometry is a part of math. The continuous extrapolation to infinitely small dimensions of geometric forms does not imply anything for reality.

I think to understand the rejection of geometry as a prerequisite of philosophy we really need to understand the sort of claims that were made for it. These claims have in fact never stopped being made, and find a fascinating expression in, of all people, Abraham Lincoln;

Quote

"He studied and nearly mastered the Six-books of Euclid (geometry) since he was a member of Congress. He began a course of rigid mental discipline with the intent to improve his faculties, especially his powers of logic and language. Hence his fondness for Euclid, which he carried with him on the circuit till he could demonstrate with ease all the propositions in the six books; often studying far into the night, with a candle near his pillow, while his fellow-lawyers, half a dozen in a room, filled the air with interminable snoring." Abraham Lincoln from Short Autobiography of 1860.

The assumption here is that if one understands how to prove a geometric theorem, one will equally know how to prove a philosophical one, as here;

But this involves a logical sleight-of-hand; it employs an argument by analogy, but argument by analogy only works if things really ARE analogous. Epicurus would challenge Lincoln on this point. If he wants to argue an end to slavery, he needs to argue from a foundation of sensation, anticipations, or feelings--because people aren't triangles, they're people.

Simply put, geometry as a foundation of philosophy is an invitation to casuistry. Nevertheless, I will always enjoy a wonderful performance by Mr. Daniel Day-Lewis!

Thanks Cassius! I thought DeWitt had made the same point but wouldn't have known where to grab the citation.