SHOULD I READ POINCARE OR ABOUT POINCARE, OR ABOUT THE DEBATES POINCARE WAS ACTI

SHOULD I READ POINCARE OR ABOUT POINCARE, OR ABOUT THE DEBATES POINCARE WAS ACTIVE IN??? 😉

—“Hey Curt – here’s a question for you: what of Poincare’s should I read? Since I know you like him!”—Davin Eastley

Great question. Although, Poincare was, like Hilbert, so successful, that we live in a mathematics that you probably know of so thoroughly it is really old hat to you. So reading about his biography might be interesting. Reading about his philosophy might be interesting. But reading about his math? You’ve already learned it all.

Poincare is interesting in the debate on the foundations of mathematics and against that of Cantor. I view him along with Menger (marginalism), Mises(praxeological constructivism), Brouwer (Mathematical intuitionism and later, Constructivism), Bridgman (scientific operationalism), and Popper (Scientific falsificationism – his attempt at completing the scientific method, as part of the tribe attempting to solve the problem of pseudoscience that arose out of the excessive use of statistical analysis in the 19th century, and in particular, the use of probability by Keynes to circumvent moral (reciprocity) testing of each action in a network of transactions.

So that said, I would suggest reading the SEP articles on Constructive Mathematics and Intuitionism first, in the context of the struggle to define the foundations of mathematics. Then to read the SEP articles on all the rest of theh players above for the same reason. Then to read Poincare’s book …. (wait… I’ll look it up, it’s escaping me)… “Science and Hypothesis”.

There is a very great similarity between the economic calculation debate against classical economics and the intuitionist-constructivist against classical mathematics.

Once you see the parallel you will see how this is not a problem of math or economics but of epistemology that popper suggested: it is increasinly difficult to make truth propositions that are dependent upon deductions, unless we can also construct the result we have deduced without the need for deduction.

Stated in those terms I think its understandable. Particularly because we tend to work today in high causal density fields, with far greater categorical variation than classical mathematics operated under.