Talk:Formalism (philosophy of mathematics)

Expert need
This page needs the help of an expert.
 * The definition given of formalism appears to me incorrect, the real definition sounds something like "statements of mathematics are considered as strings of symbols, and proofs (or deductions) are games about such strings, performed according to prescribed rules".
 * The very title of the page is not correct (not even consistent with the given definition), since this notion of formalism belongs to the philosophy of mathematics, not to mathematics itself.
 * It is strongly dubious that deductivism is part of formalism.
 * The actual version of the page creates confusion between formalism and Hilbert's program; the two issues are of course related, but very different (formalism is a philosophy of mathematics, Hilbert's program is a very precise program, its aim is to prove a certain statement).
 * Among other possible issues.--Popopp (talk) 16:11, 25 February 2011 (UTC)

Neutral point of view required
I will tag this article as POV for the following reasons that extent the concerns of the preceding post: This list of biases is probably incomplete, but suffices for tagging the article. --D.Lazard (talk) 13:12, 31 March 2019 (UTC)
 * Formalism is presented as a trend in philosophy of mathematics, but no notable formalist (if any) is cited or quoted.
 * There is no definition of formalism given by a proponent of this theory. There is only a definition aimed as presenting it as ridiculous.
 * There are two opposite definitions of formalism that are not distinguished in the article:
 * Formalization is required for insuring correctness of mathematics
 * Mathematics is nothing else than a succession of formal assertions and deductions The first assertion is supported by all modern mathematicians, while the second one is, presently, not really supported by notable mathematicians. The article is far to be neutral as suggesting that the dominant point of view is the second one
 * Hilbert supported the first view on formalism, but there is no evidence that he supported also the second. On the contrary, all his mathematical work suggest the contrary.

Article revisions
I believe the section on logicism needs to be removed entirely. Logicism and formalism are not the same thing. I also believe the article can be more focused by organizing the sections as follows: early formalism; Hilbert's formalism; the formalism of Wittgenstein in the Tractatus, Quine & Goodman's formalism, Carnap & Tarski's formalism; Criticisms of formalism TL (talk) 21:22, 25 May 2019 (UTC)