9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
8751 | Only applicability raises arithmetic from a game to a science [Frege] |
9631 | Formalism fails to recognise types of symbols, and also meta-games [Frege, by Brown,JR] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
21570 | Numbers are just verbal conveniences, which can be analysed away [Russell] |
6425 | Formalism can't apply numbers to reality, so it is an evasion [Russell] |
6424 | Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell] |
13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
1616 | Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine] |
10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
10063 | Formalism is a bulwark of logical positivism [Musgrave] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |