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Full Idea
Formalism is a bulwark of logical positivist philosophy.
Gist of Idea
Formalism is a bulwark of logical positivism
Source
Alan Musgrave (Logicism Revisited [1977], §5)
Book Ref
-: 'British Soc for the Philosophy of Science' [-], p.120
A Reaction
Presumably if you drain all the empirical content out of arithmetic and geometry, you are only left with the bare formal syntax, of symbols and rules. That seems to be as analytic as you can get.
| 10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
| 10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |