more on this theme | more from this thinker
Full Idea
Formalism seems to exclude from consideration all creative, growing mathematics.
Gist of Idea
Formalism seems to exclude all creative, growing mathematics
Source
Alan Musgrave (Logicism Revisited [1977], §5)
Book Ref
-: 'British Soc for the Philosophy of Science' [-], p.119
A Reaction
[He cites Lakatos in support] I am not immediately clear why spotting the remote implications of a formal system should be uncreative. The greatest chess players are considered to be highly creative and imaginative.
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] |