20 ideas
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] |
14650 | Maybe proper names involve essentialism [Plantinga] |
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] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
14648 | Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
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] |
14647 | Surely self-identity is essential to Socrates? [Plantinga] |
14646 | An object has a property essentially if it couldn't conceivably have lacked it [Plantinga] |
14649 | Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga] |
14642 | Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga] |
14643 | 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga] |
14651 | What Socrates could have been, and could have become, are different? [Plantinga] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |