28 ideas
13479 | Given that thinking aims at truth, logic gives universal rules for how to do it [Burge] |
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] |
8132 | We now have a much more sophisticated understanding of logical form in language [Burge] |
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] |
17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
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] |
10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
8126 | Anti-individualism says the environment is involved in the individuation of some mental states [Burge] |
8127 | Broad concepts suggest an extension of the mind into the environment (less computer-like) [Burge] |
10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
8129 | Anti-individualism may be incompatible with some sorts of self-knowledge [Burge] |
8131 | Some qualities of experience, like blurred vision, have no function at all [Burge] |
3115 | Are meaning and expressed concept the same thing? [Burge, by Segal] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
14349 | If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus [Burge, by Corry] |