23 ideas
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
13479 | Given that thinking aims at truth, logic gives universal rules for how to do it [Burge] |
8132 | We now have a much more sophisticated understanding of logical form in language [Burge] |
17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
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] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
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] |
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] |
20082 | Bodily movements are not actions, which are really the tryings within bodily movement [Hornsby, by Stout,R] |
14349 | If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus [Burge, by Corry] |