15 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 10163 | Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman] |
| 10760 | With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg] |
| 16189 | The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen] |
| 15132 | The Barcan formulas fail in models with varying domains [Kripke, by Williamson] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 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] |
| 17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
| 17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |
| 17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |