14 ideas
291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
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] |
17824 | The master science is physical objects divided into sets [Maddy] |
17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |