29 ideas
1749 | If all laws were abolished, philosophers would still live as they do now [Aristippus elder] |
9921 | 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen] |
9924 | Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen] |
9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
9928 | Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen] |
9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
3558 | Only the Cyrenaics reject the idea of a final moral end [Aristippus elder, by Annas] |
5835 | The road of freedom is the surest route to happiness [Aristippus elder, by Xenophon] |
3018 | People who object to extravagant pleasures just love money [Aristippus elder, by Diog. Laertius] |
1751 | Pleasure is the good, because we always seek it, it satisfies us, and its opposite is the most avoidable thing [Aristippus elder, by Diog. Laertius] |
1755 | Errors result from external influence, and should be corrected, not hated [Aristippus elder, by Diog. Laertius] |
9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |