30 ideas
| 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] |
| 13134 | We negate predicates but do not negate names [Westerhoff] |
| 9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
| 9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
| 9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
| 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] |
| 13117 | How far down before we are too specialised to have a category? [Westerhoff] |
| 13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
| 13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
| 13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
| 13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
| 13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
| 13124 | Categories can be ordered by both containment and generality [Westerhoff] |
| 13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
| 13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
| 13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
| 13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
| 13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
| 13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
| 9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
| 9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |