23 ideas
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
16236 | Maybe our persistence conditions concern bodies, rather than persons [Olson, by Hawley] |
6669 | For 'animalism', I exist before I became a person, and can continue after it, so I am not a person [Olson, by Lowe] |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |