25 ideas
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
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] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
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] |
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] |
12184 | Logical necessity overrules all other necessities [McFetridge] |
15083 | The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale] |
15084 | In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale] |
12180 | Logical necessity requires that a valid argument be necessary [McFetridge] |
12181 | Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge] |
12183 | It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge] |
12192 | The mark of logical necessity is deduction from any suppositions whatever [McFetridge] |
12182 | We assert epistemic possibility without commitment to logical possibility [McFetridge] |
12187 | Objectual modal realists believe in possible worlds; non-objectual ones rest it on the actual world [McFetridge] |
12186 | Modal realists hold that necessities and possibilities are part of the totality of facts [McFetridge] |
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] |
16570 | Elements are found last in dismantling bodies, and first in generating them [Albert of Saxony] |