32 ideas
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
18767 | Free logics has terms that do not designate real things, and even empty domains [Anderson,CA] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
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] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
18763 | Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA] |
18771 | Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA] |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
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] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
18769 | Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA] |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
18770 | We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA] |
18766 | 's is non-existent' cannot be said if 's' does not designate [Anderson,CA] |
18768 | We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA] |
18765 | Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA] |
18764 | The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA] |
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] |