9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
14248 | We could accept the integers as primitive, then use sets to construct the rest [Cohen] |
15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
18069 | Arithmetic is an idealizing theory [Kitcher] |
18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
9222 | The objects and truths of mathematics are imperative procedures for their construction [Fine,K] |
9223 | My Proceduralism has one simple rule, and four complex rules [Fine,K] |
10254 | Can the ideal constructor also destroy objects? [Shapiro] |
10255 | Presumably nothing can block a possible dynamic operation? [Shapiro] |
10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
8706 | Constructivism rejects too much mathematics [Friend] |