18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
12688 | Mathematics is the formal study of the categorical dimensions of things [Ellis] |
17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
10236 | There is no grounding for mathematics that is more secure than mathematics [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |