18176 | Pure mathematics is pure set theory [Cantor] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
8463 | Maths can be reduced to logic and set theory [Quine] |
8203 | All the arithmetical entities can be reduced to classes of integers, and hence to sets [Quine] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
15517 | Giving up classes means giving up successful mathematics because of dubious philosophy [Lewis] |
17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
10130 | Set theory can prove the Peano Postulates [George/Velleman] |
13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
10685 | Set theory is the science of infinity [Hossack] |
15360 | ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten] |
15369 | Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten] |
16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |