12339 | Aristotle removes ontology from mathematics, and replaces the true with the beautiful [Aristotle, by Badiou] |
12556 | Mathematics is just about ideas, so whether circles exist is irrelevant [Locke] |
14162 | Mathematics doesn't care whether its entities exist [Russell] |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
3663 | How can you contemplate Platonic entities without causal transactions with them? [Putnam] |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K] |
17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
8310 | Does the existence of numbers matter, in the way space, time and persons do? [Lowe] |
17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
10089 | Talk of 'abstract entities' is more a label for the problem than a solution to it [George/Velleman] |
10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |