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Single Idea 9962

[filed under theme 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism ]

Full Idea

I am unable to see how the mere existence of pure abstract entities enables us to concoct appropriate models to serve as interpretations.

Gist of Idea

How can pure abstract entities give models to serve as interpretations?

Source

Michael Jubien (Ontology and Mathematical Truth [1977], p.111)

Book Ref

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.111

A Reaction

Nice question. It is always assumed that once we have platonic realm, that everything else follows. Even if we are able to grasp the objects, despite their causal inertness, we still have to discern innumerable relations between them.

The 21 ideas with the same theme [reasons for doubting the existence of maths entities]:

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]