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Full Idea
Three objections to realism in philosophy of mathematics: mathematical objects have no space/time location, and so no causal role; that such objects are determinate, but reference to numbers aren't; and that there is no abstract/concrete distinction.
Gist of Idea
'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction
Source
Jerrold J. Katz (Realistic Rationalism [2000], Int.xxix)
Book Ref
Katz,Jerrold J.: 'Realistic Rationalism' [MIT 2000], p.-6
2510 | Traditionally philosophy is an a priori enquiry into general truths about reality [Katz] |
2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
2516 | Most of philosophy begins where science leaves off [Katz] |
2517 | Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz] |
2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
2519 | It is generally accepted that sense is defined as the determiner of reference [Katz] |
2520 | Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz] |
2518 | Sentences are abstract types (like musical scores), not individual tokens [Katz] |
2522 | Experience cannot teach us why maths and logic are necessary [Katz] |