more on this theme     |     more from this thinker

Single Idea 10567

[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence ]

Full Idea

Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects.

Gist of Idea

We can create objects from conditions, rather than from concepts

Source

Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)

Book Ref

-: 'Philosophical Studies' [-], p.373

A Reaction

The point is that no particular object is now required to make the abstraction.

The 14 ideas from 'Replies on 'Limits of Abstraction''

10569 If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K]
10565 There is no stage at which we can take all the sets to have been generated [Fine,K]
10564 We might combine the axioms of set theory with the axioms of mereology [Fine,K]
10560 Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
10563 A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K]
10561 Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K]
10562 We can combine ZF sets with abstracts as urelements [Fine,K]
10567 We can create objects from conditions, rather than from concepts [Fine,K]
10571 Concern for rigour can get in the way of understanding phenomena [Fine,K]
10568 Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]
10570 Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K]
10573 Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
10575 Why should a Dedekind cut correspond to a number? [Fine,K]
10574 Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]