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Single Idea 10568

[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism ]

Full Idea

Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation).

Gist of Idea

Logicists say mathematics can be derived from definitions, and can be known that way

Source

Kit Fine (Replies on 'Limits of Abstraction' [2005], 2)

Book Ref

-: 'Philosophical Studies' [-], p.374

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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]