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Single Idea 13655

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L ]

Full Idea

Putnam claims that the Löwenheim-Skolem theorems indicate that there is no 'fact of the matter' whether all sets are constructible.

Gist of Idea

The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate

Source

report of Hilary Putnam (Models and Reality [1977]) by Stewart Shapiro - Foundations without Foundationalism

Book Ref

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.109

A Reaction

[He refers to the 4th and 5th pages of Putnam's article] Shapiro offers (p.109) a critique of Putnam's proposal.

The 4 ideas from 'Models and Reality'

13655 The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]
9913 The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam]
9914 It is unfashionable, but most mathematical intuitions come from nature [Putnam]
9915 V = L just says all sets are constructible [Putnam]