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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.
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
10211 | Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro] |
13655 | The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro] |
9915 | V = L just says all sets are constructible [Putnam] |
13040 | Constructibility: V = L (all sets are constructible) [Kunen] |
13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |