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Single Idea 10211

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

Full Idea

Quine suggests that V = L be accepted in set theory because it makes for a cleaner theory, even though most set theorists are skeptical of V = L.

Gist of Idea

Quine wants V = L for a cleaner theory, despite the scepticism of most theorists

Source

report of Willard Quine (works [1961]) by Stewart Shapiro - Philosophy of Mathematics Ch.1

Book Ref

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.29

A Reaction

Shapiro cites it as a case of a philosopher trying to make recommendations to mathematicians. Maddy supports Quine.

The 6 ideas with the same theme [possible axiom saying all sets are constructible]:

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]