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Single Idea 13023

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI ]

Full Idea

The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support.

Gist of Idea

The Power Set Axiom is needed for, and supported by, accounts of the continuum

Source

Penelope Maddy (Believing the Axioms I [1988], §1.6)

Book Ref

-: 'Journal of Symbolic Logic' [-], p.486

A Reaction

The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one?

The 5 ideas with the same theme [axiom for a new set from any given set]:

13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
15936 The Power Set is just the collection of functions from one collection to another [Lavine]
18845 If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt]