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Single Idea 10779

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension ]

Full Idea

If φ contains no bound second-order variables, the corresponding comprehension axiom is said to be 'predicative'; otherwise it is 'impredicative'.

Gist of Idea

A comprehension axiom is 'predicative' if the formula has no bound second-order variables

Source

Øystein Linnebo (Plural Quantification Exposed [2003], §1)

Book Ref

-: 'Nous' [-], p.73

A Reaction

['Predicative' roughly means that a new predicate is created, and 'impredicative' means that it just uses existing predicates]

The 5 ideas from 'Plural Quantification Exposed'

10778 Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
10779 A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo]
10781 A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo]
10782 The modern concept of an object is rooted in quantificational logic [Linnebo]
10783 Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]