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Single Idea 9950

[filed under theme 5. Theory of Logic / G. Quantification / 1. Quantification ]

Full Idea

The contribution of the quantifier to the truth conditions of sentences of which it is a part cannot be adequately explained if it is treated as other than a second-level predicate (for instance, if it is viewed as name).

Gist of Idea

A quantifier is a second-level predicate (which explains how it contributes to truth-conditions)

Source

report of Gottlob Frege (Begriffsschrift [1879]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2

Book Ref

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.23

A Reaction

They suggest that this makes it something like a 'property of properties'. With this account it becomes plausible to think of numbers as quantifiers (since they do, after all, specify quantities).

The 20 ideas from 'Begriffsschrift'

7622 In 1879 Frege developed second order logic [Frege, by Putnam]
7729 Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner]
9991 For Frege the variable ranges over all objects [Frege, by Tait]
10536 Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege]
9950 A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman]
13609 Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan]
7730 Frege introduced quantifiers for generality [Frege, by Weiner]
7742 Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh]
13824 Proof theory began with Frege's definition of derivability [Frege, by Prawitz]
17855 It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C]
10607 Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P]
11008 Existence is not a first-order property, but the instantiation of a property [Frege, by Read]
22280 Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter]
7741 The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner]
22270 Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege]
8939 We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher]
17745 For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki]
7728 Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner]
4971 I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege]
16881 The laws of logic are boundless, so we want the few whose power contains the others [Frege]