Single Idea 9874

[catalogued under 5. Theory of Logic / G. Quantification / 4. Substitutional Quantification]

Full Idea

The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual.

Gist of Idea

Contradiction arises from Frege's substitutional account of second-order quantification

Source

comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.217


A Reaction

In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it.

Related Idea

Idea 9871 Frege always, and fatally, neglected the domain of quantification [Dummett on Frege]