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Ideas for 'Natural Goodness', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'What Mary Didn't Know'

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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

9874	Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
	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.
	From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17
	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.