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Ideas for 'fragments/reports', 'Thinking About Logic' and 'Introduction to Mathematical Logic'

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2 ideas

5. Theory of Logic / G. Quantification / 1. Quantification

11007	Quantifiers are second-order predicates [Read]
	Full Idea: Quantifiers are second-order predicates.
	From: Stephen Read (Thinking About Logic [1995], Ch.5)
	A reaction: [He calls this 'Frege's insight'] They seem to be second-order in Tarski's sense, that they are part of a metalanguage about the sentence, rather than being a part of the sentence.

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

10978	In second-order logic the higher-order variables range over all the properties of the objects [Read]
	Full Idea: The defining factor of second-order logic is that, while the domain of its individual variables may be arbitrary, the range of the first-order variables is all the properties of the objects in its domain (or, thinking extensionally, of the sets objects).
	From: Stephen Read (Thinking About Logic [1995], Ch.2)
	A reaction: The key point is that the domain is 'all' of the properties. How many properties does an object have. You need to decide whether you believe in sparse or abundant properties (I vote for very sparse indeed).