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Ideas for 'teaching', 'Logic in Mathematics' and 'Lecture on Nominalism'

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2 ideas

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic

21698	All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
	Full Idea: Much of the theory of relations can be developed as a virtual theory, in which we seem to talk of relations, but can explain our notation in terms {finally] of just the logic of truth-functions, quantification and identity. The exception is ancestrals.
	From: Willard Quine (Lecture on Nominalism [1946], §8)
	A reaction: The irreducibility of ancestrals is offered as a reason for treating sets as universals.

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

16865	'Theorems' are both proved, and used in proofs [Frege]
	Full Idea: Usually a truth is only called a 'theorem' when it has not merely been obtained by inference, but is used in turn as a premise for a number of inferences in the science. ….Proofs use non-theorems, which only occur in that proof.
	From: Gottlob Frege (Logic in Mathematics [1914], p.204)