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Ideas for 'Defending the Axioms', 'Reason, Truth and History' and 'Science without Numbers'

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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

10260	Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro]
	Full Idea: Field defines logical consequence by taking the notion of 'logical possibility' as primitive. Hence q is a consequence of P if the conjunction of the items in P with the negation of q is not possible.
	From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2
	A reaction: The question would then be whether it is plausible to take logical possibility as primitive. Presumably only intuition could support it. But then intuition will equally support natural and metaphysical possibilities.