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Ideas for 'Clitophon', 'Truth-makers' and 'Philosophies of Mathematics'

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2 ideas

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

10129	A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman]
	Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true.
	From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7)
	A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true.

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms

10105	Differences between isomorphic structures seem unimportant [George/Velleman]
	Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant.
	From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
	A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters?