display all the ideas for this combination of philosophers
2 ideas
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. |
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? |