display all the ideas for this combination of philosophers
3 ideas
| 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. |
| 10819 | Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H] |
| Full Idea: Model theory must choose the denotations of the primitives so that all of a group of sentences come out true, so we need a theory of how the truth value of a sentence depends on the denotation of its primitive nonlogical parts, which Tarski gives us. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §1) |
| 10827 | Model theory is unusual in restricting the range of the quantifiers [Field,H] |
| Full Idea: In model theory we are interested in allowing a slightly unusual semantics for quantifiers: we are willing to allow that the quantifier not range over everything. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], n 5) |