display all the ideas for this combination of texts
2 ideas
12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
Full Idea: The typical semantic account of validity for propositional connectives like 'and' presupposes that meaning is given by truth-tables. On the natural deduction view, the meaning of 'and' is given by its introduction and elimination rules. | |
From: Graeme Forbes (The Metaphysics of Modality [1985], 4.4) |
15328 | A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten] |
Full Idea: A theory is 'non-conservative' if it allows us to prove mathematical facts that go beyond what the background mathematical theory can prove on its own. | |
From: Leon Horsten (The Tarskian Turn [2011], 01.4) | |
A reaction: This is an instance of the relationship with mathematics being used as the test case for explorations of logic. It is a standard research method, because it is so precise, but should not be mistaken for the last word about a theory. |