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Ideas for 'On What Grounds What', 'The Metaphysics of Modality' and 'The Tarskian Turn'

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2 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and

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)

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

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.