Combining Philosophers

Ideas for Roderick Firth, Robert Owen and Stephen Read

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5 ideas

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

14187	If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read]
	Full Idea: The topic-neutrality of logic need not mean there is a pure subject matter for logic; rather, that the logician may need to go everywhere, into mathematics and even into metaphysics.
	From: Stephen Read (Formal and Material Consequence [1994], 'Logic')

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

10986	Not all validity is captured in first-order logic [Read]
	Full Idea: We must recognise that first-order classical logic is inadequate to describe all valid consequences, that is, all cases in which it is impossible for the premisses to be true and the conclusion false.
	From: Stephen Read (Thinking About Logic [1995], Ch.2)
	A reaction: This is despite the fact that first-order logic is 'complete', in the sense that its own truths are all provable.

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

10972	The non-emptiness of the domain is characteristic of classical logic [Read]
	Full Idea: The non-emptiness of the domain is characteristic of classical logic.
	From: Stephen Read (Thinking About Logic [1995], Ch.2)

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

11024	Semantics must precede proof in higher-order logics, since they are incomplete [Read]
	Full Idea: For the realist, study of semantic structures comes before study of proofs. In higher-order logic is has to, for the logics are incomplete.
	From: Stephen Read (Thinking About Logic [1995], Ch.9)
	A reaction: This seems to be an important general observation about any incomplete system, such as Peano arithmetic. You may dream the old rationalist dream of starting from the beginning and proving everything, but you can't. Start with truth and meaning.

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics

10985	We should exclude second-order logic, precisely because it captures arithmetic [Read]
	Full Idea: Those who believe mathematics goes beyond logic use that fact to argue that classical logic is right to exclude second-order logic.
	From: Stephen Read (Thinking About Logic [1995], Ch.2)