Combining Philosophers

Ideas for Pittacus, Ned Block and David Bostock

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5 ideas

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

18108	First-order logic is not decidable: there is no test of whether any formula is valid [Bostock]
	Full Idea: First-order logic is not decidable. That is, there is no test which can be applied to any arbitrary formula of that logic and which will tell one whether the formula is or is not valid (as proved by Church in 1936).
	From: David Bostock (Philosophy of Mathematics [2009], 5.5)

18109	The completeness of first-order logic implies its compactness [Bostock]
	Full Idea: From the fact that the usual rules for first-level logic are complete (as proved by Gödel 1930), it follows that this logic is 'compact'.
	From: David Bostock (Philosophy of Mathematics [2009], 5.5)
	A reaction: The point is that the completeness requires finite proofs.

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

13346	Truth is the basic notion in classical logic [Bostock]
	Full Idea: The most fundamental notion in classical logic is that of truth.
	From: David Bostock (Intermediate Logic [1997], 1.1)
	A reaction: The opening sentence of his book. Hence the first half of the book is about semantics, and only the second half deals with proof. Compare Idea 10282. The thought seems to be that you could leave out truth, but that makes logic pointless.

13545	Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock]
	Full Idea: In very general terms, we cannot express the distinction between what is finite and what is infinite without moving essentially beyond the resources available in elementary logic.
	From: David Bostock (Intermediate Logic [1997], 4.8)
	A reaction: This observation concludes a discussion of Compactness in logic.

13822	Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock]
	Full Idea: Discourse about fictional characters leads to a breakdown of elementary logic. We accept P or ¬P if the relevant story says so, but P∨¬P will not be true if the relevant story says nothing either way, and P∧¬P is true if the story is inconsistent.
	From: David Bostock (Intermediate Logic [1997], 8.5)
	A reaction: I really like this. Does one need to invent a completely new logic for fictional characters? Or must their logic be intuitionist, or paraconsistent, or both?