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Ideas for 'fragments/reports', 'Presidential Address of Am. Math. Soc' and 'Intermediate Logic'

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4 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

10247	We have no adequate logic at the moment, so mathematicians must create one [Veblen]
	Full Idea: Formal logic has to be taken over by mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so.
	From: Oswald Veblen (Presidential Address of Am. Math. Soc [1924], 141), quoted by Stewart Shapiro - Philosophy of Mathematics
	A reaction: This remark was made well after Frege, but before the advent of Gödel and Tarski. That implies that he was really thinking of meta-logic.

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?