Combining Philosophers

Ideas for Oswald Veblen, Frank P. Ramsey and Friedrich Schelling

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3 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 / D. Assumptions for Logic / 4. Identity in Logic

13427	Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
	Full Idea: In 'a = b' either 'a' and 'b' are names of the same thing, in which case the proposition says nothing, or of different things, in which case it is absurd. In neither case is it an assertion of a fact; it only asserts when a or b are descriptions.
	From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1)
	A reaction: This is essentially Frege's problem with Hesperus and Phosphorus. How can identities be informative? So 2+2=4 is extensionally vacuous, but informative because they are different descriptions.

5. Theory of Logic / L. Paradox / 1. Paradox

13334	Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
	Full Idea: Group A consists of contradictions which would occur in a logical or mathematical system, involving terms such as class or number. Group B contradictions are not purely logical, and contain some reference to thought, language or symbolism.
	From: Frank P. Ramsey (The Foundations of Mathematics [1925], p.171), quoted by Graham Priest - The Structure of Paradoxes of Self-Reference 1
	A reaction: This has become the orthodox division of all paradoxes, but the division is challenged by Priest (Idea 13373). He suggests that we now realise (post-Tarski?) that language is more involved in logic and mathematics than we thought.