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Ideas for 'works', '09: Galatians' and 'The Foundations of Mathematics'

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3 ideas

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 / E. Structures of Logic / 1. Logical Form

4730	For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
	Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality.
	From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4
	A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional.

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.