Combining Texts

All the ideas for 'works', 'The Logic of Infinity' and 'Mathematical Logic (revised)'

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4 ideas

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

12221	'Corner quotes' (quasi-quotation) designate 'whatever these terms designate' [Quine]
	Full Idea: A 'quasi-quotation' [corner quotes, Quine quotes] designates that (unspecified) expression which is obtained from the contents of the corners by replacing the Greek letters by the (unspecified) expressions which they designate.
	From: Willard Quine (Mathematical Logic (revised) [1940], 1.6)
	A reaction: Filed under 'variables', as they seem to be variables that can refer to actual expressions, like algebra. Quine was determined to distinguish clearly between 'mention' and 'use'. 'Half-hearted substitutional quantification', says Fine.

5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated

19321	We might do without names, by converting them into predicates [Quine, by Kirkham]
	Full Idea: Quine suggests that we can have a language with just predicates and no names. Thus for 'Ralph is red' we say 'x Ralphises and x is red'.
	From: report of Willard Quine (Mathematical Logic (revised) [1940]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.6
	A reaction: Kirkham discusses this as a way of getting round the lack of names in Tarski's theory of truth (which just uses objects, predicates and quantifiers). Otherwise you must supplement Tarski with an account of what the names refer to.

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

13007	Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
	Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
	From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
	A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism

18203	Avoid non-predicative classifications and definitions [Poincaré]
	Full Idea: Never consider any objects but those capable of being defined in a finite number of word ...Avoid non-predicative classifications and definitions.
	From: Henri Poincaré (The Logic of Infinity [1909], p.63), quoted by Penelope Maddy - Naturalism in Mathematics II.4