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Ideas for 'fragments/reports', 'Mathematical Logic (revised)' and 'Lecture on Applicability of Mathematics'

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4 ideas

5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens

8078	Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
	Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
	A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true.

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

6023	Every proposition is either true or false [Chrysippus, by Cicero]
	Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38
	A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc.

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.