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Ideas for 'fragments/reports', 'Remarks on the definition and nature of mathematics' and 'Properties'

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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 / 1. Logical Form

10407	Logical Form explains differing logical behaviour of similar sentences [Swoyer]
	Full Idea: 'Logical Form' is a technical notion motivated by the observation that sentences with a similar surface structure may exhibit quite different logical behaviour.
	From: Chris Swoyer (Properties [2000], 4.2)
	A reaction: [Swoyer goes on to give some nice examples] The tricky question is whether each sentence has ONE logical form. Pragmatics warns us of the dangers. One needs to check numerous inferences from a given sentences, not just one.

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

17807	To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
	Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
	A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.