Combining Texts

Ideas for 'fragments/reports', 'Interview with Baggini and Stangroom' and 'Meditations'

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3 ideas

5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
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 / C. Ontology of Logic / 3. If-Thenism
Arithmetic and geometry achieve some certainty without worrying about existence [Descartes]
     Full Idea: Arithmetic, geometry and sciences of that kind only treat of things without taking any great trouble to ascertain whether they are actually existent or not, and contain some measure of certainty.
     From: René Descartes (Meditations [1641], §1), quoted by Alan Musgrave - Logicism Revisited §4
     A reaction: This is Musgrave's earliest quotation which seems to take the if-thenist view.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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.