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Ideas for 'fragments/reports', 'Metaphysics: an introduction' and 'On the Syllogism IV'

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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 / 6. Relations in Logic
17744 De Morgan started the study of relations and their properties [De Morgan, by Walicki]
     Full Idea: De Morgan started the sustained interest in the study of relations and their properties.
     From: report of Augustus De Morgan (On the Syllogism IV [1859]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1
13501 De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD]
     Full Idea: There was a prejudice against relations (in favour of properties) but De Morgan and others that impeccable inferences turn on relations and elude Aristotle's syllogistic. Thus: All horses are animals. Hence, all heads of horses are heads of animals.
     From: report of Augustus De Morgan (On the Syllogism IV [1859]) by William D. Hart - The Evolution of Logic 4
     A reaction: This is actually an early example of modern analytic philosophy in action. You start with the inferences, and then work back to the ontology and the definition of concepts. But in pinning down such concepts, do we miss their full meaning?