Combining Texts

Ideas for 'fragments/reports', 'Interview with Baggini and Stangroom' and 'Guidebook to Wittgenstein's Tractatus'

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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 / 1. Bivalence
23484 Bipolarity adds to Bivalence the capacity for both truth values [Morris,M]
     Full Idea: According to the Principle of Bipolarity, every meaningful sentence must be capable both of being true and of being false. It is not enough merely that every sentence must be either true or false (which is Bivalence).
     From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 3D)
     A reaction: It is said that early Wittgenstein endorses this. That is, in addition to being true, the sentence must be capable of falsehood (and vice versa). This seems to be flirting with the verification principle. I presume it is 'affirmative' sentences.
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 / G. Quantification / 1. Quantification
23494 Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite [Morris,M]
     Full Idea: There are two problems with defining the quantifiers in terms of conjunction and disjunction. The general statements are unspecific, and do not say which things have the properties, and also they can't range over infinite objects.
     From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 5C)
     A reaction: That is, the universal quantifier is lots of ands, and the existential is lots of ors. If there only existed finite objects, then naming them all would be universal, and the infinite wouldn't be needed.