Combining Texts

Ideas for 'fragments/reports', 'Theories of Truth: a Critical Introduction' and '18: Book of Job'

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4 ideas

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
19315 In quantified language the components of complex sentences may not be sentences [Kirkham]
     Full Idea: In a quantified language it is possible to build new sentences by combining two expressions neither of which is itself a sentence.
     From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4)
     A reaction: In propositional logic the components are other sentences, so the truth value can be given by their separate truth-values, through truth tables. Kirkham is explaining the task which Tarski faced. Truth-values are not just compositional.
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 / I. Semantics of Logic / 4. Satisfaction
19317 An open sentence is satisfied if the object possess that property [Kirkham]
     Full Idea: An object satisfies an open sentence if and only if it possesses the property expressed by the predicate of the open sentence.
     From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4)
     A reaction: This applies to atomic sentence, of the form Fx or Fa (that is, some variable is F, or some object is F). So strictly, only the world can decide whether some open sentence is satisfied. And it all depends on things called 'properties'.