Combining Texts

Ideas for 'fragments/reports', 'Modality' and 'From Metaphysics to Ethics'

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4 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic

8077	Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin]
	Full Idea: In Stoic logic propositions are treated the way atoms are treated in present-day chemistry, where the focus is on the way atoms fit together to form molecules, rather than on the internal structure of the atoms.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
	A reaction: A nice analogy to explain the nature of Propositional Logic, which was invented by the Stoics (N.B. after Aristotle had invented predicate logic).

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

20791	Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius]
	Full Idea: Chrysippus has five indemonstrables that do not need demonstration:1) If 1st the 2nd, but 1st, so 2nd; 2) If 1st the 2nd, but not 2nd, so not 1st; 3) Not 1st and 2nd, the 1st, so not 2nd; 4) 1st or 2nd, the 1st, so not 2nd; 5) 1st or 2nd, not 2nd, so 1st.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.80-81
	A reaction: [from his lost text 'Dialectics'; squashed to fit into one quote] 1) is Modus Ponens, 2) is Modus Tollens. 4) and 5) are Disjunctive Syllogisms. 3) seems a bit complex to be an indemonstrable.

4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC

5737	Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets [Melia]
	Full Idea: First-order predicate language has four connectives, two quantifiers, variables, predicates, equality, names, and brackets.
	From: Joseph Melia (Modality [2003], Ch.2)
	A reaction: Look up the reference for the details! The spirit of logic is seen in this basic framework, and the main interest is in the ontological commitment of the items on the list. The list is either known a priori, or it is merely conventional.

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic

5744	First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia]
	Full Idea: First-order predicate calculus is an extensional logic, while quantified modal logic is intensional (which has grave problems of interpretation, according to Quine).
	From: Joseph Melia (Modality [2003], Ch.3)
	A reaction: The battle is over ontology. Quine wants the ontology to stick with the values of the variables (i.e. the items in the real world that are quantified over in the extension). The rival view arises from attempts to explain necessity and counterfactuals.