Combining Texts

Ideas for 'fragments/reports', 'Goodbye Descartes' and 'A Defense of Presentism'

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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).

8085	Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin]
	Full Idea: Where Aristotle had 19 different inference rules (his valid syllogisms), modern propositional logic carries out deductions using just one rule of inference: modus ponens.
	From: Keith Devlin (Goodbye Descartes [1997], Ch. 4)
	A reaction: At first glance it sounds as if Aristotle's guidelines might be more useful than the modern one, since he tells you something definite and what implies what, where modus ponens just seems to define the word 'implies'.

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.

8086	Predicate logic retains the axioms of propositional logic [Devlin]
	Full Idea: Since predicate logic merely extends propositional logic, all the axioms of propositional logic are axioms of predicate logic.
	From: Keith Devlin (Goodbye Descartes [1997], Ch. 4)
	A reaction: See Idea 7798 for the axioms.