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Ideas for 'works', 'Goodbye Descartes' and 'Metaphysics: the logical approach'

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6 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
8081 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin]
     Full Idea: Most people find it hard to find any conclusion that fits the following premises: 'No councillors are bankers', and 'All bankers are athletes'. There is a valid conclusion ('Some athletes are not councillors') but it takes quite an effort to find it.
     From: Keith Devlin (Goodbye Descartes [1997], Ch. 2)
     A reaction: A nice illustration of the fact that syllogistic logic is by no means automatic and straightforward. There is a mechanical procedure, but a lot of intuition and common sense is also needed.
4. Formal Logic / B. Propositional Logic PL / 1. Propositional 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
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.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
3326 Set theory attempts to reduce the 'is' of predication to mathematics [Benardete,JA]
     Full Idea: Set theory offers the promise of a complete mathematization of the 'is' of predication.
     From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.13)
3327 The set of Greeks is included in the set of men, but isn't a member of it [Benardete,JA]
     Full Idea: Set inclusion is sharply distinguished from set membership (as the set of Greeks is found to be included in, but not a member of, the set of men).
     From: José A. Benardete (Metaphysics: the logical approach [1989], Ch.13)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3335 The standard Z-F Intuition version of set theory has about ten agreed axioms [Benardete,JA, by PG]
     Full Idea: Zermelo proposed seven axioms for set theory, with Fraenkel adding others, to produce the standard Z-F Intuition.
     From: report of José A. Benardete (Metaphysics: the logical approach [1989], Ch.17) by PG - Db (ideas)