Combining Texts

Ideas for 'fragments/reports', 'On the Moral and Legal State of Abortion' and 'Naturalism in Mathematics'

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7 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 / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
18194 'Forcing' can produce new models of ZFC from old models [Maddy]
     Full Idea: Cohen's method of 'forcing' produces a new model of ZFC from an old model by appending a carefully chosen 'generic' set.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.4)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
18195 A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
     Full Idea: A possible axiom is the Large Cardinal Axiom, which asserts that there are more and more stages in the cumulative hierarchy. Infinity can be seen as the first of these stages, and Replacement pushes further in this direction.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.5)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
18191 Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
     Full Idea: The axiom of infinity: that there are infinite sets is to claim that completed infinite collections can be treated mathematically. In its standard contemporary form, the axioms assert the existence of the set of all finite ordinals.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
18193 The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
     Full Idea: In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
18169 Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
     Full Idea: The Axiom of Reducibility states that every propositional function is extensionally equivalent to some predicative proposition function.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)