Combining Texts

Ideas for 'fragments/reports', 'Later Letters to Dedekind' and 'Propositions'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

5 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 / D. Modal Logic ML / 1. Modal Logic
19209 Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks]
     Full Idea: Logical consequence guarantees preservation of truth. The Converse Barcan, a theorem of Simple Quantified Modal Logic, says that an obvious truth implies an obvious falsehood. So SQML gets logical consequence wrong. So SQML is mistaken.
     From: Trenton Merricks (Propositions [2015], 2.V)
     A reaction: I admire this. The Converse Barcan certainly strikes me as wrong (Idea 19208). Merricks grasps this nettle. Williamson grasps the other nettle. Most people duck the issue, I suspect. Merricks says later that domains are the problem.
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
19208 The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks]
     Full Idea: The Converse Barcan Formula has a startling result. Simple Quantified Modal Logic (SQML) has the following as a theorem: □∀xFx → ∀x□Fx. So 'everything exists necessarily' is a consequence of 'necessarily, everything exists'.
     From: Trenton Merricks (Propositions [2015], 2.V)
     A reaction: He says this is blatantly wrong. Williamson is famous for defending it. I think I'm with Merricks on this one.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17831 Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake]
     Full Idea: Cantor gives informal versions of the axioms of ZF as ways of getting from one set to another.
     From: report of George Cantor (Later Letters to Dedekind [1899]) by John Lake - Approaches to Set Theory 1.6
     A reaction: Lake suggests that it should therefore be called CZF.