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Ideas for 'fragments/reports', 'Go Figure: a Path through Fictionalism' and 'Thinking About Logic'

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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 / c. Derivation rules of PL
10987 Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read]
     Full Idea: Three traditional names for rules are 'Simplification' (P from 'P and Q'), 'Addition' ('P or Q' from P), and 'Disjunctive Syllogism' (Q from 'P or Q' and 'not-P').
     From: Stephen Read (Thinking About Logic [1995], Ch.2)
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 / 3. Modal Logic Systems / a. Systems of modal logic
11004 Necessity is provability in S4, and true in all worlds in S5 [Read]
     Full Idea: In S4 necessity is said to be informal 'provability', and in S5 it is said to be 'true in every possible world'.
     From: Stephen Read (Thinking About Logic [1995], Ch.4)
     A reaction: It seems that the S4 version is proof-theoretic, and the S5 version is semantic.
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
11018 There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read]
     Full Idea: In fuzzy logic, besides fuzzy predicates, which define fuzzy sets, there are also fuzzy quantifiers (such as 'most' and 'few') and fuzzy modifiers (such as 'usually').
     From: Stephen Read (Thinking About Logic [1995], Ch.7)
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
11011 Same say there are positive, negative and neuter free logics [Read]
     Full Idea: It is normal to classify free logics into three sorts; positive free logics (some propositions with empty terms are true), negative free logics (they are false), and neuter free logics (they lack truth-value), though I find this unhelpful and superficial.
     From: Stephen Read (Thinking About Logic [1995], Ch.5)
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
11020 Realisms like the full Comprehension Principle, that all good concepts determine sets [Read]
     Full Idea: Hard-headed realism tends to embrace the full Comprehension Principle, that every well-defined concept determines a set.
     From: Stephen Read (Thinking About Logic [1995], Ch.8)
     A reaction: This sort of thing gets you into trouble with Russell's paradox (though that is presumably meant to be excluded somehow by 'well-defined'). There are lots of diluted Comprehension Principles.