Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Stephen Read and D.H. Mellor

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5 ideas

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 / 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.