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Ideas of Leslie H. Tharp, by Text

[American, fl. 1975, Taught at MIT.]

1975 Which Logic is the Right Logic?
§0 p.35 In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and'
§1 p.36 Completeness and compactness together give axiomatizability
§2 p.37 Logic is either for demonstration, or for characterizing structures
§2 p.37 Elementary logic is complete, but cannot capture mathematics
§2 p.37 Soundness would seem to be an essential requirement of a proof procedure
§2 p.37 A complete logic has an effective enumeration of the valid formulas
§2 p.38 Effective enumeration might be proved but not specified, so it won't guarantee knowledge
§2 p.38 Compactness blocks infinite expansion, and admits non-standard models
§2 p.38 Compactness is important for major theories which have infinitely many axioms
§2 p.38 Second-order logic isn't provable, but will express set-theory and classic problems
§2 p.38 If completeness fails there is no algorithm to list the valid formulas
§2 p.39 The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals)
§3 p.39 There are at least five unorthodox quantifiers that could be used
§3 p.40 The axiom of choice now seems acceptable and obvious (if it is meaningful)
§5 p.41 The main quantifiers extend 'and' and 'or' to infinite domains
§7 p.43 Skolem mistakenly inferred that Cantor's conceptions were illusory