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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

10762

In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and'

§1

p.36

10763

Completeness and compactness together give axiomatizability

§2

p.37

10764

A complete logic has an effective enumeration of the valid formulas

§2

p.37

10765

Soundness would seem to be an essential requirement of a proof procedure

§2

p.37

10766

Logic is either for demonstration, or for characterizing structures

§2

p.37

10767

Elementary logic is complete, but cannot capture mathematics

§2

p.38

10769

Secondorder logic isn't provable, but will express settheory and classic problems

§2

p.38

10768

Effective enumeration might be proved but not specified, so it won't guarantee knowledge

§2

p.38

10770

If completeness fails there is no algorithm to list the valid formulas

§2

p.38

10771

Compactness is important for major theories which have infinitely many axioms

§2

p.38

10772

Compactness blocks infinite expansion, and admits nonstandard models

§2

p.39

10773

The LöwenheimSkolem property is a limitation (e.g. can't say there are uncountably many reals)

§3

p.39

10774

There are at least five unorthodox quantifiers that could be used

§3

p.40

10775

The axiom of choice now seems acceptable and obvious (if it is meaningful)

§5

p.41

10776

The main quantifiers extend 'and' and 'or' to infinite domains

§7

p.43

10777

Skolem mistakenly inferred that Cantor's conceptions were illusory
