Combining Texts

Ideas for 'Mind and Its Place in Nature', 'Which Logic is the Right Logic?' and 'Realism in Mathematics'

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7 ideas

5. Theory of Logic / K. Features of Logics / 3. Soundness

10765

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

5. Theory of Logic / K. Features of Logics / 4. Completeness

10763

Completeness and compactness together give axiomatizability [Tharp]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

10770

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

5. Theory of Logic / K. Features of Logics / 6. Compactness

10771

Compactness is important for major theories which have infinitely many axioms [Tharp]

10772

Compactness blocks infinite expansion, and admits non-standard models [Tharp]

5. Theory of Logic / K. Features of Logics / 8. Enumerability

10764

A complete logic has an effective enumeration of the valid formulas [Tharp]

10768

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