Combining Texts

Ideas for 'works', 'The Unimportance of Identity' and 'Foundations without Foundationalism'

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5 ideas

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

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'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro]

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

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We can live well without completeness in logic [Shapiro]

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

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Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro]

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Compactness is derived from soundness and completeness [Shapiro]

5. Theory of Logic / K. Features of Logics / 9. Expressibility

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A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro]