Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'There is No A Priori (and reply)' and 'Foundations without Foundationalism'
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6 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]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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We can live well without completeness in logic [Shapiro]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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We have no argument to show a statement is absolutely undecidable [Koellner]
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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]
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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]
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