Combining Texts

All the ideas for 'Lectures on the History of Philosophy', 'Chapters on Scepticism' and 'On Second-Order Logic'

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9 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
21757 Philosophy is the conceptual essence of the shape of history [Hegel]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
1799 If we can't know minds, we can't know if Pyrrho was a sceptic [Theodosius, by Diog. Laertius]