Combining Texts

All the ideas for 'Aristotle and Descartes on Matter', 'Philosophy and Scientific Image of Man' and 'On Second-Order Logic'

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10 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
21829 Philosophy aims to understand how things (broadly understood) hang together (broadly understood) [Sellars]
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]
7. Existence / C. Structure of Existence / 2. Reduction
6550 Reduction requires that an object's properties consist of its constituents' properties and relations [Sellars]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
19399 Prime matter is nothing when it is at rest [Leibniz]