Combining Texts

All the ideas for 'Wiener Logik', 'On Second-Order Logic' and 'The Theory of Relativity and A Priori Knowledge'

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11 ideas

2. Reason / D. Definition / 2. Aims of Definition
18261 A simplification which is complete constitutes a definition [Kant]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
22275 Logic gives us the necessary rules which show us how we ought to think [Kant]
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]
12. Knowledge Sources / B. Perception / 5. Interpretation
18278 Kant showed that our perceptions are partly constructed from our concepts [Reichenbach]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
18260 If we knew what we know, we would be astonished [Kant]