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Ideas for 'works', 'On What There Is' and 'Russell's Mathematical Logic'

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8 ideas

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
We study bound variables not to know reality, but to know what reality language asserts [Quine]
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein]
Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
Names can be converted to descriptions, and Russell showed how to eliminate those [Quine]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]