Combining Texts

All the ideas for 'Space and Time', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'Letters to Frege'

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14 ideas

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell]
Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
18. Thought / C. Content / 6. Broad Content
We don't assert private thoughts; the objects are part of what we assert [Russell]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
27. Natural Reality / C. Space / 6. Space-Time
Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski]