Combining Texts

All the ideas for 'Comments on a Certain Broadsheet', 'Substance' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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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]
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]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
A substance is, roughly, a basic being or subject at the foundation of reality [Robb]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
If an object survives the loss of a part, complex objects can have autonomy over their parts [Robb]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
What experience could prove 'If a=c and b=c then a=b'? [Descartes]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
The mind's innate ideas are part of its capacity for thought [Descartes]
Qualia must be innate, because physical motions do not contain them [Descartes]
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]