Combining Texts

All the ideas for 'fragments/reports', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'Reply to Fifth Objections'

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15 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 / a. Substance
Knowing the attributes is enough to reveal a substance [Descartes]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
Our thinking about external things doesn't disprove the existence of innate ideas [Descartes]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
A blind man may still contain the idea of colour [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]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Possible existence is a perfection in the idea of a triangle [Descartes]
Necessary existence is a property which is uniquely part of God's essence [Descartes]