Ideas from 'Grundgesetze der Arithmetik 1 (Basic Laws)' by Gottlob Frege [1893], by Theme Structure

[found in 'Translations from the Writings of Gottlob Frege' by Frege,Gottlob (ed/tr Geach,P. /Black,Max) [Blackwell 1980,0-631-12911-1]].

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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification
6. Mathematics / A. Nature of Mathematics / 3. Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses
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
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic
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 took the study of concepts to be part of logic