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 1980,0631129111]].
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
13733

Frege considered definite descriptions to be genuine singular terms

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9874

Contradiction arises from Frege's substitutional account of secondorder quantification

6. Mathematics / A. Nature of Mathematics / 3. Numbers / g. Real numbers
18252

Real numbers are ratios of quantities, such as lengths or masses

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
18271

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
10623

Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions

9975

Frege ignored Cantor's warning that a cardinal set is not just a conceptextension

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18165

My Basic Law V is a law of pure logic

18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9190

A concept is a function mapping objects onto truthvalues, if they fall under the concept

13665

Frege took the study of concepts to be part of logic
