### 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,M) [Blackwell 1980,0-631-12911-1]].

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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 [Fitting/Mendelsohn]
###### 5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
 9874 Contradiction arises from Frege's substitutional account of second-order quantification [Dummett]
###### 6. Mathematics / A. Nature of Mathematics / 3. Nature of 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 / 5. Definitions of Number / c. Fregean numbers
 10623 Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Hale/Wright]
 9975 Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait]
###### 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 truth-values, if they fall under the concept [Dummett]
 13665 Frege took the study of concepts to be part of logic [Shapiro]