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]].


Frege considered definite descriptions to be genuine singular terms [Fitting/Mendelsohn]
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
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 / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait]
My Basic Law V is a law of pure logic
A concept is a function mapping objects onto truth-values, if they fall under the concept [Dummett]
Frege took the study of concepts to be part of logic [Shapiro]