Gratitude extended to Dan Isaacson for compiling the following:

Essay Questions

Expound Mill's account of mathematics and logic, and assess Frege's criticisms of Mill.


Frege declares that never losing sight of the distinction between concept and object is one of three fundamental principles he kept to in the Foundations (Introduction, p. X ). Expound Frege's distinction between concept and object and assess its importance for his Foundations of Arithmetic.


Expound Frege's definition of natural number, and consider whether, on the basis of such a definition, we can know that the numbers exist.


Assess Frege's claim that, "arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one" (Foundations of Arithmetic, §87, p. 99). Include some account of Frege's development of logic in Begriffsschrift, and his definition in Part III of Begriffsschrift of "y follows in the φ-series after x", and his adoption of Basic Law V in Grundgesetze and its inconsistency.


Contact details

Department of Philosophy
Main Quadrangle A14
University of Sydney
NSW 2006

email: sebastian.sequoiah.grayson {at}