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AbstractThis paper aims to show that Frege's and Hilbert's mutual disagreement results from different notions ofAnschauungand their relation to axioms. In the first section of the paper, evidence is provided to support that Frege and Hilbert were influenced by the same developments of 19th-century geometry, in particular the work of Gauss, Plücker, and von Staudt. The second section of the paper shows that Frege and Hilbert take different approaches to deal with the problems that the developments in 19th-century geometry posed for the traditional Kantian philosophy of mathematics. Frege maintains thatAnschauungis a source of knowledge by which we acknowledge geometrical axioms as true. For Hilbert, in contrast, axioms provide one of several correct "pictures" of reality. Hilbert's position is thereby deeply influenced by epistemological ideas from Hertz and Helmholtz, and, in turn, influenced the neo-Kantian Cassirer.

Frege's essays "Function and Concept," "On Sense and Meaning," and "Concept and Object" form a unity in terms of both their origins and their reception history, and have long established themselves as two of the key texts of analytical philosophy. This volume presents and provides commentary on them together. Also conceived of as a course book, this volume provides access to Frege as an eminent, lively classic author