March 8th at 17:30, in Science Park 107 F1.15
The idea of this talk is to provide an introduction to some philosophical ideas behind Frege’s Begriffsschrift. We first expound the epistemological considerations which led to the development of Frege’s logic and put forward the claim that the logical laws he proposes have to be understood as normative rules which guide rational inquiry in general. As these rules apply quite differently in different domains of research this leads to a re-description of the Frege’s notorious ‘realms’ in epistemological rather than ontological terms.
This will serve as a background to address the classical textbook problem attributed to Frege: The problem of the (un-)knowability of objects in the mathematical realm. We will proceed by a discussion of his attempts to define number in Foundations of Arithmetic. The main protagonist in this story will be the famous ‘context principle’ as a consequence of which we need not perceive mathematical objects via a mysterious sixth sense, but can access them in the way mathematicians usually do it – by proving theorems containing them. Hence all of us can know things about mathematical objects, not only Gödel.
People with philosophy and math backgrounds are equally welcome. Acquaintance with Frege’s Begriffsschrift is not required. Neither is excessive knowledge of philosophical tech-talk.