Dedekind Abstraction: Towards a Logical Reconstruction and Defense

Explore a comprehensive seminar on Dedekind abstraction and its logical reconstruction in this 2-hour 17-minute talk from the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics. Delve into Erich Reck's presentation, which examines various structuralist positions in recent philosophy of mathematics, including eliminative and non-eliminative versions. Investigate Dedekind's unique form of structuralism, both as "methodological structuralism" and as a distinctive "abstractionist" non-eliminative approach. Analyze the concept of Dedekind abstraction as a method for reifying mathematical entities in mathematical practice. Compare this approach to previous attempts, particularly the work of Linnebo & Pettigrew, and discover how Reck's reconstruction aims to overcome limitations and offer additional advantages. Gain insights into the ongoing collaboration between Reck and Linnebo, and broaden your understanding of mathematical philosophy and logic through this in-depth exploration of Dedekind's ideas and their modern interpretations.