My MA Thesis in Philosophy, entitled The Frege-Hilbert Controversy on the Foundations of Geometry, was defended in Summer, 2006, under the supervision of Francois Tournier (Professor Emeritus of philosophy at Université Laval).
This memoir presents some axiological debates of philosophy of logic underlying the Frege-Hilbert controversy on the foundations of geometry. Against the philosophical bias according to which logic is an achieved discipline, a contextualized presentation of the respective positions of Frege and Hilbert is done in order to show that incommensurable paradigms are found in their view of logic, that is due to the influence of various philosophical and scientific traditions. From this standpoint, Frege is the defender of the traditionalist view of logic as the universal medium of science, as embodied in Euclidean geometry. In this perspective, Frege’s symbolic logic is seen as the achievement of a refined means to counter the 19th-century perversion of science with the purpose of defending the traditional conception of the role of science. On the other hand, Hilbert’s metatheoretical approach represents the so-called algebraic modern conception of logic as developed in the 19th century under the influence of metamathematics. Following this, parallels between Hilbert’s approach and the model-theoretical and categorical conceptions of logic are drawn to show their proximity.