@article{Fernández de Castro_2018, title={The controversy between Frege and Hilbert}, volume={57}, url={https://revistas.ucr.ac.cr/index.php/filosofia/article/view/35084}, abstractNote={<p>In this paper, I shall focus my attention on two subjects of the debate between Frege and Hilbert held around 1900 concerning the foundations of geometry: a) the difference between axioms and definitions, b) the proofs of independence of axioms. Concerning the first point, I will hold that Hilbert and Frege had different conceptions of ‘concept’ and that Hilbert’s position is problematic. Later, I shall explore Patricia Blanchette’s interpretation that Frege’s objections to Hilbert’s proofs of consistency and independence arise from his different notions of logical consequence. I will suggest that this interpretation is not correct, even if it fits well with most of the textual evidence, because it gives rise to certain puzzling consequences.</p>}, number={147}, journal={Revista de Filosofía de la Universidad de Costa Rica}, author={Fernández de Castro, Max}, year={2018}, month={oct.}, pages={113–128} }