Revista de Filosofía de la Universidad de Costa Rica ISSN Impreso: 0034-8252 ISSN electrónico: 2215-5589

The controversy between Frege and Hilbert
Plutón y Proserpina

Palabras clave

Proof of independence and consistency
Logical consequence

Cómo citar

Fernández de Castro, M. (2018). The controversy between Frege and Hilbert. Revista De Filosofía De La Universidad De Costa Rica, 57(147), 113–128. Recuperado a partir de


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.




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