2026-09-25T04:05:26Zhttps://api.repository.cam.ac.uk/server/oai/request

oai:www.repository.cam.ac.uk:1810/2774382024-06-26T13:53:47Zcom_1810_273com_1810_256061col_1810_221775

The Common Foundation of Neo-Logicism and the Frege-Hilbert Controversy 10.17863/CAM.24749 Doherty, Fiona Teresa Potter, Michael In the first half of the thesis I investigate David Hilbert's early ontology of mathematics around the period 1899-1916. Hilbert's early views are of significant philosophical interest and have been largely ignored due to his later, more influential work. I suggest that, in this period Hilbert, can be understood as an early structuralist. In the second half of the thesis, I connect two important debates in the foundations of mathematics: Hale and Wright's neo-Fregean logicism and the Frege-Hilbert controversy. Using this connection, I adapt Frege's objections to Hilbert and apply them to Hale and Wright's account. By doing this, I show that the neo-Fregean logicists have long abandoned the Fregean element of their program in favor of a structuralist ontology. I conclude that our ontological conception of what exists in mathematics and what it is like constrains the foundations we use to characterise mathematical reality. University of Cambridge 2017-03-08 Thesis Doctoral Doctor of Philosophy (PhD) en AHRC full scholarship. https://www.repository.cam.ac.uk/handle/1810/277438 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/86a546bb-6523-4e22-816c-100ce7090af9/download 87eda9de84448d1f82354d60eee3eb5f https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/3f56b94a-5d91-4eaf-8651-6f26ca820e1b/download 17190293a31b7295645db73b11f8abf6 https://www.rioxx.net/licenses/all-rights-reserved/ Metaphysics of mathematics Neo-Logicism The Frege-Hilbert Controversy