The Common Foundation of Neo-Logicism and the Frege-Hilbert Controversy

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.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2017

Author dc:creator

• Doherty, Fiona Teresa

Advisor dc:contributor.advisor

• Potter, Michael

• Metaphysics of mathematics
• Neo-Logicism
• The Frege-Hilbert Controversy

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/86a546bb-6523-4e22-816c-100ce7090af9/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

en

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.24749

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/277438