The Common Foundation of Neo-Logicism and the Frege-Hilbert Controversy
type: CreativeWork
description: 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.
abstract: 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.
author: Doherty, Fiona Teresa
language: en
keywords: Metaphysics of mathematics, Neo-Logicism, The Frege-Hilbert Controversy
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/86a546bb-6523-4e22-816c-100ce7090af9/download
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2017-03-08
date modified: 2026-07-22T22:24:14Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.24749