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Title: The common foundation of neo-logicism and the Frege-Hilbert controversy
Author: Doherty, Fiona Teresa
ISNI:       0000 0004 7226 0215
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2017
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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.
Supervisor: Potter, Michael Sponsor: AHRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: Metaphysics of mathematics ; Neo-Logicism ; The Frege-Hilbert Controversy