id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_a3q3uy2ibjaaniqbnaq2rhwc3e	Mark Burke	Frege, Hilbert, and Structuralism	2015	239	.pdf	application/pdf	129153	7682	61	fixing the references of mathematical terms in his unique ontology of functions and objects. Frege's somewhat more traditional view of mathematical truth, that ―If the arbitrarily postulated axioms [of With Hilbert's work on the foundations of geometry, a new conception of mathematics as the views of geometry and axiomatics, then turn to an analysis of Frege's criticisms of Hilbert. axiomatic system, on Hilbert's view, we cannot speak of the truth of mathematical axioms Hilbert's interest here is in the structure determined by the axioms of Euclidean geometry, Frege himself viewed axioms as unprovable truths, and definitions as a kind of logical entities of the appropriate type(s); Frege viewed (first-level) concepts as functions which take objects as that thoughts do not possess non-logical structure; simply that, in his work, Frege is only There are several ways to define the natural numbers in terms of many general algebraic structures, not just set mathematical objects like Frege's Caesar problem.	./cache/work_a3q3uy2ibjaaniqbnaq2rhwc3e.pdf	./txt/work_a3q3uy2ibjaaniqbnaq2rhwc3e.txt