id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
en-wikipedia-org-893		Hume's principle - Wikipedia			.html	text/html	1001	123	65	This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Hume's principle or HP—the terms were coined by George Boolos—says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence (a bijection) between the Fs and the Gs. HP can be stated formally in systems of second-order logic. Hume's principle appears in Frege's Foundations of Arithmetic (§73), which quotes from Part III of Book I of David Hume's A Treatise of Human Nature (1740). Concerning one of these, proportion in quantity or number, Hume argues that our reasoning about proportion in quantity, as represented by geometry, can never achieve "perfect precision and exactness", since its principles are derived from sense-appearance. The principle that cardinal number was to be characterized in terms of one-to-one correspondence had previously been used to great effect by Georg Cantor, whose writings Frege knew.	./cache/en-wikipedia-org-893.html	./txt/en-wikipedia-org-893.txt