tag:blogger.com,1999:blog-3891434218564545511.post3758371090779439232..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: ArithmeticAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3891434218564545511.post-69592397140981039112008-12-30T04:04:00.000-06:002008-12-30T04:04:00.000-06:00FWIW I agree with both of you. Neo-logicism was al...FWIW I agree with both of you. Neo-logicism was all the rage in Scotland, when I was there recently, and my reaction to it was as in your post.<BR/><BR/>Hume's principle is analytic insofar as it's conditional - if there were N things and another M things, and those two classes corresponded one-to-one, then N = M - but to use that to build up the numbers from nothing you need to get rid of the conditionality, which seems to me to get rid of the analyticity.<BR/><BR/>Arithmetic seems to be about the structural possibilities inherent in the concept of an individual. The connection with logic is pretty deep because such a concept is also presupposed by classical logic. Perhaps that's how the neo-logicists get away with playing games with equivocations. If only more philosophers were as perceptive as you two, is what I think.Martin Cookehttps://www.blogger.com/profile/11425491938517935179noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-29542414780272375952008-12-29T10:17:00.000-06:002008-12-29T10:17:00.000-06:00I am inclined to agree.I am inclined to agree.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-40551695440089558302008-12-29T09:18:00.000-06:002008-12-29T09:18:00.000-06:00FWIW, I think philosophy of mathematics ought to b...FWIW, I think philosophy of mathematics ought to begin from the observation that in ordinary language, the numbers are quantifiers ("two oranges") but in arithmetic-speak, they are singular terms ("two plus two"). This indicates to me that arithmetic is a kind of second-order language for representing patterns in the first-order language. There are probably other ways to go, too, but the linguistic observation is important.Heath Whitehttps://www.blogger.com/profile/13535886546816778688noreply@blogger.com