tag:blogger.com,1999:blog-23478689.post1961410290995345657..comments2008-07-30T07:09:12.106ZComments on Logic Matters: Parsons's Mathematical Thought: Sec 13, Nominalism...Peter Smithhttp://www.blogger.com/profile/03957579588136008664noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-23478689.post-53493384671007907542008-07-30T07:09:00.000Z2008-07-30T07:09:00.000ZWhat happens to your logic when you enter the stat...What happens to your logic when you enter the state of deep dreamless (formless) sleep?<BR/><BR/>Such a state being the very essence of what or who you are, before you identify with the body-mind and all of its automaticities and its never-ending thinkety-think thinking. with its yes-no-maybe "possibilities".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-23478689.post-54277745813284993642008-07-23T08:22:00.000Z2008-07-23T08:22:00.000ZPS. You say "but then the supposed ontological ga...PS. You say "but then the supposed ontological gain of interpreting the second-order quantifiers via plurals is lost"<BR/><BR/>Shouldn't 'gain' be 'lost' :-)Ochamhttp://www.blogger.com/profile/07583379503310147119noreply@blogger.comtag:blogger.com,1999:blog-23478689.post-38067686298784416002008-07-23T08:17:00.000Z2008-07-23T08:17:00.000ZInteresting, and ties in with your previous questi...Interesting, and ties in with your previous question about whether we simply have to agree 'which sentences [containing a grammatically singular term] are true', or whether we need to decide whether an object corresponds to the singular term or not. I suggest the latter. Consider 'there are only a dozen things'. Does the grammatically singular 'a dozen' denote a thing? We can't decide this from the structure of the sentence alone. We have to agree that the sentence is logically equivalent to 'there are only twelve things', from which it immediately follows that 'a dozen' is not logically singular, even though grammatically singular. (Argument: clearly the dozen, if singular, is not identical with any of the twelve things, therefore if it is singular it must be a thirteenth thing, therefore 'there are only twelve things' is false, therefore 'a dozen' is not logically singular). But note this nominalist argument does not involve examining objects. Rather, it involves translating some true sentence p into a sentence p* which does not have the existential commitment that p apparently has, proving that the existential commitment is in fact apparent, not real.<BR/><BR/>The question is whether words like 'way' or 'combination' are like 'dozen' or not. E.g. we agree there are six possible ways of combining three objects a, b and c. Does the term 'the combination a and b' or ''the combination a and c' refer to some singular object different from a b or c? Or is it like 'a dozen'?Ochamhttp://www.blogger.com/profile/07583379503310147119noreply@blogger.com