tag:blogger.com,1999:blog-6432111.post7566135808412887120..comments2023-10-24T09:18:35.229+01:00Comments on Theories 'n Things: Eliminating singular quantificationRobbie Williamshttp://www.blogger.com/profile/02081389310232077607noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6432111.post-58982926668627198952007-02-26T09:24:00.000+00:002007-02-26T09:24:00.000+00:00I was going to mention this but didn't fit neatly ...I was going to mention this but didn't fit neatly into a single comment. Of course, non-distributive predicates seem to be a problem. But they are not. 'John carried the piano with Jim' is true when the singular predicate '- carried the piano with Jim' applies to John, and also true when the singular predicate 'John carried the piano with -' applies to Jim. <BR/><BR/>The only difference is that with distributive predication you can split predication over a conjunction, tyically 'and'.Edward Ockhamhttps://www.blogger.com/profile/07583379503310147119noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-56173094763536525022007-02-23T12:04:00.000+00:002007-02-23T12:04:00.000+00:00Hi all,Thanks for this, and apologies for the dela...Hi all,<BR/><BR/>Thanks for this, and apologies for the delay in getting back to you. I managed to pick up a copy of McKay's stuff, and so will be able to see what's going on there soon. Yi's stuff looks good too. <BR/><BR/>On the non-count noun stuff: I really haven't thought about it! I guess the way I've got things set up at the moment, the predicates are mostly natural construed as involving count-nouns. The idea then is to define the singular application ("is an elephant") as a limiting case of plural application ("are elephants"). <BR/><BR/>Suppose we've got a non-count predicate like "is water". How will that interact with the machinery? Well, there does seem to my naive ear to be both plural and singular applications of mass nouns like "water": we can make sense "those puddles are water" as well as "that puddle is water". So you might hope that the same story would go through here. But I'm aware that this might be hopelessly naive (I just don't know much about the syntax or semantics of mass nouns and the like). Henry: is there a feature of non-count nouns that makes things especially problematic? What's the best place to go to find out about it?<BR/><BR/>Ocham. Interesting. So the idea is that you reduce plurally quantified sentences (substitutionally) to plural named sentences, and then reduce those further to singular stuff. Be interesting to see how this would work out in detail for e.g. the Geach Kaplan sentence "some critics admire only one another". <BR/><BR/>I've got one worry of principle. Some plural predications don't seem to "divide down" to singular predications in the way you sketch. E.g. on one reading, "John and Jim carried a piano" doesn't entail "John carried a piano"; in the way that "John and Jim are human" does entail "John is human" and "Jim is human". That threatens to block the final stage of your procedure. I guess the standard names are "collective" and "distributive" plural predication respectively.Robbie Williamshttps://www.blogger.com/profile/02081389310232077607noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-17776480380830520592007-02-23T11:30:00.000+00:002007-02-23T11:30:00.000+00:00Hello Robbie. I've been thinking about this probl...Hello Robbie. I've been thinking about this problem for years, is it not the other way round? Can we not reduce plural quantification to the singular kind. Intuitively, singular terms are basic. Mill argues that sentences like 'Peter and Paul preached in Galilee and Jerusalem' reduce to four sentences (Peter preached in Galilee & Peter preached in Jerusalem &c). We connect plural reference to plural quantification by some appropriate substitution rule, e.g. just as we move from 'any x is an apostle' to 'Peter is an apostle ', so we move from 'any x's are apostles' to 'Peter and Paul are apostles'. I.e. substitute for 'any x's' any expression consisting of concatenated proper names (perhaps with the limiting case being a single proper name). <BR/><BR/>That does not mean there exists some 'Peter and Paul' thingy, only that we can make that substitution. This implies 'Peter is an apostle and Paul is an apostle', as above. Thus, only singulars exist.Edward Ockhamhttps://www.blogger.com/profile/07583379503310147119noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-89994834886985086902007-02-12T21:53:00.000+00:002007-02-12T21:53:00.000+00:00Thom McKay's Plural Predication develops a languag...Thom McKay's Plural Predication develops a language in which plural predication is primitive and singular quantification is had in the way you propose: i.e. [Exx : (yy)(if yy < xx then xx < yy]. He calls `<' `among'.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6432111.post-72179349317028835092006-12-29T23:22:00.000+00:002006-12-29T23:22:00.000+00:00My memory is failing me at the moment, but I think...My memory is failing me at the moment, but I think a logic that takes plural predication as primitive has been worked out by Beyong-Uk Yi (see his recent [=last couple of years] Logic and Meaning of Plurals (I), (II)" in <i>Journal of Philosophocal Logic</i>) and I forget what Smiley and Oliver do in their recent article in the same journal, but it might be what you're thinking of, too. <br /><br />Sorry if I've sent you on a wild goose chase, but perhaps this is what you are looking for.Greg Frost-Arnoldhttps://www.blogger.com/profile/08563986984421570652noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-5761162826279942322006-12-29T16:08:00.000+00:002006-12-29T16:08:00.000+00:00hi Robbie - well this is a good start [commenting ...hi Robbie - well this is a good start [commenting on the quantification issue / plural count nouns]. Have you thought about incorporating non-count nouns as well? I have something of a vested interest in that myself. best, Henry LaycockAnonymousnoreply@blogger.com