From a.rosta@pmail.net Fri Mar 3 05:20:01 2000 X-Digest-Num: 382 Message-ID: <44114.382.2151.959273826@eGroups.com> Date: Fri, 3 Mar 2000 13:20:01 -0000 From: "And Rosta" Subject: RE: Sets etc. X-Yahoo-Message-Num: 2151 Bastard Onelist unsubbed me for a fortnight, but wading through the archives I found this very interesting messsage from pc. > Finally, a class may be viewed collectively, and then the properties > attributed to it have little to do with the properties of the individual > but rather with matters like how many there are of them or (more related to > their proerties) what toher classes they belong to -- cardinality, > inclusion, and the like -- set theoretic properties, in short, which only > rarely have value in ordinary discourse. It strikes me that the victory/defeat of a sports team is a collective rather than additive or distributive property, yet is not what I would think of as a set-theoretic property. I am wondering whether it is possible to find additive:collective contrasts for a given predicate. That is, are additive:collective two aspects of the same thing, which contrasts with distributive? Or are they different? If same, then cardinality -- being a collective property -- would be a property of masses (because collective is equivalent to additive, and additive properties are masses'), and sets proper would be redundant. If not, then sets proper (lo'i etc.) are useful, because they'd be used for collective rather than additive properties. I expect to be disagreed with, but I look forward to reading the reasons why I'm wrong. I also forget whether there's a significant difference between pi ro loi and pi su'o loi. And if so, is pc failing to take it into account? Jorge? > As for JCB's lo -- it was a muddle and everyone -- even JCB -- knew it was > a muddle of half a dozen different ideas floating around in his > head. I think we now have most of them sorted out in Lojban, though we still > seem to get into fights over a few from time to time (and pretty > generally, having forgetten how we solved it the last time, come up with the > opposite solution the next). I inferred from Jorge's recent description that Loglan lo is used for Mr Rabbit; what I in bygone times called a 'myopic singularizer'. I think that's a Good Thing, although, as with masses, the logical properties are a bit hard to work out. The conceptual basis for the myopic singularizer is that a category is viewed as an individual, and members of the category are merely aspects of the individual. Just as we think of the suns that appear in the sky on different days as all the same individual -- the same sun returning each day -- so we can think of lots of rabbits as Mr Rabbit popping up all over the place. When you start to analyse this logically, it looks very similar to masses, but at least one difference is that the pi ro/pi su'o distinction makes no sense for myopic singulars, just as pi ro/su'o la djan kau,n makes no sense (if la djan kau,n denotes John Cowan rather than merely his corporeal substance). A further difference from masses is that whereas heterogeneous individuals can be massified, they can't be myopically singularized. I also agree with Jorge that Lojban lo'e is probably the thing for this (and also le'e for its **nonveridical** counterpart). [Emphasis because le/lo and lei/loi is primarily a specificity difference, whereas lo'e and le'e is only a veridicality difference.] Canonical Lojban has not solved the Mr Rabbit issue, though; only Llambian/ Llambiasian Lojban has. -- As in so many other respects too, of course. --And.