From @uga.cc.uga.edu:lojban@cuvmb.bitnet Wed Jun 28 22:54:41 1995 Received: from punt3.demon.co.uk by stryx.demon.co.uk with SMTP id AA3644 ; Wed, 28 Jun 95 22:54:37 BST Received: from punt3.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Tue, 27 Jun 95 22:21:55 GMT Received: from uga.cc.uga.edu by punt3.demon.co.uk id aa25350; 27 Jun 95 23:20 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 5014; Tue, 27 Jun 95 18:18:50 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 1053; Tue, 27 Jun 1995 17:51:18 -0400 Date: Tue, 27 Jun 1995 17:54:13 EDT Reply-To: jorge@phyast.pitt.edu Sender: Lojban list From: jorge@phyast.pitt.edu Subject: Re: ci gerku nicte X-To: lojban@cuvmb.cc.columbia.edu To: Iain Alexander Message-ID: <9506272320.aa25350@punt3.demon.co.uk> Status: R la djer cusku di'e > my sentence: > >> ci remna ku so gerku zo'u ra pencu ri > > xorxes translation: > >For each of exactly three humans, there are nine dogs that the human > >touches. (Not necessarily the same ones for each human.) > > OK, from this I conclude that there can be more than 9 dogs, since on > your interpretation human-1 can touch dog-1 to dog-9, and human-2 can > touch others, "not necessarily the same ones for each human". Right. For each human, there are exactly nine dogs that the human touches, but in the whole universe, there are many more than three humans or nine dogs. > Numbers are expressed in predicate calculus by long combinations of > quantifiers and variables. Numbers are exact numerical claims, i.e. "3" > means no more than three and no less than three. It means there are > only 3 things in our universe of discourse. The shorthand way to > express these is this notation: E!=1, E^!2=2, E^!3=3, etc. E^!9(y) > gerku(y) asserts that there are exactly 9 objects satisfying gerku(y). > > I am translating the sentence as: > > E^!3(x)(remna(x) E^!9(y)(gerku(y) & pencu(x,y))) That is not a good translation, because the Lojban sentence does not claim that only three objects satisfy remna(x). All the sentence says is that exactly three objects, out of all of those that satisfy remna(x), do something. And the same for the dogs. There is no claim that only nine objects are dogs. The only claim is that for each of three humans, there are nine objects out of all that satisfy gerku(y), such that the human touches them. > The scope of the quantifier on y is to the end of the sentence. It > includes the y in pencu(x,y). The question is whether for each different x, the quantifier on y selects nine dogs again, or whether they are selected once and for all for all the x's. The consensus we seem to be reaching is that they are selected separately for each x. The other option is also logical, all we have to do is choose one of the interpretations. > We have asserted for the entire length > of the sentence that there are exactly 9 dogs. No, that is not asserted in any of the two interpretations. The sentence only limits the number of dogs that are touched, not the number of dogs that there are in all. > Where do the extra dogs come from? They were there all the time. > I just don't think that the lojban covers the situation where at O hours > gmt I touch 9 dogs in LA, you touch 9 dogs in Pittsburgh, and pc touches > 9 dogs in Washington(?), for a total of 27 dogs. There are only 9 dogs > in this universe of discourse. {so gerku} means {so lo ro gerku}, "nine of all the dogs of the universe of discourse". There is no limitation in that sentence as to the number of dogs in the universe of discourse. Jorge