Received: from minerva.phyast.pitt.edu (minerva.phyast.pitt.edu [136.142.111.2]) by locke.ccil.org (8.6.9/8.6.10) with SMTP id QAA17684 for ; Sun, 27 Aug 1995 16:37:35 -0400 From: jorge@phyast.pitt.edu Received: from clueless.phyast.pitt.edu by minerva.phyast.pitt.edu (4.1/1.34) id AA02718; Fri, 25 Aug 95 16:02:54 EDT Received: by clueless.phyast.pitt.edu (4.1/EMI-2.1) id AA15259; Fri, 25 Aug 95 16:03:20 EDT Date: Fri, 25 Aug 95 16:03:20 EDT Message-Id: <9508252003.AA15259@clueless.phyast.pitt.edu> To: pcliffje@crl.com Subject: Re: sumti summary Cc: cowan@locke.ccil.org, jorge@phyast.pitt.edu Status: OR X-From-Space-Date: Sun Aug 27 16:38:17 1995 X-From-Space-Address: jorge@phyast.pitt.edu Some comments on pc's summary. > Logical individuals are both unique and atomic, so that no kind > of quantifier applies to them: there is only one of each and it > has no parts. The apparent fractional quantifiers for the > descriptors of these individuals are to be understood metaphorically > , then. pisu'o lo'i broda is not part of the set of broda but > rather another (usually) set, a non-empty subset of lo'i broda. I agree with that. > Similarly, pisu'o loi broda is not a part of loi broda or even > the massification of a part of lo'i broda, but the massification > of a subset (or , better for now, some collection of possibly less > than all brodas. I also agree. > I think it follows from this that the implicit quantifier (if we > insist there is one) on lo'/le'i/loi/lei/ lo'e/le'e is _piro_; Here is where I disagree. I don't think that follows at all. I think {pisu'o loi broda} (as defined above) is an argument that appears much more often than {piro loi broda} (as defined). We are much more likely to talk about "some apples" as a mass than about "all apples" as a mass. The reason why {pisu'o loi plise} is more useful than {piro loi plise} is the same reason why {su'o lo plise} is more useful than {ro lo plise}: we very rarely want to talk about all the apples there are in the universe. I would also say that {pisu'o lo'i plise} "a set of apples" would be more useful than {piro lo'i plise} "the set of all apples", if I thought that talking about sets of apples was useful at all. Since I don't think so, outside a discussion of logic or set theory, then I don't care much which is the default there. For the case of {lei}, I agree that {piro} is the best, for the same reason that {ro} is best for {le}. In this case, we are talking about all of the ones we have in mind, and for definiteness it is much better that we talk about the whole thing. > The properties of masses appear best in the whole; whether > they carry over to submasses (i.e., massifications of subsets > of the set originally massified -- it really is hard not to > talk this way, but nothing hangs on it, I think, at this > point) is variable with properties and sorts of things > involved. What properties of masses appear best in the whole? If I say that I carry, buy, take, give, ask for, eat some apples, it is clear that I'm not talking about the mass of all apples in the universe. > I take the quantifiers on le/lo (and la?) seriously (logicians gotta) > and literally. That is, I understand any sentence containing such > expressions as being general claims about things of the designated > kind, not mentioning or referring to any particular ones. The > particular cases are covered only insofar as they fall under the > general claim. Since we can presumably (certainly with le) get the > kind designated down to encompassing just the particular cases > intended, we lose no assertive power by the fact that we cannot refer > directly to individuals. But the language does get more complicated, > because of the necessity of dealing everywhere with quantifier scope, > rather than less restrictive direct referential expressions. Could you give an example where using {le re gerku} as a direct referential expression relieves us of the necessity of dealing with scope? I can't imagine how that could be possible, unless you mean to say that we would interpret it as {lei re gerku}. > [...] Thus, it does seem that the move from embedded > expressions of this sort to logical representations, which must pass > through the prenex stage, does not pass through that stage simply by > pulling the expressions out to prenex position and replacing them by > anaphoric argument forms. It will be interesting to know what is the mechanism to interpret the "embedded" expressions. I can't think of anything simpler than the direct fronting to the prenex. > For I take it (after months of discussion) > that the embedded form and the prenex form above do not mean the same > thing nor even related things on the same path to explicitness (the > consensus is that the embedded form covers three men and from three to > nine dogs, three for each man; the prenex form, by logic, covers three > men and three dogs, the same for each man). I suppose that "by logic" means "by the usual convention used in logic", since there seems to be nothing illogical with the other possible convention. > On the subject of quantifiers, I take it the standard logic rules > apply: the universe of discourse -- the range of unrestricted > quantified variables -- is nonempty, as is any explicitly restricting > set, the broda of da poi broda. Thus, ro implies su'o in all > contexts. I think that's unfortunate. For the cases when the speaker knows that there are no broda, it doesn't really matter much, because no one would want to use {ro broda} in that case unless with intent to mislead. But the problem appears when the speaker doesn't know. For example, I couldn't say "I promise to pay an extra dollar to everyone who finishes their work before noon", unless I am also promising that at least someone will finish before noon, which is not normally what I would want to do. > _le [n] lo broda_ covers conjunctively (unless specified with _su'o_) > [...] I am not sure whether the [n] has to be explicit: > is _le lo broda_ legal? No, it isn't legal, the [n] has to be explicit. > I now gather that for xorxes > lu'a attached to an expression that denotes a mass would be "at least > one component of that mass". Thus (I will not keep repeating my > caveat "if I understand aright") lua lo'i broda would be, in effect, > lo broda. That's how I understand it, yes. > But also, if _le girzu_ refers to some mass (as it seems to do most > often), then lu'a le girzu would cover "at least one component of > whatever mass _le girzu_ covers." If this is right, then this would > be non-problematic if there is only one group covered, but less > comfortable if there are several (at least one component of all = of > the massification of the intersection of the underlying sets?) though > still intelligible and useful (barring the worry about whether any one > thing is a component of all those masses). If there is no such thing, then the speaker is talking nonsense, just like talking about "the fifth leg of that cat". > So, if le girzu covered back to le ci gerku, lu'a le girzu would > amount to just su'o le ci gerku. But it is not clear what would > happen if le girzu covered le ci nanmu and le ci gerku. Same thing. At least one of the six individuals. > Nor is it clear what to do with lu'a le/lo broda generally, i.e., > when le/lo broda does not obviously cover masses or sets (xorxes > has the set cases working like the mass, with "member" in for > "component"). The problem is analogous to the meaning of fractionators attached to these things. I would not use it unless there are indentifiable components. > Xorxes' lu'o may seem to agree pretty much with what I took to be the > official line above: lu'o is "at least one mass whose > components are ." But, for a given bunch of individuals, > there is only one such mass, of course, Unless the individuals are not being referred to, but simply quantified over. {lu'o ci gerku} is a mass of three dogs, but there are more than one possible mass of three dogs. > so the wording leads to the > question whether this means that lu'o lo broda (for example) is loi > broda or rather takes the implicit su'o into account and so covers > mases that have only some of the brodas in, what is elsewhere > described as pisu'o loi broda That's my intent, yes. With the added benefit of being able to quantify over them, which is not possible for {[pisu'o] loi broda}. Jorge