In a message dated 9/25/2001 11:37:53 AM Central Daylight Time, arosta@uclan.ac.uk writes:
The property of loving the property of having a Both the mother-of function and the property of having a mother are functions, one to mothers and one to propositions. This seems to me a crucial difference, since I don't send propositions mother's day card, for example, even the proposition that I have a mother. Lojban does, of course, grant a special status to item valued functions: they are sumti (just as in formal logic), though the connection is not as tidy as might beliked, as witnes the question of {pendo be c'eu} -- a puzzling _expression_,ill-formed as it stands. so, presumably what is wanted is this _expression_ with some gadri in front. But what gadri? If {le} we usedin this case, the result would not be unique, unless there some use of the"the ONE I mean" ploy of {le}; {lo} would be worse; {loi} introduces the dubious "thing" the mass, but otherwise works ok; {lo'i} is safe in some contexts (the ever popular {dunli} and {frica} for example) but a total miss in others. And the same applies for most cases where more than one thing satisfies the first gap for each second filler in {ce'u broda ce'u}. I am not sure what happens in these cases, when the wrong gadri is picked. With the right one, however, you get a nice function that explainsa situation succinctly. I am not too sure what happens when you pick the wrong gadri with {ka} or {ni} or ... either, though there it generally seems to be that there is only one natural and that covers all contexts (but I haven't really looks that closely yet). <Oh hang on, I think you mean {tu'odu'u/ka ce'u mamta ce'u} -- *that's* the mother-of relation> That is indeed the mother-of relation, but not the mother-of function, even though, in one sense of "extension," they ahve the same extension. The perform different roles and behave distinctly syntactically even in set theory. <#<#Clearly, we need a way of saying ^xf<x> in Lojban # #which we uncontroversially have, right?> # #Well, you seem to be amking it controversial, unless you have something else #in mind that I have forgotten about or don't know of. bigness = tu'odu'u ce'u barda is that not an example of ^xFx?> It is indeed. And the point is? The request was for an example of ^xf<x> (I am writing a paper for my website on the language ofLogic and how it relates to the logical language to remind or inform people who get into these discussions just what it is we are talking about.) <However, normally a bridi preserves its meaning when subordinated (e.g. placed within an abstraction), so if {la djoun mamta ke'a} and {la djoun mamta ce'u} have a certain meaning as main clauses then that meaning ought to preserved when the bridi is subordinate. And that would then seem to stymie the meaning that ce'u and ke'a already have when within ka/du'u and noi bridi.> I don't find this particularly persuasive, since it is inside out. We have these critters well-defined in subordinate positions and not as main clauses, so we can't say that the main clause meaning stymies the subordinate meaning. We might say that it is hard to imagine a main clausemeaning that would not stymie the subordinate clause meaning, and that maybe true of {kea}. I am less sure about {ce'u}. And, of course,we know exactly how it works for interrogatives, which are more or less related to {ce'u} (scope aside). But arguing from what we hard a hard time imagining to "it ain't so" is generally an awfully weak argument, sinceit collapses so easily to someone with a bit more imagination. <We also need to remember that ke'a and ce'u were chosen from among competing implementations of semantically equivalent devices, and not all devices would have raised the questions you're raising. For example, if we had an explicit way of binding variables to NOI and to ka/du'u -- call it "goi'i" then we could replace ke'a and ce'u by da variables: NOI .... ke'a = NOI goi'i da ... da ka/du'u ... ce'u = ka/du'u goi'i da .... da That would have been longerwinded than the current system, but would have overtly and explicitly expressed the way I understand ke'a and ce'u to work.> Well, I don't think that is historically accurate about how {ke'a} and {ce'u} were selected nor do I know of any devices of the sort you mention (other than {zo'u} constructions like the ones I used -- but those give the wrong sorts of things, as ordinary bound variables seem likely to do), still there could be such a system, and, indeed, the Lojban system may be one such. But that is not specified anywhere that I can find and the use of "lambda variable" cuts against it in the case of {ce'u} (less so for {kea} where the binding is by the gadri -- though this is never said outright). <#I don't understand what it would mean for ce'u to be transitive or #intransitive.> # #If it is in a construction within a construction then it is in the outer #construction, rather than being confined to the inner. Okay. Well then, yes, in a sense I want ke'a and ce'u to be sometimes transitive and sometime intransitive. But I think it is fairer to say that I want them to always be intransitive relative to the 'operator' that binds them, and transitive relative to everything else. da-series variables work exactly the same way.> This presupposes that {ka} et a few cetera bind {ce'u}, but, aside fromthe fact that {ka} requires {ce'u} and some others permit it (maybe even require it, but I don't think so -- {ka} really is, as I have said all along, peculiar here), I don't see that it binds {ce'u} in the way that LE binds{ke'a}. On the contrary, {ce'u} seems to contain its own binding operator (the lambda), as witness the fact that it is different each time it occurs (cf. {ma}, which is bound by nothing but itself -- and similarly all the interrogatives). <Okay. Well at least I see your position now. In a sense, on your position ka seems redundant: if {ka ce'u goi cy zo'u da prami le mamta be cy} is the property of having a beloved mother, then would not {da poi ke'a seprami be de gi'e mamta be ce'u} do equally well?> Well, no, since they are different syntactic categories in Lojban (and do the sumti really have to have {be} in poi clauses -- and if so, why doesn't {ke'a}? -- or is this one of the messes with {gi'e}?): one a predicate, the other a sumti (or, I would say, sumti function). However, I see that the same situation underlies the two. I don't think they are intertranslatable, however. <And your position opens many cans of worms. For example, does a "le mamta be ce'u be'o poi xendo" mean "the property of having a kind mother" or "the kind property of having a mother"? Do we really want to have to grapple with all these problems that simply don't exist on the standardstory about ce'u?> Neither, of course -- no properties here. What is the rule in general? I recall that it is that {poi} clauses modify the whole sumti, so it would be "the mother-of function that is kind" not "the kind-mother-of function." To be sure, I suppose that the distinction is hard to make in ordinary cases : the friends of Jerry who are kind are probably Jery's kind friends, and so on. <It must be me that is missing something, since, as I say above, I think the way is {tu'odu'u/ka ce'u mamta ce'u}. This is standard uncontroversial Lojban.> And again, what you are missing is that that is a function which gives propositions (as the {du'u} versions says) while we are talking (well, I am; you are confused) about a function that gives individuals. |