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| In a message dated 10/10/2002 3:31:18 PM Central Daylight Time, cowan@hidden.email writes: << What if ni is to jei as ka is to du'u? >> And how exactly is that (i.e., what is the relation between {ka} and {du'u})? I don't see any reason to think there is a special connection between {ni} and {jei} beyond the possibilities -- but not necessities outlined elsewhere. le ka ce'u kusru la djim. = the property of being cruel to Jim >> I assume the next to last is meant to be {le jei la djan kusru la djim}. I think focusing on {le ka/ni/du'u jei} maybe leading us off a bit: all these abstractions are predicates, which extensions are, therefore, sets of what? For the most part, we think that these predicates apply to exactly one thing (though I can think of reasons to doubt this for {nu} and {du'u} at least). But what is that thing in each case? Are we reduced to the tautologous (well, almost) {le ka broda cu ka broda}? The classes with {ni} and {jei} -- and in this they are similar -- are of ordered pairs of a number of some sort (including maybe vagues ones or fuzzy ones) and an "epistemology" (way of assigning such numbers to situations or propositions, presumably). We assume that the whole is a function from epistemologies to numbers for each inserted [bridi] (and, indeed, tend to take the complete _expression_ outside the [bridi] as a function from [bridi] to numbers). Taking {jei} as the fulfillment of {ni} is taking the membership function as the truth function of the membership claim. You can do that, of course, but there is no necessity to it and, except for early fuzzy logics and conventional bivalent logic (where there aren't a lot of choices), the two can be related in a variety of ways (see something somewhere else -- the convergence here is making it hard to keep threads straight; I hope nothing about the translation wiki is impinging on this). The presentation here also raises the question of how {ni ce'u kusru la djim} and {ni la djan kusru ce'u} are going to be related to {jei la djan kusru la djim}, for they should be somehow. When we throw in the {ce'u}s, which we have avoided doing pretty much up to now, we get an added problem that what we seem to have created is a function from things x (to be named in the {ce'u} spot) to, I suppose, numbers: the number assigned in one case to the value for the resultingly named situation, in the other for the resulting proposition (? since the lists say just "[bridi]" in both cases without ever clarifying whether "[bridi]" refers to the string of words, the situation it depicts or the propostion is puts foreward -- with different reading being natural for different abstractors). {du'u [bridi]} has ordered pairs of a proposition and a sentence, the proposition being (like {ka}) apparently only le du'u bridi and the sentence being any sentence at all - even in any language at all -- but typically the one laid out in [bridi] And, in this case, it is important that {du'u} is not a function, since we want to be able to say that a given sentence expresses more than one proposition (or fails to express uniquely any of several). Sticking a {ce'u} in here, gives a function again, whose values are presumably sets of propositions (assuming that the {ce'u} is uniformly replaced in [bridi] and x2 -- and all manner of complications as we go round the various places). So {ka ce'u broda} has the form of a function which gives whatever {ka ko'a broda} gives, when {ce'u} is replaced by a referring _expression_. But like the other abstractors, it has the grammar of a predicate, and is taken to mean "the property expressed by [ce'u bridi]" (strictly, I suppose, "a property..." but we are operating under the illusion that predicate expressions have only a single meaning). So, rather than a function to whatever (notice: not propositions, which would be what was expected if {ka ce'u} was a property of properties), it is simply a property. The extension of {ka ce'u broda} is apparently a function from objects (or names) to propositions. The extension of {le ka ce'u broda} then is a set of ordered pairs of names/things and paropositions. But the extension of the property of being broda is thes et of things that are broda, lo'i broda. Somewhere in all this something is wrong. xod: << Do you intend your usage of ka to abstract out EVERY possible quality associated with that bridi? Or just one or two of them, and without a clue to the reader which one(s)? Concrete example: Godzilla's Walk is historical as well as being earthshaking. >> Sure, why not? Though "associated with" is a little too vague and "bridi," as noted, is ambiguous. I'd say "all the properties of an event described by [bridi] (a linguistic item). If that gets too messy, I'd start to develop the notion of nuclear properties for this purpose as well (I'm not perfectly sure, for example, that the fact that I thought about Godzilla's walk is a property of that walking). << This is why I've repeatedly insisted that the ce'u-less ka, which is your "item 1" above, is ill-defined. You yourself admit that it refers to a class of properties, not a single property. What use is it? >> Actually, I'm now in the position (which I hope to work my way out of soon) of holding that {ce'u}-less {ka} makes pretty good sense, but that {ce'u}'d {ka} is flaky. The use of {ce'u}-less {ka} is precisely to refer to the set of properties had by some situation. Althoug I admit that it is odd that we cannot as readily refer to the set of properties had by any other kind of object: what is the shortest way to say that Sherlock Holmes has exactly the properties ascribed to him in The Canon? It seems bound to be longer than saying, using {ka}, that this explosion had all the properties of a normal 100 gram C-12 explosion. << Unless we can use ka me la godziras; "all the qualities of Godzilla", to mean the identity of Godzilla; something I've been hacking with su'u gy. co'e kei be lo kamsevzi, in my perpetual obsession with finding ways to avoid makau. >> And that looks like at least a giant part of the solution. But the event of being (an instance of) Godzilla may -- since it is an event, not a dragon -- have properties that Godzilla does not have. And the property of being (an instance of) Godzilla doesn't seem to be a whole set. cowan: << The extension of {ka ce'u broda} is presumably a set of things, lo'i > broda, in fact. By no means. le mlatu na ka ce'u broda .iku'i le mlatu cu ckaji le ka ce'u broda. Properties are as abstract as propositions, and in fact belong to a hierarchy: >> Agreed except for the "By no means." What can that mean? Ahah! SHEEEYIT:use-mention and my bad. The set is the extension of {broda}, whose intension is the property and the property is a function from objects to propositions. Thanks. I don't think that helps much with the others yet but maybe it will. xorxes << >It may be only that >{ka [bridi]} is shorter than {se ckaji le nu [bridi]} At least we have a clear definition for the competing meaning for {ka}. I suggest {tu'o} instead of {le} for the definition though, since probably we don't want this in-mind selection as part of {ka}. >> Well, I'm not sure the conditions for {tu'o} are met, since {nu} predicates may cover many things, so far as I can tell (I know you opine differently but I'd take it as undecided at the moment). So, I'd let the in-mind fit right in -- there are enough problems with "[bridi]" that being the in-mind one may be about the only everywhere satisfactory solution for now. << I still prefer the other ka: {ka ce'u broda} = {se ckaji tu'o broda} >> All that rises must converge, I suppose --this is five threads over (and I am not counting official bidness or stuff about twiki) and a week back. Here the conditions for {tu'o} definitely aren't met, since there are lotsa broda, usually, and the number we pick out does make a difference. I suppose you mean what you used to mean by {lo'e broda} here, but, while I can make some sense of that -- and have, to nobody's satisfaction, I don't understand the connection to {tu'o} at all. << >The extension of {ka ce'u broda} is presumably a set of things, lo'i >broda, in fact. No, that would be the extension of And's {poi'i ce'u broda}, see http://nuzban.wiw.org/wiki/index.php?poi%27i I also proposed using {se ka} for this. >> I don't know about And's bit, but lo'i broda is the extension of {broda} (see above) and probably not much else. {se ka} does not literally make much sense, since there is no second place to flip to, and I am not sure what is meant here anyhow. xod (on cowan): << > le ni ce'u kusru la djim = the amount of cruelty to Jim > le ni la djan. ce'u kusru = the amount of being a victim of John Do these two make any sense? It seems these are begging for another place, that indicates what the ce'u refers to, essentially collapsing them down to the jei case. I can't wrap my head around a quantity that's detached from a *thing* that exhibits that quantity. >> Well, again, these would be functions, giving values for each ot the things, though Cowan's pesentation makes it sound like a summation across all those values -- how much cruelty Jim gets or John gives altogether, which I suppose is a possible reading, but not a natural one (not that natural seems to be doing much here anyhow). |