<<
: if you have a set of things of any sort, then
>you
>can quantify over the members of that set. What does the fact that the set
>contains abstract things have to do with denying this triviality?
Nothing, but I think you're mixing levels here. Given a set
(of whatever elements: concrete, abstract, real, imaginary,
whatever you like), given that set, you can quantify over its
extension, or you can use its intension (the intension that
defines the set, not the particular intensions that might be
involved in otherwise defining any of the members). To use the
intension of that set and not its extension, I can't have a
quantifier running over that set, no matter what type of things
its elements are.
>>
Oh, is that what you are doing? Is this just use-mention again in a more muddled way? What is the intension of a set? The set itself is the extension of the expression which gives its defining property. The defining property is the intension of that expression, I suppose (I also suppose someone could split a hair or two here, but this is close enough for now). Now how do we *use* this intension? It's a property, say, so we apply it to objects to see whether they have it or not and we work with it in the general field of concepts to relate it to other properties and relations. What does this have to do with what we have been talking about (though I admit I may have lost the original point after all this time and all the gymnastics that you have gone through to avoid giving clear answers)? Why does using the "intension of a set," if I have understood what you mean, prevent quantifiers running over the members of the set? (And, if I haven't understood yet again, what -- yet again -- do you mean?) I think that if you say "Nothing" I will just go scream for a while, because then why did you bring it up? I agree that, if you are using the "intension of the set," the expression you use, whatever it may be, will most likely not be one that involves quantifier expressions over members of the set. And so? Nothing interesting seems to flow from this. What am I missing?
<<
>But, why should the quantifier not be there?
Because the quantifier immediately brings forward the extension
>>
But the cases we were discussing were -- I thought -- about getting one token of a type out of a set of such tokens -- each of them being in fact an event type. That still seems to me to be inherently extensional for all that the extension is made up of intensional objects.
<<
>Even if ythe set has only one
>member, quantification is still meaningful -- indeed, even if the set has
>no
>members.
But the sets we're talking about have many members in general:
a set of chocolates, a set of events of eating. I don't want
to quantify over the extensions of those sets, I want to use the
intensions.
>>
Well, we have moved up to allowing that the set has many members. Maybe we need to set up some terminology so that the various sorts of intensions are sorted out.
I don't know what the intension of a set is unless it is the intension of the expression whose extension is the set. Calling that the sense or designation would take it out of the mass of things going on here. It is an intensional object, meaning that various operations -- fronting, quantifier binding, and Leibniz's law -- don't apply in expressions referring to it. Let's keep "intension" as a general term for objects which are referred to by expressions with those properties.
Types and tokens are another matter entirely, though perhaps practically related. The lowest level token is a concrete individual at a given moment. From there on up, the type relative to a given token is an abstract and quasi-intensional object which the relative token manifests or however you want to put it. The two share some properties and these are defining for the type -- and they typically "have" them in different ways, though the terminology here is muddier than usual: the token typically is subject of the property, the type contains the property (to take what seems to me the least confusing pair of possibilities). The quasiness of the intensionality comes about from the fact that some real-world truths affect the issue of what tokens may fall under a given type: the fact that Jill is Jack's bitchy sister means that the proposition that Jack's bitchy sister is asleep falls under the same type as the proposition that Jill is asleep, even though they are not the same proposition. I take it that {du'u la djil sipna} is the predicate satisfied by all the propositions that fall under the same proximate type as that Jill is asleep does. I suppose that the sense of that predicate expression is pretty close to just that, the property of falling under that proximate type.
Against this background, what are you trying to say? Or what background is needed to make out what you are trying to say, if this does not fit some part of your scheme?
<<
>It surely is meaningful when the set has an indefinite number of
>members.
We agree then. In those cases, I use {lo'e} when I don't want
to quantify over the extension of the set.
>>
In what cases? When the set has an indefinite number of members (I just meant that we have no particular idea how many there are, not some peculiar kind of number)?
Why not, in complete generality, use {le du'u ce'u broda} in this case (assuming that this refers to the sense corresponding to the reference lo'i broda, i.e., the sense of {broda}, which it ought do)?
I don't know what you think we agree about; certainly not that {lo'e} plays any role in all this (it might, I suppose refer to some type, but that does not seem to be its most useful function and there seem to be clearer ways of doing this even aside from the Lojban meaning of {lo'e}). I suppose that "when I don't want to quantify over the extesion of the set" means "when I want to talk about the sense of the expression delimiting to the set rather than to the set itself or its members"
Someone complimented you (I think it was you, anyhow) for leaving out all the messy braces, but this all suggests that leaving them out gets one into trouble in these kinds of discussions. And muddling the levels and the categories makes it even worse.
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