* Sunday, 2011-09-04 at 18:22 -0300 - Jorge Llambías <jjllambias@gmail.com>:
> On Sun, Sep 4, 2011 at 4:53 PM, Martin Bays <mbays@sdf.org> wrote:
> >
> > Fragments of it are easy enough to treat - in particular, a sizable
> > fragment translates directly to usual first-order predicate logic.
>
> Yes, and while the collective/distributive issue is not so easy to
> treat in the usual (singular) first-order predicate logic, the issue
> of generics is much simpler in that respect, as long as we keep the
> domain of discourse restricted to what is relevant.
I remain hopeful that this restriction, which would be very hard to
formalise, will turn out not to be necessary - or rather, that it can be
done away with at the expense of making the logic a bit more
complicated.
> > Pre-xorlo, {lo} was part of that fragment. I'd like to understand what
> > modifications to the semantics are required to handle xor{lo}.
>
> Pre-xorlo "lo" was just a synonym of "su'o". There's not much point in
> having two words for the same quantifier. xorlo "lo" is not a
> quantifier, rather what it does is create a referring expression out
> of a predicate, and the only requirement is that the referent(s) of
> that expression satisfy that predicate. But what those referrents
> are will change from context to context.
Right. But it's important that the range of possible/likely referents is
understood by the listener. If the convention is that individuals with
a priori bizarre properties, like Kinds or lo'e-typicals or any of the
various flavours of masses/groups/whatever, are plausible referents,
then this convention needs to be commonly understood. Moreover, if the
properties of these magic individuals, or the conditions under which
they become plausible members of the domain of discourse, are not
ill-specified, then the semantics of the language is correspondingly
ill-specified.
> In some contexts the referrents of "lo gerku" will be some particular
> dog or dogs, in some other context it will be something like the
> single referrent of the English "dogs". That has no effect on
> first-order predicate logic.
> From the point of view of first-order predicate logic, all we have in
> "lo gerku" is a constant.
>
> > But what I meant was that you seemed to be upsetting the very
> > foundations of a model-theoretic formal semantics - that we can judge
> > truthhood of statements against a fixed model (fixed at least
> > throughout a sentence, whether or not throughout the whole discourse).
> >
> > I hope this isn't necessary.
>
> I don't think I'm doing that, at least not with respect to this issue
> of generics.
You seemed to be.
To repeat the problem which you seemed to be getting around by invoking
a varying domain of discourse: suppose I'm showing you my flea circus,
consisting of 100 fleas almost all of which are black, but which
contains a few freaks of other colours. Then the following exchange
seems reasonable, if we don't play tricks with domain of discourse and
treat generics just like other individuals:
M: .o'a pa no no da vi cinki
X: za'a lo vi cinki cu xekri
M: .ua mi jifsku .i su'o pa no pa da vi cinki
> >> >> And this works because, as Carlson points out, bare plurals are never
> >> >> actually ambiguous as to what reading they should be given. The
> >> >> predicate normally selects for which reading is the one called for,
> >> >> and when it doesn't it's because the predicate itself is ambiguous, as
> >> >> can be shown with the same predicate acting on non-bare plural
> >> >> arguments.
> >> >
> >> > Yes, but you don't want this to translate directly to Lojban, do you?
> >>
> >> I'm not sure I follow what you mean by "this" here.
> >
> > The ambiguity being in the predicate rather than the sumti.
>
> The type of ambiguous predicates I was thinking about were things like
> Carlson's example "... ate figs" (he used some other food item, but I
> don't recall what now
(kelp, oddly)
> ) which has the two possible readings for bare
> plural subjects in English, but it also has the two readings for an
> ordinary subject like "John", so it doesn't make sense to attribute
> the ambiguity to the bare plural, unless you want to say that "John"
> is also ambiguous in the relevant sense. In Lojban the disambiguation
> could be something like "...pu ta'e citka lo figre" vs. "... pu co'i
> citka lo figre".
Right, but using tenses like this only works for the John case - unless
you want to redefine the tense system to apply to "stages" as well as
times... is that really what you're doing?
> Plain "citka lo figre" would probably have to remain ambiguous between
> at least those two.
Based on this and some other things in this mail, I'm taking you as
saying that you want this to hold also when John is replaced by {lo
gerku} read generically, though this seems not to accord with your
answer to me question about dogs being small and hungry (a question
I asked precisely for the purpose of probing whether you wanted this
predicate-based ambiguity! But I guess that was unclear). Could you
confirm that I'm now reading you right? i.e. if {lo broda} is read
generically in {lo broda cu brode}, then the latter is ambiguous between
saying that some "stage" of {lo broda} brodes, and saying that the
generic itself brodes - the truth conditions for which are unclear, but
probably have something to do with typicality.
> >> My Lojban translation for "poets write some poems, but most poems are
> >> written by non-poets" might be something like: "lo pemfi'i cu finti
> >> su'o pemci .i ku'i so'e pemci cu se finti lo na'e pemfi'i"
> >
> > Right. So that wouldn't work with lo giving 'the typical', nor with it
> > giving some individuals as a constant - so this kind of Kind really is
> > something new. And its semantics are only getting more and more alien to
> > me as you give more examples...
>
> What I'm saying is that it's (similar to) the usual semantics of the
> English bare plural, at least as analysed by Carlson.
So you read {so'e pemci cu se finti lo na'e pemfi'i} as
MOST (x:poem(x)). EX (s:[s is a stage of {lo na'e pemfi'i}]. finti(s,x)
?
> In our domain of dioscourse we have one element (poets), another
> element (non-poets), and some indefinite number of other elements,
> each of which is a poem, and we claim that poets write some poems, and
> non-poets write most poems. Nothing deeper than that.
>
> The problem (if it's a problem) is when you try to connect this with a
> different domain of discourse which contains many people each of which
> is either a poet or a non-poet.
Yes. I'd call this a problem.
> But that's a different domain of
> discourse, not the one we need to interpret this sentence. The
> relationship that holds between an individual like "poets" and the
> many individuals each of which is a poet, when they occur in the same
> domain of discourse, does have its complications. But it's not like we
> are deviating from first-order predicate logic when we consider the
> simpler domain where "poets" has a single referent, who happens to
> write some but not most poems.
>
> > For a while, I thought your generics might be something like elements in
> > an elementary extension, i.e. that adding them doesn't change the truth
> > value of any sentence (or maybe: of any sentence which is short enough
> > and doesn't use any too high numbers (so we can add generics to large
> > finite sets)).
>
> No, we don't add generics to sets. When we have a generic, it will
> typically be the only member of "its set".
(I meant something like a generic {lo vi cinki} in the above, being
a new member of {x | x vi cinki})
> > But now it seems you would want that {ro pemci cu se finti lo finti}. So
> > {da finti ro pemci} becomes true on adding this generic.
>
> Yes, as long as we don't shift to a domain of discourse where we have
> more than the generic "authors". If you are going to go down that
> road, it would make more sense to start with "ro pemci cu se finti
> su'o finti", which of course does not license "su'o finti cu finti ro
> pemci"..
So if I were to say, out of the blue, {da finti ro pemci}, what would
you make of it? Would you think I was making the innocuous claim
regarding generics, or that I was crazy, or that I was referring to
a special form of poem which does indeed have only one author? Most
importantly: how would I disambiguate to indicate that I really mean
"someone wrote all poems"?
> > Probably I should have said "dogs are small and the dogs are hungry".
> > This isn't in your list of possibilities. Just to check - was that
> > deliberate?
>
> Yes, the x1 of "cmalu" and the x1 of "xagji" in "lo gerku cu cmalu
> gi'e xagji" has to be the same, and in "dogs are small and the dogs
> are hungry" you are changing subjects. "Dogs are small and they are
> hungry" would work.
(as mentioned above, I don't see how this fits with your other
statements)
> > Do you mean that there are *two ways* in which {lo plise cu farlu} could
> > be analysed as saying that some (particular) apples are falling - the
> > first being where {lo plise} is read as referring to some apples and
> > {farlu} as a distributive predicate, and the second being where {lo
> > plise} is read as a generic, and {farlu} is read as applying to some
> > stages of this generic?
>
> "lo plise cu farlu" could mean "apples fall" or "apples are falling",
> yes (among other things). One way of disambiguating would be "lo plise
> cu ta'e farlu" vs "lo plise cu ca'o farlu", i.e. by making the
> predicate, rather than its argument, more explicit.
Again... {ta'e} for stages??
Martin
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