On Sun, 13 Jan 2008, Pat Hayes wrote:
> At 3:28 PM 0600 1/13/08, Christopher Menzel wrote:
>> On Jan 13, 2008, at 1:15 PM, Pat Hayes wrote:
>>> ... McCarthy claims that anddistribution applies to both:
>>>
>>> (ist c (p & q)) iff ( (ist c p) & (ist c q) )
>>>
>>> but there are certainly some cases of timecontext where this
>>> fails, eg there was one day last year when I was (at various times)
>>> in five states, but I have never been in five states all at once.
>>> So apparently
>>>
>>> (ist thatDay (Pat in Mississippi)) & (ist thatDay (Pat in
>>> Kentucky))
>>>
>>> but not
>>>
>>> (ist thatDay ((Pat in Mississippi) & (Pat in Kentucky)))
>>
>> Not so clear to me that this is a counterexample to anddistribution.
>> Seems to me that one _could_ do the semantics of ist visavis
>> temporal contexts so that something that is true with respect to a
>> given interval t has to be true with respect to all subintervals of
>> t.
>
> Yes, you can. And McCarthy uses that semantics, and so concludes (and
> takes it as axiomatic) that ist distributes over conjunction. But
> examples from natural language seem to often obviously have the dual
> interpretation, as here. So for example there is a famous Italian
> movie, "Last year in Marienbad", all about something that happened in
> Marienbad the previous year. But it didn't happen everywhere in
> Marienbad, for the entire year. Examples of this kind of
> 'contextualization' are rampant in natural language: so what supports
> the claim that the dual form must be correct, so correct indeed that
> it is a logical truth? (01)
Well (not that you of all people don't know this), "logical truth" is
largely a term of art. What counts as a logical truth is often only
decided after we fix a particular semantics. Natural language shows
that there are at least two senses of "this happened at that time" and,
as you point out, we could take either as primitive (though see below),
so it doesn't seem to me that there is necessarily a preanalytic fact
of the matter about the logical truth of anddistribution. The
important thing is that our semantics is able to provide analyses that
can account for the intuitive data. Whether or not, e.g.,
anddistribution turns out to be a logical truth seems to be incidental. (02)
> In the case of the quantifiers and the modalities, natural language
> itself has explicit markers for the two dual notions: every vs. some,
> necessarily vs. possibly. But for the dual interpretations of temporal
> relativity, there seems to be nothing to lead to one being preferred
> over the other as the fundamental notion. If anything, I'd say that
> the 'Marienbad' interpretation is far more common. If we take that as
> the basic idea, so that (ist t P) means that there is a subinterval of
> t with P true in it, then ist does not satisfy McCarthy's axiom.
>
>> On such a semantics
>>
>> (ist thatDay (Pat in Mississippi)) & (ist thatDay (Pat in
>> Kentucky))
>>
>> would be false. Granted, in ordinary language, if you travelled from
>> Mississippi to Kentucky on, say, January 5, one can say both that Pat
>> was in Mississippi on Jan 5 and that Pat was in Kentucky on Jan 5.
>> But one could capture this ordinary usage  and preserve your
>> intuitive data above  by _defining_ a related notion ist* such that
>> (ist* t P) just in case (ist t' P) for _some_ subinterval t' of t
>
> Or more directly by dualization, (ist* t P) == (not (ist t (not P))). (03)
It's a bit off the point, but I'm dubious about this analysis in
general, since (I think) it presupposes that excluded middle holds
"internally", that is, that for every context t and proposition P,
either (ist t P) or (ist t (not P)). I don't think that is a viable
principle for at least some notions of contexts (though it's probably ok
if we're simply identifying contexts with time intervals with no spatial
restrictions). (04)
> But my point is not that his cannot be done  obviously it can  but
> to question why it is considered axiomatic that ist should be the
> &transparent case, rather than ist*? There is a complete logical
> symmetry between these two ideas.
>
>> (which seems to be the semantics you are assigning to ist directly
>> above). anddistribution then rightly fails for ist*: it is
>> unproblematically true that
>>
>> (ist* thatDay (Pat in Mississippi)) & (ist* thatDay (Pat in
>> Kentucky))
>>
>> and just as clearly false that
>>
>> (ist* thatDay ((Pat in Mississippi) & (Pat in Kentucky))),
>>
>> Moreover, the reason for the failure would be analyzable in simple
>> firstorder terms as an instance of the general failure of
>>
>> (exists (x) (P x) & (exists (x) (Q x))
>>
>> to imply
>>
>> (exists (x) ((P x) & (Q x))).
>
> Er, yes. Of course. That was the whole point (and the notation) of my
> paper on context mereology. (05)
You'll have to forgive me if it appeared otherwise, but I was quite
certain I wasn't saying anything you were unaware of, Pat. However, it
struck me that your claim that "there are certainly some cases of
timecontext where [anddistribution] fails" without any further
qualification was misleading insofar as it suggested (even if you didn't
so intend) that one *couldn't* find a reasonable semantics for "ist" on
which anddistribution was valid and in terms of which the apparent
counterexamples could be explained. (06)
> But now, which of these is the correct view of a timeinterval as a
> 'context'? They can't both be. (07)
Well, it should be pretty clear at this point that I'm leery of the idea
that there is such a thing as "the correct view" here. What we need to
do is account for the intuitive data. There might be more than one way
of doing that. (08)
> In fact, its clear that timeintervalsascontexts are not even one
> kind of context, but (at least) two. There are (at least) two notions
> of 'true in an timeinterval'. And of course there are more than two:
> there are notions such as "true almost everywhere" or "true during
> subintervals which are normal for that kind of proposition" (as in "he
> was furious for a whole week"), all of which have a valid claim to be
> a notion of 'true during an interval'. Which was my main point: there
> is no axiom which is true for ALL of these notions. (09)
Agreed, certainly, though it doesn't follow that there isn't a single
notion in terms of which one can give datapreserving *analyses* of the
other notions  which, of course, is not to say there *is* such a
notion either. ;) (010)
chris (011)
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