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 and-distribution applies to both:
>>
>> (ist c (p & q)) iff ( (ist c p) & (ist c q) )
>>
>> but there are certainly some cases of
>> time-context 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 and-distribution.
>Seems to me that one _could_ do the semantics of ist vis-a-vis
>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. (01)
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? (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. (03)
>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 (04)
Or more directly by dualization, (ist* t P) ==
(not (ist t (not P))). 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. (05)
>(which seems to be the semantics you are assigning to ist directly
>above). and-distribution 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
>first-order 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))). (06)
Er, yes. Of course. That was the whole point (and
the notation) of my paper on context mereology.
But now, which of these is the correct view of a
time-interval as a 'context'? They can't both be.
In fact, its clear that
time-intervals-as-contexts are not even one kind
of context, but (at least) two. There are (at
least) two notions of 'true in an time-interval'.
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. (07)
Pat (08)
>
>-chris
>
>
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