I think I agree with Waclaw, and also with Ingvar's recent comments.
It seems that the statement "p is true in context C" would be true under
Pat's consideration, even though p is, in fact false, in context "reality".
This, as I think Waclaw implies, becomes awkward, even if understandable after
considerable explanation. It would make more sense to me to include the
context as a part of the proposition, perhaps implicit (but more usefully to be
made explicit), to be able to allow a proposition to have an unequivocal
truth value (even if it's a truthlikeness other than fully true or false), just
as a proposition stated in the present tense can be seen to have an implicit
context of the time it is stated as part of its meaning. In that sense, a change
in context BECOMES a change in meaning of a proposition, which allows (preserves
the ability for) one to consider the truth value of the full proposition's
meaning (i.e. of the proposition, including the context that is an implicit or
explicit part of the proposition) to be invariable. A proposition that can
change meaning in different contexts would then be a sort of open proposition,
without all referents (implicit or explicit) fully defined, without a definable
truth value. The propositions full truth-assignable meaning would be defined
only in the appropriate context, in which the open proposition becomes "closed"
and takes on a truth value, just as a proposition with unspecified indexicals
does not have a truth value until the indexicals are specified.
(Please correct terminological issues here, if there are any, with my use
of "open," "closed" etc.)
Ken
Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx writes:
Pat
Hayes wrote:
>> John F. Sowa schrieb:
>>> Wacek and
Ingvar,
>>>
>>> It happens that English has no
tenseless verb forms.
>>> In predicate calculus, you could
write:
>>>
>>> ~(Ex)(rose(x) &
blue(x)).
>>>
>>> This statement has no
reference to any time or place.
>>> In English, it is
possible to make a statement without
>>> reference to place,
but not to time.
>>>
>> And isn't this the
reason why Quine introduced his notion of 'eternal
>> sentence'? And
propositions expressed by eternal sentences cannot change
>>
truth-values, can they?
>>
>>> vQ> The sentence
"no roses are blue" was true some time ago,
>>> >
and is false now; but does it correspond to the
same
>>> > proposition in both
cases?
>>>
>>> I would like to express the
proposition stated by the
>>> above formula in predicate
calculus. That statement
>>> is independent of any
time, place, or context. The
>>> proposition it states
has no unbound variables that
>>> could be bound, explicitly
or implicitly, to any context.
>>>
>>> Yet that
proposition can have different truth values
>>> in different
contexts despite the fact that its meaning
>>> does not
change.
>>>
>> Are you denying the old
truth: 'same meaning, same reference'?
>
> Yes. The whole point
of introducing 'contexts' is
> to provide for alternative views of what
is true
> and what is not. The very same proposition may,
> in
another context, have a different truthvalue.
> That is not to say it
ACTUALLY has that
> truth-value: the ACTUAL truthvalue of any
>
proposition is a given. But there is some utility
> in allowing the
existence of entities which
> correspond to alternative ways the world
might be
> (it allows one to reason about counterfactual or
>
fictional circumstances, for example.) And when
> one does allow such
things, it is pointless to
> insist that they must correspond to the
way
> things actually are. So, we allow that a
> proposition may
have a different truthvalue "in"
> a context than it has in fact. This
does not
> actually make its truthvalue different from what
> it
is, it simply introduces a new notion of
>
truth-in-a-context.
From this and the previous explanations, I think I
get the point.
Thanks for the explanation, I did get the idea
wrong.
Would it not be better to say that a proposition p has a
truth-value --
*the* truth-value of p -- which is not context-dependent in
any way, but
that in different contexts it may be *said* to have another
truth-value?
I think that "we allow that a proposition may have a different
truthvalue "in" a context than it has in fact" and "the very same
proposition may, in another context, have a different truthvalue" would
inevitably be misleading to most users, despite your clear (to me now)
intentions.
Kenneth
Cliffer, Ph.D.
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