>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". (01)
NO!! This is a central point. There are two ways
to go, when speaking of contexts and truth in
contexts, and it is important not to get them
confused. (02)
One is to say that assertions and truth are
inherently contextual, so that 'reality' is
simply one context among many. That gives one a
context logic, and there has been a lot of recent
interest in such formalisms. In a context logic,
there are no eternal sentences, as *every*
assertion is made in some context or other. One
cannot say 2+2=4 in a context logic: one has to
specify which context it is being asserted in.
Even a quantification over all contexts it itself
contextual, and may change its meaning between
contexts (since the universe of contexts may
itself change between contexts). (03)
The other is to follow traditional logic and
treat plain assertions as being 'eternal'
sentence, assertions made outside of any context,
and define truth and its derivative notions
(satisfaction, validity, etc.) noncontextually;
and then to introduce 'truth-in-a-context' as a
different, derivative, notion. It turns out to be
simply a relation between things called
'contexts' (which are now merely individuals of a
certain sort) and propositions, so the logic
needs to admit propositions as first-class
entities; but apart from this, it is a purely
classical logic, with a purely classical notion
of truth. (04)
IKL takes the second path. For a discussion of
the consequences, read the 'IKL guide'. I
strongly believe that this is the best way to
proceed for ontology engineering purposes, but
that discussion would take us beyond a single
email. But my present point is that in this
second viewpoint, truth is NOT 'true in the
reality context'. (One could define a 'reality
context' such that truth in it was coextensive
with actual truth, but this would have no
utility; and more to the point, it would not
actually *be* the logical reality, but instead
would be an individual thing in the universe of
that reality.) The difference is exactly that
between two readings of the English neutral
present tense: the contextual reading understands
it as really about the present, the classical
reading understands it as being an eternal
statement made independently of time. "It is
raining" is naturally understood in the first
way, and "Two plus two is four" in the second
way. But classical logic has no tenses; a
hallmark of an 'eternalist' reading. (05)
This is not a matter of degree of truth or
'truthlikeness'. It is more to do with the idea
of a 'context'. The classical logical view
amounts to the perspective that logic itself is
above, or outside, contextual matters, rather
than embedded inside a context. Context logic
puts the context as primary, and warps the logic
to fit inside it: classical logic takes logic as
primary and uses it to talk about contexts (as
about everything else.) (06)
>This, as I think Waclaw implies, becomes awkward (07)
I really don't agree. If one is used to thinking
contextually it may take some getting used to,
but anyone familiar with the use of classical
logic to model reality will find it immediately
compelling. (08)
>, 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 (09)
Propositions DO have unequivocal truth values in
IKL. They also bear relations to other entities,
including contexts. Truth-in-a-context is simply
a relation: it is not actual truth. (010)
> (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. (011)
Quite. If a sentence really is in the tensed
present, then it does not express a proposition.
One gets a proposition only when all possible
indexicality is filled in, so that the sentence
is 'eternal'. IKL is of course not a tensed
language, so the issue does not come up directly. (012)
>In that sense, a change in context BECOMES a
>change in meaning of a proposition (013)
No, that is muddled. That is exactly what does
NOT happen. A proposition never changes its
meaning. The SENTENCE expresses different
propositions. (014)
>, 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. (015)
Exactly. And what you are calling 'full
propositions' are the only propositions. There
are no non-full propositions, only indexical or
otherwise 'localized' or 'contextually
incomplete' SENTENCES. (016)
>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. (017)
Which is exactly why such things, if they were to
be contemplated, would NOT be propositions. If
you want them in IKL, you can model them
explicitly as functions with propositions as
values. (018)
>The propositions full truth-assignable meaning
>would be defined only in the appropriate context, (019)
NO!! Full propositions - that is, propositions -
are not defined in ANY context. If they were,
they would be parameterized by the context, and
hence not full propositions. (020)
>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. (021)
But this is incoherent, since propositions are
'bearers of truth values'. If something cannot be
given a truthvalue, it ain't a proposition. Maybe
its a contextual propositional function or
something, but its not an actual proposition. (022)
Pat (023)
>
>(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.
>
>
>
>
>See what's free at <http://www.aol.com?ncid=AOLAOF00020000000503>AOL.com.
>
>
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