[Top] [All Lists]

Re: [ontolog-forum] Ontology, Information Models and the 'Real World': C

To: KCliffer@xxxxxxx
Cc: ontolog-forum@xxxxxxxxxxxxxxxx
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 30 May 2007 13:34:09 -0700
Message-id: <p06230902c28389a10320@[]>
>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" 
>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)
>Kenneth Cliffer, Ph.D.
>See what's free at <http://www.aol.com?ncid=AOLAOF00020000000503>AOL.com.
>Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ 
>Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ 
>Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>Shared Files: http://ontolog.cim3.net/file/
>Community Wiki: http://ontolog.cim3.net/wiki/
>To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
>    (024)

IHMC            (850)434 8903 or (650)494 3973   home
40 South Alcaniz St.    (850)202 4416   office
Pensacola                       (850)202 4440   fax
FL 32502                        (850)291 0667    cell
phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes    (025)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (026)

<Prev in Thread] Current Thread [Next in Thread>