John and Pat, as well as others:
Thanks for your thoughts, and for your patience in explaining things with
which I have not been familiar, and in which I have had misconceptions or have
been imprecise in my use of "natural" language. I try to confine my
comments to things that I know enough about to provide useful input.
Nevertheless, I sometimes stray into territory unfamiliar enough
to me that I risk comments from a too-naive position. I think one
of the reasons I was invited to join here was to provide a perspective from
another point of view - which happens to be that of a natural
scientist/educator, rather than primarily a philosopher or information
scientist. Thanks for bearing with me.
Ken
In a message dated 5/30/2007 9:54:33 P.M. Eastern Daylight Time,
sowa@xxxxxxxxxxx writes:
Wacek,
Ken, Pat, Ingvar, et al.,
I agree that one should use technical terms
in a way that stays
fairly close to traditional usage. But the
tradition has a lot
of branches. In some branches, a proposition is
fairly close
to a sentence, but with the option of considering a
restatement
in a different language to be "the same" proposition.
I
take that to mean that a proposition is the language-independent
"meaning"
or "intension" of a sentence, and that the truth value
is evaluated in
terms of some "extension" or universe of discourse.
If somebody changes the
extension or universe of discourse, then
the truth value may change.
But the intension remains fixed.
That interpretation is consistent with
most 20th-century work
on modal and other kinds of intensional
logics. Montague, for
example, defined the intension of a sentence to
be a function
that maps possible worlds to truth values. Different
possible
worlds are different extensions, but the function
(intension)
remains fixed.
Although I prefer Dunn's semantics of
laws and facts to a
Kripke-Montague version with possible worlds, Dunn's
approach
produces exactly the same truth values for the same
sentences.
That implies that the same sentence with the same
intension
(proposition) may have different truth values in
different
circumstances. (I don't care whether anyone chooses to
use
the terms 'possible worlds', 'universes of discourse', or
'contexts'
for those circumstances.)
As Ingvar pointed out, Quine requires
propositions to have
fixed truth values. But that follows from the
fact that he
does not allow different possible worlds or
contexts.
Although I do not like the notion of possible world, I
would
agree with the modal logicians that any theory of modal
logic
should permit the same intension (proposition) to have
different
truth values in different extensions (universes of
discourse).
I also agree with Pat that the word 'context' has been
used
in too many confused and confusing ways. But I don't
like
either of the following ways of talking:
KC>> In that
sense, a change in context BECOMES a
>> change in meaning of a
proposition
PH> No, that is muddled. That is exactly what does NOT
happen.
> A proposition never changes its meaning. The SENTENCE
>
expresses different propositions.
I wouldn't say that a proposition
changes its meaning
because I would prefer to say that a proposition *is*
the
meaning of a sentence. I also would not say that a
sentence
whose indexicals were resolved to specific referents
could
express two or more different propositions.
I'm sure that one
can find logicians such as Quine who would
disagree with this
interpretation. But I believe that it is
consistent with those
logicians who are more tolerant of modal
logic. And since I want to
represent modal sentences in NL,
I prefer to accommodate their usage (even
though I use Dunn's
semantics rather than
Kripke's).
John
In a
message dated 5/30/2007 4:34:56 P.M. Eastern Daylight Time, phayes@xxxxxxx
writes:
>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".
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.
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).
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.
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.
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.)
>This, as I
think Waclaw implies, becomes awkward
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.
>, 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
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.
> (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.
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.
>In that sense, a change in context
BECOMES a
>change in meaning of a proposition
No, that is
muddled. That is exactly what does
NOT happen. A proposition never changes
its
meaning. The SENTENCE expresses different
propositions.
>, 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.
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.
>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.
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.
>The propositions full truth-assignable meaning
>would be defined only in the appropriate context,
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.
>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.
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.
Pat
Kenneth
Cliffer, Ph.D.
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