Re: [ontolog-forum] Scheduling a Discussion [was: CL, CG,On Fri.
Jan. 18, 2008, at 11:23 AM, Pat Hayes wrote:
>At 11:38 PM -0500 1/17/08, John Black wrote:
>>On Wed. Jan. 16, 2008, at 9:18 PM, Pat Hayes wrote:
>>>At 4:32 PM -0500 1/16/08, Deborah MacPherson wrote: (01)
PH>>>>> RE: ......is there any kind of thing that could NOT be a
context,
>>>>> or part of a context, in this third sense? Or can a context
>>>>> be anything,
>>>>> or perhaps any set of any things? If (as I suspect) the
>>>>> latter, then this
>>>>> is not a definition of anything, as it does not identify
>>>>> any actual category. (02)
DM>>>> Hi Pat, can you please explain why the identification of
an actual
>>>> category is the ultimate or preferred result of well-defined
>>>> context
>>>> (whether words or "any collection of things"). (03)
PH>>> Not sure I understand the question. The identification of a
category
>>> is what a definition does. The category in question is
>>> "context". (04)
PH>>> Heres my point, let me illustrate it with a parable. Joe
comes along
>>> and says, we need to discuss foodles. Its important to have a
>>> general
>>> theory of foodles. And I say, hmm, what are foodles? And Joe
>>> says,
>>> everything is a foodle. (05)
PH>>> At this point, I conclude that what Joe wants is
impossible, because
>>> there isn't anything useful to be said that applies to
>>> everything. Anything
>>> non-trivial will be true of some things and false of others:
>>> it will divide the
>>> universe into examples and non-examples. It will be a
>>> category. (06)
PH>>> Do you see the point? (07)
JB>> I think Joe might not have said that everything is a foodle,
but that
>> anything may be foodle. And he might say that it is not a
>> category but
>> a member of a relation between two sets of things. (08)
PH> Ah, good. Now we are getting somewhere. So "what are
contexts?" or
> "how do we define context?" is the wrong question. What makes
> something
> a context is that it stands in a contextual relationship to
> something else,
> what you are calling the focus. That makes more sense, I agree. (09)
JB>> He may say it was like the figure and the ground of
perceptual
>> psychology. We can not define any fixed category "ground" by
>> your
>> criteria either, could we?. Everything may at some point in
>> time be
>> the ground to some figure, and everything may be the figure,
>> but
>> nothing may be both the figure and the ground at once. What
>> matters
>> is the relation between the two. (010)
JB>> To switch back to the topic at hand, anything may be
context, or
>> anything may be the focus, but nothing may be both the focus
>> and
>> the context at once. (011)
PH> OK. Though do we really want to say that anything can be the
> focus? John Sowa wants to restrict it to cases where the focus
> is
> textual (in a fairly broad sense: 'symbolic' might be an
> alternative
> word to use.) That makes more sense to me. (012)
'Textual' will work, 'symbolic' may be better. Recently I came
across the term 'biosemiotic framework' in a paper titled
"Cellular Semiotics and Signal Transduction" by Luis Emilio
Bruni, which "sees biological processes from a sign-theoretic
perspective." So as long as we understand 'textual' to include
molecular, in addition to Unicode encodings, I'm good with that. (013)
JB>> However, for what its worth, to fully capture my own
intuitions about
>> it, speaking of sets (014)
PH> er...why are we speaking of sets? (015)
JB>>, there must be one set that is in focus, and at least two
sets that
>> are (possible) contexts. If there were a focus set and only
>> one other
>> set, we would not call the second, non-focus set a "context",
>> we
>> would call it the foundation, or cause, or conditions of the
>> focus set. (016)
PH> You've lost me now. I have two sets, and therefore one of
them is
> a cause of the other (?) (017)
Instead of 'cause' I now see I can probably only say the
*relation* between a context and a focus set. I guess that would
be T2 in John Sowa's framework, the axioms that explain the
relation between T1 and X. (018)
But, the idea, I suspect, may well be defined by your separation
axiom, A7. Lets call possible context sets 'peripheral-sets' and
say that: if there is only one peripheral-set that makes a
difference in the values of the elements of the focus-set, then
that peripheral-set is not a context-set for the focus-set. One
alternative is to say, as I think Chris Menzel was suggesting
when elements of a focus-set are all logical truths or
contradictions, that such a singular peripheral-set would be a
*trivial* context-set for the focus-set. I would like to
eliminate trivial contexts. As a picture of this type of trivial
context, imagine a strange world where I am the only person able
to speak. When I state that "I am named 'John Black'" in such a
world, the peripheral-set is the state of affairs that I just
described, namely that I am the speaker and the only one able to
speak. That peripheral-set does allow the "I" to be resolved to
myself, since I am the speaker, and make the proposition true -
but it *always* resolves to me. The value of "I" cannot vary. So
the resolution of "I" is established by the peripheral-set but
there is no other peripheral-set that would make it resolve to
someone else who is not named 'John Black' which would make the
proposition false. The question for me is, does our concept of
the contextual relationship include this? Is this kind of fixed
expansion of meaning all that is required for a relation to count
as contextual? Or does a contextual relation require variability
of the values of elements of the focus-set when the context
changes? I'm inclined to say that variability is required. So I
might say that in such cases the peripheral-set was in an
'environmental', but not a contextual realtion to the focus-set.
That was what I was trying to say above. (019)
Well, after several hours of work, I can't seem to make it more
clear than that. In particular, the example minces together two
types of "context", indexical resolution and truth value
determination, in a way that seems to make it useless. Let me try
to use John Sowa's simple framework. For any given text (or
focus-set) T1, there must be at least two contexts X and Y and
they must result in a difference in at least one element in T1 -
Otherwise there is no point in calling X a "context" and we
should call it something else, perhaps the "environment" of T1.
I think this would be better than calling X a trivial context.
Thats all. (020)
JP>> Furthermore, a context set must, when held in relation to
the
>> focus set, force differences in the truth, interpretation, or
>> perception
>> of the focus set, and these differences must be different for
>> each
>> context set. (021)
JP>> In other words, my intuition says that in this case:
>> (ist today (and A (not A))), today is not a valid context for
>> that
>> tautology because there is no other context, which if it took
>> the
>> place of "today", would change the value of that tautology. (022)
PH> Did you mean to have (or A (not A)) as your tautology? (023)
Yes, I completely botched that. I grabbed for a very simple
tautology and got instead the simplest of contradictions. But, as
Chris Menzel correctly grasped in spite of my egregious error, it
would work (if it works at all) with either a logical truth or
logical falsehood, the point being they are context-independent.
Again, as I said, Chris suggested that such propositions could be
considered to be true in all contexts, but I think it would be
better to say they are not members of any contextual relations.
I'm trying to decide if that matters and what consequences it
would have. (024)
JP>> This is pragmatic, to count as a context it must make a
difference (025)
PH> If I understand you, I agree. In fact, that is the basic
content of one
> of the axioms in the note on context mereology
> http://www.ihmc.us:16080/users/phayes/context/ContextMereology.html
> which I called the 'separation axiom' (A7). In words, it can be
> phrased
> as follows: If one context C is not wholly contained in (or, if
> you prefer,
> is not a part of) another context D, then there must be a
> proposition
> which is true in D but not in C. From which it follows that
> if every
> proposition which is true in D is also true in C, then D must
> be a part
> of C, which is exactly the case you give below. (026)
I'm re-reading that paper now. And yes, you have nailed that
intuition quite well. (027)
JB>> , and there must be an alternative context that makes a
different
>> difference. (028)
PH> And that follows from this axiom and another, if we assume
that we
> can always negate a proposition and that contexts are
> internally consistent. (029)
JB>> For example, to me right now, 'yesterday' is a valid
context,
>> because I can think of things that are different between that
>> interval
>> and 'today'. But 'yesterday-10:32am-to-10:42am' is not a valid
>> context
>> because I cannot think of anything (without further
>> investigation) that
>> falls into that particular interval. (030)
PH> I bet you can. For example, the proposition "It is now 10.40
am" is
> true in there but not outside it. But maybe you don't want to
> count that
> as a 'real' proposition, fair enough. (031)
Right, and as soon as I read that I realized that I could, given
an infinite lifetime, come up with such a proposition for any
time interval whatsoever. Or, as I just now read in your paper,
if we had a clock that spits out such propositions for us, we
could generate the distinctions that would create those contexts
that way. But harking back to the restrictions you placed on what
embodies an assertion, I'm not sure that such a clock counts as
the kind of agent that can assert propositions. (032)
> Pat (033)
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