|To:||"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>|
|From:||Pat Hayes <phayes@xxxxxxx>|
|Date:||Fri, 18 Jan 2008 10:23:45 -0600|
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:
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. - Pat Hayes
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").
PH> Not sure I understand the question. The identification of a category is what a definition does. The category in question is "context".
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.
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.
PH> Do you see the point?
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.
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.
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.
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.
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.
However, for what its worth, to fully capture my own intuitions about it, speaking of sets
er...why are we speaking of sets?
, 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.
You've lost me now. I have two sets, and therefore one of them is a cause of the other (?)
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.
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.
Did you mean to have (or A (not A)) as your tautology?
This is pragmatic, to count as a context it must make a difference
If I understand you, I agree. In fact, that is the basic content of one of the axioms in the note on context mereology
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.
, and there must be an alternative context that makes a different difference.
And that follows from this axiom and another, if we assume that we can always negate a proposition and that contexts are internally consistent.
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.
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.
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