On Jul 25, 2012, at 3:41 PM, doug foxvog wrote: (01)
> On Wed, July 25, 2012 13:07, Pat Hayes wrote:
>> On Jul 25, 2012, at 6:25 AM, John F Sowa wrote:
>>> On 7/25/2012 12:45 AM, Pat Hayes wrote:
>>>> JMcC's point was that there was no single "theory" of contexts; that
>>>> contexts are not a natural kind, and a "context" is just anything
>>>> that anyone cares to use in a context kind of a way, ie as something
>>>> that influences truth values and denotations.
>>>
>>> I agree with that idea.
>>>
>>>> my (often repeated) objection that time, for example, and belief,
>>>> for example, were very different kinds of thing and influenced
>>>> truth in very different kinds of ways...
>>>
>>> I also agree with that.
>>>
>>>> his response was always that the point of a context logic was not
>>>> to capture the essence or nature of contexts, but rather to be simply
>>>> a general framework for stating inferences which might be influenced
>>>> by *any* kind of context.
>>>
>>> And I have no objection to that idea.
>>
>> Ah, but I do. It presupposes that there IS a single overarching framework
>> which covers temporal, epistemic, ... and many other kinds of reasoning,
>> under one common umbrella.
>
> If there is such a presupposition of an overarching framework, it is merely
> (imho) that what is true in one "context" is not necessarily true in some
> other "context". (02)
OK, so you are assuming it makes sense to speak of truth "in" a context, as
opposed simply to truth. So we have to ask, what does this mean exactly? What
is "truth in" that is different from truth, simpliciter? Lets look at some
examples that have been suggested. The most obvious is truth in a
time-interval. That seems fairly clear: things can be true at one time but not
at another, *provided* we agree that we are talking in a language that is
time-embedded, or as it is often phrased, a tensed language. So if we say, "it
is raining", this means it is raining *at the time of utterance*, ie it can be
paraphrased as "it is raining *now* ". So, being true-in a time makes sense for
tensed sentences, but less so for untensed ones. Note that traditional boolean
logic is not considered to be a tensed language. Another example: the context
might be a place or location, and the sentence then is assumed to be
geographically indexical, so that "it is raining" means "it is raining (now),
*here* ". So this makes sense as long as our language is understood to be
spatially sensitive, what one might call a located language. Again, traditional
boolean logic is not considered to be a located language. We can repeat this
exercise for any kind of "context", and what we always find is that the idea
makes sense provided that the language is understood to be contextually
sensitive in the appropriate way. But classical logics are not considered to be
sensitive in these ways: they are used to represent simple truths, not
temporally or spatially located assertions. This is why all the talk about data
being contextual misses the point. If the data is asserted in a simple boolean
logic (such as CL or IKL or RDF or OWL), and if that data is understood to be
time- or location-sensitive, then it is just badly stated. It is using the
specifications of the language incorrectly. Information represented in CL or
IKL or RDF or OWL is asserted to be true, simpliciter, not true-in some kind of
context. If the data is time-sensitive then it should have a time record
included in it somewhere; if it is geographically sensitive then it should have
the location included in it somewhere. And so on. In a noncontextual logic, it
simply does not make sense to talk of truth-in something: one has to speak
simply of truth. One does not say, it is raining; one says, it rains in
Pensacola in the evening of the 25 July 2012. And that is simply true, not
true-in something. (03)
>> And I strongly suspect that in fact, there
>> isn't. That is, the common framework of 'context reasoning' is empty,
>> null, vacuous.
>
> I basically agree. A statement made in one context would have no bearing
> on a statement made in any other context (04)
That is not my point. My point was that the various *kinds* of context have
nothing in common, so that any suggested *general* logic of contexts will be
vacuous. (05)
> except in so far as specific
> rules provide for such reasoning between the two contexts.
>
> The same set of rules would not apply to any pair of contexts in general.
> General classes of rules could be made for sets of mutually compatible
> temporal contexts, while others could be made for sets of mutually
> compatible epistemic contexts, etc. (06)
Indeed? Can you suggest, or cite, any plausible such rules? I have never seen
any that are anything but completely trivial. To take one of the simplest
examples, suppose P is true in T, where T is a time-interval, and let S be a
subinterval of T. Is P true in S? Why? (HInt: it depends on P. Some are, some
aren't.) (07)
> Unless some statement specified
> that two contexts were mutually compatible (in some way) they would
> not be.
>
>> Certainly, the logics that Makarios was talking about at
>> the IKRIS meetings had got to that point. ANYTHING (including logical
>> contradictions) was allowed to be "true" in any context;
>
> Doesn't IKL allow ANYTHING (including logical contradictions) for
> propositions? One can then state (ist c ANYTHING). (08)
Yes, you can. IKL allows you to write axiomatic theories about contexts, but it
does not impose any *logical* conditions on them. Interestingly, I havn't seen
many suggestions for a nontrivial axiomatization of contexts, though I tried
hard to make one in a later AAAI symposium paper, which AFAIK is the most
thorough axiomatic investigation of the idea yet attempted: (09)
www.ihmc.us/users/phayes/SS05HayesP.pdf (010)
but even the simplest suggested axioms were vulnerable to objections from some
"context theorists". When challenged to suggest alternatives, neither John McC
nor Selene Makarios were able to come up with any. (For the record, Selene
objected to my axiom 2, and John to my axiom 5.) (011)
>> NOTHING could be
>> inferred about truth on one context from truth in any other context;
>
> In general, i'd agree. Rules would be necessary to conclude something
> in one context from something in another. (012)
I'll believe it when I see some examples. But in any case, you can't state
rules like this in a context *logic* because in such a logic everything is
stated relative to a context, so the "rules" would not apply outside the
context they were asserted in. (013)
>
>> there
>> was no way to state even a simple tautology without stating it in some
>> context which provided no guarantee that it would be true elsewhere.
>
> Unless there were some universal context which every context must
> inherit, yes. But would one want such a universal context? If one
> could state a tautology, why couldn't one state (P & (not P)) -- or
> something more complex that a reasoner could not automatically
> reject, but which entails such a falacy? (014)
I am not following you here, I'm afraid. Suppose I want to axiomatize
arithmetic. Which context do I assert my axioms in? How do I do sums in a
different context? (015)
>> This is not a logic,
>
> Agreed. It is a way of relating (or not) different sets of statements,
> each of which can be separately reasoned about in a logic. (016)
But we can do this is normal classical logic. We don't need a new formalism to
reason logically about a set of statements. That is what logics are for. (017)
>> it is a systematic denial of the possibility of there even
>> being a logic.
>
> I don't see this at all. (018)
It has no logical principles. There are no tautologies in a general context
logic. None, zip, nada. (019)
>> It is utterly without semantic or rational principles of
>> any kind, and it was completely useless even as a working notation. And
>> you get to this point because every suggestion
>> that one might make for any rational principle has some kind of
>> counterexample. (P & (not P)) must be "satisfiable" because if the
>> context is a document, that document could contain a contradiction (so it
>> would in this odd sense be "true" in that "context".)
>
> Note that in IKL:
> (ist c (and P (not P)))
> can be true even though "ist" means since the second argument is a
> proposition. (020)
Well, IKL puts no conditions on the relation "ist", which is just a neutral
relational symbol until you provide axioms for it, so technically you are
right. But I would suggest that if (021)
(ist c (that (and (P) (not (P))))) (022)
can be true, then one should not read "ist" as saying "is true in". False is
not true in anything. (023)
> This does not cause the problem mentioned below.
> Inter-context reasoning is similar.
>
>> No matter that this
>> is logically impossible in all temporal and indeed almost all other kinds
>> of "context": one example from one odd corner of the space of "contexts"
>> is enough to ensure that it must be allowed as a counterxample to
>> thousands of years of intuitions about truth.
>
> That would be true ONLY if there was a rule that such a statement in ANY
> context would be true in EVERY context -- which is totally in violation of
> any definition of "context" which i have ever seen. (024)
Again, I fail to follow you here. My point has nothing to do with rules. (025)
>
>> The rational conclusion to
>> draw, it seems to me, is that truth at times (for example) and "truth"
>> understood to mean asserted by a document, are different notions with
>> different logics based on different, and indeed incompatible,
>
> I'm not sure that they need to be incompatible. (026)
Think about it. Are the "true" in "true at a time" and the "true" in "true if
the world according to Arthur Conan Doyle were actual" really the same notion?
Is tense a kind of fiction, or fiction a kind of tense? (027)
>
>> intuitions,
>> so to force them into a single common theory is a rather obvious
>> intellectual mistake.
>
> A general rule for such would be such a mistake. But a rule designed
> for individual cases is a different matter (imho). (028)
I agree, which is why I am arguing that to be aiming to create a *general*
logic, as opposed to logics for the various special cases, is a mistake. (029)
>
>> But if one's goal and ambition is to find or create
>> the ultimate "context logic" then this rather obvious conclusion is ru
>> led out a priori.
>
> "The ultimate context logic" seems like a straw man to me. (030)
But that is what "context logic" claims, and is intended, to be: a *single*
logic which subsumes tensed logic, epistemic logic, spatial logic, a
(hypothetical) logic of fiction, a logic of conversational topic structure, a
logic of cultural relativity, a logic of lexical ambiguity and a myriad other
things that have nothing in common. (031)
> The
> only such logic i could envision is a set of rules such as:
>
> (implies
> (and
> (intercontextRelationBetween ?Context1 ?Context2 ICRelation1)
> (ist ?Context1 (and <set of conditions>))
> (ist ?Context2 (and <another set of conditions>)))
> (ist ?Context1 <conclusion>))
>
> can be stated in some context and a reasoner in that context can use such
> rules to derive conclusions.
>
>> The very use of this pernicious and meaningless word
>> blinds people to the obvious richness and heterogenaity of the world they
>> are looking at.
>
> ? (032)
If you think that times, places, fictions and documents are all kinds of
"context" then you have made negative progress. In fact, there isn't anything
that these are all kinds of. This was taken to be obvious by everyone before
the use of the word "context" as a classifier somehow made a mass hallucination
take place where people thought they were actually saying something useful by
referring to "contexts". (033)
>
>> This can even be seen in the history of the formalisms developed. Modal
>> tense logics have been around now since the 1920s and have been
>> *thoroughly* well-understood since the 1960s. Epistemic logics have a
>> similar history.
>
> Of course, we should build on prior work. Sowa constantly emphasizes
> this. (034)
It is not "building on" prior work to re-name the topic and then use this
re-naming as an excuse to ignore all prior work. (I risk offending people if I
take this much further, but there are entire doctoral theses which simply
re-iterate, in new language, facts that were considered fairly obvious 50 years
earlier.) (035)
>> I have had conversations with graduate students who saw
>> themselves as working on "context reasoning" who were utterly ignorant of
>> all this work (and had been slowly, and awkwardly, re-discovering the
>> basics of it about 70 years late) because, they explained to me, they were
>> developing a new CONTEXT logic as opposed to a mere logic of time or of
>> belief. By taking "context" to refer to something, they thought they were
>> doing original research, when in fact they were simply re-doing old work,
>> badly.
>
> Just because someone does something poorly ignoring prior art, doesn't
> mean that someone knowledgeable in prior art could not do better. (036)
My point is that there is an entire intellectual culture now in existence which
takes "context reasoning" to be a well-defined research topic (for example,
enough to justify a series of international research symposia, a journal and
many doctoral theses) and by virtue of this entirely specious claim, justifies
ignorance of previous work which happened to not use the term "context". This
is like declaring that stone, bricks, steel and wood are all kinds of
"materials" and then inventing a general science of "material" which ignores
the particulars of bricks, stone, steel and wood in order to develop a general
theory of "material". (037)
Pat (038)
>
> -- doug
>
>> Pat
>>
>>
>>>
>>> JFS
>>>>> "(that p)" is a kind of quasi-quotation that allows
>>>>> variables in p to be bound to quantifiers outside of p.
>>>
>>> PH
>>>> Hmm, I don't think it is correct to think of it as quasi-quotation.
>>>> Rather than quoting the sentence, it treats it as defining a
>>>> zero-ary predicate, and creates a term denoting that entity.
>>>
>>> The backquote in LISP can be applied to any expression. The IKL
>>> 'that' operator can be implemented in LISP
>>
>> Sorry, can't let that go by. No, it can't be implemented in LISP, in this
>> or any other way.
>>
>>> by applying backquote
>>> to sentences in some version of logic.
>>>
>>> That is an explanation that is meaningless to anybody who does
>>> not know LISP. But LISP aficionados like that way of talking.
>>
>> Maybe, but that still doesn't make it right. :-)
>>
>> Pat
>>
>>>
>>> In any case, I agree that your definition is the proper way
>>> to define 'that' in purely CL or IKL terms.
>>>
>>> John
>>>
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