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. (01)
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)
> And I strongly suspect that in fact, there
> isn't. That is, the common framework of 'context reasoning' is empty,
> null, vacuous. (03)
I basically agree. A statement made in one context would have no bearing
on a statement made in any other context except in so far as specific
rules provide for such reasoning between the two contexts. (04)
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. Unless some statement specified
that two contexts were mutually compatible (in some way) they would
not be. (05)
> 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; (06)
Doesn't IKL allow ANYTHING (including logical contradictions) for
propositions? One can then state (ist c ANYTHING). (07)
> NOTHING could be
> inferred about truth on one context from truth in any other context; (08)
In general, i'd agree. Rules would be necessary to conclude something
in one context from something in another. (09)
> 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. (010)
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? (011)
> This is not a logic, (012)
Agreed. It is a way of relating (or not) different sets of statements,
each of which can be separately reasoned about in a logic. (013)
> it is a systematic denial of the possibility of there even
> being a logic. (014)
I don't see this at all. (015)
> 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".) (016)
Note that in IKL:
(ist c (and P (not P)))
can be true even though "ist" means since the second argument is a
proposition. This does not cause the problem mentioned below.
Inter-context reasoning is similar. (017)
> 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. (018)
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. (019)
> 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, (020)
I'm not sure that they need to be incompatible. (021)
> intuitions,
> so to force them into a single common theory is a rather obvious
> intellectual mistake. (022)
A general rule for such would be such a mistake. But a rule designed
for individual cases is a different matter (imho). (023)
> 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. (024)
"The ultimate context logic" seems like a straw man to me. The
only such logic i could envision is a set of rules such as: (025)
(implies
(and
(intercontextRelationBetween ?Context1 ?Context2 ICRelation1)
(ist ?Context1 (and <set of conditions>))
(ist ?Context2 (and <another set of conditions>)))
(ist ?Context1 <conclusion>)) (026)
can be stated in some context and a reasoner in that context can use such
rules to derive conclusions. (027)
> The very use of this pernicious and meaningless word
> blinds people to the obvious richness and heterogenaity of the world they
> are looking at. (028)
? (029)
> 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. (030)
Of course, we should build on prior work. Sowa constantly emphasizes
this. (031)
> 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. (032)
Just because someone does something poorly ignoring prior art, doesn't
mean that someone knowledgeable in prior art could not do better. (033)
-- doug (034)
> 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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