On Jul 25, 2012, at 6:25 AM, John F Sowa wrote: (01)
> 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. (02)
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. And I strongly suspect that in fact, there isn't. That is, the
common framework of 'context reasoning' is empty, null, vacuous. 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; NOTHING could be inferred about truth on one context from truth in
any other context; 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. This is not a logic, it is a systematic denial of the possibility of
there even being a logic. 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".) 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. 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, intuitions, so to force them into a
single common theory is a rather obvious intellectual mistake. But if one's
goal and ambition is to find or create the ultimate "context logic" then this
rather obvious conclusion is ruled out a priori. The very use of this
pernicious and meaningless word blinds people to the obvious richness and
heterogenaity of the world they are looking at. (03)
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. 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. (04)
Pat (05)
>
> 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 (06)
Sorry, can't let that go by. No, it can't be implemented in LISP, in this or
any other way. (07)
> 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. (08)
Maybe, but that still doesn't make it right. :-) (09)
Pat (010)
>
> 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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