Pat, (01)
Your enormous stream-of-consciousness lists of quibbles with every
word or phrase make it difficult to keep volume down on the list. (02)
Briefly: (03)
If I thought idiosyncratic tagging schemes were the answer for
universal comprehension, or I would use one. (04)
The halting problem will obviously apply to a universal computer, but
it will not only apply to a universal computer. (05)
If you don't understand "what the problem is supposed to be" I can
only assume you haven't read the thread back to my original comment to
Ali. (06)
And from your earlier note: I was talking about computational
linguistics, broader linguistics recognizes a problem, without
agreeing on a solution (generally "grammars" of meaning/purpose,
Cognitive/Functional Linguistics etc.) (07)
-Rob (08)
On Tue, Jan 26, 2010 at 10:18 PM, Pat Hayes <phayes@xxxxxxx> wrote:
>
> On Jan 25, 2010, at 10:47 PM, Rob Freeman wrote:
>
>> On Mon, Jan 25, 2010 at 12:02 PM, Christopher Menzel <cmenzel@xxxxxxxx>
>> wrote:
>>>
>>> On Jan 23, 2010, at 9:46 PM, Rob Freeman wrote:
>>>
>>>> Why anyone would characterize undecidability as a "limit of
>>>> computation", I don't know.
>>>
>>> That's quite clear. Let me help: A problem is undecidable if it cannot
>>> be solved by any
>>> computer, even in theory. So the existence of undecidable problems (like
>>> the halting
>>> problem) shows that there are limits to the problems that computers can
>>> solve; you
>>> know, limits to computation or, better, to computability.
>>
>> This is perhaps the center of the issue. That decidability expresses
>> only a "limit of computation" is also the only "substantive claim" you
>> have made.
>>
>> Your argument is that I don't know what I am talking about because I
>> don't see the problem this way.
>
> I believe that Chris' point was more that you are using technical language
> in a nonstandard way. He is using "decideable", etc. in the way that these
> words are used in textbooks, technical meetings, research groups, etc..,
> whereas you seem to be using them in a different sense.
>
> I take it that you feel that you are speaking from a different, er,
> perspective? Put another way, you are talking about a different topic. It
> would be helpful, therefore, if you could use a different terminology, or at
> least flag your non-standard uses of the usual terminology. In another
> forum, a similar difficulty arose over the word "representation", and we now
> routinely use there such locutions as tag:representation,
> awww:representation, etc., to clarify our intended meanings.
>
>>
>> My question was of course rhetorical. I wanted people to think about
>> the problem from the opposite perspective.
>
> I for one am not yet sure what this other perspective is, however.
>>
>> The idea undecidability expresses a "limit of computation" only makes
>> sense from the point of view of a theory within which a "decision" is
>> valid. Without a theory, you cannot have "decidability".
>
> Im not sure what you mean by 'theory' here, but the notion of
> undecideability seems fairly well-defined already. But perhaps
> rf:undecideability has a different meaning.
>
>>
>> Looked at from the other perspective, from the point of view of the
>> computation,
>
> "point of view of the computation" ?? Can a computation be said to have a
> point of view? If you mean, using the ideas of computation theory, that is
> exactly what the standard notion does.
>
>> it is the idea of theory which is limited. From this
>> perspective "undecidability" becomes what Wolfram calls "computational
>> irreducibility".
>>
>> For instance the halting problem might be seen as the "theory" that a
>> program either halts or it doesn't.
>
> No, that is simply a tautology.
>
>> Well, Turing tells us that in
>> general this is unknowable, in finite time.
>
> Not exactly. Many programs' halting is completely knowable. The program
>
> begin
> L: goto L;
> end
>
> does not halt, for example, and this is knowable. Turing's result is that
> there is no *single* program which can determine the termination of *all*
> programs.
>
>> That's just a fact about
>> the world.
>
> True.
>
>> Does this then mean computation has failed? No
>
> Um... did anyone every say that it meant that? It does mean that computation
> has certain limits on what it can do. I don't myself think they are very
> important or significant limits, but they do have some philosophical
> implications that some folk have found important. Some people for example
> have argued that this shows that computers can never match human abilities,
> but these arguments are flawed [1]
>
>> , the way to
>> understand this is not to say that computation is unable to provide an
>> answer, the way to understand it is to say that the question
>> halting/not halting may not make sense.
>
> Oh, but it *does* make sense. As a matter of fact, it is true of every
> program either that it halts or that it does not halt. This is another fact
> about the world.
>
>> Absolute knowledge of halting
>> or not halting is not a valid theory of the world.
>
> Universal *knowledge* , at least computably defined, is not possible. But
> for every program, either it halts or it does not. In fact, it does not
> follow from Turing even that this is impossible to determine; only that
> there is no *single* method which works for all programs. But there may be
> an infinite sequence of halt-detection methods, such that for any program P
> at all, there is a method in the sequence which determines the halting of P.
> But there cannot be a single program that generates this sequence.
>
>>
>> It is a bit like quantum mechanics. QM "fails" to tell us whether we
>> should think of light as a wave or a particle.
>
> It (well, the Copenhagen interpretation) tells us that we *must* think of
> every physical thing on *both* ways.
>
>> But is this a "limit of
>> quantum mechanics" (by analogy with the "limit of computation")? No,
>
> Again, did anyone ever suggest it was? Or that these might be analogous?
>
>> we just have to come to terms with the reality light is both. What is
>> wrong is the question itself. The either/or wave or particle theory is
>> not a valid model of the world (in general.)
>>
>>> See ya. I'm done trying to help.
>>
>> Thanks for participating. At least you are willing to express the
>> traditional point of view, which helps put the solution in context.
>
> So far, I havn't seen any other point of view expressed, nor do I know what
> the solution is, not what it is supposed to be a solution to, ie what the
> problem is supposed to be.
>
> Pat Hayes
>
> [1] Laforte, Hayes & Ford, Why Godel's Theorem cannot refute
> computationalism. http://www.ihmc.us/users/phayes/Pub/LaforteHayesFord.pdf
>
>
>>
>> -Rob
>>
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>
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> (09)
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