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"david petry" <david_lawrence_petry@xxxxxxxxx> writes:
> Jesse F. Hughes wrote:
>
>> Say, you seem to have missed a few of my questions. Let me helpfully
>> reprint them here. For simplicity's sake, let me also change from the
>> Busy Beaver function to the halting problem.
>>
>> Is the phrase "The halting problem cannot be computed" meaningful?
>
> We've already discussed this question in this thread.
Then why not answer the question?
>
> Notice that all by itself, the statement "The halting problem cannot be
> computed" does not deny the possibility that there is a very short,
> simple, and efficient algorithm that takes any computer program of less
> than, say, a zillion squared lines, and tells us whether or not that
> program halts. Doesn't that suggest to you that that statement has
> nothing concrete to say about the phenomena we can observe?
I didn't ask about that statement.
By the way, there *are* indeed results that show that what you suggest
is impossible (if a zillion is big enough, anyway). These theorems
say something like: if n is large enough, then no program much smaller
than n can solve the up-to-n length halting problem.
Are those theorems meaningless, too?
Is it possible to use a meaningless statement to justify another
(meaningful) statement? If "The Busy Beaver function (or halting
problem) is uncomputable" is *literally meaningless*, then can one
reasonably write something like "Since the Busy Beaver function is
uncomputable, blah blah blah" or is he just babbling?
--
Jesse F. Hughes
"Truth is common stuff, ready to your hand, but lies you have to make
yourself, and you can't be sure they are any good until you've
used them --- and then it's too late." John Steinbeck
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