Re: Halting Problem for Humans



LauLuna says...
There is a crucial difference between the case you propose and the
halting problem. The halting problem is a well defined question while
your questions to Peter and Daryl are not.

Not really.

Daryl McCullough wrote:
Yes, really, if by "not-well-defined" we mean "not reasonably
translatable into a TM-like paradigm" (which is, after all, a very
powerful definitional framework).

Imagine that Peter and Daryl are both robots,
and their behavior is completely specified by a computer
programs,

That means we might was well call them the PTM and the DTM.
And, imagine further that they are THE SAME program, except for
a version-code (P in one case, D in the other)
that doesn't affect the behavior of either program,
but simply suffices to ensure that their names and source-codes are
different strings. This STRONGLY highlights the difference between
the TM world, which does NOT have indexicals or demonstratives,
and the natural-language one, which does. If you give EITHER of
the PTM or the DTM *any* input-
string whatsoever, THEY ALWAYS produce THE SAME output. BUT if
you ask of them, "What is your output when you are given YOUR OWN code
as an input-string?" then despite the fact that you are asking what
looks
like "the same question" to both of these machines, you may get
DIFFERENT outputs (assuming 'P' and 'D' are in both input-alphabets)
because the natural-language "your own code"
translates to DIFFERENT input-strings for the two machines, when
you cross over to the other paradigm.

and that both Peter and Daryl have access to
each other's programs. In that case, it is exactly analogous
to the halting problem.

No, NOT exactly, because it asks about "the next" response AS OPPOSED
to the response for some known input string, which is a thing that
CANNot be "next".

In the case of real humans, it only becomes fuzzier because
we lack perfect knowledge about the mechanisms by which each
of us makes decisions.

Each of them is circularly defined. Trying to complete the text of the
question to Peter (which I suppose you think contextually completed)

The question was already complete. Peter was asked whether
Daryl's next utterance will be "yes".

That is NOT complete. It is not even TM-translatable AT ALL.
If you try to take the time out of it (and put it back into TM-speak)
then you will see that you get a mutual recursion (NON-founded).

.

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