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. Imagine that Peter and Daryl are both robots,
and their behavior is completely specified by a computer
programs, and that both Peter and Daryl have access to
each other's programs. In that case, it is exactly analogous
to the halting problem.

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". Daryl was asked whether
Peter's next utterance will be "no". That's a complete question.

we would obtain:

'Will Daryl answer 'yes' to the question whether you will answer 'no'
to the question whether Daryl will answer 'yes' to the question
whether...?'

Yes, you can expand any question into an equivalent longer question.
The point is, there is no ambiguity about what each is asked to do.

'Will Daryl answer 'yes' to the question whether you will answer 'no'
to this question?'

Now the self-reference only makes the circularity still more evident.

What difference does it make whether it is self-referential or not?
There is no ambiguity in what each is being asked to do.

If they were completely described by computer programs, then
it is clear what is being asked:

Daryl is being asked: Will Peter's response to string S be "no"?
Peter is being asked: Will Daryl's response to string S be "yes"?

where string S is just the description of the game. There is no
uncertainty or ambiguity here, other than the fact that (in the
case of humans) we each only have partial knowledge of the behavior
of others.

The halting problem contains no circularity in its definition because
it poses a purely syntactical or mechanical question with no semantic
or intentional dimension.

There is no semantic dimension here, either. Human beings are physical
systems that work through natural laws. If we had perfect understanding
of those laws (and of the initial conditions), then we would know what
Peter's response will be (or else, his response could be nondeterministic,
in which case we could make probabilistic predictions).

In contrast, and using phenomenological terms, we can say that no
intentional act of thinking can be its own intentional object; call
'PNS' that proposition; so according to PNS, it is not the case that
any intentional act is a possible object for any thinking subject.

I'm not sure what you are talking about. The question of what
Peter's response to the game will be is a purely physical question.
There is a causal chain from the act of Peter being told the rules
to Peter producing certain sounds from his mouth. We only have partial
knowledge of that causal chain, but I don't see how in principle there
is any difference between asking a question about the response of
a human being and asking a question about the behavior of a computer
program.

This is why your questions to Peter and Daryl cannot be well defined
questions for none of them:

They are completely well-defined questions. Either Peter's response will
be "no", or it won't. Either Daryl's response will be "no" or it won't.
There is no third possibility. (Well, actually, the third possibility
is that they will not answer, or will answer using an illegal reply
such as "I don't know"---but in that case, it is false that the answer
is "yes" and it is also false that the answer is "no").

trying to answer them correctly would force them to consider their
own attempt to answer and this would be phenomenologically impossible.

No, that's not correct. For Daryl to answer the question, he only
needs to know how *Peter's* mind works. It's not self-referential
in that respect. Daryl only needs to know what Peter *believes*.
Those beliefs may not be correct.

Maybe we've met here an essential difference between thinking behaviors
and machines: only the latter are always possible objects for the
former.

I think that's incorrect.

--
Daryl McCullough
Ithaca, NY

.

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