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In article <12240@venera.isi.edu> smoliar@vaxa.isi.edu.UUCP (Stephen Smoliar) writes:
>In article <90Mar3.152728est.6160@neat.cs.toronto.edu> radford@ai.toronto.edu
>(Radford Neal) writes:
>>
>>Let's say that one day Penrose announces that he is able to solve, say,
>>the word problem for semi-groups - a well-known non-computable problem.
>>
>. . .  I realize that, to some extent, these issues conflict
>with a personal tendency to try to abstract the world into deductive
>operations; . . .

When I built the argument on which Radford is commenting, I was *very*
careful to apply deductive abstractions *only* to logical or
epistemological issues.  Kuhn, Feyerabend, Kitcher, and many others have
made it very clear that there can be no general method for defining the
appropriate formal abstraction in which to describe natural phenomena.
This point holds for abstraction in engineering as well as in science,
I believe.

However, deductive reasoning still has an indispensable role in all
argumentation, including scientists' arguments with each other over
theories.  I would caution against any application of the concept of
deduction outside the context of an analysis of arguments.


>Let me illustrate the difficulty by constructing what I hope is a valid
>analogy:  Penrose announces that he can solve the general medical diagnosis
>problem.  For any case from the medical literature we give him, he responds
>with the correct answer.  If you were running a hospital, would you want him
>going on rounds through your wards?

A small point: Diagnosing a case from a textbook description is different
from diagnosing a case from clinical observation.  Interpreting X-rays
is very tricky, for example.  Clinical skill is not implied by inferential
skill.  This issue is not central to the rest of your example, but I
thought it was worth mentioning.

Assuming that Penrose can magically (or whatever) diagnose from clinical
observations, he would constitute a case of a measuring device without
a theoretical explanation.  A "mysterious correlation".


>The point I am trying to get at here is that there is more to reasoning than
>getting the right answer.  If Penrose says (using whatever reasoning powers
>"work" for him), "This patient has a malignant brain tumor which will be fatal
>if not corrected by surgery within one hour," would YOU rush the patient into
>the operating room WITHOUT ASKING ANY QUESTIONS?  Whether you are an
>administrator or a fellow physician, chances are, you would want some
>kind of JUSTIFICATION for Penrose's decision before taking any hasty
>action;  and if, when confronted with the question of justification,
>Penrose were to respond, "I just know it," you would be in quite a quandary.
>(Believe me, I have no idea how I would respond in such a situation,
>particularly if I knew that Penrose's track record had been flawless
>prior to this incident.)

This example brings up an issue which is very important for AI, but is
well outside anything Penrose addresses in his book.  When a belief is
to be used as the basis for a practical decision, one's confidence in the
belief is only one factor.  The risks entailed by taking action must
also be considered, as well as the cost of the action, missed
opportunities, etc.  The rationality of an action is by no means
determined solely by the rationality of the beliefs which direct it.

It is interesting to notice the variation in the points of view of the
several actors in Stephen's story.  A consulting physician could
rationally refuse to take any position at all (moral considerations aside)
if his primary concern were his reputation.  The administrator must
consider the hospital's liability, which will be decided at least partly
on the grounds of the hospital's scientific efforts to establish Penrose'
reliability.  The patient is in quite a pickle.  Considerations of
epistemic purity are likely to have little influence on his decision.

Penrose, Neal, and I have been discussing a case in which epistemic
purity alone is relevant.  This is appropriate, since we are considering
a (fairly) well-defined hypothesis - can a robot controlled by a
computer program exhibit behavior indistinguishable from natural human
behavior.  The parameters of the discussion are also (fairly) clear -
the computer is to be allowed any finite speed, storage, and number of
processors, and is otherwise constrained only by computability theory.
The human's behavior is contrained only by the laws of physics.

As I understand Radford's objection, he is insisting that any claim that
computers are capable of modeling all real processes must address the
issues of (a) other laws of physics and (b) phenomena which are
describable but not explainable.  Since I constructed my argument in terms
of making measurements, and science proceeds by constructing abstract
deductive theories, tested by measurement and observation, I think the
argument stands.  Deduction is by no means the whole of science, but
it cannot be abandoned by scientists.

My argument (before the Peano Piano) is not based on the limitations of
the processes to be modeled, but on the limitations of the the observers'
ability to make persuasive objections to the model.

>I think the point we have to confront here is that CONVINCING reasoning lies at
>neither extreme.  If we are talking about "the process by which real
>mathematicians [or any other thinkers, for that matter] establish new
>truths," then we have no reason to believe that deductive systems are
>the only mechanisms which may kick in.

Stephen, with this point you have returned to the epistemic issue of
discovering new truths.  Your example, which involved a practical
decision, does not directly bear on the epistemic issue.  That said,
I agree with this point entirely.  (I am amazed at the difficulty I am
having in finding an area of disagreement with you, given the volume
of objections and counter-objections.  I suspect that I am not making
clear how narrow is the scope of my generalizations, which leads to
you citing the broad range of phenomena which you (rightly) believe
to be relevant to AI as a whole.)

Let me emphasize again how important the issue of practical reason is.
Although practical decision-making can be overlooked in *some* theoretical
contexts, in the daily behavior of human beings, it is absolutely
impossible to separate epistemic from practical issues.  I cannot
recommend the work of Donald Davidson too highly on this issue.  His
essay "Belief and the Basis of Meaning", in _Inquiries into Truth and
Interpretation_ is irreplaceable.  He concludes that we cannot ascribe
beliefs to an agent without also ascribing desires, and rational pursuit
of those desires.

>                                        Instead, as Marvin Minsky pointed
>out in THE SOCIETY OF MIND, such systems for formal reasoning are better
>qualified to SUMMARIZE and JUSTIFY those "new truths," once they have been
>encountered.

Could you give me a page or chapter reference on this?

>              The question then reduces to whether or not there are MECHANISMS,
>deductive or otherwise, for establishing (or even hypothesizing) them.  AI
>argues that such mechanisms do, indeed, exist;

It is certainly the case that no *effective* finitary mechanisms exist
for establishing new truths in general, although partially effective
mechanisms might.

Do you have Edelman in mind here?  Natural selection is a fine example of
a partially effective finitary mechanism (heredity at least is finitary,
though the selection process can involve non-finitary interactions with
the environment).  Whether selection can be totally effective is a very
interesting issue.  That may not even be necessary.

I mean by "effective" a property of processes analogous to recursiveness
in functions.  Before a semantic notion such as "truth", or a logical
notion such as recursiveness (or finiteness, for that matter) can be
applied to a process or its results, the process must be interpreted as
being at least linguistic.  "Truth", "effectiveness", et al are examples
of normative concepts.

>                                              but, because we have given
>so much of our attention to deductive systems, we are probably still a far
>cry from a better understanding of their nature.

At the risk of tedium (who said "that's a certainty" :-) let me emphasize
again that deduction must be applied only in models of argumentation.
In the case of determinist metaphysics, deduction is *not* applied to
the relation between objects, states, processes, or any other real thing,
but only to assertions about those things.  I can't speak for anyone
else's use of "deduction", but (excepting mistakes) my use of "deduction"
(and all logical terms) is restricted to the case of assertions.

Ken Presting