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AIList Digest Volume 8 Issue 028
AIList Digest Wednesday, 27 Jul 1988 Volume 8 : Issue 28
Today's Topics:
Free Will:
Undecidability
How to dispose of the free will issue
How to dispose of naive science types (short)
Free Will (long)
----------------------------------------------------------------------
Date: Sun, 24 Jul 88 09:42:23 PDT
From: John B. Nagle <jbn@glacier.stanford.edu>
Subject: Re undecidability
Goetz writes:
> Goedel's Theorem showed that you WILL have an
> unbounded number of axioms following the method you propose. That is why most
> mathematicians consider it an important theorem - it states you can never have
> an axiomatic system "as complex as"
> arithmetic without having true statements which are unprovable.
Always bear in mind that this implies an infinite system. Neither
undecidability nor the halting problem apply in finite spaces. A
constructive mathematics in a finite space should not suffer from either
problem. Real computers, of course, can be thought of as a form of
constructive mathematics in a finite space.
There are times when I wonder if it is time to displace infinity from
its place of importance in mathematics. The concept of infinity is often
introduced as a mathematical convenience, so as to avoid seemingly ugly
case analysis. The price paid for this convenience may be too high.
Current thinking in physics seems to be that everything is quantized
and that the universe is of finite size. Thus, a mathematics with infinity
may not be needed to describe the physical universe.
It's worth considering that a century from now, infinity may be looked
upon as a mathematical crutch and a holdover from an era in which people
believed that the universe was continuous and developed a mathematics to
match.
John Nagle
------------------------------
Date: 24 Jul 88 1526 PDT
From: John McCarthy <JMC@SAIL.Stanford.EDU>
Subject: free will
[In reply to message sent Sun 24 Jul 1988 02:00-EDT.]
Almost all the discussion is too vague to be a contribution. Let me
suggest that AI people concentrate their attention on the question of how
a deterministic robot should be programmed to reason about its own free
will, as this free will relates both to its past choices and to its future
choices. Can we program it to do better in the future than it did in the
past by reasoning that it could have done something different from what it
did, and this would have had a better outcome? If yes, how should it be
programmed? If no, then doesn't this make robots permanently inferior to
humans in learning from experience?
Philosophers may be excused. They are allowed take the view that
the above questions are too grubbily technical to concern them.
------------------------------
Date: 24 Jul 88 23:20:24 GMT
From: amdahl!pyramid!thirdi!metapsy!sarge@ames.arpa (Sarge Gerbode)
Subject: Re: How to dispose of the free will issue
In article <421@afit-ab.arpa> dswinney@icc.UUCP (David V. Swinney) writes:
>The "free-will" theorists hold that are choices are only partially
>deterministic and partially random.
>
>The "no-free-will" theorists hold that are choices are completely
>deterministic with no random component.
If my actions were random, I would not consider myself to have "free will".
Only if my actions were self-determined would I so consider myself. As Bohm
pointed out: "The laws of chance are just as necessary as the causal laws
themselves." [*Causality and Chance in Modern Physics*]
I think most would agree that we have at least some degree of self-determinism,
and beyond that, we have some degree of causativeness over our own natures,
e.g. our habits and our understanding. That is the basis upon which laws
concerning negligence rest.
How far this "second-order" self-determinism extends is an open question, but
the issue of randomness doesn't, I think, enter into it.
--
Sarge Gerbode -- UUCP: pyramid!thirdi!metapsy!sarge
Institute for Research in Metapsychology
950 Guinda St. Palo Alto, CA 94301
--
Sarge Gerbode -- UUCP: pyramid!thirdi!metapsy!sarge
Institute for Research in Metapsychology
950 Guinda St. Palo Alto, CA 94301
------------------------------
Date: 24 Jul 88 23:36:25 GMT
From: buengc!bph@bu-cs.bu.edu (Blair P. Houghton)
Subject: Re: How to dispose of naive science types (short)
In article <531@ns.UUCP> logajan@ns.UUCP (John Logajan x3118) writes:
>gilbert@cs.glasgow.ac.uk (Gilbert Cockton) writes:
>> logajan@ns.UUCP (John Logajan x3118) writes:
>> >unproveable theories aren't very useful.
>
>> most of your theories [...] will be unproven,
>> and unproveable, if only for practical reasons.
>
>Theories that are by their nature unproveable are completely different from
>theories that are as of yet unproven. Unproveable theories are rather
>special in that they usually only occur to philosophers, and have little to
>do with day to day life. You went on and on about unproven theories but failed
>to deal with the actual subject, namely unproveable theories.
>
>Please explain to me how an unproveable theory (one that makes no unique
>predictions) can be useful?
>
Rudy Carnap wrote _The Logical Syntax of Language_ in 1937. In it
he described the development of an all-encompassing, even recursive
syntax that could be used to implement logic without bound.
One of the simplest examples of unproveability is the paradox
"This sentence is false."
It drives you nuts if you analyze it semantically; but, it's blithering
at a very low level if you hit it with logic: call the sentence S;
the sentence then says
"If S then not-S."
Even a little kid can see that such a thing is patent nonsense.
The words in the sentence--the semantics--confuse the issue; while
both sentences say exactly the same thing in different semantics.
Carnap's thesis in the book was of course that the logic of communication
is in the syntax, not the semantics.
I'm correcting myself: now that I look at it, the paradox really says
"S = not-S."
Carnap's mistake (what makes him horribly obscure these days) is
that he did all of this amongst a sea of bizarre symbolic definitions
designed as an example of the derivation of his syntactical language;
but he did it, and it's a definition of _everything_ necessary to
carry on a logical calculus without running into walls of description.
It even defines itself without resorting to outside means; sort of
like writing a C compiler in C without ever having to write one in
assembly, and running it on itself to produce the runnable code.
Of course, the computer is a semantic thing...
I would hope some stout-hearted scientists would apply this sort of thing
to unproveable theories; we might find out about god, after all.
--Blair
"To be, or not to be;
that requires one TTL gate
at a minimum, but you could
do it with three NAND-gates,
or just hook the output
to Vcc."
------------------------------
Date: 25 Jul 88 12:02:06 GMT
From: l.cc.purdue.edu!cik@k.cc.purdue.edu (Herman Rubin)
Subject: Re: How to dispose of naive science types (short)
In article <6032@bunny.UUCP>, rjb1@bunny.UUCP (Richard J. Brandau) writes:
> > gilbert@cs.glasgow.ac.uk (Gilbert Cockton) writes:
> > Please explain to me how an unproveable theory (one that makes no unique
> > predictions) can be useful?
< Perhaps you mean a NONDISPROVABLE theory. An "unproveable" theory is
< a very special thing, often much harder to find than a "proveable"
< theory. If you can show that a theory is unprovable (in some axiom
< set), you've done a good day's science.
> No theories make "unique predictions" about the real, (empirical)
> world. Are quarks the ONLY way to explain the proliferation of
> subnuclear particles? Perhaps a god of the cyclotron made them
> appear. The difference between the scientific and religious theories
> is that the scientific one can be DISproven: it makes predictions that
> can be TESTED.
>
> You may, if you like, apply this distiction to the beliefs that
> determine your behavior. Since you can't disprove the existence of
> God, you may choose to chuck out all religion. Since you CAN think of
> ways to disprove f=ma, you may avoid being run over by a bus.
It is recognized that any non-trivial complete theory cannot be exactly true.
If I say that there will be some history of the universe, this is a trivial
untestable theory, and is completely useless. If I say that the motion of
the planets is describable by Newton's law of gravity, this is clearly false,
but is quite adequate for spaceship navigation. Even with relativistic
corrections it is false, because it ignores such things as tidal friction.
Furthermore, we do not know the precise form of gravitation in a relativistic
framework, and even less the modifications due to quantum mechanical considera-
tions.
In the strict sense, we will never have a correct theory. The proper question
about a theory is whether its errors should be ignored at the present time.
And it is quite possible that for some purposes they should and for others
they should not. But unless the theory provides predictive power or insight,
its accuracy is unimportant.
--
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)
------------------------------
Date: Mon, 25 Jul 88 13:22 EST
From: steven horst 219-289-9067
<GKMARH%IRISHMVS.BITNET@MITVMA.MIT.EDU>
Subject: Free Will (long)
A few quibbles about some characterizations of free will and
related problems:
(1) D.V.Swinney (dsinney@galaxy.afit.af.mil) writes:
> The "free-will" theorists hold that are (sic) choices are only
> partially deterministic and partially random.
>
> The "no-free-will" theorists hold that are (sic) choices are
> completely deterministic with no random component.
I'm not really sure whether Swinney means to equate free will with
randomness, but if he does he is surely mistaken. On the one hand,
there are some kinds of randomness that are of no use to the free
will theorist: the kind of randomness suggested by quantum physics,
for example, does not give the free will theorist what he wants.
One can believe in quantum indeterminism without believing in
free will. On the other hand, the term "choice" is ambiguous between
(a) the ACT OF CHOOSING and (b) THAT WHICH IS CHOSEN (in this case,
let's say the behavior that results from the choosing). It's not
clear which of these Swinney means. I think that what the free will
theorist (at least some free will theorists, at any rate) would say
is that the CHOOSING is not determined (in the sense of being the
inevitible result of a previous state of affairs governed by a
universal law), but the resulting behavior IS, in a sense, determined:
it is determined by the act of choosing and the states of the
organism and its environment that allow what is chosen to be carried
out. (There is a fairly large philosophical corpus on the subject
of "agent causation".)
What the advocate of free will (we'll exclude compatibilists for
the moment) must not say is that choices freely made can receive
an adequate explanation in terms of natural laws and states of
affairs prior to the free act. So Swinney is right that
(non-compatibilist) free will theorists are not determinists. But
randomness just doesn't capture what the free will theorist is after.
And I think the reason is something like this: human actions can be
looked at from an "external" perspective, just like any other events
in the world. As such, they either fall under laws covering causal
regularities or they do not, and so from this perspective they are
either determined or random. But unlike other events in nature,
the actions (and mental states) of thinking beings can also be
understood from an "internal" or "first-person" perspective. It is
only by understanding this perspective that the notion of FREEDOM
becomes intelligible. Moreover, it is not clear that the two
perspectives are commensurable - so it isn't really clear that one
one can even ask coherent questions about freedom and determinism.
At any rate, the notions of "freedom" and "bondage" of the will
are not reducible to indeterminism and determinism.
(2) John Logan (logajan@ns.uucp) writes that
> Unproveable theories aren't very useful.
and that
> Unproveable theories are rather special in that they usually only
> occur to philosophers.
If we were talking about logic or mathematics, Logan's assertions
might be correct, though even there some of the most interesting
"theories" are not known to be proveable. But in the sciences, NO
interesting theories are proveable, as Karl Popper argued so
persuasively (and frequently and loudly) for many years. The nature
of the warrant for scientific theories is a complicated thing.
(For those interested, I would recommend Newton-Smith's book on
the subject, which as I recall is entitled "Rationality in Science".)
Perhaps Logan did not mean to conjure visions of the logical
positivists when he used the word "proveable", in which case I
apologize for conjuring Popper in return. But the word "proof"
really does bring to mind a false, if popular, picture of the nature
of scientific research.
Steven Horst
BITNET.......gkmarh@irishmvs
SURFACE......Department of Philosophy
Notre Dame, IN 46556
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End of AIList Digest
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