From: crawford@boole.mitre.org (Randy Crawford)
Subject: Re: Atheism and Intelligence
Organization: The MITRE Corporation, McLean, VA
Date: Tue, 22 Dec 1992 06:38:43 GMT

In article <1h5l7pINNd73@sal-sun53.usc.edu> ericjohn@sal-sun53.usc.edu (Eric Johnson) writes:
>In article <1992Dec18.062438.6456@linus.mitre.org>, crawford@boole.mitre.org (Randy Crawford) writes:
>|> In article <1992Dec16.231131.1173@umr.edu> S106495@UMRVMA.umr.edu writes:
>|> >Another alternate logic I am
>|> >speaking of is neural networks.  These are computer algortithms
>|> >where the machine takes the factors toward a given conclusion,
>|> >and thru trial and error perfects an algorithm to give a conclusion.
>
>NNs aren't 'alternate' logics, but (as you said) algorithms. Everything
>that they do can be expressed in terms of starndard logics.
>
>|> Not `a' conclusion.  NNs can only lead you to `the' predetermined 
>|> conclusion.  NNs are useful only when you know the goal state, but 
>|> don't know how to get there.
>
>You are confusing the training of a neural net with it's operation. Yes, 
>to train a NN, you must have a known goal state(s) handy, much as you 
>would need a training example to teach a human to do something. The 
>operation of a neural net isn't 'trial and error' at all; it uses 
>the relations it learns in the training phase to come to a conclusion.
>Unfortunately, these relations are expressed in a way that is not 
>directly understandable to humans - using a NN, we *still* don't know
>how to get there... Neural nets can be trained to perform logical
>inferences and deductions... the one in my head is!

Two points.  You cannot divorce the operation from a neural net from its
learning phase.  The entire process of a NN learning and then executing is
equivalent to an A* search, either algorithm will amount to nothing without
an evaluation function -- in the case of the NN, to decide whether it's
learning, and in the case of the A*, to determine how far you are from the
goal state.

This is similar to divorcing propositional or predicate logic from the
acquisition of the given propositions on which they function.  Without
the precedent truth values, all the method in the world will amount to nil.

Secondly, you assume a lot when you state that your brain is an NN.  I'm not 
at all convinced that NNs and brains have much in common, because the more
we have learned about each, the more different they appear to be.

>
>|> In no way do NNs resemble _any_ form of logic equivalent.  Trial and 
>|> error is not a form of reasoning -- it couldn't be.  In logic, you don't 
>|> yet know the conclusion you need to reach.  You have confidence that in 
>|> the use of the method (which you understand and can verify) and that you 
>|> will reach a reproducible and valid conclusion.  In trial and error, you 
>|> know the conclusion but not how to get there.  How then could you use 
>|> trial and error to reach a logic-like conclusion when you can't tell at 
>|> each step whether you have made any forward progress since you don't 
>|> know what the conclusion is nor if you're approaching it?
>
>Even discounting the fact that neural nets don't use trial and error to 
>solve problems, you are still wrong. Reasoning doesn't operate in a
>vacuum - you attempt to prove or disprove conclusions, or at least to
>derive conclusions which have certain desirable properties. Otherwise,
>your reasoning process would never produce a result. Reasoning can be
>viewed as a search problem through the space of possible conclusions, 
>and generate-and-test is one possible search strategy. You could use
>trial and error both to select likely conclusions to attempt to prove
>or disprove, and also to guide your reasoning process each step of the
>way to the solution.

Again this assumes that some magic force exists during the NN's learning 
phase which knows the goal states and thereby directs the teaching of the 
NN.  This is pretty different from logic, where the goal state is unknown.
(Although I do agree, it isn't trial and error either.)

And discounting our disagreement as to the role of learning, I still disagree
with you that generate-and-test is a viable search method unless you are given
the goal state ahead of time.  Again, how do you know you've arrived when you
don't know where you're going or how you'll know when you get there?  In
trial and error, an external oracle is necessary to raise a flag and shout 
`success!', just as in the learning phase of neural nets.  This is just not
the case in logic.

In logic, you are trying to get somewhere unknown by applying axioms to
known predicates.  You know your start state, the given predicates.  You know
something of the relationships among the agents represented by the predicates.
You don't know the goal state, nor how to get there.  You must choose among
the available logical axioms to deduce new predicates and then evaluate them
using the same predicates and axioms.  The choice of which axiom or predicate
to use is arbitrary == random.  Ultimately you will run out of enabled axioms
and predicates and then you've reached stasis.  If you don't know all you 
needed to know by then, you are out of luck.  But by no means does this 
resemble trial and error or the teaching and using of a neural net.

I am applying logical process as inherently forward chaining, proceeding from 
given truth values for specific predicates to subsequent truth values for 
other predicates based on (effectively) irrefutable axioms and lemmas.  
Clearly, if you were to convert this to a backward chaining system the process
would remain the same -- you begin with the goal state and apply the axioms
in reverse to see which antecedent predicates are resolved.  Still, you don't
know which they will be, nor do you especially care.  In the end, you will
have an exhaustive set of antecedent predicates, which will serve your needs.

If you add an oracle to this system, in order to prune away the generation
of all possible predicates and truth values, then you exceed the model which
I am referring to as logic.  I'm trying to point out that you don't _need_ to
know the goal state for logic to work.  But you do for neural nets or trial-
and-error to work.  That's why I think they're different.

>|>
>|> >Some balance must be struck
>|> >between the two for many tasks, especially   creativity and problem
>|> >solving.  There is no algorithm to come up with new ideas, but you can't
>|> >just "use the force" to get them either.  Neural networks will probably
>|> >be able to solve some problems using neither gut instinct nor syllogisms.
>|> 
>|> I don't think NNs have ever solved _any_ problems.  Nor will they ever.
>|> Like genetic algorithms, they are simply a tool for finding your way 
>|> blindly from a place you know to another place you know, via a path you 
>|> don't know, and only when you can determine whether each step takes you 
>|> nearer or farther from your destination.  You use them to search for 
>|> something, not tell you what you are searching for.
>|> 
>|> This is not to condemn neural nets or genetic algorithms in any way.  
>|> However they can never take the place of logic nor even supplement it.  
>|> They are not reasoning methods; they are search methods.  Logic is a 
>|> reasoning method -- the only one in which I have any experience or 
>|> confidence.
>
>Again, reasoning is a search method! NN and GA wouldn't replace or 
>supplement logic, but implement it.

I think you and are arguing semantics here.  I don't see logic simply as
a search method.  Search implies that you know where you're going or when
you've gotten there.  Logic doesn't.  It may be that logic isn't terribly
useful (or purposeful) without direction, but even without guidance it 
_can_ teach you new things, and that's something I'm unconvinced that NNs 
or GAs (or pure search) can ever do.

>
>I think the larger issue is partially a matter of perspective. Love is 
>ultimately the result of an extremely complex physical process, which 
>certainly follows logic. The fact that love can be reasoned about, however,
>does not mean that it is itself the result of a reasoning process. 
>Some of the factors influencing it are purely physical (perhaps the smell
>of the loved one is physically pleasurable), some are the result of 
>cognitive processes which are not reasoned (the smell triggers an 
>association with some pleasurable past memory), some are the result of 
>reasoning processes which occur below the conscious level (the loved one
>thinks highly of you, which increases you self-esteem; thus s/he helps
>to satisfy another high level 'drive'), and some are on the conscious level
>("I respect his/her integrity"). There's plenty of interplay between 
>levels, and since most of what's going on is not directly accessable to 
>the conscious mind, it's easy to believe that there's no reason for it.

I agree that you may not arrive at love as a logical consequence, but I
do believe that if you were fully cognizant of all the forces impingent
on you as well as the relationships among these (like those you enumerated)
you could explain love using logic.  If this were not so, then the scientific
method would have failed and we must conclude that either we did _not_ have
access to all the facts, did not understand all of the relationships among
the facts, or else the mechanism of love is unobservable within this universe 
-- it's magical.  And I'd be a lot more uncomfortable thinking that magic 
was at work, than that love is just another predictable/understandable 
physical process.

Otherwise, what kind of marriage counselor would you go to when the magic 
was gone?

>
>If we try to introspectively analyze the workings of some of our 
>subconscious processes, we run up against a wall. 

Analyzing yourself, perhaps so.  But Freud and most psychoanalysts wouldn't
agree that it's impossible to analyze your subconscious.  It's just harder
than analyzing your conscious.

>It's easy to say 
>that since these things just seem to appear in our minds, there's no
>reason for them, they just are. This is like primitive men saying that
>rain falls because it falls - there's no reason for it (until they 
>invent a god to explain it). If there truly were no reason for love 
>other than just because, why is it a persistant phenomenon? We don't
>randomly fall in love and out of love with toasters and farm animals
>every two minutes (well, most of at least :-)). 

Perhaps there's a magical or divine force at work.  That'll explain it 
every time.

-- 

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