Truth and (Circular) Inference -- Re: [om-list] Re: Cyc example

[Tom and other Packers]

Lee (and the rest of you OM folks):

    Don't get too caught up in the details of the discussion.  I'm just
theorising when I talk about upper and lower bounds to the number of
possible namespaces.  Theorising comes before theory, and theory comes
before practice, i.e. the practical application of theory.

    Perhaps you are distracted by the way our goal "to model any arbitrary
knowledge" may sound like "to model all knowledge everywhere".  To model all
knowledge would require a large number of namespaces, I think.  In
discussing how to model any arbitrary knowledge, we have to consider the
same large body of knowledge, and try to deal with that vastness as well as
possible, or at least acknowledge the existence of such a large possibility.
We're walking through a forest.  We want to find the best path through the
forest.  I'm going to talk about all the paths in the forest, and even try
walking on many of them, even though I have no intention of actually walking
along the full length of all of them.

    I will be more careful about how I respond to your questions, and
upbraid not, because we need you to ask your questions, and for you to
understand what we intend, without your fearing that you will be called
stupid.  Please respond again, because I'm not sure I understand your
concern.

    I agree with Mark -- except, once we do have a good model, I would like
to start working on some serious inference algorithms.  I think Mark is
right, assuming that he's talking about deductive inference.  That kind of
inference would be pretty much taken care of by a good model.  But as for
inductive inference, I think there's a lot more work to be done after the
model is "finished".

    (::MW) In geometric mathetical space, the whole process of deduction is
like the logical operator "and", i.e. the set operator "intersection".  It's
very straight forward.  You start with two or more large-volume premise
propositions and end up with a smaller-volume conclusion proposition, which
is the intersection of the premise propositions.  Induction is the opposite.
It is like the "or" or "union" of nodes/propositions in mathetical space.
It moves from small-volume to large-volume.  Somehow this process is not as
straight forward.  I think it has something to do with our problem with
infinity and with the misapplication of what I call the "continuity
heuristic" used to deal with infinity, but I won't go into that today.

    I don't think there is any other form of inference, fundamentally.  All
of human reasoning (the basis of my epistemology) is just three things:
induction, deduction, and revelation.  I've recently heard of abductive
reasoning and circumscription -- was that what it was called Mark? -- and I
don't know what they are, but I'm immediately certain that they are either
one of the fundamental kinds, or (more likely) a mixture of both.  But,
Mark, could you send me any references on those subjects, so I can find out
for sure what they are?

    (More MW preaching follows, so everyone get out their scope resolution
operators...:-)

    What we think of induction and what we think of deduction are actually
mixtures of both, because as the MME (MetaMathesis Essay) and the AHM
(Anti-Humanist Manifesto) will hopefully demonstrate, (to the point of
confounding most secularist/humanist philosophies, including the science
which is religion to many Westerners), induction is dependent on deduction,
and deduction is dependent on induction.  In order to inductively end up
with large-volume conclusions, the process of induction must operate on
small-volume premises, which had to come in the form of the small-volume
conclusions of deduction.  The reverse is true for deduction.

    In a closed physical system, without any form of inspiration, you can't
have the one form of inference without the other; you therefore can't have
truth in a closed physical system.  There is no starting point.  Like the
great and spacious building, there is no foundation.  Behold, here is
wisdom.  You cannot prove anything by mechanical/physical/explicate
inference alone.  All of humanity's reasoning is just one giant circular
argument.

    By mechanical or physical inference, I mean the induction and deduction
that takes place in the carnal human brain (the incarnate mind), or in a
computer, or anything not spirit.

    These co-dependent processes are also called "analytic" and "synthetic",
by the way, which is how I found our British friend Roger Bishop Jones.  His
web page talks about these two types of inference.  I went on the internet
looking for someone to show me that logical people are not stupid, and found
his web page.  But he does not even see the necessity of making deduction
based on induction, let alone to make induction based on deduction, so the
two of us don't get along very well.  (I'm still looking.)

    I better give you some examples.

    (1) Deduction is dependent on induction:

    This is the easy one to see.  I saw this dependency in my introductory
course on formal (symbolic) logic at Weber, and couldn't understand why no
one else ever acknowledged this dependency.  Since then I have found a few
people who do acknowledge this, including Patricia Churchland, the very
intelligent author of "Neurophilosophy", a very cool (humanist) book which
attempts to unify neurology i.e. "brain science" with philosophy, i.e. "mind
science".

    Consider the famous syllogism, which is the prototypical, proverbial
example of deductive logic:

    All men are mortal.
    Socrates is a man.
    Therefore Socrates is mortal.

    This syllogism is movement in mathetical space from large-volume
premises ("All men are mortal" involves a lot of people), to a small-volume
conclusion.  It is the process of intersecting premises.  But before you can
use deductive reasoning to prove this conclusion from these premises, you
must first prove the premises, e.g. that all men are mortal, and you would
have to do that inductively, i.e. empirically, by observing all men.  (That
would be synonymous with the process of making a large-volume
conclusion-proposition out of lots of little small-volume
premise-propositions.)  Deduction is dependent upon induction.

    (2) Induction is dependent on deduction:

    This is harder to see.  In fact -- not to be too proud or boastful,
but -- I have never heard of *anyone* who has ever seen this, except for me.
I would really like to hear about it, if any of you have ever heard or read
about this before.  I would buy whatever book you found this insight in, out
of admiration for that one statement.

    Consider the following inductive argument, as a continuation of our
example above:

    Adam was a man, and was mortal.
    Abel was a man, and was mortal.
    Cane was a man, and was mortal.
    ...
    ...
    ...
    Tom is a man, and is mortal.
    Mark is a man, and is mortal.
    Lee is a man, and is mortal.
    Jeremy is a man, and is mortal.
    Doug is a man, and is mortal.
    Chris is a man, and is mortal.
    Jared is a man, and is mortal, whether he believes it or not.
    ...
    ...
    ...
    The last man will be a man, and will be mortal.
    Therefore all men are mortal.

    Now, even if this inductive argument were valid and provable (which it
is not -- but this is just a thought experiment, so please bear with me), it
would not be provable through inductive logic alone.  You must first prove
each premise.  These premises are small-volume propositions; and how do we
prove small-volume propositions?  That's right, through deduction.  In this
case, you would need some definition for "man" and some definition for
"mortal", based on certain criteria that you could observe, and through a
long sequence of the repeated application of a modus ponens syllogism, or
some other form of deductive inference, you would prove both halves of each
of these small-volume premise-propositions to be true.  Only then could you
safely apply your inductive logic pattern-recognition algorithm to produce
the conclusion that all men are mortal by correlating the "man" and the
"mortal".  Induction is dependent upon deduction.

    And, if you wanted to keep going, the definitions of "man" and "mortal"
would also involve some large-volume abstraction, which would have to be
proven inductively.  ... And so on, and so forth, ad infinitum, ad nauseam,
until the cows come home, and perhaps a little bit longer.

    So, do you see what I mean?  There is no starting point.  There is no
foundation.  All human reasoning is circular, forever and ever.

    You've all heard of circular arguments, right?  They are thought to be a
very bad thing, in logic.  It's a strong pejorative.  They are the act of
"proving" that A exists if B exists, though B's existence is entirely
dependent on the existence of A.  If a logician finds a circular argument in
your proof, he has "proven" that you have not proven what you intended to
prove.  (You have merely made a statement whose truth is dependent on it's
own truth, which is the same thing as simply making an unsupported
statement, after transitive closure of the inference relations between
propositions within the statement.)  So consider the significance of what I
said above:  All of human reasoning is a circular argument.  In a sense, I
have "proven" that there is no such thing as proof.

    The only difference between the proofs the logicians call circular and
everything else is (1) the size of the circle, and (2) the number of
implicit/assumed premises.

    Don't confuse "implicit" with "implicate".  They are quite different.
Allow me to insult your intelligence with an explanation.

    "Implicate", i.e. "The Implicate Order", refers to metaphysical,
spiritual, unseen things from which the explicate order, or physical
reality, is "unfolded".  I therefore also say that the implicate holds the
"proof" for all explicate ideas.  The implicate is the causal and the
inferential origin of all things explicate.  (This idea is consistent with
the Mormon notion that all things were created spiritually before they were
created physically, and is consistent with the idea that knowledge is light,
and all this light comes from God through the spirit and the Light of
Christ, etc.  "Whatsoever is truth is light.  And whatsoever is light is
spirit. ...")

    "Implicit" refers to knowledge understood, or assumed, without having to
be spoken explicitly.  This, by the way, is a circular definition, since I
would also define "explicit" in terms of "implicit".  But notice how you
probably understand the definition better for my having widened the circle
of definition.  Such is the value of proofs and definitions, despite their
being circular.  The wider the circle, the better you would probably
understand the definition.  (Notice how all definitions would be circular,
if you wrote a *complete* dictionary.  There is no starting point in the
physical world.  There is no getting around this circularity, in a closed,
physical system.)

    Regarding the World's "proof", there is no truth in it, aside from the
fact that larger circular arguments (if they use sound mechanical reasoning
within the circle) provide a larger interface between the explicate
reasoning and the implicate proof, i.e. they have more "surface area"
through which the Light of Christ can confirm to an incarnate mind the truth
of the whole matter, i.e. they provide more places or more opportunities
where "self-evident" knowledge can be applied as starting points in the
inference cycle.  There is no truth *in* it, but there can be truth
*associated with* it, or *referenced by* it.  One single statement has some
ability to cause spiritual confirmation, in proportion to its truth and its
value.  But a larger statement (an long argument) has a larger ability, I
believe, as long as it's tied together by sound reasoning, making it one
large, consistent, coherent, cohesive statement which can be confirmed or
denied by the Light of Christ.

    My big reason for talking about this now is this: What are my intentions
for OM?  OM is not meant to prove truth.  It is merely meant to help us
collect a large number of statements about the world, and to tie them
together in a consistent, coherent, cohesive manner, from which we can gain
much value, inasmuch as the large monolithic "statement" has truth and
value.  The more "surface area" our statement has the better.  Does this
make any sense?

    (Just to clarify context, I'm borrowing "implicate" and "explicate" from
the physicist Dr. Bohm, via "The Holographic Universe", and fudging their
definitions to fit my own mathetical needs.  And I'm using the geometry and
surface area of a circle as metaphor.)

    Have I already written about all this before?  I don't know.  I know
I've told Warren Petty and Jared Norman about this, but that was in person.

    If I didn't write about this before, then I probably didn't go on to
mention the incredible irony or coincidence in the fact that Descartes'
famous "proof" of the existence of God and Spirit has been dismissed since
his time as being a fallacious circular argument.  The irony is, now I have
a "proof" of the existence of God and Spirit because of the very existence
of circular arguments (including Descartes' circular argument), and because
*everything* is a circular argument, and there can be no truth without some
source of knowledge outside the circle.

    My only assumption: There is such a thing as truth.

    The physical system of truth and inference is not closed.  It is an open
system, otherwise we could not know anything.  There must be input from
outside the physical, and it is probably a constant stream of input which we
rarely recognise as the inspiration that it is.  Everything we assume to be
true, being "self-evident", and which *is* true, is probably evident through
the Light of Christ and/or the Holy Ghost, and there is an awful lot of
that.

    There is obviously more to my "proof" than what I have told you in this
letter.  You'll have to wait for the MME to read it.

    And marvel not that I say unto you "here is wisdom".  But also, please
don't anybody talk about this too much, (i.e. "Show it not unto the world").
Don't spill the beans.  Don't let the cat out of the bag.  And please excuse
my blaspheme, if I'm using too strong a form of (scriptural) language.  This
is going to be one of the main conclusions of the MME, and I'm very proud
and boastful about it.  I'd like it to make a huge splash in the scientific
and education communities, in one sudden shock to the system, once I have it
all formulated in words well placed on paper, and find a publisher smart
enough to see the significance of it.

    Regarding waiting until we (OM) have a model before doing any serious
work on inference:  Actually, I'm thinking of doing my senior (BIS capstone)
research project on "machine learning", in a formal, explicit-semantic,
mainly inductive pattern-finding-and-abstracting type of "learning".  So, I
will hopefully start on this, individually, before OM does.  This is in
opposition to artificial neural network learning, in which the semantics are
implicit and hidden and virtually unextractable and meaningless -- not
*useless*, just *meaningless*.

    I envision it being a lot like multivariate statistical analysis, which
is what a certain older computer dude at Weber (a Mr. Minor I believe) told
me I should look into when I told him about my MW several years ago.

    My CS professor (Dr. Peterson) says this project might fit under "data
mining", and I know Mark has read up on that somewhat; so if he (or any of
you) could give me any good references on data mining, I'd really appreciate
it.

Meine Wenigkeit,
TomP

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2000.10.01 -- The anniversary of the death of Christian Packer.

"Omnia apud me mathesis fiunt."
(With me, everything turns into mathesis.)
an improvement of the quote by one of my heroes, Renee Descartes.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


----- Original Message -----
From: Lee Howard <redder at deanox.com>
To: Thomas L. Packer <tomp at burgoyne.com>; OM List <OM-List at onemodel.org>
Sent: Saturday, September 30, 2000 5:10 PM
Subject: Re: [om-list] Re: Cyc example


>    So, in a sense, namespace is part of the [unabbreviated] name.  I guess
>this could work.  But I envision an awful lot of namespaces, because, going
>back to my example "God": how many conceptions of god are there?  A lower
>bound would be the number of sects, religions and mythologies which have
>ever existed.  An upper bound would be the number of people who have ever
>lived (and maybe even including some which have not lived, if we count the
>opinion of spirits, if any have been recorded in scripture, for example).

Once again, I am quite confused as to the direction of this project... and
if I were to try to explain what I had *thought* that the project was after
and then try to explain how this differs from that... well, I'd be
lambasted on all sides between various insults to my intelligence.

So, I'll let it suffice to say that I am confused - again.  If this means
that I am stupid, unobservant, silly, or destructive... well, then whatever
- just don't bother telling me so.

Lee.


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