ONT Re: Re: Logic & Programming Languages
This is a continuation of the thread begun in the SUO list that started
roughly with my defense of the motto "Logic is Great, survival is better."
see http://suo.ieee.org/email/msg05672.html
From: "Chris Menzel" <cmenzel@philebus.tamu.edu>
> You are still confusing the logical issue of identity with the
> episemological problem of identification. These are distinct, orthogonal
> issues. Identification is irrelevant to logic because, well, it's not
> logic. It's epistemology. Or maybe psychology.
Yes, quite so; but that is just my point. Were you, for just a moment, to
suspend your assumption that the topic under discussion here is my
education, you might be able to grok my proposal; which, for what its worth,
is somewhat outside the box that you and your colleagues have drawn around
the subject called "logic".
> > In a more serious vein, certainly the methods of logic have been
isolated
> > from the content of its symbols: in a binary system p <=> ~~p regardless
of
> > what p stands for.
>
> No, it precisely because logic is all about content -- the meaning of the
> logical constants -- that the above is valid. Logic doesn't assign any
> fixed meaning to sentence variables and the like because they are not the
> objects whose meanings are at issue. Again, I would recommend that you
> actually study some logic before you continue your theorizing.
The decision to totally separate the methods of binding a symbol with its
referent from the methods of inference *is* the issue I have raised. This
decision to isolate these two aspects of *applying* logic just happened
historically; it did not necessarily need to be so.
> > But I don't believe this isolation necessarily serves us
> > well, for when we apply the certain methods of logic, we must abandon
our
> > methods of grounding our symbols, and when we are creating and grounding
of
> > our symbols we have no certain methods of logic. Classical logicians
pride
> > themselves on this separation;
>
> I'm not at all sure what you mean by "grounding" symbols, but if it means
> something like "giving our symbols meaning", then what you say is patently
> false. Logic, again, is all about meaning, albeit with respect to a
> restricted class of expressions. Your claim about classical logicians is
> just plain silly.
Perhaps silly, but you have affirmed and then reaffirmed my point twice in
this very email. Now Obviously I am talking about how to apply logic to
the task of survival ... perhaps you weren't reading the train when it went
off on the tangent of me defending my slogan: "Logic is Great, but survival
is better".
Let me restate my simple, and perhaps somewhat silly idea differently:
Logic consists of well formed formulas of symbols and their methods of
manipulation. These formulas are considered true of necessity regardless of
how we apply them to the real world. If we apply them to confusion (as I
frequently do), then it is not the fault of the formula that our
conclusions don't match reality ... and our logicians may feel justified in
snickering about our ineptitude. But a computer agent which follows
necessary rules has no less problem than we humans. A computer agent is
called upon to generate symbols from signs that are read from the external
world and then to apply the formulas of logic which ignore any confusion as
to for-what those symbols stand. Presumably we are to contrive that the
computer tests its hypothesis against reality and that its symbols get
adjusted to compensate and the system is magically contrived to remain
consistent such that the truisms of classical logic are still useful.
But my proposal is to combine the process of generating and testing the
binding of symbols with the mechanisms of logical inference. Where a
trusted logical formula of symbols bound by the machine to its environment
could yield a contradiction with another such formula, is it too much to ask
that our logic points our machine to mechanisms (where known) for adjusting
our symbols? Let me provide an example of this. Suppose that we have some
graph that models some aspect of NL dialogue. Let's say it performs well
within its limited domain and within that domain uses binary logic - but
what happens when a trusted assertion is introduced that contradicts the
structure ? Classical logic in this case can do no more than report the
contradiction.
But perhaps there is a logic that could do more. Suppose that the logical
state space (see figure 3 of [1]) was expanded in such contradictory
situations to three states (see figure 4 of [1]) and the search space of the
interpreter was designed to find the methods of adjusting the binding of the
symbols to the environment of the machine and to bring the structure back to
binary logical stability. I realize that this description lacks clarity,
but I was once able to make just such a system work. Suppose the search
space of the interpreter is a binary logic tree composed of just {then,
else} tests, and that contradictions can be encountered at any leaf, yet the
resolution algorithms to the contradictions are known at the branches
somewhere above the leafs. In such a case if the leaf sets the third state
of logic (call it surprise, or Oh), and if the branches are composed of the
tests {then, else, OhThen, OhElse}, then there is an interpreter that can
find and run the appropriate algorithm to resolve the contradictions as they
occur. I realize that this is very primitive, yet if a real logician
tackled this problem combining the generation and binding of variables, with
appropriate truth tables for multivalent logic, perhaps we would have a
system of logic that was more adaptable to the chaotic flux of the real
world.
[1] http://robustai.net/mentography/formOnly2.gif
> > > If I'm right, then Seth is wrong. I'm right. Therefore, Seth is
wrong.
> > About what?
> You seem to have missed the joke -- though the point was serious.
Not at all .... I had a belly laugh ... the same laugh, from another point
of view as when i declared that the rules of logic were held constant by the
policies of academic tenure.
Logic is great, survival is better.
AND
Logic could be greater, were that it compensated for its own fallibility.
Seth Russell