ONT Re: Logic & Programming Languages
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Seth Russell wrote (SR):
Chris Menzel wrote (CM):
SR: 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".
SR: http://suo.ieee.org/email/msg05672.html
Is this intended to be a reference to the Trial of Socrates?
CM: 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.
Hmm -- "episemological"? -- I like it, can I use it?
I think that you've just invented a brand new field.
SR: 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 it's worth, is
somewhat outside the box that you and your colleagues have
drawn around the subject called "logic".
Yes, I was wondering if maybe there is some sort of discipline-and-tradition-independent,
school-of-logic-independent way of framing this issue for those of us who just walked in?
SR: 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.
CM: 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.
SR: 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.
SR: 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.
CM: 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.
SR: 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".
SR: Let me restate my simple, and perhaps somewhat silly idea differently:
SR: 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.
SR: 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.
SR: 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.
SR: [1] http://robustai.net/mentography/formOnly2.gif
CM: If I'm right, then Seth is wrong. I'm right. Therefore, Seth is wrong.
SR: About what?
CM: You seem to have missed the joke -- though the point was serious.
SR: 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.
SR: Logic is great, survival is better.
AND
Logic could be greater, were that it
compensated for its own fallibility.
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