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*Monday, June 28,
2004*

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On the nature of logic and computing, is there a difference?

Key questions on Common Upper
Ontology -> .

(new beads are edited for a few days until the
grammar is correct)

Replying message from Richard
Ballard

Note by Paul Prueitt on a related issue .

From a living system's point of
view the environment is as it is. Heinz von Foerster called the environment 'an
invention of the living system' and I tend to agree.

But this invention is not
arbitrary: it is a reductionist process of establishing causalities (as axioms,
hypotheses or theories) and using causal deduction (or logic, if we have
language) to make inferences form these causalities. Establishing a causality
is, I suspect, a process of analogical inferences, (or abduction).

Adapting to the
environment could be described as an oscillating combination of synthetic
and analytic reasoning. We can also call it thinking or biological computing.

Technical computing today is
restricted to only the analytic part of the process.

The problem is that all we really
have in order to build, program and operate machines is logic. The key to
adaptive computing seems not to be another logic, but, as Gotthard Guenther was
probably the first to emphasize, another architecture of logic.

By this I mean that we need a way to
integrate as well as trace arbitrary logic domains (logic systems). This
capability will allow us to stick to logic (and thus to use computing machinery
we can build and control), but still break the Cartesian closure that restricts
logic operations to one domain at a time.

Analogic reasoning is -in my
understanding- a way to move in arbitrary hierarchies and still be connected to
all intersecting trees at every step, so you could switch trees at any step.
This requires an interconnected combinatorial space.

My intuition is that such a
structure and system actually goes beyond the Turing machine, the Lambda
calculus and Godel's recursive functions.

We, the community, need a couple
of very good mathematicians to look deeply into this matter.

The fascinating thing is that one
can build machines using logic, by building mechanisms like CPUs.

Mon-linearity is an emergent
phenomenon of the architecture of logic.

But possible complexity, properly
understood, is the secret of biological computing.

Peter Krieg