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C00002 00002	TECHNICAL MATHEMATICAL LOGICAL PROBLEMS
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TECHNICAL MATHEMATICAL LOGICAL PROBLEMS


	The object of this section is to isolate some technical
problems in axiomatization and mathematics that are relevant to
the philosophical and AI problems of this paper.  In order to
make the problems as precise as possible, some risks have been
taken that the technical problems don't capture the philosophical
or AI content of the original problems well enough for the solutions
to be directly applicable.  The reader can judge for himself.


#. When is a second order definition reducible to first order.

#. Formally define a metaphilosophical system.  It includes
a class of worlds, the sensory and motor system, and the driver
connections that can lead the "philosopher" to think but
can't tell him anything, i.e. we need to separate the heuristic
from the epistemological problem.

#. %3Generalized systems of automata%1.

	Systems of finite automata were used to model the notion
of ⊗can.  We are reconciled to their epistemological inadequacy
in that the facts a person or robot has about the world cannot often
be expressed reasonably in terms of state diagrams and states.
However, they are inadequate for theory as well.

	First, the discrete time is an embarassment since time doesn't
appear to be quantized with a universal integer valued clock.  If we
want analogies or approximations in principle, then this may not
be harmful, because if we set the time quantum at 10%5-50%1 seconds,
no present day physicist will find a disagreement with observation.
However, 

#. %3Weakly interpretable systems of sentences%1.

	Consider the sentence "John is at Stanford" which we
want to write in predicate calculus "at(John, Stanford,s)" where
⊗s is the situation about which we are making the assertion.
Suppose further that we regard John as a collectwon of matter.
It seems unlikely that it is reasonable to interpret such sentences
only in terms of some metaphysically complete model of the world.
Therefore, we need a notion of weak interpretation or partial
interpretation in terms of partial models of the world.