CONCEPTS DEFINED RELATIVE TO A THEORY


	Our idea is that the philosophical difficulties in explicating
certain concepts, especially counterfactuals and concepts involving
counterfactuals, arise from the fact that the concept cannot be
defined in terms of the world itself, but only in terms of a theory.
In spite of this, the concepts can be quite useful.  We shall
illustrate this with an example described in terms of automata.

	Let %2A%1 be a discrete automaton perhaps indeterminate.
Suppose that %2A%1 has a very large number of states say 2↑10↑25
as is reasonable for a human.  We are interested in how this
automaton changes with time, but we are not interested in the
exact state which is unobservable, but only in certain functions
of the state.  Some of these are observable, but we are not afraid
to be interested in some unobservable functions provided there
is good evidence for them.  Let us lump these functions together
by forming a vector to get a single function %2f(s)%1 where %2s%1
denotes the state of %2A%1.  We can consider the values of %2s'%1
to be the states of a new automaton %2A'%1 which will usually
be highly indeterminate.  Namely, the successors of a state are
the sets of vectors that correspond to the successors of the states
corresponding to the original vector, i.e. %2f(successor_f%5-1%2(s))%1.