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“abstract” sense) or their physical manifestations (in the “concrete” sense).
This is done to enforce a feeling for the realizability of these operations in
the structural and functional organization of either grown nervous tissue or
else constructed machines.
4. Contemplate relations, “Rel,” between representations, R, and S.
However, immediately a highly specific relation is considered, viz, an
“Equivalence Relation” between two representations. Due to the structural
properties of representations, the computations necessary to confirm or
deny equivalence of representations are not trivial. In fact, by keeping track
of the computational pathways for establishing equivalence, “objects”
and “events” emerge as consequences of branches of computation which are
identified as the processes of abstraction and memorization.
5. Objects and events are not primitive experiences. Objects and events are
representations of relations.
Since “objects” and “events” are not primary experiences and thus cannot
claim to have absolute (objective) status, their interrelations, the “environ-
ment,” is a purely personal affair, whose constraints are anatomical or cul-
tural factors. Moreover, the postulate of an “external (objective) reality”
disappears to give way to a reality that is determined by modes of internal
computations 3 .
6. Operationally, the computation of a specific relation is a representation of
this relation.
Two steps of crucial importance to the whole argument forwarded in these
notes are made here at the same time. One is to take a computation for a
representation; the second is to introduce here for the first time “recur-
sions.” By recursion is meant that on one occasion or another a function is
substituted for its own argument. In the above Proposition 6 this is pro-
vided for by taking the computation of a relation between representations
again as a representation.
While taking a computation for a representation of a relation may not
cause conceptual difficulties (the punched card of a computer program
which controls the calculations of a desired relation may serve as a ade-
quate metaphor), the adoption of recursive expressions appears to open the
door for all kinds of logical mischief.
However, there are means to avoid such pitfalls. One, e.g., is to devise a
notation that keeps track of the order of representations, e.g., “the repre-
sentation of a representation of a representation” may be considered as a
third order representation, R (3) . The same applies to relations of higher
order, n: Rel (n) .
After the concepts of higher order representations and relations have
been introduced, their physical manifestations are defined. Since represen-
tation and relations are computations, their manifestations are “special
purpose computers” called “representors” and “relators” respectively. The
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