ABSTRACT
My comments have received a “reply” from Dr. Suppes (Suppes, 1969b). Rather than start an infinite chain of counterreplies, I invite the reader to take the note itself as reply, while drawing the following to his attention: One gains more insight by viewing Suppes’ theorem as a simple corollary of the statement “for each stimulus-response table there is a stimulus-response model that asymptotically becomes isomorphic to it” than by giving a complex proof directly from axioms from which the above statement may be derived as a theorem. Suppes’ theorem has only been proved subject to the conditions which have been made explicit in this paper, so that Suppes’ use of his theorem to back up statements about stimulus-response theory is not always valid--in particular, we must disallow Suppes’ TOTE corollary for all but those simple TOTE hierarchies which satisfy Conditions b and c. As for the rest, it is certainly not my belief that memory must be fed back through the input--I just explicate the mechanism which Suppes and I used to deduce his theorem. As was stated in my paper, I do not even regard the TOTE hierarchy as an adequate model for learning. But the reader must not expect a theory of learning to be presented in a short theoretical note--I refer him instead to the author's forthcoming book The Metaphorical Brain (Arbib, 1972) and warn him that even that formulation will be provisional. In conclusion, I might say that I am charmed by the willingness of stimulus-response theorists--in their drive to avoid positing directly some m internal states to a finite automaton with p inputs--to accept p2(m+1)p conditioning states in the Markov chain they use in explaining learning.
