ON WORDS AND WORLDS: COMMENTS ON THE ISARD AND SMITH PAPERS

The following remarks are my comments on the exciting papers by Walter Isard and 'Tony Smith2 I think their papers make a very nice piece, for in my mind they carry the seeds of their own destruction. From reading and discussing them we are therefore bound to learn, for to learn is to become so self-conscious about our work that we eventually negate it. Here--as so often recently--I am reminded of Hegel, who argued that the essential nature is to be the reverse of what it wants to be and who claimed that our activities pass into the opposite of what they immediately are. Where in the Isard-Smith works do I see these seeds of self-destruction? I see them in several places, but nowhere as clearly as in their definitions of homomorphism, numerical representation, and separability of order structures. These definitions of homomorphism, counting, and identity are then reflected in all subsequent derivations and most clearly in the three axioms, which together constitute the theory of spatial discounting. It is in fact the clarity of the authors' presentations that makes us realize that whatever they say in their paper tells us more about the language and culture they are talking in than about the subject matter they are talking about. This is, of course, nothing peculiar, for it is generally the case that our thoughts and actions reflect the categorical scheme by which we impose mental structures on the phenomena with which we are dealing. It is in this light that I shall evaluate [sard's claim that after a quarter of a century he finally has found a reasonable rationale for explaining gravity model trip behavior. This rationale is that of mathematical economics or to use his own words--it is a maximizing rationale for ordinary people. This, then, is the structure of the net in which the authors try to catch--not themselves, for everybody knows that that is impossible--but all us others, that is, you and me, our children and our parents, those we think we love and those we think we hate. There are many problems built into this reasoning net, but the most forbidding are those connected with the principles of transitivity and separability. These two principles of orderly reasoning go back a long time. Indeed they have never been specified more succinctly than in Leibniz's definition of identity and identity substitution. These principles are themselves embedded in the law of the excluded middle and they say that everything is identical to itself and nothing is identical to anything else. The problem here is how we can know that what you hold to be