same-species fallacy

(suggested new terminology)

(synonym: culmination-type fallacy)

– the false belief that those performing the culmination of an activity of members of a given species must themselves also belong to that species. The simplest counterexample is that the sequence of positive integers converges to infinity, but infinity is not a number. Another counterexample is the fact that the pointwise limit of a sequence of continuous functions need not be a continuous function. (And there is a myriad of other examples, both technical and social.) Succumbing to this fallacy is the basis of the perceived paradox that while quanta are not subject to chaos, their limit, that is, the realm of objects of classical physics, is. (“If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics?”) Thus, being subject to chaos can be said to be the Achilles’ heel of higher-order systems, enforcing the general conservation principle that you don’t get something for nothing.