Russell and the Newman Problem Revisited

In his 1927 Analysis of Matter and elsewhere, Russell argued that we can successfully infer the structure of the external world from that of our explanatory schemes. While nothing guarantees that the intrinsic qualities of experiences are shared by their objects, he held that the relations tying together those relata perforce mirror relations that actually obtain (these being expressible in the formal idiom of the Principia Mathematica). This claim was subsequently criticized by the Cambridge mathematician Max Newman as true but trivial, insofar as from a closed body of observations (or “Ramsey sentence”) one can always generate other equally-satisfactory networks of relations, provided they respect the original set’s cardinality. Since any model thus generated will be empirically adequate, “[t]he defence is therefore driven back from the fairly safe fictitious-real classification to the much less tenable ‘trivial’ and ‘important’” (Newman 1928). Given the definitional rigour afforded by the initial appeal to isomorphism (via one-to-one correspondences in extension), the received assessment, shared by Russell himself, is that retreating to a pragmatic adjudication would betoken a fatal blow. However, I suggest that reliance on “importance” can be avoided if we incorporate an impersonal criterion of diachronic precedence. When collecting observations, an ordinality emerges alongside the cardinality which gives that underived structure an irrevocable epistemological privilege. Hence, I argue that, all other things being equal, any construct parasitic on an antecedent theory ought to be regarded as inferior/dispensable, since it was generated by an algorithm lacking the world-involving pedigree of its host structure.