### Physics Avoidance & Cooperative Semantics: Inferentialism and Mark Wilson’s Engagement with Naturalism Qua Applied Mathematics

*Ekin Erkan*

#### Abstract

Mathematics' abilities to capture nature's unfolding processes within its own conceptual terms rests upon its capacities for supplying algorithms that can graphically engage in deduction numerically, bolstered by the hope of paralleling natural processes. Inter alia, Mark Wilson's project in *Physics Avoidance* shows that nature presents us with a multiplicity of manifolds that simply can not be smoothly mapped. Thus, even our most basic/fundamental modes of effective mathematical reasoning falls short of the ‘real extent' of natural processes. Mathematicians have developed sophisticated strategies that string together patchworks of numerical *approximation*, despite the algorithmic limitations upon our concrete reasoning capacities. There is, in turn, a trans-historical element to Wilson's pursuit in *Physics Avoidance*, one which is driven by a self-correcting (Sellarsian) scientificity-directed at knowledge, while constantly refining itself both methodologically and substantively. Kindling the critiques of twentieth-century thinkers such as Clifford Truesdell and Walter Noll on the essential idealization thesis of physics (i.e., that ‘physics always idealizes') while simultaneously parsing a distinction that was conceived of with the nineteenth-century distinctions between rari-constant and multi-constant approaches to elasticity (associated with the derivational methods pursued by Navier and Cauchy, respectively), Wilson approaches limits and infinitesimals qua multi-scalar localization. Meticulously engaging with Wilson's rendering of the problem of the physical infinitesimal, we not only set out to complicate the historical discussion of matter-which has bedeviled the entire epoch of classical mechanics' reign-but also to hold a candle to a novel methodological means of approaching the philosophy of language. Henceforth, we shall seek to illuminate the developmental exigencies that have not only lacerated and left scars upon modern philosophy of science but also the conceptual consideration of scientific laws via counterfactual grounding. Just as Sellars is pellucid in demonstrating how correspondence rules ought not be treated as definitions of theoretical expressions in terms of their observation language expressions-underscoring the semantic autonomy of theoretical expressions that cannot be captured in observation language-so too will we examine semantics and applied mathematics-cum-physics correspondence rules as proposals for reconsidering our observational vocabulary. In doing so, we will closely engage with Wilson's (and Robert Batterman's) research, reviewing his work while prodding it into a unique trajectory so as to carve an analytic and rationalist theory of media vis-à-vis set theory, while accepting an inherent contrast between *norms of correctness* and *effective thinking routines*.

Full Text: PDF