Mark Wilson

Mark Wilson presents a highly original and broad-ranging investigation of the way we get to grips with the world conceptually, and the way that philosophical problems commonly arise from this. He combines traditional philosophical concerns about human conceptual thinking with illuminating data derived from a large variety of fields including physics and applied mathematics, cognitive psychology, and linguistics. Wandering Significance offers abundant new insights and perspectives for philosophers of language, mind, and science, and will also reward the interest of psychologists, linguists, and anyone curious about the mysterious ways in which useful language obtains its practical applicability

Let us begin with the simple observation that applied mathematics can be very tough! It is a common occurrence that basic physical principle instructs us to construct some syntactically simple set of differential equations, but it then proves almost impossible to extract salient information from them. As Charles Peirce once remarked, you can’t get a set of such equations to divulge their secrets by simply tilting at them like Don Quixote. As a consequence, applied mathematicians are often forced to pursue roundabout and shakily rationalized expedients if any useful progress is to be made. Often these provisional and quasi-empirical procedures within applied mathematics loom large in motivating the “anti-realist” or “anti-unificationist” conclusions of Nancy Cartwright and allied authors.

Following Jacques Hadamard, applied mathematicians typically investigate their models in the form of well-set problems, which actually consist of a family of applicational circumstances that vary in specific ways with respect to their initial and boundary values. The chief motive for investigating models in this wider manner is to avoid the improper behavioral conclusions one might reach from the consideration of a more restricted range of cases. Suitable specifications of the required initial and boundary variability typically appeal to previously established experimental conclusions as to how the target system will behave under a range of eternally applied manipulations of the form “If the conditions pertaining to S were altered in manner M, internal features X would/would not alter”. In his investigations of causal reasoning within other parts of science, our first author has emphasized the conceptual importance of counterfactuals of this nature, for which he was been often criticized by authors of a self-styled “metaphysical” inclination. The purpose of this note is to argue, pace these objections, that closely analogous considerations have long been part of the practice of investigating differential equation models in a sensible way.