A traditional view of mathematical modeling holds, roughly, that the more details of the phenomenon being modeled that are represented in the model, the better the model is. This paper argues that often times this ‘details is better’ approach is misguided. One ought, in certain circumstances, to search for an exactly solvable minimal model—one which is, essentially, a caricature of the physics of the phenomenon in question.

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. (shrink)

The use of idealizations and approximations in scientific explanations poses a problem for traditional philosophical theories of confirmation since, strictly speaking, these sorts of statements are false. Furthermore, in several central cases in the history of science, theoretical predictions seen as confirmatory are not, in any usual sense, even approximately true. As a means of eliminating the puzzling nature of these cases, two theses are proposed. First, explanations consist of idealized deductive-nomological sketches plus what are called modal auxiliaries, i.e., arguments (...) showing that if the idealizations used in the initial conditions are improved, then there will be an improvement in the prediction. Second, a theory is confirmed if it can be shown that its idealized sketches can be improved; similarly, a theory is disconfirmed if its idealized sketches cannot be improved. Several examples are given to illustrate both confirmation and disconfirmation achieved by means of the modal auxiliary. These cases are compared with Scriven's bridge example. (shrink)