WHAT CAN ONE CONCLUDE ABOUT A THEORY DEVELOPED USING MAXWELL'S METHOD?
Let us divide the assumptions made by a theory postulating unobservables into two sorts: those for which there are independent warrant arguments and those for which there are not.
In Maxwell's method the most fundamental assumptions of the theory should be of the first sort. If they are, and if the arguments supplied are sufficiently strong, then one can claim to be justified in believing them to be true, even if the assumptions postulate unobservables, and even if the assumptions cannot at the time be proved experimentally. And if a range of observed phenomena is explained by derivation from these assumptions, then justification for the assumptions can be claimed not only on the basis of the independent warrant but also on the basis of the explained phenomena.[215]The assumptions for which no independent warrant is given are ones for which conditional claims are usually made: if we assume such and such, then we can derive the following result, which may or may not be testable. If it is not testable, then we certainly cannot conclude that we are justified in believing the assumptions leading to that result, or the result itself (e.g., Maxwell's assumptions leading to his distribution law). If the result is testable and determined to be true but there is no warrant for the assumptions, then, since Maxwell explicitly rejects the method of hypothesis, he will not conclude that one is justified in believing the explanatory assumptions. What, then, can one conclude about such assumptions?
For Maxwell, nothing epistemic. Yet an important way of defending a theory is by showing how it can be developed theoretically. According to Maxwell this involves formulating assumptions precisely, often mathematically; adding new theoretical assumptions about the unobservables postulated in response to questions about the properties and behavior of those entities; and deriving consequences.
Frequently in such a development new theoretical assumptions are introduced for which no independent warrant is given, and theoretical consequences are drawn that are not testable. In response to questions he posed regarding molecular velocities, Maxwell developed his theory by adding (unargued for) assumptions about the independence of component molecular velocities, leading to a derivation of his (untestable) molecular distribution law. In doing so he did not provide any new or increased epistemic reason to believe his general molecular assumptions or the specific ones needed for the derivation. Nor is such theoretical development what some have called an “aesthetic” criterion of goodness that adds beauty or simplicity to the theory. (A particular theoretical development may be quite complex and unbeautiful.[216]) Nor is a theoretical development of this sort engaged in simply to show that the theory is “worthy of pursuit.” In telling us much more about the entities and properties introduced than is done in central assumptions, its purpose is to add some measure of completeness to theory by answering a range of questions that might be prompted by considering the fundamental assumptions, and to do so with precision. Completeness and precision are nonepistemic virtues Maxwell regards as valuable for their own sake and not just for leading to conditional explanations and predictions of phenomena (if they even do so) or for leading to tests of the theory (again if they do), or just for providing reasons to pursue the theory.[217] Without a theoretical development, he suggests, the basic assumptions are “vague,” in the sense of being underdeveloped and imprecise.Accordingly, in using “the method of physical speculation” one may be able to conclude that a theory is defensible both epistemically and nonepistemically. It has the epistemic virtue that its fundamental assumptions and perhaps others have independent warrant; and, depending on the strength of this warrant and on the known phenomena derived from them, this may be enough for one to be justified in believing those assumptions. It has the nonepistemic virtue of being developed with some measure of completeness and precision.
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