Thinking

Theory

A good theory explains why something holds; it has as few moving parts as possible, each of which is critical to the explanation, and none of which can be sacrificed without doing great violence to the explanation. Moreover, a good theory is (usually) consistent with other good theories; good theories fit together in a sensible way. Furthermore, a good theory usually has greater reach than it was formulated to solve. That is, it solves problems that were thought to be unrelated to the original problem that the theory was meant to solve. For instance, the explanation that the seasons are caused by the tilting of the earth’s axis is a good explanation. It explained the seasons in an elegant way that was straightforward and impossible to fiddle with without destroying the explanation; it also explained why opposite seasons prevailed in the northern and southern hemispheres.

In other words, a good theory resolves an unresolved problem; and in comparison to rival explanations — especially ones that are empirically indistinguishable — it is parsimonious (has fewer variables), straightforward, tighter (harder-to-vary), and applies with greater generality. Einstein’s general theory of relativity resolves the problem of perihelion of Mercury’s orbit which had been shown to be anomalous with Newtonian physics; it is straightforward, specifying simply that the stress-energy tensor equals the curvature tensor of spacetime; it is parsimonious: gravity is explained entirely by the curvature of spacetime; it is tight – which is why Einstein realized that introducing the cosmological constant was his greatest blunder;  and holds in much greater generality: both special relativity and Newtonian physics live on as limiting cases — when curvature is trivial, special relativity applies; when curvature is trivial and the velocities of test particles are low compared to the speed of light, Newtonian physics continues to reign.

These properties together provide us ample reason to regard such theories as good because of the intelligibility of nature; an assumption that is basically a prerequisite for talking about reality in a rational manner. The search for better theories is what drives the growth of knowledge.

Suppose we have a good explanation for a phenomena. If this theory is testable, that is, empirically falsifiable, then there is no problem; there is no tension between the search for intelligibility that drives the growth of knowledge and the scientific method. Now, suppose that it is not testable. We may still hold it to be true for all practical purposes (always tentatively and subject to falsification) if it is the best explanation in the sense outlined above. On the other hand, we may have candidates that hint at potential resolutions but fall short of solving the puzzle in a compelling way. Should we give any credence to such theories? The problem with such theories (string theory comes to mind) is that not only are they are not testable, but because they have so far failed to solve the problem (basically the incompatibility of quantum theory and general relativity), we have no way of knowing if they are even on the right track.

What, then, is the right position to hold for a natural philosopher in such matters? In other words, what is the right philosophical position for an unresolved problem? I think that it is vital that we recognize that we do not have a solution. There is nothing wrong with saying: we do not yet know. There is a good reason why most speculative theories fail to resolve fundamental problems: even slight variations of the right theory at a given level of abstraction differ wildly in their logic, applicability, and predictions. Due to the tightness of the laws of nature, once one has found the right theory, it quickly becomes obvious that one has discovered the right formulation. This is why Wheeler said

Behind it all is an idea so simple, so beautiful, and so elegant that when we grasp it — a decade, a century, a millennium from now — we will all ask ourselves, how could it have been otherwise?

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