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At this point, it seems appropriate to address explicitly one debate in the philosophy of science—that is, whether science can, or should try to, do more than predict consequences. One view that held considerable influence during the first half of the twentieth century is called the predictivist thesis: that the purpose of science is to enable accurate predictions and that, in fact, science cannot (or need not) actually achieve more than that. The test of an explanatory theory, therefore, is its success at prediction, at forecasting. This view need not be limited to actual predictions of future, yet to happen, events; it can accommodate theories that are able to generate results that have already been observed or, if not observed, have already occurred. Of course, in such cases, care must be taken that the theory has not simply been retrofitted to the observations that have already been made—it must have some reach beyond the data used to construct the theory.

In 1960, Stephen Toulmin attacked the “predictivist thesis,” a philosophical approach that he claims he once shared. Foresight and Understanding, pp.22–3. He asserted: “Forecasting…is a craft or technology, an application of science rather than the kernel of science itself. If a technique of forecasting is successful, that is only one more fact, which scientists must try to explain, and may succeed in explaining… . [A] novel and successful theory may lead to no increase in our forecasting skill; while, alternatively, a successful forecasting-technique may remain for centuries without any scientific basis. In the first case, the scientific theory will not be necessarily any the worse; and, in the second, the forecasting-technique will not necessarily become scientific … .” Id., p.36. He explained how historically several theories that have been rejected were capable of more precise predictions than the theories that superseded them, such as Babylonian astronomy and Kepler’s laws of planetary motion, the tables of the times and heights of tides. Id., pp.27–34.

Now these methods of forecasting were the result essentially of the compilation of data reflecting apparent patterns or regularities in the phenomena under examination combined with the assumption that the patterns would repeat themselves, which they have. The techniques are mechanical (or, as Toulmin characterized them, merely “arithmetical”); they do not otherwise explain the successes or the failures of the forecasts. Id., pp.28, 29. “The Babylonians acquired great forecasting-power, but they conspicuously lacked understanding. … [Newton gave us] a number of general notions and principles which make sense of the observed regularities, and in terms of which they all hang together.” Id., pp.30, 33. (As discussed later, however, one might question the extent to which Newton’s theories actually gave us explanations; but, there clearly is a rather profound sense in which Newton’s theories were an improvement.) Toulmin describes the aims of science as lying “in the field of intellectual creation.” Id., p.38.

My discussion has been in terms of prediction and explanation, words that I think are more modest than foresight and understanding. Toulmin’s concepts seem to include greater grasps of the causal relationships involved. Thus, while prediction includes mechanical techniques that generate accurate forecasts, forecasting suggests (at least to me) some element of vision or appreciation of the factors at work in the relationships and, often, a sense of the likely outcome prior to the complication of a precise computation. Similarly, understanding suggests an appreciation of the relationships that is deeper than mere explanation. So, I shall stick with my more humble words.¹⁶

Some scientists do take an interest in these issues, at least when writing for the general public. For example, contemporary physicist David Deutsch recently set out an attack on the philosophical view that “denies that what I have been calling ‘explanation’ can exist at all.” He claims that “during the twentieth century, most philosophers, and many scientists, took the view that science is incapable of discovering anything about reality. Starting from empiricism, they drew the conclusion … that science cannot validly do more than predict the outcome of observations, and that it should never purport to describe the reality that brings those outcomes about.” The Beginning of Infinity, p.15.

Deutsch asserts, to the contrary, that the physical world—reality—really does exist and that it is accessible to rational inquiry. Id. Furthermore, he says that the aim of science is explanation which enables us to understand the external world and that the use of theories permeates man’s mental activities.¹⁷ The dramatic progress in understanding has been the result of the development of a “tradition of criticism,” which has been embraced by post-Enlightenment intellectuals and scientists. Criticism has enabled the differentiation between good and bad explanations. “Bad explanations” (like myths) tend to have a flexibility that accommodates new evidence and experience without changing the substance of the explanation. As a result, bad explanations thwart progress. (In contrast, a good explanation is “hard to vary, because all of its details play a functional role.” Id., p.24.)

Proper scientific methods allow for the detection and correction of errors in theories. However, scientific theories, providing explanations, originate as conjectures or guesses; the discovery of theories is an act of intellectual creation by man. Id., pp.1–30. Finally, he concludes, scientific progress is always (and will always be) a work in progress, as existing explanations get replaced by better explanations which will themselves be replaced by better explanations in the endless quest for the best explanation. Id. Deutsch provides a somewhat simplistic view of the philosophy of science developed by Karl Popper and others in the twentieth century. But, as noted below, the philosophy has a tendency to be forgotten when Deutsch discusses scientific theories themselves.

As we shall discuss below, developments in quantum theories in the second half of the twentieth century gave rise to an increasing emphasis on the predictive successes and testability of the mathematical models being employed, as opposed to the concepts of explanation and understanding. However, it would appear that there are among the current generation of leading physicists some who seem to see the possibility of explanatory models that can be grasped by the intelligent layman—or, at least, the marketability of books that purport to present such explanations.

For example, Columbia University Professor of Physics and Mathematics Brian Greene recently wrote: “There’s a difference between making predictions and understanding them. The beauty of physics, its raison d’être, is that it offers insights into why things in the Universe behave the way they do. The ability to predict behavior is a big part of physics’ power, but the heart of physics would be lost if it didn’t give us a deep understanding of the hidden reality underlying what we observe.” The Hidden Reality, p.271. Albert Einstein, we can assume, would have wholly agreed.

Interestingly, there is a similar contrast or tension in the philosophy of mathematics among types of proof. Ian Hacking, Why Is There Philosophy of Mathematics at All?, pp.21–40. At one end, there are long, detailed proofs that appear to establish a proposition and can be carefully checked step by step. These proofs are often identified with Leibniz (1646–1716). At the other end, there are proofs that can be absorbed as a whole and which are compelling in their simplicity. This type of proof is associated with Descartes. The point of interest here is that the Cartesian proofs are thought to impart understanding—“they enable one to see not only that something is true, but why it is true. They give a feeling of understanding of the fact proven.” Id., p.32.

But, what does it mean to “make sense” of the observed regularities, to create a sense of insight or understanding? Natural scientists and many social scientists seem to aspire to the ideal of the deductive theory, and much of modern science appears in the mathematical forms to which a deductive theory lends itself. However, what we mean by an explanatory theory in the sense here is not necessarily or even primarily a mathematical model of the phenomena under investigation.

Toulmin argues that the notion of explanation “…involves appeal to some principle of regularity or ideal of natural uniformity.” Foresight and Understanding, pp.41–42. And, he acknowledges that those “notions” will reflect the paradigms and ideals of the persons involved. Toulmin attributes to Copernicus the objective of a scientific theory as “consistent with the numerical data” while being “absolute” and “pleasing to the mind.” Id., pp.41, 115. In more contemporary language, a satisfactory explanatory theory will be based upon circumstances that the observer considers to be natural or self-evident, circumstances that require no further explanations or raise no questions. See, id., p.41.

Toulmin refers to “ideals of natural order,” which are perceptions of circumstances or events—such as motion or change—that are in the natural order of things and that, therefore, require no explanation. The goal is to explain new data or observations of events that differ from the natural order in terms that make sense of the differences. Id., pp.44–82. Of course, man’s perception of what is the natural order of things is a historical/cultural phenomenon that can and does vary among men and over time. Again, those perceptions necessarily shape the questions that are asked (i.e., the observations that “need” explanation) and the nature and content of the theories that are developed to provide the explanations. This notion clearly introduces a significant subjective element into a field of intellectual inquiry (or “creation”) that we like to think of as “objective.” Hacking says, “[O]thers talk of the proof explaining the fact that is proved. Such words—understand, why, explain—are sound, but do little more than point to a satisfying phenomenon that is experienced, rather than one that can be well defined.” Why Is There Philosophy of Mathematics at All?, p.32. I return to this issue below.