Most religious conversations between believers and non-believers lead to a contrast between religion and science. “Science is based upon reason; religion relies upon faith,” the agnostic will assert, believing that this in some way damages the respectability of belief. In fact, he is only echoing Thomas Aquinas who taught that theology is done on the light of faith while philosophy—including the philosophy of nature and hence modern science—is based upon the natural light of reason.
This, of course, is not what the non-believer wants to say. In contrasting religion and science, he is implying that the believer is a victim of superstition who fails to acknowledge that only science can lead to true knowledge because it alone is based on empirical verification and rigorous testing.
How is the believer to respond? Is it true that science alone is rational because it is based on demonstration and logical reasoning?
Most people would agree that religious faith is grounded in truths that cannot be demonstrated empirically using the scientific method. For the Catholic, these beliefs of faith are justified because they are accepted as true on the revelation and authority of God, who can neither deceive nor be deceived. What is not obvious is that scientific knowledge too must be grounded in essential, non-provable beliefs about the nature of the universe.
What follows is a brief summary of the scientific method that grounds the scientific enterprise. As many philosophers of science have shown, the success and justification of the method rests on premises which cannot be demonstrated. Instead these premises are accepted as true by the scientific community because science would be unable to function without them. These premises constitute the essential beliefs of every scientist—his natural faith—and reflect his implicit acceptance of classical metaphysics.
The first step in the scientific method involves the process of induction. The scientist looks around himself, collects data, then makes a probable conclusion. For example, all the swans he sees are all white. He therefore proposes the hypothesis that all swans are white. But using this process of induction alone, the scientist can never assert truths with absolute certainty. No great number of white swans could rule out the possibility that the next swan could be black. Consequently, the scientist often constructs his hypothesis so that it can be verified and tested through experimentation. The experiment is then thought to confirm or dismiss the hypothesis.
But even this safeguard cannot guarantee the truth of scientific conclusions. This is illustrated by a simple example used by the philosopher Richard Swinburne (Simplicity as Evidence of Truth, . Marquette University Press , 15–19). Let us say that a scientist is analyzing data composed of four pairs of numbers, the first number in each set being designated “x” and the second “y”: (1,2), (2,4), (3,6), and (4,8). He wants to determine the relationship between the first and the second numbers in the series where x increases by 1 and y increases by 2.
Using induction, he compares the pairs of numbers and proposes that y = 2x. It is a reasonable hypothesis, but he resorts to more testing and comes up with two more pairs of numbers, (5,10) and (6,12). They seem to confirm his hypothesis, and he rejoices. What is not usually realized, however, is that this series of paired numbers can be adequately explained by an infinite number of alternate equations of the form y = 2x + x(x-1)(x-2)(x-3)(x-4)(x-5)(x6)z, where z can be a constant or another function of x. No further testing and collecting of data would be able to distinguish between these alternative equations and the basic equation y = 2x.
In choosing y = 2x as his hypothesis, the scientist has made an assumption: He has assumed that simplicity is a marker for truth.
James D. Watson, describing his discovery with F. H. C. Crick of the double helical structure of deoxyribonucleic acid, or DNA, said it was “an adventure characterized by youthful arrogance and by the belief that the truth, once found, would be simple as well as pretty” (Watson The Double Helix, Athenaeum , ix). And despite the absence of any definitive data that would favor the heliocentric over the geocentric model for the solar system, Copernicus believed that his hypothesis that the Earth revolved around the sun was true because it was simpler. These are only two examples that suggest that the simplest theories are most likely to be true. Most scientists believe this. Why?
Swinburne discusses three possible answers (Simplicity, .44–51). First, some might claim that there are reasons why scientists choose simple theories beyond the greater probable truth of a simple theory. But examples from the history of science suggest this is not true. As Watson believed, simplicity itself is thought to be a marker of truth.
Second, some might argue that the presumption of simplicity is justified because history has shown that simplicity is a reasonable assumption that has worked. Swinburne points out that justifying simplicity this way itself already relies upon the criterion of simplicity and as such begs the question. He points out there are many ways of extrapolating from past historical data. “Usually simplest theories predict better than more complex theories” is one way, but “Usually theories formulated by Greeks in the bath, by Englishmen who watch apples drop, or Germans who work in patent offices . . . predict better than other theories” is another way. (Swinburne is referring here to Archimedes, Newton, and Einstein.) This second explanation of past data explains history equally well but is obviously absurd. The first alternative, the simpler one, has to be preferred. However, since simplicity itself is presumed, the appeal to history cannot be used to justify simplicity.
The third possibility is that some mathematical or logical theorem justifies belief in simplicity. This, in fact, is only a more sophisticated way of saying that some mathematical formula can be devised to demonstrate that induction can give rise to certain knowledge. But, as the skeptic philosopher David Hume said, “There can be no demonstrative arguments to prove that those instances of which we have had no experience resemble those of which we have had experience” (Treatise on Human Nature. 1:3:6).
The future always remains contingent. Ultimately, if the principle of simplicity is true, it is a fundamental, undemonstrable truth that must be accepted on faith by the scientist. It allows him to do science.
The quote from James Watson above is a reminder that the conviction that truth is simple is not the only belief held by the scientist. Closely related to this is the belief that the truth is beautiful or, using Watson’s word, “pretty.” The mathematical physicist Paul M. Dirac—after recalling that the greatest modern physicists have looked for “beautiful theories,” “beautiful equations,” and “beautiful generalizations” to explain nature—recounts the case of a physicist who refused to accept his mathematical theory because it did not agree exactly with the observed data. Eventually, it turned out that the mathematical solution was true and the observation was erroneous.
“I think that there is a moral to this story,” wrote Dirac, “namely, that it is more important to have beauty in one’s equations than to have them fit experiments. . . . It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress” (“The Evolution of the Physicist’s Picture of Nature,” Scientific American. 208 [May 1963], 47).
Today, theoretical physicists still use elegance and coherence, elements which reflect the beautiful, as signposts for formulating explanations for nature that may not at first be provable with empirical methods. String theory, with which scientists are attempting to unify all the fundamental forces with gravity, is one example. In fact, string theory is just one of many attempts to find a theory-of-everything, a single equation that can be emblazoned on the T-shirt of an M.I.T. student. It is a search driven by the realization that the standard model used by physicists to describe the structure of nature seems too complicated. It is not pretty enough.
Clearly, it is not easy to justify this intuitive understanding that truth is beautiful in a logical demonstration. However, alongside simplicity, beauty allows the scientists to choose among his different hypotheses. It allows him to accomplish his task.
Finally, as the Holy Father points out, the scientist takes for granted that truth exists and is the object of his endeavors. “When scientists, following their intuition, set out in search of the logical and verifiable explanation of a phenomenon, they are confident from the first that they will find an answer, and they do not give up in the face of setbacks. They do not judge their original intuition useless simply because they have not reached their goal; rightly enough they will say that they have not yet found a satisfactory answer” (Fides et Ratio 29.). Hence, for the scientist, the truth is attractive—or, in classical terminology, the truth, because it attracts, is good.
We have seen that the scientific assumption that truth is simple, beautiful, and good cannot be proved demonstratively and yet must be accepted as true. As Swinburne has pointed out, an inductive argument cannot be used to justify this belief, since it has to be assumed in order to construct any conclusions from historical data. It is a metaphysical first principle, a basic assertion about the nature of reality, which, as the ancient and medieval philosophers understood, is fundamental and non-demonstrable.
Ultimately, it is nothing more than the scientist’s implicit acceptance of classical metaphysics that equates being with truth, unity, beauty, and goodness. Every scientist has to accept that reality is ordered and intelligible. As such, simplicity, beauty, and goodness constitute non-empirical criteria that must be adopted by every scientist in order to accomplish his work. These attributes reflect common metaphysical beliefs that must be presupposed in order for anyone—scientist or philosopher or theologian—to be rational. Hence, at the very heart of science’s rationality is an act of the will—an act of faith.
Science is one example of human reasoning at its best. Most scientists would contend that their work attains truth, pointing at the successes of science—we fly planes, we cure diseases, we communicate on the Internet—to support their argument. These same scientists often fail to realize that these successes necessarily presuppose metaphysical and methodological principles that though non-demonstrable are accepted by them as true and certain.
Is it surprising that there are truths that cannot be proved? Though most scientists would be suspicious, they shouldn’t be. Kurt Gödel, one of their own, showed in 1930 that there would always be some truths whose truth or falsity cannot be established using the axioms and deductive rules of arithmetic (John Barrow, Impossibility: The Limits of Science and the Science of Limits, .Oxford University Press , 218–231). He used logic to prove that there were things that could not be proved. Some of these include the metaphysical first principles that ground the scientific enterprise.
Thus, if science is considered the paradigm of rationality as many people suppose, then one must conclude that believing is also rational. The believer can now correct the non-believer who has contrasted science and religion: Science is based primarily upon reason but, as does every rational enterprise, including religion, science relies upon principles that are grounded in faith.