The Philosophical Breakfast Club

by Laura J. Snyder

  Whewell argued further than Newton had done that even the relation between the celestial and terrestrial realms indicates the work of an intelligent Creator. The length of a solar year is determined by how long it takes for the earth to orbit the sun. As Whewell pointed out, this period of time could easily have been other than it is, if the earth were closer to or farther from the sun, or if its speed were faster or slower. If, however, the solar year were different from what it is, then it would be a disaster for fruits and vegetables. If the summer and autumn were shorter than they are, fruit would not ripen on the trees. Moreover, plants and animals are adapted to the climate of the areas in which they are found. Tropical plants and flowers thrive in the warm climate of tropical zones; but if the temperature in those zones were colder, those plants and flowers would all die off.38 Like Paley, Whewell argued that this could not all have been arranged by chance.

  Yet Whewell’s version of natural theology was more sophisticated than Paley’s, reflecting Whewell’s superior knowledge of science. The most compelling evidence to be found in nature for God’s existence, Whewell argued, was not the existence of individual cases of fitness to environment, such as the white fur of the polar bear, but the workings of natural law. “Nature acts by general laws,” Whewell explained, pointing to examples such as the law of universal gravitation—he even cited Herschel’s work on the double stars, as proving that the inverse-square law of gravitation really is a universal law, reaching beyond the confines of our solar system.39 The existence of natural law implies the existence of a law-giver, some intelligent mind that formulated a general law and created the universe in accordance with it.

  Indeed, because studying the laws of nature gives so much confidence in the existence of a law-giving God, science is not only consistent with religion, but is an important pathway to religious belief. Whewell thus embarked on a discussion about the proper way to do science, showing that the use of an inductive method was most likely to lead to the strengthening of religious faith. In two chapters, Whewell contrasted what he called the inductive and deductive “habits of the mind,” arguing that the former are more likely than the latter to lead to belief in God. With Rose’s criticisms of scientific inquiry in mind, Whewell was trying to show that science—properly done science—does not lead to irreligious views. As far as it is true that some men of science have been atheists, Whewell insisted, they have been mainly from the camp of deductive, not inductive, thinkers.40 This section of his Bridgewater Treatise was very much part of the Philosophical Breakfast Club’s project of defeating the “downwards mad” writers who wished to make scientific method primarily deductive; here he is giving a religious justification for following an inductive scientific method.

  The inductive mind, Whewell reminded his readers, studies the facts of nature in order to try to discover lawful connections between them. As he had put it in his review of Herschel’s Preliminary Discourse two years earlier, the facts of nature are like individual pearls, which need to be strung on a connecting thread, an organizing principle, or law. When the scientist discovers a law of nature, what happens is that “a mass of facts which before seemed incoherent and unmeaning assume, on a sudden, the aspect of connexion and intelligible order.”41 All facts are suddenly seen as “exemplifications of the same truth”—as when Newton realized that falling bodies, projectiles, orbiting planets, and the movement of the tides were all particular instances of the inverse-square law of gravitation. “This step,” Whewell explained, “so much resembles the mode in which one intelligent being understands and apprehends the conceptions of another, that we cannot be surprised if those persons in whose minds such a process has taken place, have been most ready to acknowledge the existence and operation of a superintending intelligence.” That is, our recognition of the lawlike nature of the world almost forces us to the realization that the world must have been created by an intelligent being who imposed these laws on His Creation.

  Whewell allowed that deductive reasoning is valuable in science. Once a law is discovered by inductive reasoning, it is important to use deduction to find “a train of consequences,” or empirical predictions, that can be used to test the truth of the law. As Bacon, and more recently Herschel, had argued, there is a “double ladder,” requiring ascent (to a law) by induction and descent (to testable consequences of the law) by deduction.42 Whewell went out of his way to praise mathematicians, “men well deserving of honor,” who, Whewell emphasized, “have labored with such wonderful success in unfolding the mechanism of the heavens”—d’Alembert, Clairault, Euler, Lagrange, Laplace.43 But this deductive work does not add to knowledge anything not already contained in the laws themselves; it is like unfolding “right triangles have 180 degrees” out of the law “all triangles have 180 degrees.” Deduction is useful for testing theories arrived at by induction; but deduction itself, as Babbage, Herschel, Jones, and Whewell had all argued against the Ricardian political economists, cannot be used for finding new truths in the first place.

  So the man of science who uses only deductive reasoning is not a real discoverer, not someone who will uncover new laws of nature. The deductive scientist is also at a disadvantage in religious belief. By not doing the work of discovering new laws of nature, the deductive scientist or mathematician is not in a position to realize that there must have been an intelligent law-giver who created the world. It was not surprising, Whewell concluded, that many famous mathematicians (mostly French, as it happens) have been atheists.44

  Whewell was most concerned about the reception of these two chapters.45 Gilbert, who had commissioned the work from him, told Whewell that he was delighted with the book. He was “much pleased” with the chapters on the inductive and deductive habits of the mind, Gilbert assured him, but warned, “I hear that some mathematicians are quite violent against them.”46 He surely had in mind Babbage—who had recently published his screed against the Royal Society—as one of these “violent” mathematicians.

  To Babbage, ever on the lookout for slights aimed at him, this book seemed to be denigrating his very essence as a mathematician—indeed, it appeared to him that Whewell was dismissing his Difference Engine, created in order to perfect and mechanize mathematical reasoning, a form of deductive thought. In expressing his anger toward Whewell, Babbage made it clear that the project of the Philosophical Breakfast Club—to bring about a revolution in science, partly by promoting inductive scientific method—had become secondary to Babbage’s main project: his own self-promotion.

  ON BEHALF OF mathematicians everywhere, Babbage resolved to show that deductive reasoning—even when done by a machine—did not inevitably lead to atheism. He may have argued as an undergraduate at Cambridge that “God was a material agent,” but he was not about to concede the realm of religion to Whewell. In response to his friend’s work he wrote what he cheekily called his Ninth Bridgewater Treatise—cheeky because it was not one of the books in the official Bridgewater series—published in May 1837. The title page of this work displayed the quotation from Whewell’s Bridgewater Treatise that had most provoked Babbage: “We may thus, with the greatest propriety, deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the universe; we have no reason whatever to expect from their speculations any help, when we ascend to the first cause and supreme ruler of the universe.”

  On the contrary, Babbage believed, deductive reasoning could be used in support of religious views. Specifically, one could use deductive mathematical reasoning to demolish Hume’s famous argument against the existence of miracles, making a much stronger case against it than Paley had done in his Evidences of Christianity. Indeed, one must use mathematics to defeat this argument, Babbage claimed, making mathematical reasoning actually necessary for religious belief.

  Hume had famously argued that the existence of miracles—defined as specific acts outside the laws of nature created by God—could not be rationally supported. Given t
he evidence for any such miracle, which generally includes the testimony of witnesses, it is always more reasonable to believe that the miracle did not in fact happen. Witnesses can be incorrect, or lying.

  Making reference to works on mathematical probability theory by Laplace, Poisson, and De Morgan, Babbage translated the issue into statistical terms, noting that Hume’s argument amounts to the claim that miracles are extremely improbable. Once Babbage does this, he can use mathematical reasoning to show that the argument is fallacious. If “miracle” means something very improbable, then it follows that one should believe in miracles if the evidence in their favor makes them more probable than the evidence against them.

  Babbage considered Hume’s example of Christ’s alleged resurrection. Babbage claimed that the improbability of this event was 200 billion to one against its occurrence. (Babbage reached the number 200 billion by estimating the number of human beings who had ever lived; the probability of only one of them being resurrected was supposed, therefore, to be 200 billion to one.) Babbage next showed that if there are six normally reliable, independent witnesses (that is, none is influenced by the testimony of the others) to a miraculous event, the probability of all six lying is 1006 to one, or 1 trillion to one (assuming that each witness will tell a falsehood one out of one hundred times, making the probability of lying in a given situation for each witness one hundred to one, according to Babbage). So it is actually far more probable that the miracle is true than that all six witnesses are lying: specifically, it is five times more improbable that all the witnesses are lying than that the dead man rose up (one trillion to one versus two hundred billion to one).47

  Herschel complained to Babbage about these calculations: Why should he count only the total number of human beings who have ever lived, and not the total number of mammals, or other vertebrates, or indeed all other living things, since only one living thing has ever been resurrected? Moreover, he chided Babbage that “I have objections in toto to any application of the calculus of probabilities to the case in question, as a ground for belief one way or the other.”48 As Herschel complained to Jones, “The real fact is that it is not a question of which any numerical computation applies at all!”49

  Babbage also took issue with Whewell’s view of miracles. Whewell’s position on this topic was not fully articulated in his Bridgewater Treatise. In that work, Whewell had mainly described God as acting in a lawful way, by creating a world that runs by natural laws; indeed he argued that the existence of these universal laws, which do not require God’s constant intervention, is the best evidence for the existence of a law-giver. From this it would seem to follow that God does not need to intervene each time an object is dropped, or every time a projectile is flung, or during the never-ceasing orbits of the planets. Rather, God merely had to create the law of universal gravitation that governs these actions.

  However, in his reviews of both volumes of Lyell’s Principles of Geology, published in 1831 and 1832, Whewell had claimed that God sometimes performs miracles outside of—and contrary to—natural law. Lyell had argued that the fossil record showed not only evidence of now-extinct animals, but also the “succession of different races of animals,” suggesting that not only did species become extinct, but also that new species arose to take their place. Whewell agreed that the evidence seemed to confirm this. But, he cautioned, Lyell must show how one world of animal forms was exchanged for another, how the earth went from being populated by plesiosaurs and pterodactyls to paleotherians and mastodons. To Whewell, the inescapable conclusion was that God intervened miraculously, creating new species after the old became extinct. We see in this fossil record, Whewell argued, “a distinct manifestation of creative power, transcending the operation of known laws of nature.”50

  In his three-volume work History of the Inductive Sciences, published only a few weeks before Babbage’s Ninth Bridgewater Treatise—so that it is possible Babbage had not yet seen the book when he finalized his manuscript—Whewell made this point even more explicitly. “We must,” Whewell insisted, “believe in many successive acts of creation, and extinction of species, out of the common course of nature; acts which, therefore, we may properly call miraculous.”51 That is, new species were most likely created by specific interventions of God himself, not through any purely natural process. Appealing to miracles in explaining the origin of new species was not denial of scientific method, Whewell insisted, because the appearance of new species was in the realm of religion rather than science. In trying to explain such origins, geology “says nothing, but she points upwards [i.e., to God].”52

  Here Whewell was clearly in the majority among scientists at the time, who were reluctant to give up their belief that species were individually created by God, even as the evidence of new species found in the fossil record mounted. Whewell felt that his view was scientifically supportable as well; he knew that Newton, the greatest of all the natural philosophers, had also argued that God must constantly intervene in the natural world. Newton had even argued this point against Leibniz, who believed that God had made a perfect world that required no further intervention. (Voltaire’s Pangloss, who believes that this is the “best of all possible worlds,” was created to poke fun at Leibniz and his rosy view of things.) On the contrary, Newton argued in his Opticks, God’s intervention is necessary in order to keep the planetary orbits moving in their paths; without God’s continual action, he believed, the orbits would become more and more irregular over time. In a letter to Caroline of Ansbach (the wife of the future King George II of England), Leibniz had mocked this view, noting that Newton believed “God Almighty wants to wind up his watch from time to time, otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion.”53

  In his Ninth Bridgewater Treatise, Babbage agreed with Leibniz (another inventor of a calculator!) that God does not need to work in such an unlawful and messy way. To attribute this kind of constant meddling in His Creation to God was, as Leibniz had noted, “by implication denying to Him the possession of that foresight which is the highest attribute of omnipotence.”54 God is not a tinkerer, but a divine planner. Babbage disagreed with Hume’s characterization of miracles as events outside natural law; for Babbage, miracles were events inside natural law, because God has created the law with the supposed miracle built in. Babbage’s main example in the book of this kind of preordained miracle was his Difference Engine with the feedback mechanism, just as he had been demonstrating at his soirées in order to show that God was, in Babbage’s conception, a divine programmer, who set up the laws of the universe such that unexpected, seemingly “miraculous,” events were part of the initial program. (Babbage did not, however, use the term “program” or “programmer” in this book; these terms had not yet been created, because there was as yet nothing concrete to which they could refer.)

  Provocatively, Babbage made it clear in his book, as he had at his parties, that the origin of new species was one of these so-called miraculous events that could be explained as the result of God’s divine program.55 Just as the laws of the caterpillar give way to the laws of the butterfly, and that of the tadpole to that of the frog, so, too, the laws governing a land covered with vegetation could be replaced by laws governing the appearance of animal forms, some of which die out and are replaced by newly arising forms. “To have foreseen all these changes, and to have provided, by one comprehensive law, for all that should ever occur … manifests a degree of power and of knowledge of a far higher order” than would be required by a being who continuously tinkered with His creation, Babbage insisted.56

  Babbage enlisted Herschel’s aid in arguing against Whewell. Lyell had shown Babbage a letter from Herschel on this topic, as well as Lyell’s reply, and Babbage reprinted portions of these letters as an appendix to his Ninth Bridgewater Treatise.57 In his letter to Lyell, Herschel had referred to “that mystery of mysteries, the replacement of extinct species by others.” In his view, we are led by analogy with ho
w God’s laws work in the natural world to suppose that God acts through “intermediate” or physical causes, and thus that “the origination of fresh species … would be found to be a natural in contradistinction to a miraculous process.”58 In this letter, Herschel made it clear that he believed it possible that the appearance of a new species could be a matter of natural law, not a special case of divine intervention.

  The crux of the disagreement between Babbage, Herschel, and Whewell over the creation of new species rests on this point. Babbage and Herschel believed that new species could arise through a lawful, natural process, just as they conceived the planets moving in their orbits due to a law set by God at the start of His Creation—the law of universal gravitation. Whewell, on the other hand, was much more skeptical, and thought it likely that God had to intervene each time a new species arose, in an act of “special creation” outside natural law—similar to the view of modern proponents of intelligent design. At the same time, however, Whewell did not absolutely shut the door on the possibility that new species might have arisen through natural law, without God’s intervention; indeed, after reading the History of the Inductive Sciences, Lyell optimistically reported to Herschel that Whewell “appears to me to go nearly as far as to contemplate the possibility at least of the introduction of fresh species being governed by general laws.”59 (Jones, the fourth member of the Philosophical Breakfast Club, seems not to have expressed any view on this topic in writing.) The four friends had disagreed with each other over other issues, such as public financing for science and the importance of reforming the Royal Society and creating the British Association, but this was the first serious fissure in the group, both philosophically and personally.