William of Occam is a hero of the skeptical movement, and the importance of Occam’s razor to skeptical analysis is well known to readers of this magazine. But just who William of Occam actually was and what he actually said is less well known. Johnjoe McFadden’s book not only provides a biography of William but a history of the influence his ideas have had since he lived in the fourteenth century. The book is divided into four sections: Discovery (six chapters), The Unlocking (six chapters), Life’s Razors (three chapters), and The Cosmic Razor (four chapters).
The first section provides a biography of William and his influences on early philosophy and theology. It will probably contain the most new information about William of Occam for most readers. William led an interesting life! In 1327, he accused the pope of being a heretic—a surefire way to get oneself in serious trouble with the Catholic Church. He was duly summoned to Avignon, then the seat of the Papacy, to answer for this accusation. Things did not go well. In 1328, William fled Avignon and found sanctuary in the Court of Louis IV, the Holy Roman Emperor, in Germany. William never returned to his native England.
William’s heresy was to challenge the Church’s view that theology was a real science, the “Queen of the Sciences” according to Thomas Aquinas. He attacked the idea proposed by Plato that things we experience in our world are only faint sorts of shadows of the real objects that existed … somewhere. Plato termed these “real” objects Forms, and “St. Augustine had already imported Plato’s Forms into the early medieval Church where they became ideas in the mind of God” (42). Later, Aristotle modified the Forms into “universals,” which were thought to be the “essence” of an object or concept. Thus, “all fathers partook of the essence, or universal, of fatherhood” (42). In William’s time, Catholic theology had adopted the idea of universals. But William argued that Forms and universals were not necessary and that “entities should not be multiplied beyond necessity.” It was simpler to say that a father was a father because he had children. There was no need for any sort of vague, abstract “entity” of which all fathers took part.
This line of reasoning was a big problem for the Church—but not because of what modern skeptics might think: that there is no need for any gods in the first place. William never went that far. Rather, William’s position threatened classic proofs of the existence of God. Aquinas had relied heavily on Aristotle’s ideas of universals for his five proofs of God’s existence. Now here was William saying that this basic idea of Aristotle was bogus, thereby calling into question Aquinas’s proofs. In contrast, William held that God was, more or less by definition, unknowable.
Another major point of conflict between William and the Church was over the nature of human rights, specifically the right to own property. The Church held that Jesus had owned his own purse and transferred ownership of the purse and, by extension, all the world to the Church when he died. This allowed the Church to own vast wealth and to claim dominion over the whole world. Thus, “Pope Alexander VI divided ownership of the New World between the Spanish and Portuguese crowns, based on this notion of divinely appointed domination” (69). William, on the other hand, believed that Jesus did not own a purse and that “natural rights could not be annulled by pope or emperor, even voluntarily, as ‘no one can remove the rights and liberties conceded to the faithful by God and nature’” (71). It’s easy to see how this position would have been extremely threatening to a vastly wealthy and powerful Church hierarchy. McFadden’s discussion of this point made me understand, for the first time, why the seemingly absurd question of whether Jesus did or did not own something was so important at the time.
Sections two through four follow the success of the concept of simplicity through the history of science from William’s time to the present. It’s a delightful trip with each section describing the relevant problems solved by Occam’s razor. As an added bonus, fascinating tidbits of information are scattered here and there.
The second section covers the development of models of the solar system going, as is well known, from the frighteningly complex to the much simpler modern understanding. McFadden points out that the earlier, more complex models worked pretty well. Furthermore, highly complex models are hard to disprove or falsify because, with so many degrees of freedom, almost any new finding can be incorporated into the model by twiddling with one or more of the variables. This raises the question of “which system, if any, provided a correct physical model of the heavens.” Michael Mastlin, under whom Kepler had studied, “had taught him [Kepler] that each was a mere mathematical tool with no claim on the unknowable reality of the heavens. Kepler disagreed” (127). This issue, of how close a model is to reality, even if the model works very well in making predictions, is certainly still with us.
It is in the second section that a most intriguing quote from Copernicus appears. Copernicus is complaining about the complexity of astronomical calculations and says that the “experience was just like someone taking from various places hands, feet, a head, and other pieces [to make] a monster rather than a man” (110). Could Mary Shelley have read this passage?
The third section examines the role of the concept of simplicity in the biological sciences. It begins with the story of Alexander von Humbolt’s attempts to collect electric eels in South America for his scientific studies and the question that vexed early scientists: What is life? McFadden notes the position of the biologist Hans Westerhoff that “life is too complex, even ‘irreducibly complex’ … for Occam’s razor to be of any use” (5). In the three chapters in this section, McFadden does an excellent job of refuting this position. By the middle nineteenth century, the use of the razor “had become so much second nature that most scientists were unaware that they were working in that way.” Thus, in 1866 Mendel commented that “Experiments with seed characteristics give the results in the simplest and most certain way” (253).
Physics and cosmology are the focus of the final section. There is a discussion of Bayes’ Theorem (cleverly referred to as “The Probability Razor”) with one of the clearest nonmathematical explanations of this theorem I’ve read. McFadden has little patience with postmodernists who argue that we can never know anything for certain, saying, “a thousand observations of the sun rising does not provide us with certainty, but it does provide us with the high likelihood that the simplest hypothesis—that it will rise again tomorrow—will turn out to be true” (310).
The final chapter delves into two profound questions to which the author brings to bear the concept of simplicity and the razor. The first is whether our universe is as simple as it could possibly be. This question is difficult to answer; even if the current universe appears, on whatever grounds, to be as simple as possible, that doesn’t mean that there couldn’t be a simpler one, even if we can’t image how that might be. Nonetheless, McFadden invokes the principle of least action (that is, the stationary action principle) to argue that the current universe is pretty close to as simple as can be. This is because from the principle of least action it is possible to derive numerous other fundamental physical laws. These include Newton’s laws of motion, “classical conservation laws as well as Noether’s theorem and the gauge theories of particle physics. For quantum particles, such as photons, the principle of least action delivers Richard Feynman’s path integral method of calculating motion” (317) among other things. Pretty cool! This section ends with a discussion of why, if the universe is simple, there are neutrinos, which seem to have little to do with much of anything.
The second question is why the basic physical constants in our universe are what they are and not different—differences that would not allow life to evolve or our universe even to exist. Following Lee Smolin, McFadden proposes a “cosmic ecology” in which multiple universes are formed and only some survive to allow life to exist. There are obvious problems here. What is the universe-based equivalent of reproduction? How is the “genetic” information of a universe passed on to succeeding generations of universes? How does this information mutate to create new universes with different values for the physical constants?
The discussion of the evolution of universes is based on the idea of a multiverse in which an infinite, or at least an extremely large, number of universes have existed, exist now, or will exist in the future. It has always struck me that such a hypothesis is extraordinarily unparsimonious. But I suppose if the issue is to minimize the complexity of our little universe and not worry about parsimony elsewhere, it sort of makes sense.
Life is Simple brings the life of William of Occam to light and gives a description of his influence on the theology of his time and his profound influence on science up to the present. It is an excellent book that covers an impressive range of topics. It is well written and exciting in its entirety.