Elliott Sober’s recent monograph Ockham’s Razors: A User’s Manual examines the epistemic status of the principle of parsimony and its application across philosophy and the sciences. In particular, Sober defends a reductionist thesis about parsimony—parsimony is epistemically relevant only insofar as it contributes to the achievement of some more fundamental epistemic goal—and applies this thesis to phylogenetic inference in biology, chimpanzee mind reading in psychology, and a number of philosophical debates invoking Ockham’s razor. The book is Sober’s most comprehensive treatment of the subject, revisiting earlier writings and tackling new topics. As such, the monograph is a welcome contribution to the philosophical literature on parsimony. By perusing Ockham’s Razors, the reader will get a clear idea of how to use formal epistemological principles originating from the statistical literature to clarify philosophical and scientific arguments invoking parsimony.
The book is structured as follows. Chapter 1 sets the scene by providing an abridged tour through the history of parsimony from Aristotle to the British psychologist C. Lloyd Morgan at the turn of the twentieth century. Chapter 2 reviews different schools of statistical inference, including Bayesian, likelihoodist, and frequentist (or, more precisely, model-selection) approaches, and develops a reductionist view of parsimony. In particular, Sober identifies two ‘paradigms’ that attribute epistemic relevance to parsimony. The first paradigm originates from likelihoodism: more parsimonious theories have higher likelihoods. According to the second paradigm, parsimony is relevant to estimating a model’s predictive accuracy since models with fewer adjustable parameters are less prone to “overfitting,” that is, less prone to describe random noise in the data rather than the true relationship of the variables of interest. So, considerations invoking parsimony are epistemically relevant only insofar as they reflect likelihoods (first paradigm) or refer to the number of adjustable parameters in a model (second paradigm).
While Sober advocates parsimony paradigms based on likelihoodist and model-selection ideas, Bayesianism is the odd one out. Sober considers Jeffreys’s simplicity postulate (i.e., the idea that simpler hypotheses should have higher prior probabilities) and Bayesian Ockham’s razor (i.e., the idea that simpler hypotheses have larger marginal likelihoods) and finds them both wanting.
In chapter 3, Sober’s reductionist view of parsimony is nicely mirrored by attempts in the biological literature to provide independent justifications for the maximum parsimony (MP) method in phylogenetic inference. MP infers phylogenetic trees that minimize the total number of evolutionary changes. Again, the law of likelihood figures prominently in this chapter, since the question as to when and how MP mirrors maximum likelihood (ML) based phylogenetic inference has led to a vivid and ongoing debate among biologists.
As the precise relationship between MP and ML is still investigated in the biological literature, Sober also discusses whether MP can be justified on the basis of other criteria such as statistical consistency and reliability. Informally, a statistical procedure is said to be consistent if it identifies the truth when applied to infinitely large data sets. MP fails to be statistically consistent in simple evolutionary models, but the question of MP’s consistency in more complex models is yet to be explored in detail. Reliability, as understood here, requires that MP has a higher probability of inferring the correct character states of a common ancestor than using the prior probability distribution over these states as one’s guess. It turns out that MP is more reliable than guessing only under rather restrictive assumptions about the evolutionary process.
Chapter 4 turns to psychology and addresses the question whether psychological experiments on chimpanzees support the hypothesis that chimpanzees are mind readers (i.e., they form mental representations of the mental states of others) over the hypothesis that they are behavior readers (i.e., they form mental representations of the behavior of others). In particular, Sober evaluates the view that the mind-reading hypothesis is more parsimonious than the behavior-reading hypothesis, as well as arguments asserting the opposite. Sober sides with the behavior readers in the sense that on the basis of the model-selection paradigm, behavior reading is more parsimonious than mind reading. In a model-selection framework, however, parsimony is only part of the story, as simplicity measured by the number of adjustable parameters of a model stands in competition with the goodness of fit of the model. As such, the debate between proponents of behavior reading and mind reading is not settled by reference to parsimony alone. Data from psychological experiments still have an important role to play in resolving the debate.
Finally, chapter 5 reviews a number of philosophical debates in which parsimony-based arguments have figured, such as the problem of evil, the mind-body problem, moral realism, and the debate between nominalists and Platonists about mathematics. While chapters 3 and 4 have more of a specialist character and will attract interest mainly from philosophers of biology and philosophers of mind, the final chapter offers a potpourri of thought-provoking arguments that should appeal to more generally minded analytic philosophers.
Ockham’s Razors illustrates both the depth and the width of Sober’s thinking on parsimony. I particularly enjoyed going through the individual arguments of chapter 5 and found the open-ended nature of the chapter appealing but stumbled when reading the discussion of the indispensability argument. The indispensability argument in the philosophy of mathematics asserts that the empirical evidence that confirms a scientific theory also confirms the purely mathematical consequences of the theory. For instance, the observations that confirm relativity theory are said to also confirm the existence of numbers since relativity theory entails that numbers exist. Sober (274) thinks that proponents of the indispensability argument, at least tacitly, presume the special consequence condition (SCC), which says that if evidence E confirms theory T and T has the logical consequence C, then E confirms C. While Sober rightly points out that SCC is false under the incremental notion of Bayesian confirmation (i.e., E confirms T if and only if P(T|E) > P(T)), SCC is a valid form of inference given the absolute notion of Bayesian confirmation (i.e., E confirms T if and only if P(T|E) > k for some threshold value k). While modern Bayesians typically adopt the incremental rather than the absolute notion of confirmation, the absolute notion still plays an essential role in some recent accounts of evidence and confirmation (Sherrilyn Roush, Tracking Truth: Knowledge, Evidence, and Science [Oxford: Oxford University Press, 2005]). Hence, there is good reason to put this view on confirmation on the table.
By adopting the absolute notion of confirmation, one also has the resources to reply to Sober’s second worry about the indispensability argument. Sober (274) claims that the argument falls prey to what he calls “selective attention”: if the empirical success of relativity theory confirms the existence of numbers, then why does the empirical failure of other mathematical theories not disconfirm their existence? It follows from the axioms of the probability calculus that the probability of a logical consequence of a theory is greater than or equal to the probability of the theory itself. Hence, it is possible for the theory to be disconfirmed by the evidence on the basis of the absolute account, while the consequence is not. More generally, it seems important to assess whether the validity of the indispensability argument is sensitive to the adopted account of confirmation.
To sum up, apart from the primary objective of shedding light on the status of Ockham’s razor in science and philosophy, the book serves two further aims in my view. First, it highlights a unifying theme of Sober’s philosophical work over the past decades. The monograph illustrates that philosophical and scientific debates invoking parsimony can be clarified, and at times resolved, by applying formal epistemological principles, such as the law of likelihood. Second, the book revisits a number of themes from Sober’s earlier writings and supplements them with new ideas and results (e.g., chap. 3 combines arguments from Elliott Sober, Reconstructing the Past: Parsimony, Evolution and Inference [Cambridge, MA: MIT Press, 1988], with novel discussions on the justification of MP and new mathematical results on the relationship between MP and ML).
I see three groups of readers as particularly benefiting from the book. First, any philosopher or scientist interested in Ockham’s razor should have a look at Sober’s take on the subject. Second, readers who are familiar with Sober’s earlier work, and would like to keep up-to-date with recent developments or to get a more comprehensive view on Sober’s thinking on parsimony, will find the book helpful. Finally, I view this monograph as an ideal introduction to Sober’s philosophy. This is helped by Sober’s clear and entertaining style of writing: Ockham’s Razors is a pleasure to read. As such, I recommend the book to any graduate student with interests in the philosophy of science, the philosophy of probability or the philosophy of biology. Furthermore, the book is suitable for a graduate seminar on Ockham’s razor, and individual chapters can be used for specialist graduate courses in the philosophy of probability, the philosophy of biology, and the philosophy of mind.
