Elliott Sober

Ockham's razor, the principle of parsimony, states that simpler theories are better than theories that are more complex. It has a history dating back to Aristotle and it plays an important role in current physics, biology, and psychology. The razor also gets used outside of science - in everyday life and in philosophy. This book evaluates the principle and discusses its many applications. Fascinating examples from different domains provide a rich basis for contemplating the principle's promises and perils. It is obvious that simpler theories are beautiful and easy to understand; the hard problem is to figure out why the simplicity of a theory should be relevant to saying what the world is like. In this book, the ABCs of probability theory are succinctly developed and put to work to describe two 'parsimony paradigms' within which this problem can be solved.

The problem of simplicity involves three questions: How is the simplicity of a hypothesis to be measured? How is the use of simplicity as a guide to hypothesis choice to be justified? And how is simplicity related to other desirable features of hypotheses -- that is, how is simplicity to be traded-off? The present paper explores these three questions, from a variety of viewpoints, including Bayesianism, likelihoodism, and the framework of predictive accuracy formulated by Akaike (1973). It may turn out that simplicity has no global justification -- that its justification varies from problem to problem.

Realists persuaded by indispensability arguments af- firm the existence of numbers, genes, and quarks. Van Fraassen's empiricism remains agnostic with respect to all three. The point of agreement is that the posits of mathematics and the posits of biology and physics stand orfall together. The mathematical Platonist can take heart from this consensus; even if the existence of num- bers is still problematic, it seems no more problematic than the existence of genes or quarks. If the two positions just described were the only ones possible, there could be no objection to this melding of numbers with genes and quarks. However, the position I call contrastive empiricism (Sober 1990a) stands opposed to both realism and to Van Fraassen's em- piricism. As it turns out, contrastive empiricism entails that coalesc- ing mathematics with empirical science is highly problematic. I believe that there is an important kernel of truth in abductive ar- guments for genes and quarks. But no counterpart argument exists for the case of numbers. Of course, the existence of this third way would be uninteresting, if contrastive empiricism were wholly implausible. However, I will argue that contrastive empiricism captures what makes sense in standard versions of realism and empiricism, while avoiding the excesses of each. This third way is a middle way; it cannot be dismissed out of hand.

“Absence of evidence isn’t evidence of absence” is a slogan that is popular among scientists and nonscientists alike. This article assesses its truth by using a probabilistic tool, the Law of Likelihood. Qualitative questions (“Is E evidence about H ?”) and quantitative questions (“How much evidence does E provide about H ?”) are both considered. The article discusses the example of fossil intermediates. If finding a fossil that is phenotypically intermediate between two extant species provides evidence that those species have a common ancestor, does failing to find such a fossil constitute evidence that there was no common ancestor? Or should the failure merely be chalked up to the imperfection of the fossil record? The transitivity of the evidence relation in simple causal chains provides a broader context, which leads to discussion of the fine-tuning argument, the anthropic principle, and observation selection effects.

Darwin claims in the Origin that similarity is evidence for common ancestry, but that adaptive similarities are ‘almost valueless’ as evidence. This second claim seems reasonable for some adaptive similarities but not for others. Here we clarify and evaluate these and related matters by using the law of likelihood as an analytic tool and by considering mathematical models of three evolutionary processes: directional selection, stabilizing selection, and drift. Our results apply both to Darwin’s theory of evolution and to modern evolutionary biology. 1 Introduction2 The Likelihood Framework3 A Sufficient Condition for a Similarity to Favour Common Ancestry over Separate Ancestry4 The 1/p Criterion and Its Limitations5 Directional Selection versus Drift6 Stabilizing Selection versus Drift7 Going beyond Two Taxa8 ConclusionsAppendix.