Absence of Evidence and Evidence of Absence: Evidential Transitivity in Connection with Fossils, Fishing, Fine-Tuning, and Firing Squads

Elliott Sober examines the logical relationship between absence of evidence and evidence of absence, challenging the common philosophical dictum that "absence of evidence is not evidence of absence." Through careful analysis of probability theory and Bayesian reasoning, Sober demonstrates that this principle requires significant qualification and often fails to hold in scientific and philosophical contexts.

The article begins by distinguishing two interpretations of the absence/evidence relationship. Under one reading, the claim concerns whether failing to find evidence for a hypothesis constitutes evidence against that hypothesis. Under another, it addresses whether the absence of observable effects provides evidence against their causes. Sober argues that both interpretations yield instances where absence of evidence does constitute evidence of absence, provided certain probabilistic conditions obtain.

Central to Sober's analysis is the concept of evidential transitivity. If evidence E supports hypothesis H1, and H1 makes H2 more probable, then E provides at least some evidence for H2. However, Sober identifies important exceptions to this transitivity principle, particularly when dealing with existential claims and observational limitations. He employs four key examples to illustrate these complexities: fossil evidence for evolutionary theory, fishing in a lake to determine fish presence, fine-tuning arguments for divine design, and Paley's firing squad analogy.

The fine-tuning discussion proves particularly relevant to natural theology. Sober examines whether the precise cosmic constants necessary for life provide evidence for divine design. He argues that while fine-tuning might support the existence of multiple universes or divine intention over single-universe chance hypotheses, the evidential relationships become complex when considering observation selection effects. The anthropic principle introduces complications that can block evidential transitivity from fine-tuning to design hypotheses.

Sober's analysis carries significant implications for debates about divine hiddenness and arguments from evil. If absence of evidence can constitute evidence of absence under specific conditions, then the apparent absence of divine intervention might, given certain probability assignments, provide evidence against theistic hypotheses. However, Sober carefully notes that such inferences depend critically on prior probability assumptions and the specific observational contexts involved.

The article's contribution lies in its rigorous probabilistic framework for evaluating evidential relationships. Rather than endorsing blanket principles, Sober advocates careful attention to the specific probabilistic dependencies between hypotheses and evidence. This methodological precision proves invaluable for assessing both scientific theories and philosophical arguments about unobservable entities, including divine beings.