Paradox (review)

What is a paradox? In her illuminating and exactly argued treatise on paradox, Olin distinguishes between two types. In type I: apparently, a sound argument leads to a false conclusion; in type II: apparently, two sound arguments lead to conclusions that are mutually inconsistent. Thus, Achilles and the tortoise is type I; Monty Hall and Ship of Theseus are type II. Resolution of some paradoxes of either type is uncontroversial; Ship of Theseus is an example where the resolution is controversial. What is needed for an adequate resolution? Olin rightly insists that a resolution should show why a premise in the paradox is not true or why an argument in it is not valid or why a conclusion of it is not false, and, equally important, it should explain why appearances are otherwise.

Her analysis assumes that a statement cannot be both true and false. However, paraconsistent logic suggests that paradoxes may be resolved precisely by rejecting this assumption. Olin defends the law of non-contradiction in a separate chapter by arguing that paraconsistent logic cannot make fully intelligible the difference between accepting and rejecting a statement, that some classically valid inferences fail to be truth-preserving in this logic, and that meaningful statements in this logic fail to exclude any possibility. In the next six chapters Olin examines in detail the resolutions proposed in the literature for each of six deep paradoxes: the prediction (or 'surprise examination'), the preface, the lottery, Newcomb's problem, the prisoner's dilemma, and the sorites. Her probing discussion demonstrates that they are deep, because their resolution, if possible at all, must engage central unresolved issues in epistemology, metaphysics, and semantics.

This book would make an excellent text for an advanced undergraduate seminar in epistemology. Though it presupposes familiarity with truth-functional connectives, the book would also be appropriate for bright beginning students, because Olin's presentation of the paradoxes and their possible resolutions is accessible, despite the sophistication of the reasoning, for someone who has no acquaintance with the literature. Opposing positions are set out accurately and simply, and their merits fairly assessed based on the internal logic of the puzzle. It is, in my view, a model of how to think and teach philosophically. Olin takes particular pains to enable the reader to appreciate the scope of the issues that lie at the heart of paradoxes. We see how, for example, the lottery paradox challenges our understanding of justifying evidence, even to the point of calling into question a weak principle of deductive closure: If S is justified on the evidence in believing each of a set of statements, these statements jointly entail Q, and S recognizes this entailment, then S is justified on the evidence in believing Q. Those unacquainted with the paradoxes will be enthralled; those already acquainted, even if they have published on them, may find much that is new and gripping.

Is there room to quarrel? Of course. The fallibility argument, a version of the preface paradox, points out that I am justified in believing, on the basis of finding errors in past justified beliefs, that some of my justified beliefs are false. Since this meta-belief is one of my justified beliefs, the total set of my beliefs is inconsistent. (One of them has to be false.) Thus, paradoxically, there is rational basis for having inconsistent beliefs. Olin takes issue with this 'radical' view. Her problem is that the induction from past error is illegitimate. Suppose I arrive at my beliefs by reading tea-leaves. That method has led to error, yet the inference that new beliefs so formed are likely to be in error is, on her view, a mistake. Why? Because the set of beliefs that are the negations of the former beliefs would not be less likely to be in error. True enough, but that is because the connection between tea-leaf reading and truth is random. Given that, the likelihood of error is great in either set, but this fact in no way undermines the original inference.

But the places where I...