Michael Clark

_Paradoxes from A to Z, Third edition_ is the essential guide to paradoxes, and takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo, and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus’ Ship, and the Prisoner’s Dilemma, taking in subjects as diverse as knowledge, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at likely solutions. This third edition is revised throughout, and adds nine new paradoxes that have important bearings in areas such as law, logic, ethics and probability. Paradoxes from A to Z, Third edition is an ideal starting point for those interested not just in philosophical puzzles and conundrums, but anyone seeking to hone their thinking skills.

Attempts to solve the Trolley Problem by means of a single principle have proved unpersuasive. Nor can the intuition about Transplant be adequately grounded in the hypothetical dissent of rational contractors. It is explained by the initial liability principle, that loss should lie where it falls unless there is sufficient reason to shift it. If we did not think we should accept misfortune in such cases and thought that minimising loss of life was sufficient reason to shift the loss we should not be according others the minimum respect and treatment we feel is their due. The intuition about Trolley is explained by the affinity of that case to the pure case where the choice is between saving many and saving fewer, where minimising misfortune is the only credible option. But these considerations are not yet enough to accommodate the cases that lie between the extremes of Trolley and Transplant. We can handle the intermediate cases by attempting to assimilate them to one or other paradigm and to one another with a sensitivity to morally relevant and irrelevant differences that seeks initially to be faithful to the values reflected by our moral intuitions. Those intuitive judgements are unlikely to survive such an examination wholly unmodified.

Do we have the right to defend ourselves against innocent aggressors? If I amattacked in a lift by a knife‐wielding lunatic, may I kill or maim him to protect my own life? On one view the insane man’s plight is his bad luck and I am under no obligation to let it be transferred to me. On the opposing view it is my bad luck to be under attack and I have no right to transfer it to an innocent man by killing him to protect myself. It is perhaps becauseneither of these opposing viewpoints is obviously preferable to the other that there is no consensus about the question. Nevertheless we can find considerations for favouring the first view over the second.

In the final chapter of his recent book, <it>The Construction of Social Reality</it> (1995), John Searle denies that the minimalist theory, as elaborated for example by Paul Horwich 1990, gives the entire content of the truth predicate, and vigorously defends the correspondence theory against it. He stigmatises minimalism as "wildly counterintuitive' and believes it is unsustainable. Although he agrees that, when a statement S means that P, S corresponds to the facts iff P, and that once we have established that P we have thereby established that S corresponds to the fact that P, he maintains that the truth predicate is not redundant, even with the qualifications incorported in the minimalist account. We shall see that his argument fails.

Nicholas Rescher claims that rational decision theory “may leave us in the lurch”, because there are two apparently acceptable ways of applying “the standard machinery of expected-value analysis” to his Dr. Psycho paradox which recommend contradictory actions. He detects a similar contradiction in Newcomb’s problem. We consider his claims from the point of view of both Bayesian decision theory and causal decision theory. In Dr. Psycho and in Newcomb’s Problem, Rescher has used premisses about probabilities which he assumes to be independent. From the former point of view, we show that the probability premisses are not independent but inconsistent, and their inconsistency is provable within probability theory alone. From the latter point of view, we show that their consistency can be saved, but then the contradictory recommendations evaporate. Consequently, whether one subscribes to evidential or causal decision theory, rational decision theory is not in any way vitiated by Rescher’s arguments.

Previous claims to have resolved the two-envelope paradox have been premature. The paradoxical argument has been exposed as manifestly fallacious if there is an upper limit to the amount of money that may be put in an envelope; but the paradoxical cases which can be described if this limitation is removed do not involve mathematical error, nor can they be explained away in terms of the strangeness of infinity. Only by taking account of the partial sums of the infinite series of expected gains can the paradox be resolved.