Michael Clark

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.

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.

The question “What is humour?” has exercised in varying degrees such philosophers as Aristotle, Hobbes, Hume, Kant, Schopenhauer and Bergson and has traditionally been regarded as a philosophical question. And surely it must still be regarded as a philosophical question at least in so far as it is treated as a conceptual one. Traditionally the question has been regarded as a search for the essence of humour, whereas nowadays it has become almost a reflex response among some philosophers to dismiss the search for essences as misconceived. Humour, it will be said, is a family-resemblance concept: no one could hope to compile any short list of essential properties abstracted from all the many varieties of humour— human misfortune and clumsiness, obscenity, grotesqueness, veiled insult, nonsense, wordplay and puns, human misdemeanours and so on, as manifested in forms as varied as parody, satire, drama, clowning, music, farce and cartoons. Yet even if the search for the essence of humour seems at first sight unlikely to succeed, I do not see how we can be sure in advance of any conceptual investigation; and in any case we might do well to start with the old established theories purporting to give the essence of humour, for even if they are wrong they may be illuminatingly wrong and may help us to compile a list of typical characteristics

_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.

Traditionally Kant's theory of punishment has been seen as wholly retributive. Recent Kantian scholarship has interpreted the theory as more moderately retributive: punishment is deterrent in aim, and retributive only in so far as the amount and type of penalty is to be determined by retributive considerations (the ius talionis). But it is arguable that a more coherent Kantian theory of punishment can be developed which makes no appeal to retribution at all: hypothetical contractors would have no good reason to endorse punishment distributed retributively. This position is first sketched behind Rawls's neo‐Kantian ‘veil of ignorance’, and it is suggested that the same theory will emerge from Scanlon's more relaxed neo‐Kantian position.