Several different approaches to the conceptual analysis of causation are guided by the idea that a cause is something that makes a difference to its effects. These approaches seek to elucidate the concept of causation by explicating the concept of a difference-maker in terms of better-understood concepts. There is no better example of such an approach than David Lewis’ analysis of causation, in which he seeks to explain the concept of a difference-maker in counterfactual terms. Lewis introduced his counterfactual theory (...) of causation with these words: 'We think of a cause as something that makes a difference, and the difference it makes must be a difference from what would have happened without it. Had it been absent, its effects—some of them, at least, and usually all—would have been absent as well.' (Lewis 1973b: pp. 160-1) According to Lewis, a cause c makes a difference to an effect e in the sense that if the cause c had not occurred, the effect e would not have occurred either. All we shall see in section 2, Lewis’ theory says there is more to the concept of causation than this counterfactual condition. Lewis is on the right track, I think, in saying that we think of a cause as something that makes a difference and that this thought is best explicated in terms of counterfactual concepts. However, I shall argue that the particular way in which Lewis spells out the concept of a cause as difference-maker is unsatisfactory. For Lewis’ articulation of this concept is distorted by a specific metaphysical assumption: specifically, that causation is an absolute relation, specifiable independently of any contextual factors. The distortion induced by this assumption is reflected in the undiscriminating manner in which his theory generates countless causes for any given effect. However, commonsense judgement is much more discriminating about causes than Lewis’ theory. Accordingly, I claim that Lewis' analysis faces the problem of profligate causes and I outline some specific problem cases in section 3.. (shrink)

Anyone who has pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of this question. Adrian Moore's historical study of the infinite covers all its aspects, from the mathematical to the mystical.

Anyone who has pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of this question. Adrian Moore's historical study of the infinite covers all its aspects, from the mathematical to the mystical.

This essential guide to paradoxes 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, Hempel's Raven, and the Prisoners' Dilemma, taking in subjects as diverse as knowledge, ethics, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at likely solutions.

It’s well known that one way to cure a hangover is by a “hair of the dog” — another alcoholic drink. The drawback of this method is that, so it would appear, it cannot be used to completely cure a hangover, since the cure simply induces a further hangover at a later time, which must in turn either be cured or suffered through.

In my (2004), I argued that it is possible to drink any finite amount of alcohol without ever suffering a hangover by completing a certain kind of supertask. Assume that a drink causes drunkenness to ensue immediately and to last for a period proportional to the quantity of alcohol consumed; that a hangover begins immediately at the time the drunkenness ends and lasts for the same length of time as the drunkenness; and that at any time during which you are (...) drunk you do not suffer any hangover you might have at that time. Starting at a time at which you are not drunk and not hung over, drink a half pint of beer. Wait until you are just about to get a hangover (30 minutes, say), and then drink a quarter pint. Wait until you are just about to get a hangover again, and then drink an eighth, and so on.... After an hour you have drunk a pint, and you do not have a hangover. Every hangover you incurred happened within the hour you spent drinking; but you were drunk that whole time, so you didn’t suffer the hangovers. It seems that the old drunkard’s method of a “hair of the dog” can be effective in completely avoiding a hangover. (shrink)