ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 609 



itself, probability can have no meaning. Yet if a man bad to choose 

 between drawing a card from a pack containing twenty-five red cards 

 and a black one, or from a pack containing twenty-five black cards 

 and a red one, and if the drawing of a red card were destined to 

 transport him to eternal felicity, and that of a black one to consign 

 him to everlasting woe, it would be folly to deny that he ought to pre- 

 fer the pack containing the larger proportion of red cards, although, 

 from the nature of the risk, it could not be repeated. It is not easy 

 to reconcile this with our analysis of the conception of chance. But 

 suppose he should choose the red pack, and should draw the wrong 

 card, what consolation would he have? He might say that he had 

 acted in accordance with reason, but that would only show that his 

 reason was absolutely worthless. And if he should choose the right 

 card, how could he regard it as anything but a happy accident ? He 

 could not say that if he had drawn from the other pack, he might 

 have drawn the wrong one, because an hypothetical proposition such 

 as, " if A, then B," means nothing With reference to a single case. 

 Truth consists in the existence of a real fact corresponding to the true 

 proposition. Corresponding to the proposition, " if A, then B," there 

 may be the fact that whenever such an event as A happens such an 

 event as B happens. But in the case supposed, which has no parallel 

 as far as this man is concerned, there would be no real fact whose 

 existence could give any truth to the statement that, if he had drawn 

 from the other pack, he might have drawn a black card. Indeed, 

 since the validity of an inference consists in the truth of the hypotheti- 

 cal proposition that if the premises be true the conclusion will also 

 be true, and since the only real fact which can correspond to such a 

 proposition is that whenever the antecedent is true the consequent is 

 so also, it follows that there can be no sense in reasoning in an isolated 

 case, at all. 



These considerations appear, at first sight, to dispose of the diffi- 

 culty mentioned. Yet the case of the other side is not yet exhaust- 

 ed. Although probability will probably manifest its effect in, say, a 

 thousand risks, by a certain proportion between the numbers of suc- 

 cesses and failures, yet this, as we have seen, is only to say that it 

 certainly will, at length, do so. Now the number of risks, the num- 

 ber of probable inferences, which a man draws in his whole life, is a 

 finite one, and he cannot be absolutely certain that the mean result 

 will accord with the probabilities at all. Taking all his risks collec- 

 tively, then, it cannot be certain that they will not fail, and his case 

 does not differ, except in degree, from the one last supposed. It is an 

 indubitable result of the theory of probabilities that every gambler, 

 if he continues long enough, must ultimately be ruined. Suppose he 

 tries the martingale, which some believe infallible, and which is, as I 

 am informed, disallowed in the gambling-houses. In this method of 

 playing, he first bets say $1 ; if he loses it he bets $2 ; if he loses that 



VOL. XII. S9 



