Science and method / by Henri Poincaré ; translated by Francis Maitland ; with a preface by Bertrand Russell.

Date:
[1914?]
Catalogue details

Licence: In copyright

Credit: Science and method / by Henri Poincaré ; translated by Francis Maitland ; with a preface by Bertrand Russell. Source: Wellcome Collection.

Provider: This material has been provided by the Royal College of Physicians of Edinburgh. The original may be consulted at the Royal College of Physicians of Edinburgh.

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    inch in the cause produces a difference of a mile in the effect. If I am to win in case the effect corre- sponds with a mile bearing an even number, my probability of winning will be Why is this ? Because, in order that it should be so, the cause must correspond with an inch bearing an even number. Now, according to all appearance, the probability that the cause will vary between certain limits is proportional to the distance of those limits, provided that distance is very small. If this hypothesis be not admitted, there would no longer be any means of representing the probability by a continuous function. Now what will happen when great causes produce small effects? This is the case in which we shall not attribute the phenomenon to chance, and in which Lumen, on the contrary, would attribute it to chance. A difference of a mile in the cause corresponds to a difference of an inch in the effect. Will the probability that the cause will be comprised between two limits n miles apart still be proportional to «? We have no reason to suppose it, since this dis- tance of n miles is great. But the probability that the effect will be comprised between two limits n inches apart will be precisely the same, and ac- cordingly it will not be proportional to n, and that notwithstanding the fact that this distance of n inches is small. There is, then, no means of repre- senting the law of probability of the effects by a continuous curve. I do not mean to say that the curve may not remain continuous in the analytical sense of the word. To infinitely small variations of the abscissa there will correspond infinitely small variations of the ordinate. But practically it would