Page:The Foundations of Science (1913).djvu/244

226 very far away from the first, happens the phenomenon $$\beta$$, which causes as consequence the effect $$\beta'$$. The phenomena $$\alpha$$ and $$\beta$$ are simultaneous, as are also the effects $$\alpha'$$ and $$\beta'$$.

Later, the phenomenon $$\alpha$$ is reproduced under approximately the same conditions as before, and simultaneously the phenomenon $$\beta$$ is also reproduced at a very distant place in the world and almost under the same circumstances. The effects $$\alpha'$$ and $$\beta'$$ also take place. Let us suppose that the effect $$\alpha'$$ happens perceptibly before the effect $$\beta'$$.

If experience made us witness such a sight, our postulate would be contradicted. For experience would tell us that the first duration $$\alpha\alpha'$$ is equal to the first duration $$\beta\beta'$$ and that the second duration $$\alpha\alpha'$$ is less than the second duration $$\beta\beta'$$. On the other hand, our postulate would require that the two durations $$\alpha\alpha'$$ should be equal to each other, as likewise the two durations $$\beta\beta'$$. The equality and the inequality deduced from experience would be incompatible with the two equalities deduced from the postulate.

Now can we affirm that the hypotheses I have just made are absurd? They are in no wise contrary to the principle of contradiction. Doubtless they could not happen without the principle of sufficient reason seeming violated. But to justify a definition so fundamental I should prefer some other guarantee.

But that is not all. In physical reality one cause does not produce a given effect, but a multitude of distinct causes contribute to produce it, without our having any means of discriminating the part of each of them.

Physicists seek to make this distinction; but they make it only approximately, and, however they progress, they never will make it except approximately. It is approximately true that the motion of the pendulum is due solely to the earth’s attraction; but in all rigor every attraction, even of Sirius, acts on the pendulum.

Under these conditions, it is clear that the causes which have produced a certain effect will never be reproduced except approximately. Then we should modify our postulate and our