Page:Popular Science Monthly Volume 71.djvu/59

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53
THE VALUE OF SCIENCE
THE VALUE OF SCIENCE

Science and Reality

By M. H. POINCARÉ
MEMBER OF THE INSTITUTE OF FRANCE

5. Contingence and Determinism

I DO not intend to treat here the question of the contingence of the laws of nature, which is evidently insoluble, and on which so much has already been written. I only wish to call attention to what different meanings have been given to this word, contingence, and how advantageous it would be to distinguish them.

If we look at any particular law, we may be certain in advance that it can only be approximative. It is, in fact, deduced from experimental verifications, and these verifications were and could be only approximate. We should always expect that more precise measurements will oblige us to add new terms to our formulas; this is what has happened, for instance, in the case of Marriotte's law.

Moreover the statement of any law is necessarily incomplete. This enunciation should comprise the enumeration of all the antecedents in virtue of which a given consequent can happen. I should first describe all the conditions of the experiment to be made and the law would then be stated: If all the conditions are fulfilled, the phenomenon will happen.

But we shall be sure of not having forgotten any of these conditions only when we shall have described the state of the entire universe at the instant t; all the parts of this universe may, in fact, exercise an influence more or less great on the phenomenon which must happen at the instant t + dt.

Now it is clear that such a description could not be found in the enunciation of the law; besides, if it were made, the law would become incapable of application; if one required so many conditions, there would be very little chance of their ever being all realized at any moment.

Then as one can never be certain of not having forgotten some essential condition, it can not be said: If such and such conditions are realized, such a phenomenon will occur; it can only be said: If such and such conditions are realized, it is probable that such a phenomenon will occur, very nearly.