'It would seem under these conditions that I ought to abstain from all publication until I had solved the problem, but after the fruitless efforts I have made for months, it appeared to me wisest to let the problem ripen while I let it alone for some years. That would have been very well if I had been sure of taking it up again some day, but at my age I could not be sure of that. Besides, the importance of the subject is too great, and the results already obtained are on the whole too considerable for me to be content to leave them altogether useless. I hope that the geometricians who will interest themselves in this problem and who will doubtless be more fortunate than I will be able to get something out of it and make use of it in finding the path they should pursue.'
"What words can be added to this scientific testament, so simple and so noble, of a life altogether consecrated, without faltering even to the last hour, to the search for truth? For the first time in half a century this unparalleled brain has found repose."
Poincaré, as we have seen, was awake to the wider aspects of science. He was interested in its effects upon human life and conduct, although he himself was engaged in one of its most remote and abstract branches. Shortly before his death he discussed a question which nowadays arouses intense interest, the question of what effect the advance and popularization of science will have on ethics. Will science in destroying superstitions, in changing utterly the traditional way of regarding the universe and man, undermine the morality which forms the foundation of our civilization? This question Poincaré answers in the negative. He believes that our moral instincts lie too deep to be affected by such a revolution in thought, but on the other hand he does not think, as some do, that science will ever be able of itself to provide the moral imperative. A few paragraphs from this essay, published posthumously in "Last Thoughts", may well serve as a conclusion to this sketch of his philosophy:
There can be no scientific morality; but no more can there be immoral science. And the reason is simple; it is a reason—how shall I say it?—purely grammatical.
If the premises of a syllogism are both in the indicative, the conclusion likewise will be in the indicative. For the conclusion to be put in the imperative, it would be necessary that at least one of the premises should itself be in the imperative. Now, the principles of science, the postulates of geometry, are and can be only in the indicative; still in this same mood are the experimental verities, and at the foundation of the sciences there is, there can be, nothing else. Hence, the most subtle dialectician may juggle with these principles as he will, combine them, frame them up one upon another; all he will get from them will be in the indicative. He will never obtain a proposition which shall say: do this, or don't do that; that is to say, a proposition which confirms or contradicts morality....
Some therefore think that science will be destructive; they fear the ruin it will make and dread lest, where it shall have passed, society can no longer survive.
Is there not in these fears a sort of internal contradiction? If it is scientifically proved that such or such a custom, regarded as indispensable to the very existence of human society, had not in reality the importance attributed to it and deceived us only by its venerable antiquity, if that be proved, admitting this proof to be possible, will the moral life of humanity be shaken? One of two things, either this custom is useful, and then a reasonable science cannot prove that it is not; or else it is useless and we should not regret it. From the moment that we place at the foundation of our syllogisms one of those generous emotions which engender morality, it is still this emotion, and consequently it is still morality which we must find at the end of our whole chain of reasonings, if this has been conducted in accordance with the rules of logic. What is in danger of perishing is the non-essential, that which was merely an accident in our moral life; the sole important thing cannot fail to be found in the conclusions since it is in the premises....
Science, right or wrong, is deterministic; everywhere it penetrates it introduces determinism. So long as it is only a question of physics or even of biology, this is unimportant. The domain of conscience remains inviolate. What will happen when morality in turn shall become the object of science?
Is all despair, or if some day morality should accommodate itself to determinism, could it so adapt itself without dying from the effects? So profound a metaphysical revolution would doubtless have much less influence upon morals than we think. It is of course understood that penal repression is not in question. What is called crime or punishment, would be called sickness or prophylaxis, but society would retain intact its right, which is not to punish, but simply the right of self-defense. What is more serious is that the idea of merit or demerit would have to disappear or be transformed. But we should continue to love the good man, as we love all that is beautiful; we should no longer have the right to hate the vicious man, who would then inspire only disgust; but is hate necessary? Enough that we do not cease to hate vice.
Apart from that, all would go on as in the past. Instinct is stronger than all metaphysics, and even though one should have laid it bare, even if one should understand the secret of its force, its power would not thereby be weakened. Is gravitation less irresistible since Newton? The moral forces which guide us would continue to guide us.[9]
HOW TO READ POINCARÉ
A complete analytical bibliography of Poincaré's writings up to 1909 will be found in Ernest Lebon's "Henri Poincaré" (Paris: Gaultier-Villars), which contains the biographical address of M. Frédéric Masson on his admission to the French Academy and other eulogies. The list comprises 436 articles and books classified as follows: Mathematical analysis, 146; analytical and celestial mechanics, 85; mathematic physics, 78; scientific philosophy, 51; necrology, 17; miscellaneous, 59; an astonishing output for thirty years' work, considering the amount and difficulty of the labor involved in some of the contributions.
The mathematical works of Poincaré are too difficult for the layman and indeed for many professional mathematicians. But there are five volumes of general interest published by Flammarion, Paris: "La Science et l'Hypothèse", "La Valeur de la Science", "Science et Méthode", "Savants et Ecrivains", and "Dernières Pensées." The first of these has had a wide popularity, having been translated into English, German, Spanish, Hungarian, and Japanese. The English translation of "Science and Hypothesis", by Professor George Bruce Halsted (New York: Science Press), which appeared in 1905, is introduced by an interesting criticism of Poincaré's philosophy by Professor Josiah Royce, of Harvard. Two years later "The Value of Science" was published in this country (Science Press). "Science et Méthode", though it contains some matter of more general interest than the others, particularly his account of the rôle played by unconscious mind in mathematical invention and his explanation of the newer conceptions of physics, has not yet appeared in English. The fourth volume, "Savants et Ecrivains", is an evidence of Poincaré's good will rather than his literary talents, as it consists of perfunctory addresses on deceased Academicians, the most extensive being that on Sully-Prudhomme, whose chair he holds. The fifth, published after his death, contains the essay on "Science and Morality" from which I have quoted, as well as interesting discussions of recent science and philosophy. The volume entitled "Foundations of Science" (published by the Science Press, New York) contains "Science and Hypothesis", "Value of Science", and "Science and Method" with the introduction by Professor Royce.
From either of the two volumes, "Science and Hypothesis" or "The Value of Science", one can get an idea of Poincaré's philosophy, which is of importance because it is not merely the philosophy of an individual but the point of view of most men of science nowadays, though rarely so definitely recognized or clearly expressed. Both books consist of a somewhat heterogeneous collection of studies on the method and logic of the mathematical and physical sciences, containing much that the general reader will have to skip because of its use of unfamiliar terms, but it will not be safe for him to skip any whole pages without looking them over carefully, for he is likely to find brilliant and suggestive sentences embedded in the most unpromising material.
Separate articles by Poincaré, forming chapters from the above-mentioned volumes, are accessible in American periodicals. "The Future of Mathematics" in Monist, Vol. XX, pp. 76-92; also in the 1909 Smithsonian Report, which is in every public library. "The Choice of Facts" in Monist, Vol. XIX, pp. 231-239. "The Principles of Mathematical Physics" in the report of the St. Louis Congress of Arts and Sciences, Vol. I, pp. 604-624, and in Monist, Vol. XV, pp. 1-24. "The Bolyai Prize" (Report on the Work of Hilbert) in Science, May 19 and 26, 1911. "Mathematical Creations" in Monist, Vol. XX, pp. 321-335. "The Value of Science" was first published complete in the Popular Science Monthly, September, 1906, and later; "Relativity of Space", "The New Logics", and "Chance" in the Monist, 1913.