[French] Poincaré: “The Last Reflections,” translated by Li Xingmin, proofread by Fan Dainian, Commercial Press, December 1996
Poincaré was such a great, even legendary, figure! Poincaré is widely regarded as the “last all-around mathematical genius,” comparable to Gauss; in fact, it would not be at all excessive to remove even the word “mathematical.” “Poincaré’s achievements in the four main branches of mathematics—arithmetic, algebra, geometry, and analysis—were all pioneering; in particular, he made outstanding contributions to branches such as function theory, algebraic geometry, number theory, the mathematics of strings, differential equations, and algebraic topology.” (p. ii) “In astronomy, Poincaré’s main work fell into three areas: the equilibrium shapes of rotating fluids; the stability of the solar system, that is, the many-body problem; and the origin of the solar system. Poincaré’s methods for solving these problems were so advanced at the time that even more than forty years later, very few people were able to master this sharp weapon of his.” (p. iii) Poincaré was even “a first-rate expert in all branches of theoretical physics,” “made direct contributions to the physical revolution,” and “was a pioneer of relativity” (p. iii). Even in the last half-year of his life, he was still “making new contributions to the dissemination and development of quantum theory” (p. iv). He also conducted specialized studies in the philosophy of science and methodology of science, and “touched on fields such as chemistry, biology, geology, physiology, psychology, and so on” (p. vi) … After Poincaré, science became increasingly specialized, its various branches becoming more and more independent and more and more in-depth, so much so that it has already become extremely difficult to span even a few branches within a single discipline, let alone to become a polymath in both science and philosophy; and the initial pioneers of these new branches of mathematics and physics were precisely Poincaré. Poincaré’s place in modern science can be compared with Kant’s place in modern philosophy—carrying forward the past and opening up the future. And what is worth noting is that the thought of these two giants has a direct connection and similarity: Poincaré’s “conventionalism” clearly retains traces of Kantian transcendental philosophy, though of course it was also greatly influenced by Mach. Like Kant, Poincaré’s “conventionalism” was not meant to destroy the reliability of science, but rather precisely to support science; they likewise held that science was not the only thing. Unlike Kant’s universalism, Poincaré’s view of ethics seems to lean toward pluralism. Although Poincaré did not discuss moral questions very much, and did so in a very unsystematic way, his views are nonetheless quite referential and illuminating for our reflection on the relation between science and ethics.
Translated from the French by John W.. Bolder Dover Publications, Inc. New
York. 1963
Preface to the Chinese translation
p. iv
In philosophy of science, Poincaré inherited the tradition of Mach and Hertz, drew on some of Kant’s ideas, and, through summarizing his own scientific research practice and pondering deeply on the scientific achievements of his time, put forward many highly illuminating new ideas. Poincaré was the founder of conventionalism, and he himself was a moderate conventionalist. ………… Conventionalism requires, on the one hand, freeing ourselves from narrow empiricism and, on the other hand, freeing ourselves from apriorism; it reflects the scientific world’s demand for free creation and bold hypotheses, and has positive significance both in science and in philosophy. Poincaré’s conventionalism and Mach’s empiricism are the philosophical foundation for the rise of logical empiricism, and therefore Poincaré is naturally regarded as one of the forefathers of logical empiricism. Poincaré was also an ardent rationalist and idealist .////——From my initial impression, Poincaré’s absorption of Kant’s thought is very obvious. In addition, as the translator says, Poincaré himself was a “moderate” conventionalist, and he differs in many ways from later conventionalists, and even more so from logical empiricists. It feels as though Poincaré’s conventionalism is still very similar to Kant’s transcendental theory.
Chapter One: The Evolution of Laws
P1 p. 3
Do natural laws change easily? If the world is in continuous evolution, is the law governing that evolution itself uniquely exempt from all change? Such a concept has never been accepted by scientists, at least not in the sense in which they may understand its meaning; unless the rationality and the real possibility of science are denied, scientists will not accept it. But philosophers retain the right to ask this question, so as to consider the various answers to which it gives rise, examine the consequences of these answers, and try to coordinate them with the reasonable requirements of scientists. I am glad to consider several aspects that the question can present. Therefore, I shall not reach so-called conclusions, but rather various ideas, which perhaps will not be uninteresting. In the process, if I casually dwell in detail on certain related questions, I hope the reader will forgive me .////——Science is devoted to discovering (or inventing) natural laws; natural laws can explain why natural phenomena are as they are, yet why natural laws themselves are as they are is a question science finds hard to answer. When great scientists such as Poincaré and Einstein touch upon this sort of question (for example, when Einstein asks, “When creating the world, did God make a choice?”), they are already asking as philosophers. Of course, the question discussed in this chapter by Poincaré—whether laws can evolve over time—may still be a scientific question, for example if one seeks ancient traces through geology, astronomy, and so on; but if one pursues the question of natural laws themselves further, it inevitably becomes a philosophical question. Another important reason I excerpted this passage is this: here Poincaré expresses some basic views about the relation between philosophy and science. Philosophers retain the right to inquire into metaphysical questions, to think through the various possible answers, and to ponder the “consequences” of those answers—that is, “if this is so, it means …” But philosophy arrives at “ideas,” not at “conclusions.” These philosophical reflections arise from questions posed by science, but philosophy should strive to coordinate with science rather than offer conclusions that oppose or direct science. This can be called the basic attitude of philosophy of science: it is neither servile nor overbearing, but just right; while the attitude that philosophy has nothing to do with science, or the attitude that philosophy can guide science, are both extreme. (By the way, the last sentence in this passage doesn’t seem very smooth …)
Chapter Two: Space and Time
P21~22 pp. 26~27
Thus, we have grasped the meaning of the principle of physical relativity: it is no longer a simple convention. It is verifiable, and therefore it may not be confirmed. It is an experimental truth, and what is the meaning of such truth? It can be easily inferred from the foregoing considerations. It means that when the distance between two bodies increases indefinitely, their mutual gravitational attraction tends to zero. It means that the behavior of two distant worlds is as though they were unrelated to each other; we can better understand why the principle of physical relativity is not as widely applicable as the principle of psychological relativity. Owing to the true nature of our intellect, it is no longer necessary; it is an experimental truth, and experiment imposes limits on this truth.
This principle of physical relativity can be used to define space; one might say that it provides us with new measuring tools. Let me make this clear for myself: how can a solid body enable us to measure space, or more precisely, how can it enable us to construct space? By moving a solid body from one position to another, we acknowledge that it may first be made to fit one figure, and then made to fit another, and we agree that these two figures may be regarded as equal. It is by virtue of this convention that geometry arises. Thus, without changing the shape and size of figures, the transformations of space itself correspond to every possible movement of a solid body. Geometry is nothing but knowledge of the relationships among these transformations. Or, in mathematical language, it is the study of the structure of the group formed by these transformations—that is, the structure of the group of solid-body motions.
P23 p. 28
A concluding remark: as we have already said, for reasons identical to those concerning the properties of natural solids, the principle of physical relativity is an empirical fact; for example, it is subject to continual correction; geometry, however, must free itself from such correction. Precisely for this reason, it must once again become a convention, and the principle of relativity must be regarded as a convention. We have already mentioned what its experimental meaning is: it means that two extremely distant systems, when their distance increases indefinitely, have mutual attraction that tends toward zero. Experience tells us that this is approximately true; experience cannot tell us that it is completely true, because the distance between two systems is always finite. But nothing prevents us from assuming that it is completely true; ………… Only by taking the principle under consideration itself as a convention can it be shielded from the impact of experience. Convention is suggested to us by experience, but we are free to adopt it.
Then what is the revolution brought about by the recent advances in physics? The principle of relativity, in its earlier aspect, has been abandoned; it has been replaced by Lorentz’s principle of relativity. …………
P24 p. 29
Another remark: previously I tried to define the relation between two events occurring in two different environments, and I said that if one time can be regarded as the cause of another time, then it can be regarded as occurring before the other event. This definition has become inappropriate. In this new mechanics, there is no action transmitted instantaneously; … it can happen that event A is neither the result of event B nor the cause of event B. …………
In light of these new ideas, what will our own view be? Must we revise our conclusions? Of course not. We have already adopted a convention because it seemed convenient, and we have said that there is no reason whatsoever compelling us to abandon it. Today, some physicists want to adopt a new convention. It is not that they are forced to do so; rather, they think this new convention is more convenient; that is all. Those who have not accepted this view can reasonably retain their old view, so as not to disturb their old habits. I believe this is what they, right here among us, will be doing for a long time to come.
////——Poincaré’s conventionalism is certainly a step beyond Kant’s apriorism. The key lies in the fact that Poincaré saw special relativity as giving entirely new interpretations to the two major a priori categories of Kant, “space” and “time.” In any case, Kant’s transcendental theory and his table of the twelve categories always need some improvement. However, has Poincaré’s conventionalism already gone beyond Kant’s transcendental theory? It seems not entirely. Poincaré’s conventionalism still seems to retain prominent traces of Kantian transcendental theory. Of course, many later conventionalists did in fact go beyond apriorism; however, whether they went too far is another question worth discussing.
Chapter Three: Why Space Has Three Dimensions
P43~44 p. 51
Truths like the axioms of order are revealed to us through intuition; but is this a matter of intuition of space itself, or of intuition of the mathematical continuum or the physical continuum in general? If we favor the first solution, we can easily reason about space, but it is much harder to reason about more complex continua, to reason about continua of more than three dimensions that cannot be described in space.
Moreover, if the first solution were adopted, the whole discussion here would become pointless; the reason we straightforwardly attribute three-dimensionality to space is that the three-dimensional continuum is the only continuum of which we can have a clear intuition.
But there is also topology beyond three dimensions. I have not said that it is an easy science; I paid enormous effort for it, without foreseeing that I would encounter so many difficulties in it. But in any case, this science is possible; it does not remain entirely on the level of analysis. If one does not continue to appeal to intuition, one cannot succeed in pursuing it. Therefore, there really is intuition of continua of more than three dimensions; compared with ordinary geometric intuition, if it demands more sustained attention, that is undoubtedly a matter of habit, and undoubtedly also the result of the sharp increase in complexity of continua as dimensions increase. Have we not seen in our middle schools students who are very good at plane geometry yet “unable to imagine space”? That is not because they lack intuition of three-dimensional space, but because they are not accustomed to using it; they need to make an effort in order to do so. And in order to imagine spatial figures, do we not successively imagine the various possible perspectives of such a figure?
I shall conclude that all of us have an intuitive concept of continua of arbitrary dimension, because we possess the ability to construct the physical continuum and the mathematical continuum; and the reason this ability exists in us prior to any experience is that without it, experience, strictly speaking, would be impossible, and would degenerate into irrational sensation unfit for any organism; because this intuition is nothing but our awareness of this instinct. However, this instinct can be employed in different ways; it can enable us to construct four-dimensional space just as we construct three-dimensional space. It is precisely the external world, precisely experience, that guides us to use it in one sense rather than another.
////——From this passage one can glimpse a feature of Poincaré’s “moderate conventionalism.” In contrast to Kant, who takes space as an intuition and says mathematics is based on construction through space and time, Poincaré treats space as a construction atop the intuition of the three-dimensional continuum. But after inverting Kant’s transcendental theory, does Poincaré still retain elements of transcendental theory? This notion that “all of us have an intuitive concept,” that we possess, “prior to any experience,” a capacity for construction, because only this capacity guarantees the possibility of experience—this “capacity” sounds almost like another way of expressing “transcendental theory.” The similarities and differences, the relation, and even the relative merits of transcendental theory and conventionalism all deserve further discussion; for now I cannot say much.
Chapter Six: Quantum Theory
P76 p. 88
Now someone asks whether it is necessary to introduce discontinuity into the laws of nature, not as an apparent law but as an essential one; we must first explain that such an extraordinary view can be established .////——It should be noted that Poincaré died in 1912. When he made these final reflections, quantum mechanics was only just beginning to emerge, and Poincaré’s profound insight is truly astonishing. Had Poincaré lived another twenty or thirty years (he lived only to 58), I believe the history of the development of quantum mechanics, written by a string of great names such as Bohr, Einstein, Heisenberg, Schrödinger, and Dirac, would have presented a completely different picture. Of course, history cannot be hypothetical…
Chapter Eight: Ethics and Science
P103 p. 118
What do we think about the fact that some people are full of hope for science while others harbor fear toward it? I answer without hesitation: both are unfounded. There can be no scientific morality; nor can there be immoral science. The reason is simple: this can be proved purely grammatically.
If both premises in a syllogism are declarative sentences, then the conclusion will also be a declarative sentence. In order for the conclusion to be expressed in the imperative mood, at least one premise itself must be an imperative sentence. … no proposition concerning an affirmed morality or a morality violated is ever obtained .////——I reserve judgment on this mode of reasoning, but I fully agree with Poincaré’s main point—that science cannot produce or derive ethics; that is to say, science alone is not enough. Of course, to say that science does not contain morality is not to say that science will not bring good or bad effects to morality.
P103 p. 118
Here lies a difficulty long encountered by moralists. They strive to prove moral precepts; we must forgive them, because that is their profession. They hope to place ethics on the basis of something, as though it could be based on something other than itself. Science shows us that, by living in such a way, a person can only diminish his own value. What if I do not care about diminishing myself, and if you take what is degenerate to be progress? Metaphysicians force us to follow the general principle of man, a principle said to have been discovered. To this one may reply: I would rather obey my own particular principle. I do not know what reply metaphysicians will make, but I can assure you that they will not have the final answer .////——At first glance, I cannot agree with this passage, because I too am trying to find a foundation for ethics in metaphysics or religious faith. But on closer thought, Poincaré’s view is still one I accept. What Poincaré opposes is dogmatic, universalist, or absolutist moral doctrine, whereas each person may have a moral principle of his own; so long as his ethics are internally coherent, there is nothing to object to. From a pluralist standpoint, each person may have different principles and aims, and as Poincaré says later, one beneficial task science can perform is to show that various different worthwhile pursuits are compatible and consistent; moreover, science can also help people reflect on their own principles and pursuits.
P104 pp. 119~120
Thus, all dogmatic ethics, all demonstrative ethics, are doomed to failure in advance; it is just like a machine with a transmission but no engine. The moral engine that can set all the rods and gears in motion can only be something felt. One cannot prove that we must sympathize with the unfortunate; but let us face suffering that should not be endured—ah, what a scene that is! Too often we shall find ourselves inflamed by the feeling of revolt; in us there will arise a force beyond the control of reason, a force that seems to violate our will and drives us on with irresistible power.
Even if it has already been proved that God is all-powerful, God can crush us; even if it can be proved that God is benevolent and that we ought to be grateful to God, that still does not prove that we must obey God. Some people regard as something detestable what is the most precious of all rights, namely freedom. But if we love God, all proofs become unnecessary; obedience may then be perfectly natural. That is why religion is powerful, while metaphysical systems are not.
When we ask for rational arguments to prove that we have good reason to love our country, we may be at a loss. But let us imagine that our army has been defeated, that France has been invaded; we are burning with rage, our eyes are filled with tears, and we will listen to nothing anymore.…………
Therefore, science cannot by itself create morality; nor can it directly and of itself weaken or abolish traditional morality. But can it exert an indirect influence?…… Science can give rise to new feelings, which is not to say that such feelings are provable; but since all forms of human activity react back upon human beings themselves, giving their souls a fuller shape. Every occupation has its professional psychology. The feelings of a peasant differ from those of a financier; likewise, the scientist has his own special psychology—I mean the psychology of his feelings—and there is something in this affective psychology that can move even those who come into contact with science only occasionally.
On the other hand, science can stir the feelings that naturally exist in human beings.…… Feeling supplies us only with the general impulse to action; it gives us the major premise of the syllogism. In suitable circumstances, this major premise will be in the imperative mood. Science, in its role, will give us the minor premise, which is in the indicative mood, while the conclusion drawn from it may be in the imperative mood. We shall consider these two points in turn.
////——Though some parts are not especially fluent (which is understandable, since this was a speech), Poincaré’s meaning is still easy to grasp—the core of morality is “feeling.” This is by no means to say that reason and argument, as the “transmission mechanism,” are unnecessary; rather, the foundation of morality, the “engine,” is “feeling.”
P105 pp. 120–121
Science keeps us in constant contact with certain things greater than ourselves; science shows us scenes that are ever new and vast, and profound. Behind the great vistas that science offers us, it leads us to conjecture something even greater; such scenes are a delight to us, and it is precisely in that delight that we reach a state of self-forgetfulness; thus science is morally noble.
Anyone who has tasted this flavor, even if he merely glimpses from afar the pre-established harmony of natural laws, will be better able than others to live with himself and to pay no heed to his petty, personal interests.…………
For such a person, what inspires him most is love of truth, and only secondarily passion.…… For deception, in the eyes of the innocent, is a base crime and the gravest corruption,…… when we have formed the habit of scientific methods, their rigorous precision, and an extreme aversion to every attempt to distort the experimental process……
P106 p. 122
Second, science has another use for us. Science is a collective undertaking;………… we feel that we are working for the benefit of humanity, and as a result, people seem more lovable to us.
P107 p. 123
There is no doubt that love of truth is a great thing; but what would it be if, in pursuit of truth, we sacrificed other things of infinite value, such as kindness, piety, and love of one’s neighbor! When we hear of any catastrophe, say an earthquake, we forget the suffering of the victims and think only of the direction and amplitude of the shock; if the earthquake reveals some unknown law of seismology, we would almost take it for good luck.
P108 p. 124
It is well known—and teachers who know and love science tirelessly teach this—that science can play a highly beneficial and highly important role in moral education. But to think that only science has such a role would be a mistake. Science can awaken feelings of kindness, and such feelings can serve as a moral force; but other disciplines can do the same. To deprive ourselves of any assistance would be, I fear, foolish;
P108 p. 125
The feelings that can serve as the basis of ethics are of a very different nature; they are also expressed in wildly different ways from one person to another.…… Some people are especially rich in sympathy;…… others subordinate everything to social harmony and public happiness;…… still others may have an ideal of beauty,……
All these tendencies are commendable; but they are different. Conflict may arise from this. If science shows us that this conflict need not be feared, if science proves that one of these aims cannot be attained without aiming at the others as well (and this is within the scope of science), then science will have done useful work; science will have given the moralist precious help.…… For science shows them that one person’s victory is everyone’s victory.
P109 p. 125
Is this the true direction of scientific progress? To hope so is permissible. Science increasingly shows us the interdependence of the different parts of the universe; it reveals to us the harmony of the universe. Is this because this harmony is real, or because it is a need of our minds and therefore a postulate of science? This is a question I do not wish to try to solve. The fact remains that science tends toward unity, and leads us toward unity. Just as science coordinates certain special laws and unites them into a more general law, does it not also bring under unity the individual ambitions of our hearts—ambitions that seem so opposed to one another, so capricious, so utterly different?
P110 p. 127
What we must fear is only that incomplete science, mistaken science, which seduces us with its empty appearance and incites us to destroy things that ought not to be destroyed, only for us to realize, when we know more, that these things destroyed would still need to be rebuilt later, but by then it is too late. Some people are enamored of an idea not because it is correct, but because it is new, because it is fashionable. These people are dreadful destroyers, but they are not…… I was about to say, they are not scientists, but I notice that many of them have made enormous contributions to science; therefore they are scientists, and they are scientists not because of this, but quite apart from it.
True science is wary of hasty generalization, wary of hasty theoretical deduction.………… Undoubtedly, we must criticize tradition, but we must by no means abandon tradition altogether.
P111 p. 128 Ethics as a science is not a moral system; it will never be a moral system; it cannot replace morality, just as a treatise on the physiology of digestion cannot replace a delicious meal.
P112 p. 129
Science is deterministic; it is a priori deterministic; it postulates determinism, because without determinism science would not exist. Science is also a posteriori deterministic; if it begins from the hypothesis of determinism, as a necessary condition of its existence as science, it later confirms determinism by means of existing facts, and every achievement of science is a victory for determinism. Perhaps a reconciliation is possible.………… Whatever the rights and wrongs of it may be, science is deterministic. Wherever science penetrates, it introduces determinism.………… What will happen on the day when ethics in its turn becomes the object of science? Ethics will inevitably become saturated with determinism, and that will undoubtedly be the collapse of ethics.
P113 p. 130
Nature is more powerful than all metaphysical systems; even if this is proved, even if the secret of its power is known, its power will not thereby be diminished. Since Newton, is gravitation not irresistible? The moral force that guides us will continue to guide us.
P113 pp. 130–131
We must now come to the conclusion that, in the strict sense of the word ethics, there is at present no scientific ethics, and there never will be one; but science can help ethics in an indirect way. Science, as ordinarily understood, cannot but help ethics; only pseudoscience is what should worry us. On the other hand, science alone is not enough, because it can see only a part of human beings, or, if you prefer, although it can see everything, it sees everything from the same angle; secondly, because one must believe that the human mind is not wholly scientific. Moreover, fear of science and excessive hopes seem to me equally unrealistic; ethics and science, so long as both are advancing, will certainly adapt to one another.
////——We see that Poincaré’s attitude toward science is quite fair and well judged, and I very much agree with it. Of course, Poincaré was clearly an idealist, and in reality it does not seem easy for science to fulfill its ideal role in assisting ethics; the dangers are obvious as well. In addition, Poincaré’s own views could also be misunderstood, especially his concepts of “nature” and “feeling.” But in any case, Poincaré’s instruction and inspiration are important.
February 9, 2006
Translated from the Chinese original with AI assistance. The original text is authoritative.
Leave a Reply