By Professor Pierre Duhem



THE Revue de Métaphysique et de Morale a little more than a year ago published an article in which the opinions I emitted on different occasions concerning physical theories were expounded and discussed.2 The author of this article, Abel Rey, has taken the trouble to study assiduously even the smallest writings in which I had expounded my thought, and he has followed the course of this thought with a great concern for accuracy; thus, he has drawn for his readers a picture whose fidelity has keenly impressed me; and surely, I shall not be bargaining with M. Rey by offering him acknowledgement of my appreciation in exchange for the sympathy with which his understanding has assimilated what I had published.

And yet (is there anyone who does not find something about which to complain in his own portrait, however accurate the painter may have been?), it seemed to me that M. Rey had solicited somewhat more than exactly the premises which I had set down and that he has drawn conclusions from them which were not altogether contained in them. I should like to apply some restrictions to these conclusions.

M. Rey terminates his article as follows:

"Our intention here has been to examine only the scientific philosophy of M. Duhem and not his scientific work itself. In order to find and formulate precisely the expression of this philosophy it seems that we may propose the following formula: In its tendencies toward a qualitative conception of the material universe, in its challenging distrust with regard to a complete explanation of this universe by itself, of the sort mechanism imagines it has, and in its animadversions, more pronounced than genuine, with respect to an integral scientific skepticism, Duhem’s scientific philosophy is that of a believer."

Of course, I believe with all my soul in the truths that God has revealed to us and that He has taught us through His Church; I have never concealed my faith, and that He in whom I hold it will keep me from ever being ashamed of it, I hope from the bottom of my heart: in this sense, it is permissible to say that the physics I profess is the physics of a believer. But surely it is not in this sense that M. Rey meant the formula by which he characterized this physics; rather did he mean that the beliefs of the Christian had more or less consciously guided the criticism of the physicist, that they had inclined his reason to certain conclusions, and that these conclusions were hence to appear suspect to minds concerned with scientific rigor but alien to the spiritualist philosophy or Catholic dogma; in short, that one must be a believer, not to mention being a perspicacious one, in order to adopt altogether the principles as well as the consequences of the doctrine that I have tried to formulate concerning physical theories. If that were the case, I should have been singularly pursuing the wrong course and failed of my aim. In fact, I have constantly aimed to prove that physics proceeds by an autonomous method absolutely independent of any metaphysical opinion; I have carefully analyzed this method in order to exhibit through this analysis the proper character and exact scope of the theories which summarize and classify its discoveries; I have denied that these theories have any ability to penetrate beyond the teachings of experiment or any capacity to surmise realities hidden under data observable by the senses; I have thereby denied these theories the power to draw the plan of any metaphysical system, as I have denied metaphysical doctrines the right to testify for or against any physical theory. If all these efforts have terminated only in a conception of physics in which religious faith is implicitly and almost clandestinely postulated, then I must confess I have been strangely mistaken about the result to which my work was tending.

Before admitting such a mistake, I should like to he allowed to glance again at this work as a whole, to fix my gaze particularly on the parts in which the seal of the Christian faith was believed noticeable, and to recognize whether, against my intention, this seal is really impressed therein or else, on the contrary, whether an illusion, easy to dissipate, has not led to the taking of certain characteristics not belonging to the work as the mark of a believer. I hope that this inquiry, by clearing up confusions and ambiguities, will put the following conclusion beyond doubt: Whatever I have said of the method by which physics proceeds, or of the nature and scope that we must attribute to the theories it constructs, does not in any way prejudice either the metaphysical doctrines or the religious beliefs of anyone who accepts my words. The believer and the nonbeliever may both work in common accord for the progress of physical science such as I have tried to define it.

1, An article published in the Annales de Philosophie chrétienne, 77th Year, 4th series , Vol 1 (Oct & Nov 1905) p 44 and p 133.

2 Abel Rey "La Philosophie scientifique de M. Duehm" Revue de Métaphysique et de Morale, XII (July 1904), 699.


We should like to prove that the system of physics which we propose is subjected in all its parts to the most rigorous requsrements of positive method, and that it is positivist in its conclusions as well as in its origins.

First, of what preoccupations is the constitution of our system the result? Is our conception of physical theory the work of a believer who is uneasy about the disparity between the teachings of his church and the lessons of reason? Does it arise from an effort that faith in divine things would have attempted in order to attach itself to the doctrines of human science (fides quaerens intellectum) ? * If so, the nonbeliever may conceive legitimate suspicions regarding such a system; he may fear that some proposition oriented toward Catholic beliefs has, unawares even to the author, slipped through the close meshes of rigorous criticism, so ready is the human mind to think true what it wishes! On the other hand, these suspicions would cease to have any ground if the scientific system occupying us were born within the very matrix of experiment and were forced on the author outside of any metaphysical or theological concern, and almost despite himself, through the daily practice and teaching of the science.

Here then we are going to relate how we were led to teach concerning the aim and structure of physical theory an opinion that is said to be brand new; we shall do so in all sincerity, not because we have the vanity to believe the career of our thought interesting in itself, but in order that the knowledge of the origins of the doctrine may make for a more exact judgment of its logical validity, for it is this validity that is in question.

* "Faith inquiring into the intellect."

Let us take ourselves back twenty-five years to the time when we received our first initiation, as physicist-to-be, in the mathematics classes of the College Stanislas. The man who gave us this initiation, Jules Moutier, was an ingenious theorist; his critical sense, ever alert and extremely perspicacious, distinguished with sure accuracy the weak point of many a system which others accepted without dispute; proof of his inquiring mind is not lacking, and physical chemistry owes one of its most important laws to him. It was this teacher who planted in us the seed of our admiration for physical theory and the desire to contribute to its progress. Naturally he oriented our first tendencies in the same direction to which his own preferences brought him. Now, although he appealed in his investigations to the most diverse methods, each in turn, it was to the mechanical attempts at explanation that Moutier returned most often with a sort of predilection. Like most of the theorists of his time he saw the ideal of physics in an explanation of the material universe constructed in the manner of the atomists and the Cartesians; in one of his writings’ he did not hesitate to adopt the following thought of Huygens: "The causes of all natural phenomena are conceived through mechanical reasons, unless we wish to give up all hope of understanding anything in physics."

Being a disciple of Moutier, it was as a convinced partisan of mechanism that we approached the courses in physics pursued at the école Normale. There we were to come under influences very different from those we had experienced until then; the jesting skepticism of Bertin struck in vain against the constantly reborn and constantly abortive attempts of the mechanists. Without going as far as to have the agnosticism and empiricism of Bertin, most of our teachers shared his mistrust regarding hypotheses about the intimate nature of matter. Past masters in experimental manipulation, they saw in experiment the only source of truth; when they accepted physical theory it was on condition that it rest entirely on laws drawn from observation.

Whereas the physicists and chemists rivalled one another in praising the method that Newton had formulated at the end of his book of Principia, those who taught us mathematics, especially Jules Tannery, worked to develop and sharpen in us a critical sense and to make our reason infinitely difficult to satisfy when it had to judge the rigor of a demonstration.

The tendencies which the instruction of the experimenters had produced in our mind and the lessons that the mathematicians had fixed in us concurred in making us conceive physical theory to be of quite a different type from what we had imagined it to be until then. This ideal theory, the supreme goal of our efforts, we wished to see resting solidly on laws verified by experiment and completely exempt from those hypotheses about the structure of matter which Newton had condemned in his immortal General Scholium; but at the same time we wished theory to be constructed with that logical rigor which the algebraists had taught us to admire. It was to the model of such a theory that we tried hard to make our lessons conform when we were given the first opportunity to teach.

We soon had to recognize how vain our efforts were. We had the good fortune to teach before an elite audience in the Faculty of Sciences at Lille. Among our students, many of whom are today colleagues of ours, the critical sense was hardly asleep; requests for clarification and embarrassing objections indefatigably indicated to us the paradoxes and vicious circles which kept reappearing in our lessons despite our care. This harsh but salutary test did not take long to convince us that physics could not be constructed on the plan we had undertaken to follow, that the inductive method as defined by Newton could not be practised, that the proper nature and true object of physical theory had not yet been exhibited with complete clarity, and that no physical doctrine could be expounded in a fully satisfactory manner so long as this nature and object had not been determined in an exact and detailed manner.

3. J Moutier, "Sur les attractions et les répu1sions des corps électrisés au point de vue de la théorie mécanique de l’électricité," Annales de Chimie et de Physique, 4th Series, Vol. xvi.

This necessity to take up again the analysis of the method by which physical theory can be developed, down to its very foundations, appeared to us in circumstances of which we retain a very vivid recollection. Little satisfied with the exposition of the principles of thermodynamics that they had encountered "in books and among men," several of our students asked us to edit for them a small treatise on the foundations of that science. While we tried hard to satisfy their desire, the radical impotence of the methods then known for constructing a logical theory came home to us more persistently each day. We then had an intuition of the truths which since that time we have continually affirmed: we understood that physical theory is neither a metaphysical explanation nor a set of general laws whose truth is established by experiment and induction; that it is an artificial construction manufactured with the aid of mathematical magnitudes; that the relation of these magnitudes to the abstract notions emergent from experiment is simply that relation which signs have to the things signified; that this theory constitutes a kind of synoptic painting or schematic sketch suited to summarize and classify the laws of observation; that it may be developed with the same rigour as an algebraic doctrine, for in imitation of the latter it is constructed wholly with the aid of combinations of magnitudes that we have ourselves arranged in our own manner. But we also understood that the requirements of mathematical rigor are no longer relevant when it comes to comparing a theoretical construction with the experimental laws which it claims to represent, and to judging the degree of resemblance between the picture and the object, for this comparison and judgement do not arise from the faculty by which we can unwind a series of clear and rigorous syllogisms.

We realized that in order to judge this resemblance between theory and empirical data, it is not possible to dissociate the theoretical construction and to submit each of its parts in isolation to the test of facts, for the slightest experimental verification puts into play the most diverse chapters of theory, and we realized that any comparison between theoretical physics and experimental physics consists in an alliance of theory taken in its entirety with the total teaching of experiment.

It was thus through the necessities of teaching, under their urgent and constant pressure, that we were led to produce a conception of physical theory markedly different from what had been current till then. These same necessities led us through the years to develop our first thoughts, to make them more precise, to explain and to correct them. It was through these necessities that our system concerning the nature of physical theory was affirmed in our conviction, thanks to the ease with which it enabled us to connect into a coherent exposition the most diverse chapters of science. And may we be pardoned for insisting here on indicating the quite special authority conferred on our principles by this test to which we have submitted them in the course of many long years? There are many persons today who write about the principles of mechanics and physics, but if someone proposed to them that they give a complete course in physics which would still agree in all particulars with their doctrine, how many of them would accept the challenge?

Our ideas about the nature of physical theory are, therefore, rooted in the practice of scientific research and in the exigencies of teaching. Deeply as we have gone into our examination of our intellectual conscience, it is impossible for us to recognize an influence exerted on the genesis of these ideas by any religious preoccupation whatever. And how could it be otherwise? How could we have imagined that our Catholic faith was interested in the evolution undergone by our opinions as a physicist? Have we not known Christians, as sincere as they were enlightened, who firmly believed in the mechanical explanations of the material universe? Have we not known some of them to be ardent partisans of the inductive method of Newton? Was it not a glaring fact to us, as to any man of good sense, that the object and nature of physical theory are things foreign to religious doctrines and without any contact with them? And, furthermore, as though better to mark to what little extent our manner of viewing these questions was inspired by our religious beliefs, have not the most numerous and liveliest attacks against this manner of viewing things come from those who profess the same faith as we do?

Our interpretation of physical theory is, therefore, essentially positivist in its origins. Nothing in the circumstances which suggested this interpretation can justify the distrust of anyone who does not share our metaphysical convictions or religious beliefs.


Our reflections on the meaning and scope of physical theories were induced by preoccupations in which metaphysics and religion had no part; they terminated in conclusions which have nothing to do with metaphysical doctrines and nothing to do with religious dogmas.

Certainly we have relentlessly fought physical theories which claim to reduce the study of the material world to mechanics; we have insisted that the physicist should admit primary qualities into his systems. Now, the doctrines which proclaimed that everything in the material world reduced to matter and motion are metaphysical; some proclaimed that every quality is essentially complex, and that it can and should always be resolved into quantitative elements. It seems that our conclusions are really in opposition to these doctrines; our manner of viewing things cannot be admitted without rejecting by that very fact these metaphysical systems, and, therefore, it seems that our physics underneath its positivistic appearances is, after all, a metaphysics. And that is what M. Rey imagines when he says: "It really seems that M. Duhem has succumbed to a common temptation: he has been metaphysical. He had an idea in the back of his head, a preconceived idea about the validity and scope of science, and about the nature of knowledge."4

If this were so—let us repeat it loudly—we should have completely failed in the attempt in which we made every effort: we should not have succeeded in defining a theoretical physics for whose progress positivists and metaphysicians, materialists and spiritualists, nonbelievers and Christians may work with common accord.

But it is not so.

With the help of essentially positivistic methods we have tried hard to distinguish sharply the known from the unknown; we never intended to draw a line of demarcation between the knowable and the unknowable. We have analyzed the procedures through which physical theories were constructed and sought to conclude from this analysis the exact meaning and proper scope or range of the propositions formulated by these theories; our inquiry concerning physics has not led us either to affirm or deny the existence and legitimacy of methods of investigations foreign to this science and appropriate for attaining truths beyond its means.

So we fought against mechanism; but on what terms? Have we postulated at the base of our reasoning some proposition not provided by the method of the physicist? Starting from such postulates have we unwound a series of deductions whose conclusion might be of the following form: mechanism is an impossibility; it is certain that we can never construct an acceptable representation of physical phenomena by means of masses and motions subject only to the laws of dynamics? By no means. What we did do was to submit to a minute examination the systems proposed by the various mechanistic schools and to note that none of these systems offered the characteristics of a good and sound physical theory, for none of them represented with a sufficient degree of approximation an extensive group of experimental laws.5

Here is how we expressed ourselves regarding the legitimacy or illegitimacy of the very principle of mechanism:

"For the physicist the hypothesis that all natural phenomena may be explained mechanically is neither true nor false, but has no meaning.

"Let us explain this proposition which might appear paradoxical.

"Only one criterion permits one in physics to reject as false a judgment which does not imply logical contradiction, and that is the noting of a flagrant disagreement between this judgment and the facts of experiment. When a physicist affirms the truth of a proposition, he affirms the fact that this proposition has been compared with the data of experiment, that among these data there were some whose agreement with the proposition under examination was not a priori necessary, but that, nevertheless, the deviations between these data and the proposition remained less than the experimental errors.

"By virtue of these principles we do not state a proposition which physics can hold as erroneous when we advance the view that all the phenomena of the inorganic world may be explained mechanically, for experiment cannot inform us of any phenomena not surely reducible to the laws of mechanics. However, neither is it legitimate to say that this proposition is physically true; for the impossibility of running down a formal and irresolvable contradiction between it and the results of observation is a logical consequence of the absolute indetermination allowed by invisible masses and hidden motions.

"So it is impossible for one who holds to the procedures of experimental method to declare the following proposition true: All physical phenomena are explained mechanically. It is just as impossible to declare it false. This proposition transcends physical method."

To assert, therefore, that all the phenomena of the inorganic world are reducible to matter and motion is to be metaphysical; to deny that this reduction is possible is again to be metaphysical.

But our critique of physical theory refrained from making such an affirmation or denial. What it affirmed and proved is that there did not exist at the time any acceptable physical theory which was in conformity with the requirements of mechanism, and that it was possible at the time, by refusing to be subject to these requirements, to construct a satisfactory theory; but in formulating these assertions we were doing the work of a physicist, not that of a metaphysician.

In order to construct this physical theory not reduced to mechanism, we had to make certain mathematical magnitudes correspond to certain qualities, and among these qualities there are some which we did not decompose into simpler qualities but treated as primary qualities. Was it by virtue of a metaphysical criterion that we regarded such qualities as primary? Did we have some means of recognizing a priori whether they were or were not reducible to simpler qualities?

By no means. All that we asserted about such qualities was what the procedures proper to physics could teach us: we asserted that we did not know at the time how to decompose them, but that it was not absurd to seek their further resolution into simpler elements. We said: "Physics will reduce the theory of the phenomena presented by inanimate nature to the consideration of a certain number of qualities, but will seek to make this number as small as possible. Each time a new effect presents itself, physics will try in every way to reduce it to qualities already defined; only after recognizing the impossibility of making this reduction will it resign itself to put into its theories a new quality and introduce into its equations a new kind of variable. Thus the chemist discovering a new body tries hard to decompose it into one of the elements already known only when he has exhausted in vain all the means of analysis the disposal of laboratories will he decide to add a name to the of simple bodies.

"The name simple is not given to a chemical substance by virtue of a metaphysical argument proving that it is by nature indecomposable; it is given to it by virtue of a fact, because it has resisted all attempts at decomposition. This epithet (simple) is an admission of present inability, and is nothing definitive and irrevocable; a body that is simple today will cease being so tomorrow if some chemist more fortunate than his predecessors, succeeds in dissociating it; potash and soda, simple bodies for Lavoisier, were compounds beginning with the work of Davy. So it is with the primary qualities admitted in physics. By calling them primary we do not prejudge them to be irreducible by nature; we simply confess that we do not know how to reduce them to simpler qualities, but this reduction which we cannot effect today will, perhaps, be an accomplished fact tomorrow."

Therefore, in rejecting mechanical theories and proposing instead a qualitative theory, we have in no way been guided by "a preconceived idea about the validity and scope of science and about the nature of the knowable"; we have not made any appeal, consciously or unconsciously, to metaphysical method. We have made use exclusively of the procedures belonging to the physicist; we have con demned theories which did not concord with the laws of observation; we have acknowledged a theory which gave a satisfactory representation of these laws; in short, we have scrupulously respected the rules of positive science.


Led by the positivistic method as practised by the physicist, our interpretation of the meaning and scope of theories has not undergone any influence either of metaphysical opinions or of religious beliefs. This interpretation is by no manner or means the scientific philosophy of a believer; the nonbeliever may admit every article of it.

Does it follow from this that the believer has nothing to gain from this critique of physical science, and that the results to which it leads have no interest for him?

It has been fashionable for some time to oppose the great theories of physics to the fundamental doctrines on which spiritualistic philosophy and the Catholic faith rest; these doctrines are really expected to be seen crumbling under the ramming blows of scientific systems. Of course, these struggles of science against faith impassion those who are very poorly acquainted with the teachings of science and who are not at all acquainted with the dogmas of faith; but at times they preoccupy and disturb men whose intelligence and conscience are far above those of village scholars and café physicists.

Now, the system we have expounded gets rid of the alleged objections that physical theory would raise to spiritualistic metaphysics and Catholic dogma; it makes them disappear as easily as the wind sweeps away bits of straw, for according to this system these objections are, and can never be anything but, misunderstandings.

What is a metaphysical proposition, a religious dogma? It is a judgment bearing on an objective reality, affirming or denying that a certain real being does or does not possess a certain attribute. Judgments like "Man is free," "The soul is immortal," "The Pope is infallible in matters of faith" are metaphysical propositions or religious dogmas; they all affirm that certain objective realities possess certain attributes.

What will be required for the possibility that a certain judgment, on one side, is in agreement or disagreement with a proposition of metaphysics or theology, on the other side? Of necessity it will be required that this judgment have certain objective realities as its subject, and that it affirm or deny certain attributes concerning them. In effect, between two judgments not having the same terms but bearing on the same subjects, there can be neither agreement nor disagreement.

The facts of experience—in the current meaning of the words, and not in the complicated meaning these words take on in physics —and empirical laws—meaning the laws of ordinary experience which common sense formulates without recourse to scientific theories—are so many affirmations bearing on objective realities; we may, therefore, without being unreasonable, speak of the agreement or disagreement between a fact or law of experience, on the one hand, and a proposition of metaphysics or theology, on the other.

6 ibid., Part 2, Gb. I: "La Physique de La Qualité." Cf. Part is, Ch. is of the present volume, on primary qualities


If for example, we noticed a case in which a Pope, placed in the conditions provided by the dogma of infallibility, issued an instruction contrary to the faith, we should have before us a fact which would contradict a religious dogma. If experience led to the formulation of the law, "Human acts are always determined," we should be dealing with an empirical law denying a proposition of metaphysics.

That being settled, can a principle of theoretical physics be in agreement or disagreement with a proposition of metaphysics or of theology? Is a principle of theoretical physics a judgment involving objective reality?

Yes, for the Cartesian and the atomist, and for anyone who makes of theoretical physics a dependency or a corollary of metaphysics; a principle of theoretical physics is a judgment which bears on a reality. When the Cartesian affirms that the essence of matter is extension in length, breadth, and thickness or when the atomist declares that an atom moves with uniform rectilinear motion so long as it does not hit another atom, the Cartesian and the atomist really mean to assert that matter is objectively just what they say it is, that it really possesses the properties they attribute to it, and that it is deprived of the properties they refuse to give it. Consequently, it is not meaningless to ask whether a certain principle of Cartesian or atomistic physics is or is not in disagreement with a certain proposition of metaphysics or of dogma; it may reasonably be doubted that the law imposed by atomism on the motion of atoms is compatible with the action of the soul on the body; it may be maintained that the essence of Cartesian matter is irreconcilable with the dogma of the real presence of the body of Jesus Christ in the Eucharist.

Yes, also, for the Newtonian; a principle of theoretical physics is a judgment involving objective reality for one who, like the Newtonian, sees in such a principle an experimental law generalized by induction. Such a person will see, for instance, in the fundamental equations of dynamics a universal rule whose truth experiment has disclosed and to which all the motions of objectively existing bodies are subject. He will be able to speak without illogicality of the conflict between the equations of dynamics and the possibility of free will, and investigate whether this conflict is resolvable or not.

Thus, the defenders of the schools of physics that we have put in combat may legitimately speak of agreement or disagreement between the principles of physical theory and metaphysical or religious doctrines. This will not be the case with those whose reason has accepted the interpretation of physical theory we proposed, for they will never speak of a conflict between the principles of physical theory and metaphysical or religious doctrines; they understand, in fact, that metaphysical and religious doctrines are judgments touching on objective reality, whereas the principles of physical theory are propositions relative to certain mathematical signs stripped of all objective existence. Since they do not have any common term, these two sorts of judgments can neither contradict nor agree with each other.

What indeed is a principle of theoretical physics? It is a mathematical form suited to summarize and classify laws established by experiment. By itself this principle is neither true nor false; it merely gives a more or less satisfactory picture of the laws it intends to represent. It is these laws which make affirmations concerning objective reality, and which may, therefore, be in agreement or disagreement with some proposition of metaphysics or theology. However, the systematic classification that theory gives them does not add or take away anything concerning their truth, their certainty, or their objective scope. The intervention of the theoretical principle summarizing and ordering them can neither destroy the agreement between these laws and metaphysical or religious doctrines when such agreement existed before the intervention of this principle, nor reinstate such agreement if it did not exist previously. In itself and by its essence, any principle of theoretical physics has no part to play in metaphysical or theological discussions.

Let us apply these considerations to an example: Is the principle of the conservation of energy compatible with free will? That is a question often debated and resolved in different ways. Now, does it even have a meaning such that a man conscious of the exact import of the terms it employs can reasonably think about answering it with either yes or no?

Of course, this question has a meaning for those who make of the principle of the conservation of energy an axiom applicable in all strictness to the real universe, either when they draw this anxiom from a philosophy of nature or when they arrive at it by starting from experimental data with the help of a broad and powerful induction. But we do not accept either side.

For us the principle of the conservation of energy is by no means a certain and general affirmation involving really existent objects. It is a mathematical formula set up by a free decree of our understanding in order that this formula, combined with other formulas postulated analogously, may permit us to deduce a series of consequences furnishing us a satisfactory representation of the laws noted in our laboratories.

Neither this formula of the conservation of energy nor the formulas that we associate with it can be said, properly speaking, to be true or false, since they are not judgments bearing on realities; all that we can say is that the theory composing a group of laws is a good one if its corollaries represent these laws we intend to classify with a sufficient degree of exactness, and that the theory is a bad one in the contrary case. It is already clear that the question; 'is the law of the conservation of energy compatible with free will or not?' cannot have any meaning for us. If it had any, in effect it would be the following: Is the objective impossibility of free acts a consequence of the principle of the conservation of energy, or not? Now the principle of the conservation of energy has no objective consequence.

And furthermore, let us insist on this. How would one go about deriving from the principle of the conservation of energy and from other analogous principles the corollary, "Free will is impossible"? We should observe that these various principles are equivalent to a system of differential equations ruling the changes of state of the bodies subject to them; that if the state and motion of these bodies are given at a certain instant, their state and motion would then be determined unambiguously for the whole course of time; and we should conclude from this that no free movement can be produced among these bodies, since a free movement would be essentially a movement not determined by previous states and motions.

Now, what is such an argument worth? We selected our differential equations or, what comes to the same thing, the principles they translate, because we wished to construct a mathematical representation of a group of phenomena; in seeking to represent these phenomena with the aid of a system of differential equations, we were presupposing from the very start that they were subject to a strict determinism; we were well aware, in fact, that a phenomenon whose peculiarities did not in the least result from the initial data would rebel at any representation by such a system of equations. We were therefore certain in advance that no place was reserved for free actions in the classification we had arranged. When we note afterwards that a free action cannot be included in our classification, we should be very naive to be astonished by it and very foolish to conclude that free will is impossible.

Imagine a collector who wishes to arrange sea shells. He takes seven drawers that he marks with seven colors of the spectrum, and you see him putting the red shells in the red drawer, the yellow shells in the yellow drawer, etc. But if a white shell appears, he will not know what to do with it, for he has no white drawer. You would, of course, feel very sorry for his reason if you heard him conclude in his embarrassment that no white shells exist in the world.

The physicist who thinks he can deduce from his theoretical principles the impossibility of free will deserves the same feeling. In manufacturing a classification for all phenomena produced in this world, he forgets the drawer for free actions!


That our physics is the physics of a believer is said to follow from the fact that it so radically denies any validity to the objections obtained from physical theory to spiritualistic metaphysics and the Catholic faith! But it might just as well be called the physics of a nonbeliever, for it does not render better or stricter justice to the arguments in favor of metaphysics or dogma that some have tried to deduce from physical theory. It is just as absurd to claim that a principle of theoretical physics contradicts a proposition formulated by spiritualistic philosophy or by the Catholic doctrine as it is to claim that it confirms such a proposition. There cannot be disagreement or agreement between a proposition touching on an objective reality and another proposition which has no objective import. Every time people cite a principle of theoretical physics in support of a metaphysical doctrine or a religious dogma, they commit a mistake, for they attribute to this principle a meaning not its own, an import not belonging to it.

Let us again explain what we are saying by an illustration. In the middle of the last century, Clausius, after profoundly transforming Carnot’s principle, drew from it the following famous corollary: The entropy of the universe tends toward a maximum. From this theorem many a philosopher maintained the conclusion of the impossibility of a world in which physical and chemical changes would go on being produced forever; it pleased them to think that these changes had had a beginning and would have an end; creation in time, if not of matter, at least of its aptitude for change, and the establishment in a more or less remote future of a state of absolute rest and universal death were for these thinkers inevitable consequences of the principles of thermodynamics.

The deduction here in wishing to pass from the premises to these conclusions is marred in more than one place by fallacies. First of all, it implicitly assumes the assimilation of the universe to a finite collection of bodies isolated in a space absolutely void of matter; and this assimilation exposes one to many doubts. Once this assimilation is admitted, it is true that the entropy of the universe has to increase endlessly, but it does not impose any lower or upper limit on this entropy; nothing then would stop this magnitude from varying from -¥ to +¥ while the time itself varied from - ¥ to + ¥; then the allegedly demonstrated impossibilities regarding an etemal life for the universe would vanish.

But let us confess these criticisms wrong; they prove that the demonstration taken as an example is not conclusive, but do not prove the radical impossibility of constructing a conclusive example which would tend toward an analogous end. The objection we shall make against it is quite different in nature and import: basing our argument on the very essence of physical theory, we shall show that it is absurd to question this theory for information conceming events which might have happened in an extremely remote past, and absurd to demand of it predictions of events a very long way off.

What is a physical theory? A group of mathematical propositions whose consequences are to represent the data of experiment; the validity of a theory is measured by the number of experimental laws it represents and by the degree of precision with which it represents them; if two different theories represent the same facts with the same degree of approximation, physical method considers them as having absolutely the same validity; it does not have the right to dictate our choice between these two equivalent theories and is bound to leave us free.

No doubt the physicist will choose between these logically equivalent theories, but the motives which will dictate his choice will be considerations of elegance, simplicity, and convenience, and grounds of suitability which are essentially subjective, contingent, and variable with time, with schools, and with persons; as serious as these motives may be in certain cases, they will never be of a nature that necessitates adhering to one of the two theories and rejecting the other, for only the discovery of a fact that would be represented by one of the theories, and not by the other, would result in a forced option.

Thus the law of attraction in the inverse ratio of the square of the distance, proposed by Newton, represents with admirable precision all the heavenly motions we can observe.

However, for the inverse square of the distance we could substitute some other function of the distance in an infinity of ways such that some new celestial mechanics represented all our astronomical observations with the same precision as the old one. The principles of experimental method would compel us to attribute exactly the same logical validity to both these different celestial mechanics. This does not mean that astronomers would not keep the Newtonian law of attraction in preference to the new law, but they would keep it on account of the exceptional mathematical properties offered by the inverse square of the distance in favor of the simplicity and elegance that these properties introduced into their calculations.

Of course, these motives would be good to follow; yet they would constitute nothing decisive or definitive, and would be of no weight the day when a phenomenon would be discovered which the Newtonian law of attraction would be inept to represent and of which another celestial mechanics would give a satisfactory representation; on that day astronomers would be bound to prefer the new theory to the old one.

This is what they did, in fact, the day when, by introducing the idea of molecular attraction, they complicated the formula of Newtonian attraction in order to be able to represent the laws of capillarity.

That being understood, let us suppose we have two systems of celestial mechanics, different from the mathematical point of view, but representing with an equal degree of approximation all the astronomical observations made until now. Let us go further: let us use these two celestial mechanics to calculate the motions of heavenly bodies in the future; let us assume that the results of one of the calculations are so close to those of the other that the deviation between the two positions they assign to the same heavenly body is less than the experimental errors even at the end of a thousand or even ten thousand years. Then we have here two systems of celestial mechanics which we are bound to regard as logically equivalent; no reason exists compelling us to prefer one to the other, and what is more, at the end of a thousand or ten thousand years, men will still have to weight them equally and hold their choice in suspense.

It is clear that the predictions from both these theories will merit equal degrees of confidence; it is clear that logic does not give us any right to assert that the predictions of the first theory, but not those of the second theory, will be in conformity with reality.

In truth these predictions agree perfectly for a lapse of a thousand or ten thousand years, but the mathematicians warn us that we should be rash to conclude from this that this agreement will last forever, and by concrete examples they show us to what errors this illegitimate extrapolation could lead us.8

The predictions of our two systems of celestial mechanics would be peculiarly discordant if we asked these two theories to describe for us the state of the heavens at the end of ten million years; one of them might tell us that the planets at that time would still describe orbits scarcely different from those they describe at present; the other, however, might very well claim that all the bodies of the solar system will then be united into a single mass, or else that they will be dispersed in space at enormous distances from one another. Of these two forecasts, one proclaiming the stability of the solar system and the other its instability, which shall we believe? The one, no doubt, which will best fit our extra-scientific preoccupations and predilections; but certainly the logic of the physical sciences will not provide us with any fully convincing argument to defend our choice against an attacking party and impose it on him.

So it goes with any long-term prediction. We possess a thermodynamics which represents very well a multitude of experimental laws, and it tells us that the entropy of an isolated system increases eternally. We could without difficulty construct a new thermodynamics which would represent as well as the old thermodynamics the experimental laws known until now, and whose predictions would go along in agreement with those of the old thermodynamics for ten thousand years; and yet, this new thermodynamics might tell us that the entropy of the universe after increasing for a period of 100 million years will decrease over a new period of 100 million years in order to increase again in an eternal cycle.

By its very essence experimental science is incapable of predicting the end of the world as well as of asserting its perpetual activity. Only a gross misconception of its scope could have claimed for it the proof of a dogma affirmed by our faith.


There you have, then, a theoretical physics which is neither the theory of a believer nor that of a nonbeliever, but merely and simply a theory of a physicist; admirably suited to classify the laws studied by the experimenter, it is incapable of opposing any assertion whatever of metaphysics or of religious dogma, and is equally incapable of lending effective support to any such assertion. When the theorist invades the territory of metaphysics or of religious dogma, whether he intends to attack them or wishes to defend them, the weapon he has used so triumphantly in his own domain remains useless and without force in his hands; the logic of positive science which forged this weapon has marked out with precision the frontiers beyond which the temper given it by that logic would be dulled and its cutting power lost.

But does it follow from the fact that sound logic does not confer on physical theory any power to confirm or invalidate a metaphysical proposition that the metaphysician is entitled to distrust the theories of physics? Does it follow that be can pursue the construction of his cosmological system without any concern for the set of mathematical formulas by means of which the physicist succeeds in representing and classifying the set of experimental laws? We do not believe so; we are going to try to show that there is a connection between physical theory and the philosophy of nature; we are going to try to show precisely in what this connection consists.

But first, in order to avoid any misunderstanding, let us make a remark. This question, Does the metaphysician have to take account of the statements of the physicist? applies absolutely only to the theories of physics. The question is not to be applied to the facts of experiment or to experimental laws, for the answer cannot be doubtful; it is clear that the philosophy of nature has to take account of these facts and of these laws.

Indeed, the propositions which state these facts and formulate these laws have an objective import which is not possessed by merely theoretical propositions. The former may then be in agreement or disagreement with the propositions constituting a cosmological system; the author of this system does not have the right either to be indifferent to this agreement, which brings valuable confirmation to his intuitions, or to this disagreement, which condemns his doctrines beyond appeal.

The judgment of this agreement or disagreement is generally easy when the facts considered are facts of everyday experience and when the laws aimed at are the laws of common sense,10 for it is not necessary to be a professional physicist to grasp what is objective in such facts or in such laws.

On the other hand, this judgment becomes infinitely delicate and thorny when it comes to a scientific fact or scientific law. In fact, the proposition which formulates this fact or law is generally an intimate mixture of experimental observation endowed with objective import and theoretical interpretation, a mere symbol devoid of any objective sense. It will be necessary for the metaphysician to dissociate this mixture in order to obtain as pure as possible the first of the two elements forming it; in that element, indeed, and in that observational element alone, can his system find confirmation or run into contradiction.

Suppose, for instance, that it is a question of an experiment on the phenomena of optical interference. The report of such an experiment contains statements bearing surely on the objective characteristics of light, for example, a certain assertion that an illumination which seems constant is in reality the manifestation of a property varying very rapidly from one instant to the next in a periodic manner. But these assertions are, through the very language used to express them, intimately bound up with the hypotheses bearing on optical theory. In order to express them the physicist speaks of the vibrations of an elastic ether or of the alternating polarity of a dielectric ether; now, we must not attribute offhand complete and entire objective reality either to vibrations of an elastic ether or to polarization of a dielectric ether, for they are really symbolic constructions imagined by theory in order to summarize and classify the experimental laws of optics.

8 See above, Part II, Ch. III, particularly the third section of that chapter.
9 Thus the trajectories of the planets under the simultaneous action of Newtonian attraction and capillary attraction might very well not differ over a period of ten thousand years to any appreciable extent from the trajectories of the same baffles subject only to Newtonian attraction; and yet, we could suppose without absurdity that the effects of capillary attraction accumulating over a period of 100 million years might appreciably disturb a planet from the path which Newtonian attraction alone would have made it follow.


And there you have the first reason why the metaphysician should not neglect the study of physical theories. He must know physical theory in order to be able to distinguish in an experimental report what proceeds from theory and has only the value of a means of representation or sign from what constitutes the real content or objective matter of the experimental fact.

Let us not go ahead and imagine, furthermore, that a wholly superficial acquaintance with theory would be enough for that purpose. Very often in the report of a physical experiment, the real and objective matter and the merely theoretical and symbolic form interpenetrate each other in so intimate and complicated a manner that the geometric mind with its clear and rigorous procedures, too simple and inflexible however to be penetrating, may not suffice to separate them. There we need the insinuating and looser methods of the subtle mind with finesse; it alone, by slipping in between this matter and this form, can distinguish them; it alone can surmise that the latter is an artificial construction created of whole cloth by theory and without any value for the metaphysician, whereas the former, rich in objective truth, is suited to instruct the cosmologist.

15 See above, Part is, Cbs. iv and v.


Now, the subtle mind here, as everywhere else, is sharpened by long practice; it is by profound and detailed study of theory that one will obtain that sort of flair thanks to which one will discern in a physical experiment what is theoretic symbol, and thanks to which one will be able to separate this form, of no philosophical value, from the genuine empirical teaching which the philosopher should take into account.

Thus, it is necessary for the metaphysician to have a very exact knowledge of physical theory in order to recognize it unmistakably when it crosses the boundaries of its own domain and intends to penetrate into the territory of cosmology; in the name of this exact knowledge he will be entitled to halt the theory and remind it that it cannot gain from his assistance nor challenge his objections. The metaphysician has to make a profound study of physical theory if he wishes to be certain that it will not exert any illogical influence on his speculations.


There are still other and more serious reasons why the teachings of physical theory impose themselves on the attention of the metaphysician.

No scientific method carries in itself its full and entire justification; it cannot through its principles alone explain all these principles. We should therefore not be astonished that theoretic physics rests on postulates which can be authorized only by reasons foreign to physics.

Among a number of these postulates is the following one: Physical theory has to try to represent the whole group of natural laws by a single system all of whose parts are logically compatible with one another.

If we limit ourselves to invoking merely the grounds of pure logic, of that logic which allows us to determine the object and structure of physical theory, it is impossible to justify this postulate; it is impossible to condemn a physicist who would claim to represent by several logically incompatible theories either diverse sets of experimental laws or even a single group of laws; all that can be required of him is not to mix up two incompatible theories, that is, not to combine a major premise obtained from one of these theories with a minor premise supplied by the other.

This conclusion, viz., the right of the physicist to develop a logically incoherent theory, is indeed one arrived at by those who analyze the method of physics without recourse to any principle foreign to this method. For them the representations of theory are only convenient summaries and only artificial devices aimed at facilitating the work of discovery. Why should we forbid the worker the successive employment of disparate instruments when he finds that each one of them is well adapted to a certain task and not well adapted to another job?

However, this conclusion greatly shocks a good number of those striving for the progress of physics; some of them wish to see in this scorn for theoretic unity the prejudice of a believer desiring to exalt dogma at the expense of science; and to support this opinion it is observed that the brilliant galaxy of Christian philosophers grouped around Edouard Le Roy readily hold physical theories to be merely recipes. In so reasoning it is too often forgotten that Henri Poincaré was the first to proclaim and teach in a formal manner that the physicist could make use, in succession, of as many theories, incompatible among themselves, as he deemed best; and I do not know that Henri Poincaré shares the religious beliefs of Edouard Le Roy.

It is certain that Henri Poincaré as well as Edouard Le Roy were fully authorized by the logical analysis of physical method to maintain their stand; it is no less certain that this doctrine with its skeptical overtones shocks most of those working for the advance of physics. Although the merely logical study of the procedures they employ does not provide them with any convincing argument in support of their way of viewing things, they feel that this way is the right one; they have an intuition that logical unity is imposed on physical theory as an ideal to which it tends constantly; they feel that any lack of logic, any incoherence in this theory, is a blemish, and that the progress of science should gradually remove this blemish.

And this conviction is fundamentally shared even by those who defend the right of theory to logical incoherence. Is there a single one among them who hesitates for an instant to prefer a rigorously coordinated theory to a junk heap of irreconcilable theories, and who in order to criticize an adversary does not strive to discover fallacies and contradictions in him? Therefore, it is not with wholehearted will that they proclaim the right to logical incoherence; like all physicists they regard the physical theory which would represent all experimental laws by means of a single, logically coordinated system as the ideal theory; and if they tend to stifle their aspirations toward this ideal, it is solely because they believe it unrealizable and because they despair of attaining it.

11 See above, Part o, Ch. iv, Sec. 10.

Now, is it right to regard this ideal as Utopian? It is up to the history of physics to answer this question; it is up to it to tell us whether men, ever since physics took on a scientific form, have exhausted themselves in vain efforts to unite into a coordinated system the innumerable laws discovered by experimenters; or else, on the other hand, whether these efforts through slow and continuous progress have contributed to fusing together pieces of theory, which were isolated at first, in order to produce an increasingly unified and ampler theory. To our mind that is the great lesson we ought to obtain when we retrace the evolution of physical doctrines, and Abel Rey has very clearly seen that that was the principal lesson we sought in the study of past theories.

When thus interrogated, what answer does history give us? The meaning of this answer is not doubtful, and here is how M. Rey interprets it: "Physical theory by no means presents us with a set of divergent or contradictory hypotheses. On the contrary, it offers as, if we follow its transformations attentively, a continuous development and genuine evolution. The theory which seems sufficient at a given time in science does not collapse as a whole when the field of science is enlarged. Adequate to explain a certain number of facts, it continues to remain valid for those facts. Only it is not so any longer for the new facts; it is not ruined; it has become insufficient. And why? Because our mind cannot grasp the complex except after the simple, the more general except after what is less so. So in order not to get lost in very complicated details masking the exact relations of things, the mind has neglected certain modalities, restricted the conditions of inquiry, and reduced he field of observation and experiment. Scientific discovery, when we really know how to understand it, only gradually enlarges this field, gradually lifts certain restrictions, and reintegrates considerations judged negligible at first."

Diversity fusing into a constantly more comprehensive and more perfect unity, that is the great fact summarizing the whole history of physical doctrines. Why should this evolution, whose law is manifested to us in this history, stop suddenly? Why should not the discrepancies we note today among the various chapters of physical theory be fused tomorrow into a harmonious accord? Why resign ourselves to them as to irremediable vices? Why give up the ideal of a completely unified and perfectly logical theory, when the systems actually constructed have drawn closer and closer to this ideal from century to century?

The physicist, then, finds in himself an irresistible aspiration toward a physical theory which would represent all experimental laws by means of a system with perfect logical unity; and when he asks of an exact analysis of experimental method what the role of physical theory is, he does not find anything in it to justify this aspiration. History shows him that this aspiration is as old as science itself, and that successive physical systems have realized this desire more and more fully from day to day. But the study of the procedures by means of which physical science makes progress does not disclose to him the entire rationale of this evolution. The tendencies directing the development of physical theory are not, therefore, completely intelligible to the physicist if he wishes to be nothing but a physicist.

If he wishes to be nothing but a physicist, and if, as an intransigent positivist, he regards everything not determinable by the method proper to the positive sciences as unknowable, he will notice this tendency powerfully inciting his own research as it has guided those of all times; but he will not look for its origin, because the only method of discovery which he trusts will not be able to reveal it to him.

If, on the other hand, he yields to the nature of the human mind, which is repugnant to the extreme demands of positivism, he will want to know the reason for, or explanation of, what carries him along; he will break through the wall at which the procedures of physics stop, helpless, and he will make an affirmation which these procedures do not justify; he will be metaphysical.

What is this metaphysical affirmation that the physicist will make, despite the nearly forced restraint imposed on the method he customarily uses? He will affirm that underneath the observable data, the only data accessible to his methods of study, are hidden realities whose essence cannot be grasped by these same methods, and that these realities are arranged in a certain order which physical science cannot directly contemplate. But he will note that physical theory through its successive advances tends to arrange experimental laws in an order more and more analogous to the transcendent order according to which the realities are classified, that as a result physical theory advances gradually toward its limiting form, namely, that of a natural classification, and finally that logical unity is a characteristic without which physical theory cannot claim this rank of a natural classification.

The physicist is then led to exceed the powers conferred on him by the logical analysis of experimental science and to justify the tendency of theory toward logical unity by the following metaphysical assertion: The ideal form of physical theory is a natural classification of experimental laws. Considerations of another sort also urge him to formulate this assertion. Very often a statement representing not an observed law but an observable law can be deduced from a physical theory. If we compare this statement with experimental results, what chance is there that the latter will be in agreement with the former?

If physical theory is nothing but what the analysis of the procedures put into operation by the physicist reveals, there is no sort of chance for the theoretically predicted law to agree with the facts. The statement deduced from the principles of the theory will be, for the physicist anxious to hazard nothing which is not tested by his customary method, exactly as though it were formulated by accident; this physicist will just as soon expect to find this forecast contradicted by observation as to see it confirmed by it; strict logic would disavow formally any preconceived idea regarding the experimental test to which this statement is to be submitted and any anticipated confidence in the success of this test.

Indeed, for logic, physical theory is only a system created by a free decree of our understanding in order to classify experimental laws already known. When in this theory we run across an empty compartment, can we conclude from this that there objectively exists an experimental law made to order to fill this compartment? We laughed at the collector who, not having prepared a drawer for white sea shells, deduced accordingly that there are no white sea shells in the world; would it be less ridiculous if from the presence in his conchologist’s cabinet of a drawer reserved for the color blue but still empty, he took it upon himself to assert that nature possesses blue sea shells destined to fill the empty drawer?

Now, in what physicist do we ever meet such perfect indifference concerning the result of a test and this absence of any prediction about the meaning of this result when it comes to comparing a law predicted by a theory with the facts? The physicist knows quite well that strict logic absolutely allows him only this indifference and that it authorizes no hope of agreement between theoretical prophecy and the facts; nevertheless, he waits for this agreement, counts on it, and regards it as more probable than the refutation. The probability that he attributes to it is so much the greater as the theory subjected to the test is more perfect; and when he lends his confidence to a theory in which numerous experimental laws have found a satisfactory representation, this probability seems to him to verge on certainty.

None of the rules governing the handling of experimental method justify this confidence in the theory’s foreknowledge, and yet this confidence does not seem ridiculous to us. Furthermore, if we harbored some intention to condemn its presumption, the history of physics would surely not take long to compel us to modify our judgment; indeed, it would cite innumerable circumstances in which experiment confirmed down to the smallest details the most surprising predictions of theory.

Why then can the physicist, without exposing himself to ridicule, assert that experiment will disclose a certain law because his theory demands the reality of this law, whereas the conchologist would be ridiculous if the mere presence of an empty compartment in his cabinet drawers devoted to the various colors of the spectrum led him to conclude there are blue sea shells in the ocean? Obviously because the classification of this collector is a purely arbitrary system not taking into account the real affinities among the various groups of mollusks, whereas in the physicist’s theory there is something like a transparent reflection of an ontological order.

Everything, therefore, urges the physicist to postulate the following assertion: To the extent that physical theory makes progress, it becomes more and more similar to a natural classification which is its ideal end. Physical method is powerless to prove this assertion is warranted, but if it were not, the tendency which directs the development of physics would remain incomprehensible. Thus, in order to find the title to establish its legitimacy, physical theory has to demand it of metaphysics.


A slave to positive method, the physicist is like the prisoner of the cave: * the knowledge at his disposal allows him to see nothing except a series of shadows in profile on the wall facing him; but he surmises that this theory of silhouettes whose outlines are shadowy is only the image of a series of solid figures, and he asserts the existence of these invisible figures beyond the wall he cannot scale.

So the physicist asserts that the order in which he arranges mathematical symbols in order to constitute a physical theory is a clearer and clearer reflection of an ontological order according to which inanimate things are classified. What is the nature of this order whose existence he asserts? Through what sort of affinity do the essences of the objects coming under his observation approach one another? These are questions he is not allowed to answer. By asserting that physical theory tends toward a natural classification in conformity with the order in which the realities of the physical world are arranged, he has already exceeded the limits of the domain in which his methods can legitimately be exercised; all the more reason why this method cannot disclose the nature of this order or tell what it is. To make out the nature of this order exactly is to define a cosmology; to display it to us is to expound a cosmological system; in both cases it is doing the work not essential to the physicist but to the metaphysician.

The methods by which the physicist develops his theories are without force when it comes to proving that a certain proposition of cosmology is true or false; the propositions of cosmology, on the one hand, and the theorems of theoretic physics, on the other hand, are judgments never bearing on the same terms; being radically heterogeneous they can neither agree with nor contradict one another.

Does it follow that the knowledge of physical theory is useless to anyone working for the progress of cosmology? That is the question we should like to examine now.

First, let us make very clear the precise meaning of this question.

We are not asking whether the cosmologist can without harm be ignorant of physics; the answer to that question would be too obvious, for it is very plain that a cosmological system cannot he reasonably constituted without any knowledge of physics.

* See Plato, Republic, Book VII

The reflections of the cosmologist and the physicist have a common starting point, namely, the experimental laws disclosed by observation applied to the phenomena of the inanimate world. Only the direction they follow after leaving from that point distinguishes the inquiries of the physicist from those of the cosmologist. The former wishes to acquire a knowledge of the laws he has discovered that is increasingly more precise and detailed, but the latter analyzes these same laws in order to lay bare when possible the essential relations they manifest to our reason.

For example, if the physicist and the cosmologist study at the same time the laws of chemical combination, the physicist will wish to know very exactly what the proportion is among the masses of the bodies entering into combination, under what conditions of temperature and pressure the reaction may take place, and how much heat is involved. The preoccupation of the cosmologist will be quite different: observation shows him that certain bodies, viz., the elements in the combination have at least apparently ceased to be, and that a new body, viz., the chemical compound, has appeared; the philosopher will strive to conceive what this change of mode of existence really consists in. Do the elements really subsist in the compound? Or do they persist in it only potentially? Such are the questions he will wish to answer.

Will the details which the physicist will have determined by his numerous and precise experiments all be useful to the philosopher? Undoubtedly not; discovered in order to satisfy a desire for detailed precision, a good number of these details will remain useless in an inquiry solicited by other needs. But will all these details be idle for the cosmologist? It would be odd if this were so, if certain facts did not serve to suggest an answer to some one of the problems which preoccupy the philosopher. When the latter for instance, attempts to pierce the mystery concealing from him the real state of the elements within the chemical compound, should he not take any account, in his attempts at solution, of certain precise details acquired by the work of the laboratories? Do not laboratory analyses proving that we can always obtain from a compound the elements which went into forming it, without the slightest loss or gain of matter, provide a basis, valuable in its rigor and solidity, for the doctrine which the cosmologist tries to constitute?

There is no doubt then that the knowledge of physics can be useful and even indispensable for the cosmologist. But physical science is composed of an intimate blend of two sorts of elements: one of these is a set of judgments whose subjects are objective realities; the other is a system of signs serving to transform these judgments into mathematical propositions. The first element represents the share of observation, the second the contribution of theory. Now, if the first of these two elements is manifestly useful to the cosmologist, it may well seem possible that the second is of no use to him, and that he must know it only in order not to confuse it with the first and never to depend on its help prematurely.

This conclusion would certainly be correct if physical theory were only a system of symbols arbitrarily created in order to arrange our knowledge according to a quite artificial order, and if the classification it establishes among experimental laws had nothing in common with the affinities unifying respectively the realities of the inanimate world.

The case is quite different if physical theory has as its limiting form a natural classification of experimental laws. There would be a very exact correspondence between this natural classification or physical theory, after it had reached its highest degree of perfection, and the order in which a finished cosmology would arrange the realities of the world of matter; consequently, the more physical theory, on the one hand, and cosmology, on the other, approach each other in their perfect form, the more clear and detailed should be the analogy of these two doctrines.

Thus, physical theory can never demonstrate or contradict an assertion of cosmology, for the propositions constituting one of these doctrines can never bear on the same terms which the propositions forming the other do, and between two propositions not bearing on the same terms there can be neither agreement nor contradiction. However, between two propositions bearing on terms of different natures it is nevertheless possible that there would be an analogy, and it is such an analogy which ought to connect cosmology with theoretic physics.

It is thanks to this analogy that the systems of theoretic physics can come to the aid of progress in cosmology. This analogy may suggest to the philosopher a whole group of interpretations; its clear and tangible presence can increase the thinker’s confidence in a certain cosmological doctrine, and its absence put him on guard against another doctrine.

This appeal to analogy forms in many cases a valuable means of investigation or test, but it is well not to exaggerate its power; if at this point the words "proof by analogy" are uttered, it is well to determine their meaning exactly and not to confuse such a proof with a genuine logical demonstration. An analogy is felt rather than concluded; it does not impose itself on the mind with all the weight of the principle of contradiction. Where one thinker sees an analogy, another, more keenly impressed by the contrasts between the terms compared than by their resemblances, may very well see opposition. In order to bring the latter to change his negation into an affirmation, the former cannot use the irresistible force of the syllogism; all he can do by his arguments is to attract the attention of his adversary to the similarities which he judges important and turn him away from the divergencies that he believes negligible. He can hope to persuade the person with whom he is arguing, but he cannot claim to convince him.

Another order of considerations also comes in to limit the range of the proofs in cosmology obtained from the analogy with physical theory.

We said that there ought to be an analogy between the metaphysical explanation of the inanimate world and the perfect physical theory arrived at the state of a natural classification. But we do not possess this perfect theory, and mankind will never possess it; what we possess and what mankind will always possess is an imperfect and provisional theory which by its innumerable gropings, hesitations, and repentances proceeds slowly toward that ideal form which would be a natural classification. Therefore, it is not physical theory as we have it but an ideal physical theory that we must compare with cosmology in order to support the analogy of the two doctrines. Now, for one who knows only what exists, how difficult it is to know what ought to exist! How doubtful and subject to caution his assertions are when he states that this doctrine is finally established in the theoretic system and will remain unshakable in the course of time, whereas that one is fragile and mutable and will be carried away by the next crop of new discoveries! Of course, in such a matter, we must not be astonished to hear physicists pronounce the most discordant opinions; and in order to choose among these opinions, we must not demand peremptory reasons, but be content with unanalyzable instinctive judgments which the mind of finesse will suggest, whereas the geometric mind will declare itself incapable of justifying them.

These few remarks suffice, we believe, to recommend to the cosmologist that he uses with extreme prudence the analogy between the doctrine he professes and physical theory; he should never forget that the analogy he sees most clearly may appear obscure to others to such an extent that they may cease having even a glimpse of it. He should fear above all that the analogy employed in favour of his proposed explanation connects this explanation merely with some provisional and shaky theoretic scaffolding rather than with a definitive and unshakable part of physics. Finally, he should keep in mind that any argument based on an analogy so difficult to judge is an infinitely frail and delicate argument, really incapable of refuting what a direct demonstration would have proven.

Here then are two points we may take as gained: The cosmologist may in the course of his reasoning employ analogy between physical theory and the philosophy of nature; he should employ this analogy only with extreme precautions.

The first precaution that the philosopher should take, before he makes too much of the analogy that his cosmology may have with physical theory, is to become very accurately and minutely acquainted with this theory. If he has merely a vague and superficial acquaintance with it, he will let himself be duped by similarities of detail, by accidental affinities, even by assonances of words which he will take as indications of a real and profound analogy. Only a science capable of penetrating theoretic physics to its most secret arcana and of laying bare its most intimate foundations will be able to put him on guard against these captious errors.

But it is not enough for the cosmologist to know very accurately the present doctrines of theoretic physics; he must also be acquainted with past doctrines. In fact, it is not with the present theory that cosmology should be analogous, but with the ideal theory toward which present theory tends by continual progress. It is not the philosopher’s task, then, to compare present-day physics to his cosmology by congealing science at a precise moment of its evolution, but rather to judge the tendency of theory and to surmise the goal toward which it is directed. Now, nothing can guide him safely in conjecturing the path that physics will take if not the knowledge of the road it has already covered. If we perceive in an instant’s glance an isolated position of the ball that a tennis player has hit, we cannot guess the end point he aimed at; but if our glance has followed the ball from the moment his hand moved to strike it, our imagination, prolonging the trajectory, marks in advance the point that will be struck. So the history of physics lets us suspect a few traits of the ideal theory to which scientific progress tends, that is, the natural classification which will be a sort of reflection of cosmology.

Consider someone, for instance, who would take physical theory just as we have it, in the year of grace 1905, presented by the majority of those who teach it. Anyone who would listen closely to the talk in classes and to the gossip of the laboratories without looking back or caring for what used to be taught, would hear physicists constantly employing in their theories molecules, atoms, and electrons, counting these small bodies and determining their size, their mass, their charge. By the almost universal assent favouring these theories, by the enthusiasm they raise, and by the discoveries they incite or attribute to them, they would undoubtedly be regarded as prophetic forerunners of the theory destined to triumph in the future. He would judge that they reveal a first draft of the ideal form which physics will resemble more each day; and as the analogy between these theories and the cosmology of the atomists strikes him as obvious, he would obtain an eminently favourable presumption for this cosmology. How different his judgment will be if he is not content with knowing physics through the gossip of the moment, if he studies deeply all its branches, not only those in vogue but also those that an unjust oblivion has let be neglected, and especially if the study of history by recalling the errors of past centuries puts him on his guard against the unreasoned exaggerations of the present time!

Well, he will see that the attempts at explanation based on atomism have accompanied physical theory for the longest time; whereas in physical theory he will recognize a work produced by the power of abstraction, these attempts at explanation will show themselves to him as the efforts of the mind that wishes to imagine what ought to be merely conceived; he will see them constantly being reborn, but constantly aborted; each time the fortunate daring of an experimenter will have discovered a new set of experimental laws, he will see the atomists, with feverish haste, take possession of this scarcely explored domain and construct a mechanism approximately representing these new findings. Then, as the experimenter’s discoveries become more numerous and detailed, he will see the atomist’s combinations get complicated, disturbed, overburdened with arbitrary complications without succeeding, however, in rendering a precise account of the new laws or in connecting them solidly to the old laws; and during this period he will see abstract theory, matured through patient labor, take possession of the new lands the experimenters have explored, organize these conquests, annex them to its old domains, and make a perfectly coordinated empire of their union. It will appear clearly to him that the physics of atomism, condemned to perpetual fresh starts, does not tend by continued progress to the ideal form of physical theory; whereas he will surmise the gradually complete realization of this ideal when he contemplates the development which abstract theory has undergone from Scholasticism to Galileo and Descartes; from Huygens, Leibniz and Newton to D’Alembert, Euler, Laplace, and Lagrange; from Sadi Carnot and Clausius to Gibbs and Helmholtz.


Before proceeding further, let us summarize what we have gained above: Between the ideal forms toward which physical theory and cosmology slowly travel, there ought to be an analogy. This assertion is by no means a consequence of positive method; although it is imposed on the physicist, it is essentially an assertion of metaphysics.

The intellectual procedure through which we judge the more or less broad analogy existing between a physical theory and a cosmological doctrine is quite distinct from the method through which convincing demonstrations are developed; they do not impose themselves.

This analogy should connect natural philosophy not to the present state of physical theory but to the ideal form toward which it tends. Now, this ideal state is not given in a plain and indisputable manner; it is hinted to us by an infinitely delicate and volatile intuition, whereas the analogy is guided by a profound knowledge of theory and its history.

The sorts of information which the philosopher can obtain from physical theory, either in favor of or against a cosmological doctrine, are therefore scarcely outlined indications; he would be very foolish who would take them as certain scientific demonstrations and be astonished to see them discussed and disputed!

After having thus definitely affirmed how much any comparison between a physical theory and a cosmological demonstration differs from a demonstration proper, after having indicated that it leaves plenty of room for hesitation and doubt, we shall be permitted to indicate the present form of physical theory which appears to us to tend toward the ideal form, and the cosmological doctrine which seems to us to have the strongest analogy with this theory. We do not maintain that this indication is to be given in the name of the positive method belonging to the physical sciences; after what we have said, it is obviously clear that it goes beyond the scope of this method, and that this method can neither confirm nor contradict it. In so doing, in penetrating thereby the domain belonging to metaphysics, we know that we have left the domain of physics behind us; we know that the physicist, after having gone along with us through the latter domain, may very well refuse to follow us into the terrain of metaphysics without violating logically imposed rules.

Which among the various ways, unequally favored by men of science, of dealing with physical theory at present is the one carrying the germs of the ideal theory? Which one already offers us through the order in which it arranges experimental laws something like a sketch of a natural classification? This theory, we have very often said, is in our opinion the one called general thermodynamics.

This judgment is dictated to us by the contemplation of the present state of physics and by the harmonious whole formed by general thermodynamics out of the laws discovered and made precise by experimenters; it is dictated to us, above all, by the history of the evolution which has led physical theory to its present state.

The movement through which physics has evolved may actually be decomposed into two other movements which are constantly superimposed on one another. One of the movements is a series of perpetual alternations in which one theory arises, dominates science for a moment, then collapses to be replaced by another theory. The other movement is a continual progress through which we see created across the ages a constantly more ample and more precise mathematical representation of the inanimate world disclosed to us by experiment.

Now, these ephemeral triumphs followed by sudden collapses making up the first of these two movements are the successes and reverses which have been experienced by the various mechanistic physical systems in successive roles, including the Newtonian physics as well as the Cartesian and atomistic physics. On the other hand, the continual progress constituting the second movement has resulted in general thermodynamics; in it all the legitimate and fruitful tendencies of previous theories have come to converge. Clearly, this is the starting point, at the time we live in, for the forward march which will lead theory toward its ideal goal. Is there a cosmology which may be analogous to this ideal we glimpse at the end of the road where general thermodynamics engages physical theory? Surely it is not the ancient cosmology of the atomists any more than it is the natural philosophy created by Descartes, or the doctrine of Boscovich inspired by the ideas of Newton. On the contrary, it is a cosmology to which general thermodynamics is unmistakably analogous. This cosmology is the Aristotelian physics; and this analogy is all the more striking for being less anticipated and for the fact that the creators of thermodynamics were strangers to Aristotle’s philosophy.

The analogy between general thermodynamics and the physics of the Aristotelian school is marked by many a characteristic whose prominence attracts one’s attention from the start.

Among the attributes of substance, equal importance is conferred by Aristotelian physics on the categories of quantity and quality; now, through its numerical symbols, general thermodynamics represents the various magnitudes of quantities and the various intensities of qualities as well.

Local motion was for Aristotle only one of the forms of general motion, whereas the Cartesian, atomistic, and Newtonian cosmologies agree in that the only motion possible is change of place in space. And notice that general thermodynamics deals in its formulas with a host of modifications such as variations in temperature or changes in electrical or magnetic state without in the least seeking to reduce these variations to local motion.

Aristotelian physics is acquainted with transformations still deeper than those for which it reserves the name of motions. Motion reaches only attributes; those transformations, viz., generation and corruption, penetrate to substance itself, creating a new substance at the same time that they annihilate a preexistent substance. Likewise, in the mechanics of chemistry, one of the most important chapters of general thermodynamics, we represent different bodies by masses which a chemical reaction may create or annihilate; within the mass of a compound body the masses of the components subsist only potentially. These features, and many others, that it would take too long to enumerate, strongly connect general thermodynamics with the essential doctrines of Aristotelian physics.

We say "with the essential doctrines of Aristotelian physics," and we must now emphasize this point.

Experimental science was in its infancy at the time when Aristotle built the impressive monument whose plan has been conserved for us in his Physics, On Generation and Corruption, On the Heavens, and Meteors; and at the time when his commentators, like Alexander of Aphrodisias, Themistius, Simplicius, Averroes, and innumerable scholastics, strove to chisel down and polish even the slightest portion of this enormous structure. The instruments which so greatly increase the extent, certainty, and precision of our means of knowing were not available to grasp material reality; man had only his naked senses; observable data came to him just as they appear first of all to our perception; no analysis had yet recognized and disentangled a frightful complication; facts, which a more advanced science was to consider as the results of a multitude of simultaneous, interlocked phenomena, were naively and hastily taken as the simple and elementary data of natural philosophy. The mark of everything which was incomplete, premature, and childish in this experimental science is necessarily in the cosmology which issues from it. One who hastily runs through the works of the Aristotelians and barely touches the surface of the doctrines expounded in these works notices everywhere strange observations, unimportant explanations, idle and fastidious discussions, in a word, an antique, worn out, deteriorated system in striking contrast with physics at present, so that it is only very remotely possible to recognize in them the slighest analogy with our modem theories.

Quite another impression is experienced by one who digs further. Under this superficial crust in which are conserved the dead and fossilized doctrines of former ages, he discovers the profound thoughts which are at the very heart of the Aristotelian cosmology. Rid of the covering bark which concealed them and at the same time held them in, those thoughts take on new life and movement; as they gradually become animated we see the mask of deterioration which disguised them disappear; soon their rejuvenated look and our general thermodynamics take on a striking resemblance.

He, then, who wishes to recognize the analogy of Aristotelian cosmology with theoretic physics today must not stop at the superficial form of this cosmology, but must penetrate to its deeper meaning.

An illustration may be brought in to clarify our thought and make it precise.

We shall borrow this illustration from one of the essential theories of Aristotle’s cosmology, from the theory of the "natural place of the elements"; and we shall consider this theory on the surface, first of all, and, so to speak, from the outside.

In all bodies we always meet, although in various degrees, four qualities: the hot and the cold, the dry and the wet. Each of these qualities characterizes essentially one element: fire is eminently the hot element; air, the cold element; earth, the dry element; and water, the wet one. All the bodies surrounding us are mixtures; to the extent to which each of the four elements, fire, air, water, and earth, enter into the composition of a mixture, it is hot or cold, dry or wet. Beyond these four elements, capable of being transformed into one another by corruption and generation, there exists a fifth essence, incorruptible and nongenerative; this essence forms the celestial orbs and the stars which are condensed portions of these orbs.

Each of the elements has a "natural place"; it remains at rest when it is in this place, but when it is removed from it by "violence," it returns to it by a "natural motion."

Fire is essentially light; its natural place is the concavity of the moon’s orb; by natural motion then it rises until it is stopped by this solid vault. Earth is the distinctively heavy element; its natural motion carries it to the center of the world which is its natural place. Air and water are heavy, but less heavy than earth; now, by natural motion the heavier tends to be placed below the lighter; the various elements will therefore be in their natural places when three spherical surfaces concentric with the universe separate water from earth, air from water, and fire from air. What maintains each element in its natural place when it is placed there? What carries it toward this place when it is removed from it? Its substantial form. Why? Because every being tends toward its perfection and in this natural place its substantial form attains its perfection; there it best resists anything which might corrupt it; there it experiences in the most favorable manner the influence of the celestial motions and astral light, the sources of all generation and of all corruption within sublunary bodies.

How childish all this theory of the heavy and the light seems to us! How plainly we recognize the first babblings of human reason trying to give an explanation of falling bodies! How dare we establish the slightest connection between these babblings of an infant cosmology and the admirable development of a science come to full vigor in the celestial mechanics of minds like those of Copernicus, Kepler, Newton, and Laplace?

Of course, no analogy appears between physics today and the theory of natural place, if we take this theory as it appears at first sight with all the details making up its external form. But let us now remove these details and break this mould of outworn science into which the Aristotelian cosmology had to be poured; let us go to the bottom of this doctrine in order to grasp the metaphysical ideas which are its soul. What do we find truly essential in the theory of the natural place of the elements?

We find there the affirmation that a state can be conceived in which the order of the universe would be perfect, that this state, would be a state of equilibrium for the world, and what is more, a state of stable equilibrium; removed from this state, the world would tend to return to it, and all natural motions, all those produced among bodies without any intervention of an animated mover, would be produced by the following cause: they would all aim at leading the universe to this ideal state of equilibrium so that this final cause would be at the same time their efficient cause.

Now, opposite this metaphysics, physical theory stands, and here is what it teaches us: If we conceive a set of inanimate bodies which we suppose removed from the influence of any external body, each state of this set corresponds to a certain value of its entropy; in a certain state, this entropy of the set would have a value greater than in any other state; this state of maximum entropy would be a state of equilibrium and, moreover, of stable equilibrium; all motions and all phenomena produced within this isolated system make its entropy increase; they therefore all tend to lead this system to its state of equilibrium.

And now, how can we not recognize a striking analogy between Aristotle’s cosmology reduced to its essential affirmations and the teachings of thermodynamics?

We might multiply comparisons of this kind, and they would authorize, we believe, the following conclusion: If we rid the physics of Aristotle and of Scholasticism of the outworn and demoded scientific clothing covering it, and if we bring out in its vigorous and harmonious nakedness the living flesh of this cosmology, we would be struck by its resemblance to our modern physical theory; we recognize in these two doctrines two pictures of the same ontological order, distinct because they are each taken from a different point of view, but in no way discordant.

It will be said that a physics whose analogy with the cosmology of Aristotle and Scholasticism is so clearly indicated, is the physics of a believer. Why? Is there anything in the cosmology of Aristotle and in that of Scholasticism which implies a necessary adherence to Catholic dogma? May not a nonbeliever as well as a believer adopt this doctrine? And, in fact, was it not taught by pagans, by Moslems, by Jews, and by heretics as well as by the faithful children of the Church? Where then is there that essentially Catholic character with which it is said to be stamped? Is it in the fact that a great number of Catholic doctors, some of the most eminent ones, have worked for its progress? In the fact that a Pope not long ago proclaimed the services that the philosophy of Saint Thomas Aquinas formerly rendered science as well as those that it may render it in the future? Does it follow from these facts that the nonbeliever cannot, without subscribing to a faith not his own, recognize the agreement of Scholastic cosmology with modern physics? Certainly not. The only conclusion that these facts impose is that the Catholic Church has on many occasions helped powerfully and that it still helps energetically to maintain human reason on the right road, even when this reason strives for the discovery of truths of a natural order.

Now, what impartial and enlightened mind would dare to testify falsely against this affirmation?