To Save the Phenomena

An Essay on the Idea of Physical Theory from Plato to Galileo

Pierre Duhem, Edmund Dolan, Chaninah Maschler

• Publisher: University of Chicago Press
• Year: 2015
• ISBN:
  9780226381657
• Topic: Scienze biologiche
• Subtopic: Scienza generale

Duhem's 1908 essay questions the relation between physical theory and metaphysics and, more specifically, between astronomy and physics–an issue still of importance today. He critiques the answers given by Greek thought, Arabic science, medieval Christian scholasticism, and, finally, the astronomers of the Renaissance.

1

Greek Science

To find the origin of the tradition whose course we mean to follow we must go back to Plato.

The transmission and application of his opinions concerning astronomical hypotheses Plato owes in the first instance to Eudoxus. Next, Eudemus, an immediate disciple of Aristotle, drawing on Eudoxus’ writings, reported Plato’s views in the second book of his History of Astronomy. It was from this book that Sosigenes, the philosopher and astronomer who later became Alexander of Aphrodisias’ teacher, borrowed them and passed them on to Simplicius. And it is from Simplicius that we have our report.⁴

In Simplicius’ Commentary we find the Platonic tradition formulated in the following terms:

Plato lays down the principle that the heavenly bodies’ motion is circular, uniform, and constantly regular.⁵ Thereupon he sets the mathematicians the following problem: What circular motions, uniform and perfectly regular, are to be admitted as hypotheses so that it might be possible to save the appearances presented by the planets? (τίνων ύποτέθεντων δι’ ὁμαλῶν καί ἐγκυκλιῶν καί τεταγμένων κινὴσεων δυνὴσεται διασωθῆναι τά περί τούς πλανωμένους Φαινόμενα;)

The object of astronomy is here defined with utmost clarity: astronomy is the science that so combines circular and uniform motions as to yield a resultant motion like that of the stars. When its geometric constructions have assigned each planet a path which conforms to its visible path, astronomy has attained its goal, because its hypotheses have then saved the appearances.

This is the problem that challenged the efforts of Eudoxus and Calippus: it was to save the appearances (σώζειν τά Φαινόμενα) that they combined their hypotheses. When Calippus modified the combination of homocentric spheres proposed by Eudoxus in certain particulars, he did so solely because the hypotheses of his predecessor did not accord with certain phenomena, and he was determined that these phenomena too should be saved.

The astronomer must declare himself fully satisfied when the hypotheses he has combined succeed in saving the apparances. But may human reason not fairly ask for more? Does it not have the power to discover and analyze some of the characteristics of the nature of the heavenly bodies? And might not these characteristics help him by pointing out certain types to which astronomical hypotheses should of necessity conform? And should not a combination of movements that cannot conform to any of these types therefore be declared unacceptable, though this very some combination would save the appearances?⁶

Along with the method of the astronomer, so clearly defined by Plato, Aristotle admits the existence and legitimacy of another such method: he calls it the method of the physicist.

In the Physics,⁷ Aristotle compares the methods of the mathematician and the physicist and lays down certain principles which have direct bearing on the question we just raised, though his remarks do not allow us to push analysis very far. Geometers and physicists, he says, frequently study the same object, whether it be the same figure or the same movement, but they regard the object from different points of view. A particular figure, a movement—the geometer views these “by themselves,” abstractly; the physicist, by contrast, studies them as the limit of such and such a body, the movement of such and such a moving thing.

This rather vague teaching does not allow us fully to grasp Aristotle’s thought concerning the method of the astronomer and the method of the physicist. Really to penetrate his thought we must examine how he put this conception to work in his writings.

Eudoxus, Aristotle’s predecessor by a few years, whose theories he studied assiduously, and Calippus, his contemporary and friend, had followed the method of the astronomer, exactly as defined by Plato. This method was, then, perfectly familiar to Aristotle. Yet he, for his part, followed another. Aristotle requires that the universe be a sphere, that the celestial spheres be hard, that each of them have a circular and uniform motion around the world’s center, and that this center be occupied by the earth, an immobile earth. These were so many restrictive conditions that he imposed upon the hypotheses of astronomers, and he would not have hesitated to reject a combination of motions that presumed to dispense with any of them. Yet it was not because he considered them indispensable to saving the appearances registered by observers that he laid down these limiting conditions, but because according to him they alone were compatible with the perfection of the material of which the heavens are formed and with the nature of circular motion. While Eudoxus and Calippus, employing the method of the astronomer, controlled their hypotheses by examining whether or not they save the appearances, Aristotle wants to govern the choice of these hypotheses by propositions that are the outcome of certain speculations about the nature of heavenly bodies. His is the physicist’s method.

What is the point of introducing this new method alongside the method of the astronomer, since it merely attempts to solve the astronomer’s problem by another route? If the astronomer’s procedure were capable of providing an altogether unambiguous answer to the question posed by Plato, one might well doubt that there was any gain. But if this is not how things stand, if it should turn out that the appearances can be saved by various combinations of circular and uniform motions, how then are we to choose from among these different, yet to the astronomer equally satisfactory, hypotheses? Must we in that case not appeal to the ruling of the physicist to make our selection, and would that not tend to show that the physicist’s method is the indispensable complement to the method of the astronomer?

Now in point of fact the appearances can be saved by means of different combinations of circular and uniform motions, and the geometric acumen of the Greeks was far too developed for this truth to remain hidden from them for very long: Even very old astronomical systems, like that of Philolaus, for example, could only have germinated in minds thoroughly convinced of this principle: that the same relative motion can be obtained from different absolute motions.

In any case, one circumstance soon enforced an exceptionally clear realization of the truth that different hypotheses may render the phenomena equally well: This circumstance presented itself in the course of Hipparchus’ investigations.

What Hipparchus proved was that the course of the sun can be represented either by supposing that this star describes a circle eccentric to the world, or by letting it be carried by an epicycle, provided the revolution of this epicycle is achieved in exactly the same time in which its center has completed a circle concentric with the world.

Hipparchus seems to have been very much struck by the agreement between the results of two such very different hypotheses. Adrastus of Aphrodisias, whose teachings have been preserved for us by Theon of Smyrna, records how Hipparchus felt about his own discovery:

Hipparchus singled out as deserving the mathematician’s attention the fact that one may try to account for phenomena by means of two hypotheses as different as that of eccentric circles and that which uses concentric circles bearing epicycles.⁸

Certainly, there is only one hypothesis that agrees with the nature of things (κατά Φύσιν). Every astronomical hypothesis that saves the appearances is in harmony with this single hypothesis to the extent that the propositions entailed by it match the results of observation. This is what the Greeks meant when, speaking of different hypotheses which yielded the same resultant motion, they said that they agreed among themselves “accidentally” (κατά συμβεβηκός):

It is obviously consistent with reason that there be agreement between the two mathematical hypotheses—the epicyclic and the eccentric—concerning the stellar movements. Both agree accidentally with the one that conforms to the nature of things, and this is what Hipparchus marveled at.⁹

Which one of these different hypotheses, “accidentally” in agreement with each other, one saving the phenomena as well as the other and therefore, in the eyes of the astronomer, equivalent, conforms to nature? It is for the physicist to decide. If we are to believe Adrastus,¹⁰ Hipparchus, more competent in astronomy than in physics, was incapable of making such a decision:

It is clear, for the reasons set forth, that, of the two hypotheses, each of which is a consequence of the other, the epicyclic appears to be the more common, more generally accepted, and better conformed to the nature of things. For the epicycle is a great circle of a rigid sphere, namely, that circle which the planet traces out as it moves on the sphere, whereas the eccentric is altogether different from the circle which conforms to nature, and it is traced out only “accidentally.” Hipparchus, convinced that this is how the phenomena are brought about, adopted the epicyclic hypothesis as his own and says that it is likely that all the heavenly bodies are uniformly placed with respect to the center of the world and that they are united to it in a similar way. Not being sufficiently knowledgeable in physics, however, he did not distinguish properly between the true movement of the stars, which conforms to the nature of things, and their accidental movement, which is only an appearance. Nonetheless, in principle he holds that the epicycle of each planet moves along a concentric circle and that the planet moves along the epicycle.

By proving that two distinct hypotheses can agree “accidentally” and save the appearances of the solar movement equally well, Hipparchus greatly contributed to a more exact delimitation of the scope of astronomical theories. Adrastus set about proving that the eccentric hypothesis is entailed by the epicyclic;¹¹ Theon proved that the epicyclic hypothesis can, inversely, be considered a consequence of the eccentric hypothesis. These propositions, according to him, point up the impossibility of astronomy’s ever discovering the true hypothesis, the one which conforms to the nature of things:

No matter which hypothesis is settled on, the appearances will be saved. For this reason we may dismiss as idle the discussions of the mathematicians, some of whom say that the planets are carried along eccentric circles only, while others claim that they are carried by epicycles, and still others that they move around the same center as the sphere of the fixed stars. We shall demonstrate that the planets “accidentally” describe each of these three kinds of circles—a circle around the center of the universe, an eccentric circle, and an epicyclic circle.¹²

If the decision that determines the true hypothesis escapes the competence of the astronomer, who attempts only to combine the abstract figures of the geometer and to compare them with the appearances reported by observers, it must then be reserved for the physicist, the man who has meditated on the nature of the heavenly bodies. He alone is competent to lay down the principles by means of which the astronomer will discern the one true hypothesis amidst the several suppositions that equally save the phenomena. This is precisely what the Stoic Posidonius asserted in his Meteorology. Geminus, in an abridged commentary on this work, reported Posidonius’ doctrine; and Simplicius, for the purpose of clarifying Aristotle’s comparison between the mathematician and the physicist, reproduces the passage from Geminus. It runs as follows:¹³

To physical theory (φυσικῆς θεωρίας) belongs the study of all that concerns the essence of the heavens and the stars, their power, their quality, their generation and destruction. And, by Zeus, physics also has the power of providing demonstrations concerning the size, shape, and arrangement of these bodies. Astronomy, on the other hand, is not prepared to say anything about the former. Its demonstrations concern the order of the heavenly bodies, taking it for granted that the heavens are truly ordered. Astronomy speaks of the shapes, sizes, and relative distances of the earth, the sun, and the moon. It speaks of eclipses, the conjunction of stars, the qualitative and quantitative properties of their movements. Now since astronomy depends on the study which considers figures in terms of quality, size, and number, it is quite right that it should require the assistance of arithmetic and geometry. And in dealing with these things, the only ones on which it is authorized to speak, astronomy must conform to arithmetic and geometry. It happens frequently that the astronomer and the physicist take up the same subject—for instance, they set out to prove that the sun is large or that the earth is round. But in such a case they do not proceed in the same way: The physicist must demonstrate every single one of his propositions by deriving it from the essence of bodies, or from their power, or from what best accords with their perfection, or from their generation and their transformation. The astronomer, on the other hand, establishes his propositions by means of “what goes with” magnitudes and figures, or by means of the magnitude of the motion in question, or the time that corresponds to it. Often the physicist will fasten on the cause and direct his attention to the power that produces the effect he is studying, while the astronomer draws his proofs from circumstances externally related to that same effect. The astronomer is not equipped to contemplate causes, unable to tell us, for instance, what cause is responsible for the spherical shape of the earth and the stars. Sometimes, as for instance when he reasons about eclipses, he does not even try to lay hold of a cause. At other times he feels obliged to posit certain hypothetical modes of being which are such that, once conceded, the phenomena are saved (καθ’ ύπόθεσιν εύρίσκει τρόπους τινάς άποδιδούς ὧν ύπαρχόντων σωθήσεται τά φαινόμενα). For example, the astronomer asks why the sun, the moon, and the other wandering stars seem to move irregularly. Now, whether one assumes that the circles described by the stars are eccentric or that each star is carried along by the revolution of an epicycle, on either supposition the apparent irregularity of their course is saved. The astronomer must therefore maintain that the appearances may be produced by either of these modes of being (τρόπους); consequently his practical study of the movement of the stars will conform to the explanation he has presupposed. This is the reason for Heraclides Ponticus’ contention that one can save the apparent irregularity of the motion of the sun by assuming that the sun stays fixed and that the earth moves in a ...