Reality Or Mathematical Fiction

Greek geometrical astronomy is accurately characterized as showing a lack of concern with the physics of the problem of planetary motions and a preoccupation with the mathematics. Given the general acceptance of Aristotle's division between physics and mathematics, and the placement of astronomy within mathematics, it could scarcely have been otherwise.

Some historians and philosophers of science imagine that it was even more. They believe that the models of planetary motions constructed by Greek geometrical astronomers were intended as purely calculating devices having nothing to do with any underlying physical reality. It is easy to agree with this opinion. It is correspondingly difficult to believe in the reality of a universe composed of planets attached to epicycles, themselves rotating uniformly, and also carried about apparently irregularly by eccentric circles actually rotating uniformly around equant points located other than at their centers.

The idea of instrumentalism runs through the history of Greek geometrical astronomy. In the instrumentalist view of the relationship between theory and observation, known empirical data are suspended and the study then becomes one of pure geometry, not solving but still relevant to the astronomical problem. All that remains are simple mathematical fictions and pure conceptions, with no question of their being true or in conformity with the nature of things or even probable. For so-called instrumentalists, it is enough that a scientific theory yields predictions corresponding to observations. Theories are simply calculating devices.

Realists, on the other hand, insist that theories pass a further test: that they correspond to underlying reality. For realists, Greek geometrical astronomers were describing concrete bodies and movements that actually were accomplished. Realists believe that scientific theories are descriptions of reality. Dogmatic realists insist on the truth of a theory. Critical realists concede a theory's conjectural character without necessarily becoming instrumentalists.

A disappointed realist may appear to be a local instrumentalist with regard to a particular failed theory retaining instrumental value but is far from becoming a global instrumentalist.

As early as the sixth century a.d. , Simplicius raised the issue of whether the astronomers' combinations of uniform circular motions were real or merely fictions:

But just as the stops and retrograde motions of the planets are, appearances notwithstanding, not viewed as realities . . . so an explanation which conforms to the facts does not imply that the hypotheses are real and exist. By reasoning about the nature of the heavenly movements, astronomers were able to show that these movements are free from all irregularity, that they are uniform, circular, and always in the same direction. But they have been unable to establish in what sense, exactly, the consequences entailed by these arrangements are merely fictive and not real at all. So they are satisfied to assert that it is possible, by means of circular and uniform movements, always in the same direction, to save the apparent movements of the wandering stars. (Duhem, To Save the Phenomena, 23)

Simplicius was considering instances in which the apparent movements were saved. Even stronger candidates for the merely fictive are planetary models that overlooked or ignored known phenomena. Because Eudoxus did not take into account changing distances, some historians and philosophers of science have concluded that his planetary theory was merely a calculating device that had nothing to do with underlying physical realities. It was not true or in conformity with the nature of things or even probable; it was a mathematical fiction. Geometers used it to render celestial motions accessible to their calculations. Hence, Eudoxus was an instrumentalist. Supposedly, scientific theories for him were simply instruments, or calculating devices.

Other historians and philosophers of science argue that Greek geometrical astronomers were describing concrete bodies and movements that actually occurred. Eudoxus's mathematical construction was a theory about the physical world. It was intended to discover and explain the real, rather than the apparent, movements of celestial bodies. Observations functioned as evidential controls on theory; astronomers tried to make the theory fit the observations. Indeed, Eudoxus's system could have been less complex had it been intended merely as a computational device. Hence, Eudoxus was a realist.

Historians and philosophers of science debate whether ancient Greek geometrical astronomers were instrumentalists or realists. A third possibility is that Eudoxus was neither a realist nor an instrumentalist. His system for saving the phenomena was far more than a mere calculating device but less than reality, at least the empirical reality of realists. Eudoxus was infatuated with Plato's paradigm and intellectually imprisoned by it in Plato's cave. He was neither a realist nor an instrumentalist, but a paradigm prisoner.

A modern example of the power of a paradigm or themata is provided by Einstein. He wrote: "I do not by any means find the chief significance of the

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