On the Determination of Planetary Distances in the Ptolemaic System

Abstract

In 1975, Imre Lakatos and Elie Zahar claimed that the determination of planetary distances represents excess empirical content of Copernicus’s theory over that of Ptolemy. This claim provoked an interesting discussion during the first half of the 1980s. The discussion started when Alan Chalmers affirmed that it is not correct to attribute this advantage to the Copernican system over the Ptolemaic. Other scholars criticized Chalmers’s assertion, reaffirming the position of Lakatos and Zahar: one went even further, asserting that Copernicus has not one but two methods for calculating distances, even though this claim was subsequently also criticized. But all participants assumed that Ptolemy has no method for calculating planetary distances. In this article, I argue that this is not correct. I argue, in fact, that Ptolemy has two independent methods for calculating the distances of some of the planets and, therefore, as far as the calculation of planetary distances is concerned, Ptolemy’s system surpasses that of Copernicus.

Acknowledgements

I would like to thank Dennis Duke and Ignacio Silva for reading previous drafts of this article and making helpful comments, and the two anonymous referees whose smart objections were very helpful for improving this article.

Notes

[1] There is a reference to this method in Lakatos and Zahar too. They assert in a footnote that ‘one may use also the Aristotelian “doctrine of plenitude” to arrive at distances; but this doctrine is again heuristically ad hoc, besides being both false and, within Ptolemy’s program, unfalsifiable’ (Lakatos and Zahar 1975, 379n72). But the horror vacui hypothesis is clearly not ad hoc in the sense of being postulated in order to obtain the distances. The reasons for its acceptance are previous and absolutely independent of others. Of course it is unfalsifiable if it is considered in isolation, but applied to the distances calculation method it becomes falsifiable. Finally, it is obviously false, but no one asks for a hypothesis to be true in order to be scientific. Cf. Thomason (1992, 187n25). Neither Chalmers in his two discussions, nor Curd, nor Hutchison mentioned Ptolemy’s methods.

[2] Hutchinson (1983, 370) quotes Neugebauer (1975, 146–147).

[3] See for example Riddell (1980, especially 131–137), who discusses with much detail many of the supposed Copernican advantages enumerated by Lakatos and Zahar (1975).