In his 1900 lecture ?On the Principles of Mechanics,? Poincar? imagined the following fable (1900b, p. 480; 1902, p.131): imagine beings living on an imaginary cloudy planet. They can never see the stars and therefore may think that their planet is the only object in the universe. How can they find out whether their planet rotates or stands still? Poincar? answers that for these beings the two conventions; ?the earth turns round? (Copernican) and ?the earth does not turn round? (Ptolemaic) are equivalent. Therefore no absolute motion can exist. Poincar? seemed to have been inspired by Mach's ideas towards offering his conventionalist above point of view (see Mawhin, 1995). Mach protested against Newton's interpretation to his famous bucket experiment in terms of absolute motions and space. He philosophically demonstrated relative motions by stating the logical equivalence of the Copernican and Ptolemaic systems. However, unlike Mach, Poincar? examined the experimental equivalence of the two conventions for beings living in the cloudy planet. According to Poincar?, beings living in the cloudy planet and performing experiments in order to discover whether their planet turns round or stands still, would always find out that the two conventions are completely experimentally equivalent. As a result of this suggestion, Poincar? had to philosophically and physically respond to a realist understanding by his audience over the years of the above conventionalist position: imagining a being standing outside Poincar?'s cloudy world and knowing that thick clouds forever cover this planet, he could readily choose between the two conventions, and he might conclude that the earth rotates or else stands still with respect to absolute space. Therefore, Poincar?'s audience could not have accepted his reasoning.
In this paper I demonstrate that in light of Poincar?'s special efforts to save his conventionalist view, he himself was also eventually not persuaded by his own arguments. He probably understood very well that his conventionalism was open to a kind of criticism regarding the possibility of the existence of an external being (standing outside his cloudy planet) for whom conventionalism did not hold any more. This criticism was embodied in the na?ve and realist response of Poincar?'s audience to his explanations. Poincar?'s last resource was therefore the ether: the cloudy planet does not rotate with respect to absolute space but with respect to the ether. In my previous paper, ?What characterizes Poincar?'s ether?? I characterized Poincar?'s obscure notion of the ether, which is based on Lorentz's stationary ether. I start this paper by analyzing Newton's famous bucket experiment and Mach's solution in terms of relative motions. I then trace Poincar?'s response to Mach's ideas and, his inner struggles and special efforts to save his conventionalist view.
