Incompatible data in Galileo's argumentation
It remains to know why, given these solutions and patterns of engagement, Galileo failed to resort to solution 2', in other words to persuade his opponents of the rationality of the heliocentric system, correlated with a metaphoric understanding of some passages in the Biblical text. One currently held view consists in indicating that Galileo's argument could not prevail because, according to the scientific standards of the times, it was neither rational nor scientific. The analysis below is based on science philosopher Paul Feyerabend's[1] Against Method and more specifically on the relation between theoretical and observed circularity.
According to then prevailing Aristotelian physics, if the earth spinned, the impact of a stone dropped from a tower should not be at the bottom of the tower but a little further due to the earth's motion during the time taken by the stone to fall. This is not the case, furnishing Galileo's contemporaries with one of their most compelling arguments in favour of the geocentric system. In order to counter this argument, Galileo developed a new theory of inertia fit to explain why the stone falls at the foot of the tower even if the earth rotates. But how is this new concept of inertia demonstrated? In that, accepting the Copernician theory, the stone dropped from a tower can be observed to reach the ground at the bottom of the tower. But why accept the Copernician theory? Because once the concept of inertia is accepted, the Copernician model predicts that the stone falls at the foot of the tower. The acceptation of one of the two theories thus depends on the acceptation of the other in order to explain a phenomenon that, in itself, poses no problem in the Ptolemaic system.
Aristotelian physics made a fundamental distinction between sublunary[2] and supralunary[3] spheres. The laws of physics operating in the sublunary sphere, where the rather chaotic movement of objects were deemed to have nothing to do with the eternal laws governing planets and fixed stars. With his spyglasses, which worked to perfection in the sublunary sphere, Galileo wanted to breach this limit and prove some celestial facts. His approach ran as follows: why should one believe that they would be a reliable instrument in the observation of the supralunary sphere? Because, answered Galileo, the spyglasses confirm the Copernician theory. But why should one subscribe to the Copernician theory? Because the spyglasses confirm it. Coincidentally, the sketches Galileo drew of the moon surface and of its craters thanks to the spyglasses do not look like the moon surface as it can now be observed thanks to modern technology.
Furthermore, it must be noted that in the Dialogue, Galileo mentions none of the most advanced geocentric models of his age, such as Tycho Brahe's[4], even though he knew of them. Now, those aimed to explain some observations Galileo used as proof of heliocentrism. For good measure, as early as 1616, he bolstered his theory with his explanation of the tides. But as his contradictors pointed out, the data provided could only explain one tide a day, which did not satisfactorily account for the facts.
The challenge taken up by Galileo, after Copernicus, was considerable: it took no small conviction to insist, in the face of common perception, that the earth rotated. Galileo relied on a circular argumentation, he put forward observations of questionable value (spyglasses) or even disproved by experience (two tides) and he infringed basic methodological norms (expunging Tycho Brahe's arguments, inaccurate drawings of the lunar surface). Brought into the power relation structure in which this affair took place, these factors explain why a fair number of his colleagues did not follow the mathematician of the Great Duchy of Tuscany. Leaving aside the issue of the greater validity of the heliocentric system over the geocentric one, it was more sensible, nay more scientific at the time not to follow Galileo.
