Galileo and prior philosophy
Introduction
The thought experiment by which Galileo destroyed the Aristotelian dogma that heavier bodies fall faster than lighter ones is a classic in the field. It sets the example, and as such it features prominently in all contemporary studies of scientific thought experiments (Brown, 1991b, Norton, 1991, Sorensen, 1992, Norton, 1996, McAllister, 1996, Gendler, 1998, Brown, 2000). However, as we will show, it does not attain the impeccable standard that is generally assumed. At first sight, it appears to refute the Aristotelian paradigm in a decisive and even awe-inspiring manner. But in fact it is flawed, both in its attempted refutation of the old, as in its attempted demonstration of the new ideas on falling bodies. One may therefore not cogently claim, as Brown and others have tried to do, that this thought experiment offers us a glimpse into a Platonic world of verities.
Let us begin with an adaptation of the thought experiment in question. Suppose we have two pieces of the same material but of different weight; a rock weighing 8 kilograms and another weighing only 4 kg. Suppose we drop them from a tower. Aristotle, who claims that the rate of fall of a body is proportional to its weight, must now infer that the heavier rock falls twice as fast as the lighter one, and thus takes half as much time to reach the ground. Suppose that we next pick up the two rocks, bind them together with a string, and drop this bound system from the tower. Then it can be shown that the Aristotelian system leads to a contradiction: on the one hand, the bound system must fall more slowly than the 8 kg piece, for the 4 kg rock, which Aristotle says has a natural tendency to fall slowly, will slow down the rock of 8 kg, which he claims to have a natural tendency to fall more quickly. Thus the time measured for the bound system to fall to the ground must be greater than that for the heavier piece alone. On the other hand, the bound system falls faster than the 8 kg rock, for weight is additive: the bound system weighs 12 kg and thus falls one-and-a-half times as fast as the 8 kg piece, and this contradicts the first conclusion. Galileo’s way out of this predicament is to reject the old idea that the rate of fall is proportional to the weight and replace it by a new claim, namely that all bodies fall at the same rate, independent of their weight.
It looks as though a pure thought experiment has destroyed an old belief and replaced it by new knowledge concerning the world, without the need for a real experiment, that is, without extra empirical input. Such a claim is indeed made by J. R. Brown. For him, Galileo’s reasoning is the thought experiment par excellence: it gives us ‘a grip on nature just by thinking’ (Brown, 2000, p. 528), it enables us to ‘go well beyond the old data to acquire a priori knowledge of nature’ (op. cit., p. 529). Thought experiments like Galileo’s are called by Brown ‘Platonic’ (Brown, 1991, p. 77), ‘the truly remarkable ones’ (op. cit., p. 34). The hallmark of such a thought experiment is that it is simultaneously destructive and constructive; it destroys an old theory and at the same time establishes a new one:
Galileo showed that all bodies fall at the same speed with a brilliant thought experiment that started by destroying the then reigning Aristotelian account … That’s the end of Aristotle’s theory: but there is a bonus, since the right account is now obvious: they all fall at the same speed … (Brown, 2000, p. 529)
In Sect. 2, we will take a first look at the textual basis for the Galilean claim, and at the extant Aristotelian writings on the subject of falling bodies. In the subsequent 3 Gendler and reconstructing Galileo’s argument, 4 Norton and the tacit assumption of Galileo, we reconstruct Galileo’s reasoning and analyze the deficiencies in it; we show that there is no purely logical objection to the Aristotelian claim that the rate of fall is proportional to the weight, nor any valid argument for the Galilean claim that all bodies fall at the same rate. In Sect. 5 we inveigh especially against Platonists, among whose ranks we must number Brown, and in a sense Galileo himself.
We close the paper with some appendices devoted to technical considerations. Their main purpose is to show that, aside from purely logical matters, Newtonian physics has definite implications for the correctness or otherwise of Galileo’s conclusions. It is not relevant that Galileo lacked the physics that we possess; the point is that empirical situations can be envisaged in which Galileo’s claims are correct, and other situations in which they are not. We can therefore state with confidence that Galileo’s double claim (namely that Aristotle’s dogma is logically inconsistent, and that his own dogma is necessarily true) is unfounded. In Appendix A we analyze the accelerated fall of bodies in a uniform gravitational field, showing that in this situation, Galileo’s conclusion is correct. In Appendix B we consider another situation, namely that of terminal motion of slowly falling bodies in viscous fluids, and in this case we show that Aristotle’s conclusion is correct. In Appendix C we return to bodies falling in vacuo, but now taking cognizance of the fact that the earth’s gravitational field is nonuniform. Here it turns out that the details of Galileo’s thought experiment can be matched, step by step, but that his grand conclusion, that all bodies fall at the same rate (i.e. with the same acceleration) is wrong. Technical details are given in Appendix D of turbulent fluid motion, these being relevant to a realistic treatment of musket shot and cannon balls falling from the leaning tower of Pisa, to cite a possibly apocryphal experiment. Appendix E is devoted to questions of both Aristotelian and Galilean source material and to commentaries upon them.
Section snippets
Galileo contra Aristotle
In his ‘Two new sciences’, Galileo presents his criticism of Aristotle’s dogma concerning falling bodies with especial clarity:
Salviati: But, even without further experiment, it is possible to prove clearly, by means of a short and conclusive argument, that a heavier body does not move more rapidly than a lighter one, provided both bodies are of the same material, and in short are such as those mentioned by Aristotle … If then we take two bodies whose natural speeds are different, it is clear
Gendler and reconstructing Galileo’s argument
Galileo’s own resolution of the imagined inconsistency in the doctrine that different bodies fall at different rates, as implied by the weak dogma, is that all bodies must fall at the same rate. Moreover, via the words of Salviati (‘even without further experiment’) he presents this as a truth that is accessible to reason, rendering experiment unnecessary.
T. S. Gendler analyzes Galileo’s thought experiment with acumen (Gendler, 1998). She first introduces the notion of the mediativity of
Norton and the tacit assumption of Galileo
The foregoing three reconstructions of Galileo’s argument seem unexceptionable. However, strictly speaking they are all non sequiturs. They are all based on a hidden assumption, namely that any other parameters determinative of natural speed are excluded. We call this ‘Galileo’s tacit assumption’. Without this assumption, Galileo’s conclusion that all natural speeds are the same does not follow from [G1]–[G3], nor from [C1]–[C3], nor yet from [Z1]–[Z3]. Even our proof that the weak set
Galileo and prior philosophy
A lively philosophical debate on the nature of thought experiments can be found in the literature from about 1990. Concerning thought experiments in natural science, Brown, Norton and Gendler made significant contributions. As we have seen, Brown adopts a clear stance. For him, the essence of a thought experiment is that it teaches us new things about the world without the use of new empirical data. Brown’s world view is denied by Norton, for whom thought experiments are disguised arguments. On
Acknowledgements
Special thanks are due to Pieter Sjoerd Hasper for an illuminating discussion of some aspects of Aristotle’s De caelo. We are grateful for the interactive contribution of audiences in Bertinoro, Gent, Groningen, Leusden and Rotterdam, and in particular for that of James McAllister, who brought Casper’s article to our attention. We acknowledge also an e-mail from Jim Cushing concerning Galileo’s reasons for not having attempted the celebrated experiment in Pisa.
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2015, Studies in History and Philosophy of Science Part ACitation Excerpt :I am not claiming here that Galileo's thought experiment constitutes a valid logical ‘proof’ for his conclusion that speed is not proportional to weight. There is now an extensive philosophical literature that reveals how Galileo's thought experiment rests on hidden assumptions, which fail to establish the conclusion it is supposed to demonstrate (Irvine, 1991; Schrenk, 2004; Atkinson & Peijnenburg, 2004). Yet, it is evident, than in presenting this argument, Galileo certainly intended to convince his reader of this conclusion by a different rhetorical means than simple appeal to everyday experience.
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