Parts of Falling Objects: Galileo’s Thought Experiment in Mereological Setting

Erkenntnis https://doi.org/10.1007/s10670-020-00263-y ORIGINAL RESEARCH Parts of Falling Objects: Galileo’s Thought Experiment in Mereological Setting Rafał Gruszczyński1 Received: 21 October 2019 / Accepted: 4 April 2020 © The Author(s) 2020 Abstract This paper aims to formalize Galileo’s argument (and its variations) against the Aristotelian view that the weight of free-falling bodies influences their speed. I obtain this via the application of concepts of parthood and of mereological sum, and via recognition of a principle which is not explicitly formulated by the Italian thinker but seems to be natural and helpful in understanding the logical mechanism behind Galileo’s train of thought. I also compare my reconstruction to one of those put forward by Atkinson and Peijnenburg (Stud Hist Philos Sci 35(1):115–136, 2004), and propose a formalization which is based on a principle introduced by them, which I shall call the speed is mediative principle. 1 The Verification of Hypotheses and Galileo’s Reasoning Confronting a scientific hypothesis which a scientist is convinced is false and lacking suitable empirical machinery to reject it, she may resort to the power of pure thought. If h is such a hypothesis and K is the body of knowledge the scientist is working with, one of the possible pure-thought strategies is to assume h obtains, incorporate it into the body of knowledge and check what the consequences of K + h are. If from K + h the scientist manages to draw a false statement, then something among K + h is false (because false sentences cannot be consequences of true ones). Since h is the main suspect, the reasonable strategy is to reject it and accept the negation of h instead as an element of one’s knowledge. Since Aristotle, and before Galileo, people had been convinced that if two falling bodies differ in weight, then their speeds must be different as well: the heavier one falls faster than the lighter. This view was (and still is) supported by everyday experience. It called for a genius of Galileo’s to break through the surface of things and to discover that if it indeed was like that, the ontological principle of consistency would be violated. B Rafał Gruszczyński 1 Institute of Philosophy, Nicolaus Copernicus University in Toruń, Toruń, Poland 123 R. Gruszczyński Whether the great thinker of Pisa performed the famous experiment dropping cannonballs from the leaning tower of his hometown is still an object of debate among the historians and the philosophers of science. What is undeniable is his thought experiment in which he demonstrates the falsity of the widespread view on falling bodies. The thought experiment depicts the following situation: (G1) Consider two falling stones, B and b, assuming that the weight of the first one is larger than that of the second. (G2) Assume that the stones are united somehow. (G3) According to Galileo (1954): “[…] on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter.” (i.e. B is retarded by b, and b is hastened by B). (G4) “[…] if a large stone moves with a speed of, say, eight, while a smaller stone moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter; an effect which is contrary to your supposition.” (G5) in other words, the united body B, b is heavier than B but moves with less speed than B. In the above, K is elementary knowledge about the behaviour of spatial things, h is Aristotle’s viewpoint. The contradictory statement (G4) (i.e., that there is an object which at the same time does have and does not have some property) allows for the repudiation of h. The Aristotelian principle has led us to a contradiction, and we are justified in rejecting it—it is not true that heavier bodies fall with greater speed than lighter ones. Since it is tacitly rejected that lighter bodies fall with greater speed than heavier ones, one may conclude that weight itself does not influence the speed of falling bodies. 2 The Nature of Thought Experiments The nature of mental operations known as thought experiments did stir a heated debated in the 80s and 90s of the previous century, with opposite views represented mainly by John D. Norton and James Robert Brown.1 To set the stage for my interpretation of the Galilean thought experiment let me recapitulate the main points of the debate. Norton (1991) defines a thought experiment as an argument which posits a state of affairs being either hypothetical or counterfactual, and invokes particulars which do not harm the generality of the conclusion of the argument. In consequence, by its very definition every thought experiment can be reconstructed as an argument, a stance which is embodied in the following Reconstruction Thesis: 1 See mainly: (Norton 1991, 1996, 1993) which is a review of (Brown 1991), with (Brown 1993); also (Brown 1986). 123 Parts of Falling Objects: Galileo’s Thought Experiment... (RT) All thought experiments can be reconstructed as arguments based on tacit or explicit assumptions. Belief in the outcome-conclusion of the thought experiment is justified only insofar as the reconstructed argument can justify the conclusion.2 From (Norton 1996) we can infer that in order to make a fully satisfactory analysis of the thought experiment we have to: (RT1) explicitly formulate all the premises incorporated in the experiment, including enthymematic ones upon which the experimenter may seem not to rely at first sight, (RT2) formulate a statement which embodies the posited hypothesis, (RT3) show that the premises are strong enough to justify the conclusion as a consequence of the premises, either in a deductive or inductive sense (in which case embrace the hypothesis as part of knowledge), or use the reductio ad absurdum method to show that the posited hypothesis is inconsistent with knowledge (and reject it),3 (RT4) last but not least, ensure that it is clear which elements of the thought experiment are essential to the point and which are mere colourful details or ’stage-setting’ to make it imaginable. Therefore, as Norton (1996) points out, “the success of the thought experiment is determined by the validity of the argument”. With reference to the opening section of this paper, the analysis of a thought experiment would require checking whether all the premises (both explicit and enthymematic) constitute an item of knowledge, formulating a hypothesis the experimenter wants to reject and finally demonstrating that from the premises and the hypothesis we can deduce some falsehood or absurdity (i.e., applying the reductio ad absurdum method). Following Norton let me observe that the thought-experiment-as-argument stance gives us precise criteria for judging the relia (...truncated)