Galileo's Failing Bodies

Galileo’s Failing Bodies: The Entification Illusion Abstract Galileo's 'falling stones' thought-experiment is likely the most famous in the history of science. Many philosophers in the present day use it as the best example of what a thought-experiment is capable of adding to our epistemic arsenal, despite the enormous range of their answers to this question. I provide what I take to be the best analysis of the thought-experiment to date. On my analysis, it has more in common with a magic-trick than an experiment, and is to that extent epistemically valueless. I draw no larger conclusions about the value of thought-experiments broadly. 1. Introduction In 1638, Galileo presented the now-famous thought experiment of the ‘falling stones,’ considered by many to have shown the falsity of Aristotelian mechanics. A subset of those people believed it to also show the truth of Galileo’s assertion that all objects fall at the same rate (at least in a vacuum). Tamar Szabó Gendler and James Brown hold these views, respectively. Others are less impressed with its epistemic, justificatory power. John Norton claims that it, like all thought experiments, is an argument and that belief in its conclusion is only as justified as is the conclusion of a proper reconstruction of the (implicit) argument. James McAllister believes that it has evidential significance, but only in the context of the Galilean ‘doctrine of phenomena.’ Julian Reiss claims that while this, like all thought experiments, can be valuable in the context of discovery, it is justificatorily inert. My principal aim in this paper is to provide what is to my knowledge a novel analysis of Galileo’s thought experiment. On my analysis, it has more in common with a magic trick than a real experiment. While I remain agnostic about whether ‘thought experiments’ as a species should be considered experiments, in this case I believe that it should not. Therefore I depart from Reiss and McAllister in their eschewing of the term ‘real experiment’ in favor of ‘concrete experiment’ as a contrast to thought experiment. The reasons for this will be made evident. I will however continue to refer to it as a thought experiment; the reader may justifiably place mental scare quotes around the term where it appears, at least in reference to the Galilean one under consideration. It will then come as no surprise that I take it to be epistemically worthless. This goes whether there are vacua or not and independently of the question whether the Aristotelian cares about them or the phenomena they isolate. 2. Galileo’s Bodies and Two Reconstructions Here is the thought experiment: imagine two stones of different weights; per Aristotle they have different natural speeds, with the heavier having the greater natural speed. Now connect them and drop them. Clearly, the faster stone will be retarded by the slower one and the slower one speeded by the faster one. Therefore the rate of their fall will be intermediate between the rates of the two isolated stones. However, the weight of the combined stones is greater than that of the heavy stone alone. Since we have just seen that the combined stones fall more slowly than the heavy stone alone, we can say that the heavier (combined) stone falls more slowly than the lighter (solitary heavy) stone. Since we reached this conclusion based on the assumption that heavier stones fall faster, this assumption is not tenable (nor would it be tenable that lighter ones fall faster). That is, stones fall at a rate independent of their weights. Brown (1991, 2000) has argued that this thought experiment is both ‘destructive’ and ‘direct,’ in that it destroys Aristotle’s theory and allows us to perceive the truth of Galileo’s by granting us direct access to Platonic laws of nature. Tamar Szabó Gendler, while eschewing the Platonic account, claims that the experiment ‘brings [one] to see’ that there is ‘no conceptual space’ for the view that rate of fall might vary with weight. ‘Galileo and the Indispensability of Scientific Thought Experiment,’ Brit. J. Phil. Sci. 49 (1998), 397-424. All Gendler references are to this work. Quotes above are taken from pp. 408 and 412 respectively. Gendler’s paper is largely a response to Norton’s view. Norton 1991 and 1996. All quotes and references are to his 1996 article, ‘Are Thought Experiments Just What You Thought?’ in the Canadian Journal of Philosophy, 26, 333-66. that thought experiments are arguments. Gendler focuses on this (canonical) thought experiment as a vehicle for showing that no argument could capture the persuasiveness of Galileo’s thought experiment (398) I agree, but in the same manner that a magician could not persuade an audience that he had made someone disappear as effectively via argument as he could by means of exploiting aspects of their perceptual apparatus. Though my main purpose is not to argue specifically for or against Norton or Gendler, Norton’s view and Gendler’s response will provide me with some useful context within which to provide my analysis of the thought experiment. Let’s begin with John Norton’s (1996) take. Norton’s view is that all thought experiments are arguments. This view involves two claims. One is the ‘Reconstruction Thesis:’ 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. (339) This is a view of the justificatory power of thought experiments. The other claim is about the ‘context of discovery’ and concerns what thought experiments ‘really are.’ This second claim is that whenever one conducts a thought experiment, one is really executing an argument, though this will of course not normally be apparent, due to abbreviation and suppressed premises. I agree with the former but not the latter claim; that will be treated later. As Brown and his Platonism is Norton’s focus of attack, and the falling body thought experiment is Brown’s favorite example of a Platonic thought experiment (one which transcends empiricism and cannot be recast as an argument) Norton gives a reconstruction of this thought experiment. Here it is: Assumption for reductio proof: The speed of fall of bodies in a given medium is proportionate to their weights. From 1: If a large stone falls with 8 degrees of speed, a smaller stone half its weight will fall with 4 degrees of speed. Assumption: If a slower falling stone is connected to a faster falling stone, the slower will retard the faster and the faster speed the slower. From 3: If the two stones from 2 are connected, their composite will fall slower than 8 degrees of speed. Assumption: the composite of the two weights has greater weight than the larger. From 1 and 5: The composite will fall faster than 8 degrees. Conclusions 4 and 6 contradict. Therefore, we must reject Assumption 1. Therefore, all stones fall alike. (341-2) Norton realizes that the move from 8 to 9 isn’t warranted without the additional assumption (8a) that the rate of fall depends only on gravity. Though Norton’s 8a says that rate of fall depends only on the weights, I will assume he means to say gravity. It would be funny if our confidence in the conclusion that weight is irrelevant to rate of fall depended on our confidence in the claim that weight is all that matters to the rate of fall. In this paper, I will act as if Norton had meant gravity rather than weight. He then argues, as the Reconstruction Thesis would have it, that our degree of belief in the outcome of the thought experiment depends on our confidence in the truth of 8a. Insofar as our belief in 8a is strong, so is the thought experiment and the argument. Norton does not mention that our degree of belief in 3 and 5 had also better be strong in order for the argument to work. Given the apparent obviousness of the dependence of the conclusion on these assumptions, Norton’s failure to address their importance cries out for explanation. I will have a go at that later, but first I turn to Gendler. Gendler’s reconstruction of the thought experiment as an argument is perfectly general and simple. The conclusion it establishes, or rather the inconsistency it points out, is immediately apparent, and so then would seem to be the options for alleviating the inconsistency. Gendler provides the Aristotelian with four ways out of the inconsistency. Only one has any attractiveness, and even that one is strikingly inferior to what would seem to be an obvious alternative, which I will argue is completely adequate. The reconstruction is as follows: ‘Natural speed is mediative.’ This just means that if two bodies have different natural speeds, then joining them will produce a body with a natural speed between the two. ‘Weight is additive.’ The weight of the combined body resulting from the joining of two bodies is the sum of the weights of the two bodies. From these premises (and the assumptions that not all natural speeds and weights are either zero or infinite) we have: ‘Natural speed is not directly proportional to weight,’ since what is mediative cannot be directly proportional to what is additive. (404) Gendler points out that ‘the only way to maintain (1), (2), and (3) simultaneously is to assume that all natural speeds are the same’ (404). Since (3) follows from (1) and (2), the assumption is required just to maintain these two premises. Gendler now proceeds to provide the Aristotelian with ‘four ways out.’ The first two ways out are to deny that ‘strapped-bodies’ have determinate natural speeds or weights, respectively. The third is to postulate a distinction between ‘united’ and ‘unified’ bodies. Bodies that are united have mediated speeds while unified bodies have additive speeds. The former are, as a matter of fact, two bodies, while the latter as a matter of fact form one body. This way out escapes contradiction but forces the Aristotelian to accept ‘radical discontinuities’ in nature, for should a united body (two bodies) happen to become unified during free-fall, its rate would suddenly increase, perhaps doubling. The final way out, one which avoids radical discontinuity, is to postulate a determinate physical property, ‘degree of connectedness.’ Degree of connectedness can range from 0 to 1, with bodies having degree of connectedness 0 (but still united) falling at fully mediated rates, bodies being completely unified having degree of connectedness 1 and falling at completely additive rates. Intermediate values of connectedness will correspond to rates of fall somewhere between these poles. The point of this exercise on Gendler’s part is to show that though there are several ways out for the Aristotelian, the thought experimental format excludes them by virtue of calling upon ‘broad, defeasible, tacit assumptions’ concerning our basic ‘representations of experienced reality’ (406). One is that weight and natural speed are physically determined and the other is that ‘entification’ (whether there are one or more objects) is not physically determined. This is supposed to show that the argumentative reconstruction provided in steps (1) – (3) cannot capture what is going on in the thought experiment; if it could, the Aristotelian would have the suggested ways out; ‘[t]hat these ways out do not seem available when the thought experiment is presented in its reconstructed form shows that this eliminative reconstruction has failed to capture its original demonstrative force’ (p. 407, italics mine). According to Gendler, ‘by evoking tacit knowledge about how the falling bodies actually behave, the thought experiment pre-emptively precludes such ways out’ (407). I want to both agree and disagree in the strongest possible terms. I want to agree that the thought experimental presentation has immeasurably more persuasive force than Gendler’s reconstructed argument. This is evident from the sheer fact that so many people, including Gendler, have supposed it to have actually refuted Aristotelian mechanics. However, Reiss (2002) provided evidence that the thought experiment doesn’t have nearly the knock-down demonstrative force it is supposed to have. My analysis hopes to show why it did not have such force in his presentation. However, if ‘demonstrative force’ implies that something has been ‘demonstrated’ or ‘established’ (as Gendler makes clear she means to imply on 408), then nothing could be further from the truth, as the thought experiment not only does not ‘establish’ the conclusion Galileo wanted, but does not require the Aristotelian to accept any radical discontinuities in nature, dubious physically determinate properties or anything unsavory whatever. In fact, a perfectly legitimate understanding of the thought experiment allows the Aristotelian to be reaffirmed in her belief that rate of fall is determined by weight alone. Gendler pointed out that (1) and (2) are sufficient to generate (3), which then leads one to the conclusion that all natural speeds are the same. Gendler then spent some time providing the Aristotelian some (pretty bad) ways out. I can think of one she missed: deny that natural speed is mediative. For Gendler, this might not have seemed an option, for she describes (1) as ‘[t]he first claim of the Aristotelian.’ However, nowhere can I find ‘the Aristotelian’ committed to this. If Aristotle (or Simplicio) was committed to this, I haven’t been able to find evidence of it. Even if this were the case, it would remain quite puzzling that nobody should have suggested that they drop this claim rather than the weight-dependence claim. In Two New Sciences, Galileo puts it this way: ‘it is evident that were we to connect the slower to the faster, the latter would be partly retarded by the slower, and this would be partly speeded up by the faster…[b]ut if this is so…’ (italics mine). Two New Sciences, S. Drake, trans. (Madison, WI: University of Wisconsin Press 1974), p. 65. If that is so, then (maybe) there’s a problem. But Simplicio (Aristotle’s surrogate) doesn’t assent to that (as he does assent to every heavy object having a natural speed) and I can’t imagine why he should. III. A Couple of Thought Experiments To deny the mediativity of natural speed seems to be all that is necessary to (quite satisfactorily) defeat Gendler’s or Norton’s reconstructed arguments. I’ll consider this my weak claim. The stronger claim is that this should have been obvious. It is sitting right there in both their arguments, quite clearly crucial for either to go through (it is fully half of Gendler’s premises). However, neither Norton nor Gendler (nor anyone else I can find), in the explicit tasks of both reconstructing the thought experiment and evaluating the justificatory power of their reconstructions, supposes that the Aristotelian might not (or should not) be committed to the proposition that natural speed is mediative. Perhaps it seems as obvious as Norton’s (5), that weight is additive. This section will show that it is not at all obvious. Then I will try to investigate how such a bizarre notion could have been thrust upon the Aristotelian for the last 400 years or so. Let me begin with a thought experiment. Consider two stones of unequal weight, the heavier on top of the lighter, the latter of which is on the ground. They are connected by five feet of string. Grab the top stone and slowly lift it straight up. At the beginning (neglecting the string), is there any difference in the difficulty of lifting this stone compared to the case in which it is connected to nothing? Specifically, does the connected, lighter stone somehow ‘mediate’ the force required to lift the heavier stone? Keep lifting. As the string becomes taut, can you perceive a (radical, discontinuous) change in the amount of force required to lift the stone(s)? How is this now different (insofar as you lift the stones straight up) than if the stones were fused into one large stone, or connected by a light, inflexible pole? Allow me one more thought experiment to drive the point home. Imagine a uniform lead sphere. Melt it, losing no mass, and reform it so that there are two ball-like bulges of differing size at either end of a thin cylinder of metal. Drop it. Do you suppose that the bulges are two objects and one retards or speeds the other? If so, consider this: imagine the original sphere dropped from arbitrary height. God, without affecting anything else, begins to transform the sphere very gradually into the figure described above. At what point shall we say that one part retards the other and is speeded by it? The Aristotelian might rightly wonder if Galileo thought her committed to the idea that for each of the infinitely many ways to imaginatively ‘divide up’ an object unequally, the heavier part retarded the remaining part, generating an infinity of contradictions in a single object. Perhaps the Galilean will be tempted to say that my examples are all single objects while his stones are two objects. One response is that if they are two objects, then there is no reason to suppose that Simplicio’s agreement that ‘every heavy falling body’ (65, italics mine) has a natural speed applies to them. A better response is to agree with Gendler that ‘[e]ntification is not physically determined’ (407). The number of objects it is has no definite answer; we may equally consider it one, two, or ‘indefinitely many objects held together by internal forces’ (407). What matters is the (relevant sort of) causal connectedness between the objects. What of the radical discontinuity in nature? The Aristotelian must say that suddenly the combined body (upon the string becoming taut) begins to fall faster than the heavier one. The Aristotelian can respond that this sort of ‘radical discontinuity’ happens all the time. In the case of my stones, upon the string becoming taut, the rate of rise (if enough force remains to lift both) will be (radically, discontinuously) slowed in direct proportion to the smaller object’s weight. The force of the earth pulling on the lighter ball will be in effect subtracted from the upward force you’re applying to the heavier ball. Now the opposite situation (it could easily be supposed) holds when they are falling. Then the force of the earth pulling on the lighter stone, once they’re causally connected in the same way, will be added to the force pulling on the heavier ball, speeding it in direct proportion to the lighter object’s weight. One might think that the Aristotelian would owe an account of relevant causal connectedness. It doesn’t seem so to me. It seems that it is sufficient for the Aristotelian to rely on the sort of causal connectedness involved in the stones example. Roughly, what seems to matter is that for the ‘objects’ to be connected in the right way, in order to move ‘one,’ the ‘other’ must move too (in the case of things connected by strings and such things, direction of movement will be relevant). This seems to be the reason why we can say entification isn’t physically determined; if an ‘object’ can be considered ‘indefinitely many objects held together by internal forces,’ then that must be because moving one part of it around moves the other parts too (on a macroscopic scale, at least). It strikes me that the Galilean owes an answer to the question why taut strings count less than molecular attractions and whatever other sorts of causal connectedness that don’t result in our wanting to call something two or more things. In the context of free-fall, of course. In that context, we might well be ambivalent about whether two people strapped tightly to each other counted as one or two objects, because of the sort of causal connectedness they have. We would not suppose that if they were similarly strapped together and singing to each other, that that sort of causal connectedness makes their entification (as between one or two bodies, or persons) indeterminate. IV. The Irrelevance of Phenomena Norton and McAllister have supposed that the question whether gravity is the only thing that affects rate of fall is crucial to the success of Galileo’s thought experiment. Norton claimed that our (justified) confidence in 8a determines our (justified) confidence in the thought experiment/argument’s outcome/conclusion. McAllister ‘The Evidential Significance of Thought Experiment in Science,’ Stud. Hist. Phil. Sci., Vol. 27, No.2, pp. 233-250, 1996. claims that the thought experiment, along with all Galilean thought experiments (any ‘idealizing’ thought experiment), has evidential significance due to the background doctrine of phenomena. This matters because if and since the Aristotelian is not concerned with (or does not believe in) fundamental phenomena underlying the hurly-burly of ordinary experience, but rather in what happens in the hurly-burly itself, he will not be interested to ‘see’ what would happen in artificial, idealized situations (such as fall of bodies in a vacuum). Norton objected that when rate of fall is affected by other things than gravity (like shape), Galileo’s theory is clearly false. Though the context of the discussion in Two New Sciences was about the possibility of a vacuum, and so Salviati (Galileo) could not have simply assumed a vacuum to exist, one might yet claim that Galileo’s thought experiment shows that in a vacuum, where the phenomenon of free-fall is isolated, weight is irrelevant to rate of fall. Even if the Aristotelian isn’t concerned with this, we can at least see that if one is concerned with phenomena, then one will give this thought experiment evidential significance (for McAllister, on par with a ‘concrete’ experiment), as it shows what must be the case when only gravity matters. Even Reiss, who attributes no justificatory power to thought experiments, comments on the success of Galileo’s thought experiment depending crucially on all effects other than gravity having been controlled for (2002, 9). As an illustration, he proposes a counter-thought experiment to Galileo’s in which the size of an object is reduced until it has the same specific gravity as the surrounding medium; Galileo’s theory says it will fall as fast as any object, though we know it will float (2003, 16). So even if Galileo’s thought experiment doesn’t allow one to conclude that all objects fall at the same rate in any medium (which is manifestly false!), it perhaps does allow one to see that they do in a vacuum. I say it does no such thing, and for what should (now) be obvious reasons. Since the Aristotelian has been given no reason to treat the combined, causally connected body as anything other than a normal heavy body (which is just to reject the 'mediativity of natural speed’ premise), there is no reason Galileo’s thought experiment ought to convince her of anything. The Aristotelian now conceives of the combined body(ies), with string taut, as functionally equivalent to one body of the very same weight. That body will ‘clearly’ fall faster than one of the stones alone. Undoubtedly that would have been the Aristotelian’s intuitive and theoretical commitment prior to the thought experiment, vacuum or not (insofar as he would have been willing to make intuitive or theoretical judgments about vacua). So the Aristotelian could care all you like about vacua and phenomena and be totally unmoved, perhaps even a bit amused, at the supposed demonstrative force of this thought experiment. Before moving to the next section, I want to make good on my claim that the Aristotelian could justifiably feel reaffirmed in her belief that weight is what matters in free fall. Our responses to Galileo’s thought experiment have helped to make explicit that entification is not physically determined. If the Aristotelian had been previously tempted to think that the number of bodies involved or whether they were connected by string or stone had some bearing on the matter, she can ‘see’ now that that doesn’t matter. Once the string is taut, it’s just as if there were two large stone bulges on either end of a thin strip of stone, which is just the same as if the stone were all one sphere. If the parts are connected in the causally relevant way, all that matters is weight, though there be one object or legion. V. How Could This Have Happened? I’d like to now consider how, if I am right about all this, this thought experiment could have come to be so famous and thought for so long to have demonstrated so much. First of all, as I mentioned before, I find it totally implausible that what was ‘really’ going on all along was a (logical) argument. Both of the arguments that I presented of Norton’s and Gendler’s are completely incapable of generating Galileo’s conclusion (Norton’s singling one of the assumptions out ‘for reductio proof’ would hardly be convincing to someone who felt free to doubt the other assumptions, notably (3)). Also, I agree with Reiss (2003, 11) that the mode of inference is not logic, but (at least partly) intuition. However, contra Gendler, it is not the case that the thought experiment is an ‘experiment-in-thought,’ in which the experimenter ‘finds out’ (414, italics in original) what would (apparently) happen in the described circumstances. Galileo’s ‘contradiction’ derives from the contradiction he imports. He presents the scenario so that the Aristotelian (and the rest of us) are led to conceive of the stones as both one and two bodies simultaneously. The image of the two stones facilitates our accepting that there are two bodies, and our physical intuitions involving what would happen if one connected a slower body to a faster one compel us to accept that the speed must be mediative in this scenario. Now the claim that there is a combined-body with an additive weight does not meet resistance because, as Gendler claims, we do not have a sense that entification is physically determined. Last, but certainly not least, we are told what the answer is! In the presentation of the thought experiment, we are told there is a contradiction (and even more importantly, we have learned as children that Galileo was right). In this, like (at least almost) all thought experiments, the ‘experimental results’ come right along with the ‘experiment.’ I have never encountered a so-called thought experiment in which the ‘outcome’ was not either explicit or implicit, normally explicit, and this one is no different. Galileo does not sit back and ‘allow’ you to ‘see’ what would happen; he leads you quite deliberately and cleverly to a situation in which you have irreconcilable intuitions and makes you think you got them from Aristotle’s theory. In addition to the arguments I have already provided to suggest this conclusion, evidence for it comes in the form of an ‘experiment’ conducted by Reiss in which he gave the ‘same’ thought experiment to a group of undergraduates in mathematical logic. He also puts ‘experiment’ in quotes, as he does not suggest that it is a well-controlled experiment. The text given the students bears quotation: According to an Aristotelian theory, a falling body falls at the rate of its so-called natural motion, which is proportional to its weight. This implies that heavy bodies fall faster than light ones. Galileo constructed a thought experiment, which, he claimed, bears on the Aristotelian theory. He asked his readers to imagine two balls of different weights to be dropped from a tower. The Aristotelian predicts that the heavier one falls faster and hits the ground first. “But now,” Galileo said, “suppose that the two balls were joined to each other by a string or rope and then dropped.” What is the outcome in this scenario? (2002, 13) The students were then asked a series of questions, including what they thought would happen in the scenario, their physics and philosophy background and whether the thought experiment had a bearing on the Aristotelian theory and if so, what it was. To oversimplify only slightly, the results were all over the map. Only one person wrote that Aristotelian theory is falsified due to a contradiction. Fourteen percent each thought the combined body would fall faster and slower than the heavier body. Some thought the heavy body would pull the light one, some that they would fall at the same rate, and some that the lighter one would land first. Having heard of the thought experiment before did not matter very much, and only twenty percent of ‘high-physics’ students said rate of fall was independent of weight. At first, I actually thought the situation was prejudicial as it said that Galileo ‘claimed’ that the experiment bore on Aristotle’s theory; this might not allow the students to simply envision the scenario and see what they came up with--as if that’s what Galileo did! Galileo tells us outright that there is a contradiction and that the theory is thus falsified. In Galileo’s experiment, the results are part and parcel of the experiment; at least Reiss did not explicitly provide the results. The difference in ‘reception’ of Reiss’s and Galileo’s version very plausibly comes down to presentation. Reiss did not refer to a ‘composite’ body, he did not claim that ‘it is evident that…the [faster] would be partly retarded by the slower,’ nor did he tell them that there is (or is not) a contradiction involved. Galileo did all these things. He did everything but allow us to ‘find out’ the answer. It might be objected that lots of (if not all) thought experiments come equipped with their results. Why was this one so compelling if it didn’t tap into some core intuitions about the physical world? It did ‘tap into them,’ in just the way a magician taps into perceptual/behavioral habits to generate an illusion. I agreed with Gendler above that we do not (tacitly) consider entification to be physically determined. That is a long way from saying that it is arbitrary. Consider two small stones a mile apart. Nobody would call these two stones a single object; in fact, I take it that while you might get people to agree that together they make up indefinitely many objects, you will have a hard time getting someone to agree that they are only one object. Now consider the same stones ten feet apart, one hundred feet in the air, tied loosely together by a string a mile long, drooping to the ground and collecting there in a slack heap. Interestingly, though Reiss declared that ‘[a]ny answer is possible, and one will always find someone who actually maintains it’ (15), nobody pointed out that if the string or rope were long enough, the scenario 'clearly' wouldn’t have any bearing on the theory. Shall we consider these two stones a composite body? We could if we liked, but we would hardly say that their weights were additive in any greater sense than the unconnected stones’ weights are additive; that is, one can add them up if she likes. Their weights are clearly not additive in the sense that even if we were Aristotelians, we would not suppose that the speed of the ‘composite body’ would be additive; nobody would be tempted to suppose that, unless the string between them became taut so that the fall of one affected the other. Neither would anyone suppose that the speeds of the bodies would be mediated by one another. It is only when the two objects are perceived to be connected in the causally relevant way that we are willing to suppose that their weights are additive, and that it is irrelevant whether we call it one or two (or more) objects. So Galileo’s calling it a composite body meets no real resistance. His calling it two bodies meets no resistance because he began the thought experiment with two ‘moveables.’ After connecting them, by referring to a slower and faster one, he keeps them distinct in the reader’s imagination. One visualizes two objects, connected by a string. Interestingly, Galileo actually said nothing about any rope or string, but only that we ‘connect’ the ‘moveables.’ Presumably they could then be fused. If they were thoroughly fused (in the limit case, reshaped so as to make a larger but otherwise indistinguishable version of the heavy stone) however, it would destroy the impression of there being two objects. That the version involving a string is the version ‘in the relevant literature’ (Reiss 2002, 9) makes one wonder if the champions of the thought experiment helped Galileo out a bit. VI. The Entification Illusion I have argued that the justificatory force of Galileo’s thought experiment relies on the ascription of a bizarre commitment to the Aristotelian, namely that natural speed is mediative. I have shown that the Aristotelian (and everybody else) would have no reason to grant that the speed is mediative, at least so long as weight is additive. Therefore, in my view the thought experiment has no justificatory force at all. However, it has had and continues to have considerable persuasive force, perhaps more than any single thought experiment in the history of science. I have suggested that its persuasive force owes much more to its similarity to a magic trick than to an argument or an experiment, insofar as it exploits aspects of the reader’s (imaginative) perceptual apparatus. As we have seen, if the objects were ‘connected’ by a thorough fusing, the thought experiment wouldn’t get off the ground (so to speak), for there would be no separate objects in imagination such that one could pull on the other, and therefore no retardation or speeding up of parts. Since the ‘contradiction’ arises from the apparent persistence of two objects (with unequal natural speeds) at the same time as one is willing to treat them as (functionally) one object, I call this ‘The Entification Illusion.’ This illusion is so powerful that it has apparently been able to put Norton’s (3) out of harm’s way, and led Gendler to offer a host of (poor) ways out for the Aristotelian, while neglecting the seemingly obvious option of rejecting one of the two premises sufficient to generate the anti-Aristotelian conclusion. The trick is clever enough to make it seem that the ‘two-ness’ of the objects is so apparent that the Aristotelian must find a way to deny the additivity of weight, and the only way to do that seems to be to deny that it is a single body. At the least, the onus seems to be on the Aristotelian to provide a non-ad hoc reason why the body isn’t composite. That natural speed is mediative, that there are two separate things (and only one at the same time!) to mediate one another seems beyond question. Interestingly, Gendler’s final, best way out for the Aristotelian denies mediativity of natural speed in the case where the bodies are totally unified (where degree of connectedness is 1). The mistake is in supposing that there was some reason to have the speeds be mediate at all until the string becomes (at least very nearly) taut, at which point they may be considered unified, and have additive speed! Rather, as we have seen, the onus is on the Galilean to say under what circumstances we have two objects such that one can ‘mediate’ the other, and more importantly, why the Aristotelian (or anyone else) should think they would actually do so. Gendler, in attempting to show that the thought experiment cannot be captured in a reconstructed argument, points out that ‘the argument from (1) and (2) to (3) is no better or worse than the argument from (not-3) to (not-1) or (not-2)’ (413). Since she thinks that the thought experiment has considerable demonstrative force, it must be coming from something else. That something else she takes to be its ‘ability to direct the reader’s attention to inadequacies in her conceptual scheme…’ (413). I think a better description would be that it has the ability to direct the reader’s attention to what the author’s left hand is doing so it does not notice what the right hand is up to. That the opposing arguments Gendler mentions are justificatorily equivalent is in my opinion a vindication of Norton’s Reconstruction Thesis insofar as the conclusion of both the thought experiment and the argument are completely unjustified without providing some justification for the ‘mediativity of natural speed’ assumption(s). The thought experiment provides only illusory justification for this assumption. VII. Concluding Remarks I have not attempted to treat thought experimentation generally, but only focused on a particular example. Though it is a (perhaps the) canonical thought experiment, I leave any larger lessons about thought experiments for another time. Galileo’s thought experiment is not like a ‘real’ or ‘concrete’ experiment, in that it does not allow us to ‘see what happens.’ The presentation of the ‘experiment’ exploits rather than makes use of our intuitions to generate desired conclusions, just as a rhetoritician exploits our emotions, prejudices, sloppy reasoning and so on to reach her conclusions. In fact, my analysis of this thought experiment suggests that it should be considered a sort of ‘visual rhetoric;’ an art of making ‘visual speeches,’ if you will. Finally, I have suggested that this thought experiment might be considered a sort of magic trick; in rare cases, a particularly gifted magician can make us believe that he is really capable of making a theory disappear. References Brown, J.R. (1991). The Laboratory of the Mind: Thought Experiments in the Natural Sciences: London and New York: Routledge. Brown, J.R. (2000). Thought Experiments In W.H. Newton-Smith (Ed.), A Companion to the Philosophy of Science. Oxford: Blackwell Publishers.Galileo Galilei (1974). Dialogues Concerning Two New Sciences, S. Drake, trans. (Madison, WI: University of Wisconsin Press), 65. (First published 1638) Gendler, T.S. (1998). Galileo and the Indispensability of Scientific Thought Experiment, The British Journal for the Philosophy of Science. 49, 397-424. McAllister, J.W. (1996). The Evidential Significance of Thought Experiment in Science. Studies in History and Philosophy of Science, 27, 233-250. Norton, John (1991). Thought Experiments in Einstein's Work. Thought Experiments in Science and Philosophy, Eds. T. Horowitz, G.J. Massey, Savage, MD: Rowman and Littlefield, 129-48. Norton, John (1996). Are Thought Experiments Just What You Thought? Canadian Journal of Philosophy, 26, 333-66. Reiss, Julian (2002). Causal Inference in the Abstract or Seven Myths About Thought Experiments. Technical Report CTR 03/02. Centre for Philosophy of Natural and Social Science, London School of Economics, London, UK. Reiss, Julian (2003). Thought Experiments and the Elimination of Experimental Artefacts. Centre for Philosophy of Natural and Social Science, London School of Economics, London, UK.