Why Empiricism Won't Work

Philosophy of Science Association Philosophy of Science Association

Why Empiricism Won't Work Author(s): James Robert Brown Source: PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1992, Volume Two: Symposia and Invited Papers (1992), pp. 271-279 Published by: The University of Chicago Press on behalf of the Philosophy of Science Association Stable URL: http://www.jstor.org/stable/192841 Accessed: 21/01/2009 07:33 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=ucpress. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].

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Why Empiricism Won't Work1 James Robert Brown University of Toronto Thought experiments present an enormous challenge to empiricism. So much so that some of us have (cheerfully) thrown in the towel and embraced good old fashioned platonism. I'll try to explain why, or at least, why one brand of empiricism won't work. Thought experimentsprovide us with scientific understandingand theoretical advances which are sometimes quite significant, yet they do this without new empirical input, and possibly without any empirical input at all. How is this possible? The challenge to empiricism is to give an account which is compatible with the traditionalempiricist principle that all knowledge is based on sensory experience. Ernst Mach (1960, 1976) thought we have "instinctiveknowledge" derived from extensive-but not yet articulated--experience, and perhapseven innate. And this instinctive knowledge is conjured up when we imagine ourselves in some thought experimentalsituation. For example, in Stevin's wonderful inclined plane thought experiment,we are asked to consider what would happen to a chain drapedover a prism-like pair of inclined frictionless planes. (Fig. l(a)) Would it slide to the left? to the right? or remain static? When the links arejoined (Fig. 1(b)) we see immediately what the answer must be: it will remain static. It is our instinctive knowledge that there couldn't be a perpetualmotion machine that provides the crucial empiricist ingredientin coming to the right conclusion.

Figure l(a)

PSA 1992, Volume 2, pp. 271-279 Copyright ? 1993 by the Philosophy of Science Association

Figure l(b)

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Mach provides one empiricist approachto thoughtexperiments,Roy Sorensen (1992) provides another. His view (which he calls naturalistand which is in some ways Machian) is that there is a difference of degree, but not of kind, between thought experiments and real ones. Knowledge derived from either is based on experience. "...thoughtexperiment is experiment (albiet a limiting case of it), so that the lessons learned about experimentationcarry over to thought experiment,and vice versa." (Sorensen 1992, p. 3) Mach and Sorensen are not the only empiricists looking at the issue. John Norton (1991) provides a different account, one which seems quite popular. The idea is simple. A thought experiment, says Norton, is an argument(deductive or inductive) with empirical premisses (which are sometimes suppressed), and with a lot of strictly irrelevant but picturesque detail (which gives it the experimental flavour). In Norton's own words, Thought experiments are argumentswhich (i) posit hypothetical or counterfactual states of affairs and (ii) invoke particularsirrelevant to the generality of the conclusion. (1992, p. 129) He provides an empiricist gloss: Thought experiments in physics provide or purportto provide us information about the physical world. Since they are thought experimentsratherthanphysical experiments, this information does not come from the reportingof new empirical data. Thus there is only one non-controversial source from which this informationcan come: it is elicited from information we already have by an identifiable argument, although that argumentmight not be laid out in detail in the statementof the thought experiment. The alternative to this view is to suppose that thoughtexperiments provide some new and even mysterious route to knowledge of the physical world. (ibid.) An illustrationseems called for. It will not only help to us to understandNorton's account, but will show its elegance, its naturalnessand its obvious appeal. Here's a very simple example, Einstein's elevator, which shows thatlight bends in a gravitationalfield.

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r / Figure2 1. An observer in an elevator cannot distinguish between being accelerated and being in a uniform gravitational field. (Principle of Equivalence) 2. If a light beam were to enter one side of the elevator and the elevator were accelerating,then the light beam would appearto bend as the elevator moved up. .'. In a gravitational field the light beam would also bend.

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This argumentgives us the conclusion that light bends in a gravitationalfield. And it seems to fit the Norton pattern, a deduction from empirical premisses. There are different versions of the elevator thought experiment. Norton reconstructs the version that establishes the Principle of Equivalence, itself. It's worth looking at since the argument in his example is more complex than in the very brief illustration that I just gave; it even includes a philosophical premiss. Norton sees the argumentas follows (1992, pp. 136-138): 1. An observer in an elevator cannot empirically distinguish between being accelerated and being in a uniform gravitational field. 2. This situationis typical; the details of the observerin the elevator are not relevant. 3. VerificationPrinciple: States of affairs which are not observationally distinct should not be distinguished by the theory. .'. Being uniformly accelerated and being at rest in a uniform gravitationalfield should not be theoretically distinguished. .'. Principle of Equivalence: Being uniformly accelerated is identical to being at rest in a gravitational field. Norton calls (2) an "inductive step". I'm not sure that the kind of patternrecognition that is involved here can reasonably be so characterized,but I'll let this point pass for now. We should also note that premiss (3) is certainly not an empirical premiss, even though many empiricists are happy to embrace it. However, we do arrive at the conclusion (the Principle of Equivalence) via an argumentfrom already accepted premisses, and that's Norton's main point. Maxwell's demon is a classic thought experiment that has a quite different structure than the others discussed here. It's an example of a thought experiment playing a mediating or illustrative role. In the 19th century James Clarke Maxwell was urging the molecular-kinetic theory of heat (Maxwell 1871). A gas is a collection of molecules in rapid random motion and the underlying laws which govern it, said Maxwell, are Newton's. Temperatureis just the average kinetic energy of the molecules; pressure is due to the molecules hitting the walls of the container;etc. Since the numberof particles in any gas is enormously large, the treatmentmust be statistical, and here lay Maxwell's difficulty. One of the requirementsfor a successful statistical theory of heat is the derivation of the second law of thermodynamicswhich says: in any change of state entropy must remain the same or increase; it cannot decrease. Equivalently, heat cannot pass from a cold to a hot body. But the best any statistical law of entropy can do is make the decrease of entropy very improbable. Thus, on Maxwell's theory there is some chance (though very small) that heat would flow from a cold body to a hot body when brought into contact, something which has never been experienced and which is absolutely forbidden by classical thermodynamics. The demon thought experiment was Maxwell's attemptto make the possible decrease of entropy in his theory not seem so obviously absurd. We are to imagine two gases, one hot and the other cold, in separate chambers, brought together; there is a little door between the two containers and a little intelligent being who controls the door. Even though the average molecule in the hot gas is faster that the average in the cold, there is a distributionof molecules at various speeds in each chamber. The demon lets fast molecules from the cold gas into the hot chamber and slow molecules from the hot gas into the cold chamber. The consequence of this is to increase the average speed of the molecules in the hot chamber and to decrease the average speed in the cold one. Of course, this just

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means making the hot gas hotter and the cold gas colder, violating the second law of classical thermodynamics.

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Figure3 The point of the whole exercise is to show that what was unthinkableis not so unthinkable after all. It is, we see on reflection, not an objection to Maxwell's version of the second law that it is statistical and allows the possibility of a decrease in entropy. Maxwell's demon helps to make some of the conclusions of the theory more plausible; it removes a barrierto its acceptance. In one sense, Norton's account fits this example perfectly. We startwith the statistical theory and we derive the probabilistic version of the second law; so we have a deductive argument. And the demon, as Norton says, is a "particular[which is] irrelevant to the generality of the conclusion." In fact, the demon is utterly unnecessary; we can derive the conclusion without invoking it at all. However, such an analysis misses the aim of the thought experiment. The point of Maxwell's demon is not to prove a conclusion hithertounestablished,but instead to provide us with that elusive thing, insight and understanding. After the demon thought experiment we see how something is possible. The mechanism of sorting fast and slow molecules is not a physical possibility, since obviously there are no demons, and given the makeup of the world, there couldn't be. But we now have a grasp of the physical situation which we lacked before. Norton is right in one sense in this example when he claims that the picturesquedetails play no role in the argument:the demon is irrelevant to the derivation of the conclusion. But the demon is not irrelevantto the understanding of that conclusion, and that's the thing Norton's account misses. I realize that to talk of "understanding"is to wade into murky waters and to court mystery mongering. There is a form of explanation in science which tries to answer the "how possible" question. Maxwell's demon is an example. In general, narrative explanations in history and in biology are paradigmaticof this form. The explanations tell a story in which the events to be explained make sense. We see how things could come about-not how they actually do or did come about. For instance, on the one hand we have the theory of evolution and on the other we have the phenomenon of giraffes with very long necks. How did this come about. The Darwinian tries to answer

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the "how is it possible?" question with a story about droughts,leaves on tree tops, early species of giraffe with relatively shorternecks, and those individuals among them with longer necks surviving at a higher rate to reproducewhile the shorternecked ones perished. The evolutionist isn't committed to this at all. The point of the story is only to show that an evolutionary route does exist thatproduceslong-necked giraffes. Similarly, Maxwell's demon thought experimentis a narrativeexplanation which answers the "how is the decrease of entropy possible?" question by telling us a story in which it makes clear sense. The truth of the how possible story-either Darwin's or Maxwell's-is quite irrelevant for the purposes of understanding.(I think truthexplains the "success of science" in a similar way. See my 1993.) Narrativeexplanations are common in the social sciences and biology. They are rare is physics; thought experiments like Maxwell's may be their only instances. Still, they do play an importantrole, one which cannot be analyzed as an argumentin the Norton mould. In his approachto thought experiments, Norton has a two-fold advantage. Empiricism has a long and successful history of explaining scientific activity. So it has the upper hand in the plausibility ratings when we turn our attentionto a new field like thought experiments. And second, Norton says that thought experiments are often disguised, not explicit arguments. So the real claim is that they can be reconstructed along his empiricist lines. Existence claims like this are devilishly difficult to defeat. I doubt that an actual refutation could ever be delivered. The most I can hope to do is make the possibility of a reconstruction look implausible. That's what I'll now try to do starting with a look at an apparentlytangential matter. Though we are concerned with thought experiments in the naturalsciences, much can be learned from some remarkableexamples in mathematicswhere pictures or diagrams play a role. The common view of diagrams in mathematicsis this: they provide a heuristic aid, a help to the imagination when following a proof. And they are thought of as no more than this. In particular,diagramscannot justify; they are not to be confused with real proofs, which are formulated in words and symbols. At most illustrationsplay a psychological role, and should never be used for making inferences. The standardaccount seems right for examples such as the Pythagoreantheorem. In Euclid's Elements the diagramwhich accompanies this theorem and its proof is merely an aid, psychologically helpful, but not necessary for the justification of the theorem. However, there are a few rare and remarkableexamples where somethingquite different is going on. The following theorem is from numbertheory;it has a standardproof (by mathematicalinduction) which uses no diagramsat all. But it can actually be proven with a diagram. (Take a moment to study the proof, to see how it works.) Theorem: +2+3+...+n=-- = --+Theorem: 1+2+3+...+n 2

Proof:

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2

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Of course, there is lots of interpretinggoing on to make this a proof. For example, we must consider the individual unit squaresas numbers and we must bring some background informationfrom geometry to the effect that a square with sides of length n has area n2. But these sorts of interpretiveassumptions are no less innocuous than those made in a typical verbal/symbolic proof. Here's anotherexample, this time a result about infinite series. 1 Theorem: -+ 2

Proof:

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Figure5 The usual proof of this theorem relies on standarde-5 techniques. But nothing like that is used here. Instead, we can simply see a pattern;we can see that the inner boxes are getting smaller,that they will eventually exhaust the unit square (without remainder), and so we see that their sum is equal to the whole square, hence equal to 1. The moral I think we should draw from examples like these is simple but profound: we can sometimesprove things with pictures. In spite of the fact that the number theory diagramseems to be a special case (n = 5), still we can see all generality in it. And the proof does not work by merely suggesting the "real"proof, since in the diagramthere is nothing which corresponds to the passage from n to n+l which is the key step in any proof by mathematicalinduction. Those who hesitate to accept these pictures as genuine proofs might think that the diagramsmerely indicate the existence of a "real"proof, a proof by mathematicalinduction or by using E-6 techniques, respectively. Perhaps they even wish to appeal to the well known distinction between discovery andjustification: the picture is part of the discovery process while true justification comes only with the verbal/symbolic proof. But consider: would a picture of an equilateral triangle make us think there is a proof that all triangles are equilateral? No. Yet the above picture makes us believe-rationally believe-that the theorem is true and even that there is a verbal/symbolic proof of the theorem to be found, if we were to hunt for it. The picture is evidence for the existence of a "real"proof (if we like to talk that way), and the "real"proof is evidence for the theorem. But we have transitivity here; so the picture is evidence for the theorem, after all. This tangentinto the mathematicalrealm has a point. Let's see how well Norton's empiricism does with such examples. Pretty clearly, these two examples fly in the face of Norton's account. A standard,traditionalproof in mathematics is an argument; it's a derivation (though often quite sketchy) of the theorem from first principles. Proofs by induction or by e-6 techniques fit the bill. However, the two proofs by diagramthat I've given here are not like this at all; there is not the hint of an argument about them. Instead, I suggest, we accept the theorem because we grasp an abstract pattern. This is a kind of intellectual "perception." I favour a platonistic ac-

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count of what's going on similar to Gidel's view (1944, 1947) (see my 1991), but I won't push this now; it is enough to know that the Norton proposal doesn't work in these mathematical cases. I would even go a step furtherand say that Norton's view of thought experiments is the analogue of the standardview of diagrams in mathematics. In both cases the picture or the visualized situation is allowed to be psychologically helpful, but plays not role in the real justification of the mathematicaltheorem or the scientific theory; justification, according to him, can only come via an argument from premisses which have already been established. Of course, Norton is interested in what goes on in science, not mathematics, so there are no morals to be drawn yet. But an interesting question does obviously arise: Do any thought experiments resemble the mathematicalcases? As you might imagine, I am now going to argue: Yes. Consider, first, my favourite example. This is Galileo's wonderful thought experiment in the Discorsi to show that all bodies, regardless of their weight, fall at the same speed (Galileo, 1974, pp. 66f). It begins by noting Aristotle's view that heavier bodies fall faster than light ones (H > L). But what would happen if a heavy cannon ball is attached to a light musket ball?

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Reasoning in the Aristotelian manner leads to an absurdconclusion. On the one hand, the light ball will slow up the heavy one (acting as a kind of drag), so the speed of the combined system would be slower than the speed of the heavy ball falling alone (H > H+L). One the other hand, the combined system is heavier than the heavy ball alone, so it should fall faster (H+L > H). We now have the absurdconsequence that the heavy ball is both faster and slower than the even heavier combined system. Thus, the Aristotelian theory of falling bodies is destroyed. But we are far from finished. We still want to know: which falls faster? The right answer is now obvious. The paradox is resolved by making them equal; they all fall at the same speed (H = L = H+L).

If we try to analyze this example from Norton's perspective we will run into trouble. The first part of the thoughtexperimentsfits his account well. We have an argument, startingfrom Aristotelian premisses, and ending in a contradiction;so it's a reductio ad absudum of those premisses. This much is certainlyacceptable to any empiricist. It's

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the second part of the though experiment that's problematicfor Norton. When we see that H = L = H+L, we grasp it immediately. It is not based upon empiricalexperience; in fact all our actual observations are to the contrary:heavy objects generally do fall faster thanlight ones. And it does not follow from otherpremisses. We are intellectually primed by the discovered absurdityin Aristotle's theory. But Galileo's conclusion does not follow from that absurdity(except in the trivial sense that anythingfollows from a contradiction-but, clearly, that's not what is going on here). In sum, I've tried to make a case against Norton's empiricism in two ways. First, there are thought experiments such as Maxwell's that try to answer "how possible?" questions and lead to scientific understanding;as explanations they are not arguments, but narrations. Second, there are thought experiments such as Galileo's which result in something like an immediate perception; they, too, are not arguments,but instead are vehicles to directing our attention so that we can simply see for ourselves-and I do mean see.

Note 1I wish to thank my co-symposiasts, David Gooding and Nancy Nersessian, and also several of my Toronto colleagues, especially Ian Hacking, my commentator,for their remarkson an earlier draft. I am also glad to acknowledge the financial help of S.S.H.R.C.

References Brown, J.R. (1991), The Laboratory of the Mind: ThoughtExperimentsin the Natural Sciences, New York and London: Routledge. _ _ _ ___ . (1993), Smoke and Mirrors: How Science Reflects Reality, New York and London: Routledge. Godel, K. (1944), "Russell's Mathematical Logic", reprintedin Benacerrafand Putnam (eds.). Philosophy of Mathematics, Cambridge:CambridgeUniversity Press, 1983. Godel, K. (1947), "What is Cantor's Continuum Problem?",in Benacerrafand Putnam (eds.). Philosophy of Mathematics, Cambridge:CambridgeUniversity Press, 1983. Galileo, (1974), Two New Sciences, (Trans. from the Discorsi by S. Drake). Madison: University of Wisconsin Press. Kuhn, T.S. (1964), "A Function for Thought Experiments",reprintedin The Essential Tension, Chicago: University of Chicago Press, 1977. Leff, H. and A. Rex (eds.) (1990), Maxwell's Demon, Princeton:Princeton University Press. Mach, E. (1960), The Science of Mechanics, (Trans by J. McCormack), sixth edition. LaSalle Illinois: Open Court.

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_ _ _ __ (1976), "On Thought Experiments", in Knowledge and Error, Dordrecht: Reidel. Maxwell, J.C. (1871), Theory of Heat, London: Longmans. Norton, J. (1991), "ThoughtExperiments in Einstein's Work",T. Horowitz and G. Massey (eds.). Thought Experiments in Science and Philosophy, Savage, MD: Rowman and Littlefield. Sorensen, R. (1992), ThoughtExperiments, Oxford: Oxford University Press.