Philosophy of the Sciences (PHIL 2130)

Lecture 2: Thought Experiments II

Please note that recommended reading may be borrowed (on a two-hourly basis) from the collection in the Department of Philosophy. There is at present a reading associated with the first two lectures (see below) and, in connection with the lectures on September 16 and 18 (Max Deutsch), a section from Karl Popper Conjectures and Refutations and Paul Thagard, Why Astrology is a Pseudo-science.

1. Last time, we considered some thought experiments in ethics, mathematics and science. There are thought experiments in many other areas of study. In law, for example. Under the common law system, new laws are invented when a case before the court lacks a precedent. But supposing we wished to invent a law not in reaction to a present case but in anticipation of events that might occur in the future? You might say, for example, that even though there has been no subversion so far in Hong Kong, we nevertheless ought to devise anti-subversion laws that would serve the purpose of warning people that certain kinds of behavior will be regarded as illegal. To devise such laws requires, presumably, envisaging possible future scenarios, and asking: `What should be our response if such and such were to occur?’ This is not an examination of actual events but of contrived ones, i.e. it is an exercise in thought-experimentation. A colleague in the American Studies programme has argued that certain kinds of novels, including, prominently, works of science fiction, are extended thought-experiments. In the theory of mind, there is a very clever thought-experiment devised by John Searle which seeks to establish that no computer, just by running a program, can understand Chinese. Though these are fascinating areas of investigation, we shall confine ourselves to thought experiments in science, and the philosophical questions that they raise.

2. The philosopher-mathematician G.W.Leibniz' (1646-1716) devised a thought-experiment for refuting Descartes' Law of Collision. Descartes said that if a smaller object hits a larger one it rebounds with equal speed; if a larger object hits a smaller one, they move together in a way that conserves the total quantity of motion. Leibniz asks us to imagine one collision in which A strikes an imperceptibly larger B (so according to Descartes, A should bounce back with equal speed while B remains stationary). But next suppose that A is slightly enlarged so that it is imperceptibly larger than B and again, we cause it to strike B. According to Descartes now the two should move off together at a speed approximately half A's initial velocity. But it is absurd to suppose that such a tiny change could have such a dramatic effect, ergo the Cartesian view is wrong.

3. Are the scientific thought-experiments we have mentioned a more or a less satisfactory way of reaching a result than normal experimentation? Are the results really obtained just by thought alone?

4. A criticism of Simon Stevin’s thought-experiment: suppose that one part of the chain were denser than the other (beads more tightly packed on the `necklace'). Would the Stevin reasoning show (wrongly) that that `necklace' would also not move when released? One answer is that, after release, the weighted necklace would reach an equilibrium position -- with the heavier part at the lowest point -- there would not be perpetual motion. But now consider the unweighted necklace. Suppose it slipped to an equilibrium position. But that position would be qualitatively indistinguishable from the starting position (because the chain is homogeneous). Therefore the chain would not move from the starting position. (I've no doubt that this reasoning could be tightened up a bit.)

5. Kathleen Wilkes (Real People, p.6 f.) argues that there is a big difference between thought experiments in science and thought experiments in philosophy. Her reason seems to be that in scientific thought experiments, just as in real scientific experiments, we can hold all variables constant and just manipulate the one that we're interested in. For example, in the Stevin thought experiment, his world of thought is exactly like our world, except that the inclines he envisages are frictionless. Here the point is proved without making any other idealizations. Compare this with an example from moral philosophy. Wilkes cites Gyges ring which enables a person to disappear at will. The purpose of this thought experiment is to determine whether morality is based entirely on self-interest (for the ring would enable a person to vanish after committing an immoral act, thereby entirely escaping the consequences). Wilkes thinks that such a thought experiment is useless, because the use of this ring brings in its train a whole host of consequences and unanswered questions, so that we no longer can keep our feet on the ground - we are in a world of fantasy where we just can't say what will happen; we can't sensibly draw any conclusions.

6. Thought experiments can be constructive, in that they establish a positive result, or they can be destructive. A destructive thought experiment shows that a conjecture is false by reducing it to absurdity. As an example of a destructive thought experiment, take Galileo's depiction of an inertial frame - this is `destructive' in that its purpose is to destroy the belief that certain contrary-to-fact consequences follow from the supposition that the Earth moves. Galileo invites us not to actually go below deck on a ship and start experimenting with fish in a bowl, a bottle dripping water etc., but just to think about it. (But can we think about it properly without having had any relevant experience?)

7. Of course, this classification would allow some thought experiments to be both constructive and destructive. If the only alternative to a given conjecture is another interesting and substantial conjecture, then, in doing the destructive work of showing one conjecture false, one is constructively showing the other to be true. For example, if Galileo succeeds in refuting the claim that bodies fall at different rates, he establishes that they fall at the same rate.

8. Back to philosophical question of how thought experiments work, one reaction would be to say that they don't - that they import illicit empirical assumptions. Take Galileo's result about falling bodies, for example. Crucial to the argument is an analogy - the lighter weight would act as a drag on the heavier one just as a slower bicyclist would slow you down if he grabbed onto you as you were overtaking him. That's a reasonable assumption, but it's not necessarily true. It's an empirically plausible assumption given what we already know about the behaviour of moving bodies. Likewise with Stevin’s experiment. We do not know a priori that the string of beads will not rotate ad infinitum. Since the planets are (apparently) in perpetual motion, why not the string of beads? From experience, we know that loss of energy, e.g. through friction, prevents perpetual motion, but Stevin's experiment is supposed to be an idealization - a frictionless plane and no other energy losses. Of course, it seems overwhelmingly plausible that the beads won't move, but that it should seem so is because of what we know empirically about the materials, and we `feel' that, in going from the real cases to ideal ones, nothing is introduced that makes a substantial difference.

9. But aren't there `pure' thought experiments e.g. Maxwell's demon (designed to show that, contrary to classical thermodynamics, there can be instances where there is heat flow from a cold body to a hot one -- the demon lets through the door into the hot chamber only those fast moving molecules from the cold chamber, and the slow molecules in the cold chamber into the hot) and also Huyghens demonstration that equal elastic masses exchange their velocities on impact?

10. It is the direct and Platonic thought experiments that are philosophically most problematic, for, in these cases, we appear to be getting `something for nothing', viz., a contingent result about the empirical world but just by using a priori thought. J.R. Brown takes a Platonist line, and argues in Chap.4 of his The Laboratory of the Mind that some of our knowledge of nature is a priori - knowledge of relations between abstract universals, as in the Armstrong-Tooley-Dretske account of the laws of nature. This is a rationalist (as opposed to empiricist) position. It is not one to which many modern scientists would subscribe. One alternative worth considering is that thought-experimental results are just the deductive or inductive consequences of reasonable extrapolations from what we already know empirically to be the case about the actual world. This account contrasts with Mach's (see Roy Sorensen, Thought Experiments, pp.53-4) that we have a purely instinctive cognition that renders superfluous real experimentation with all its flaws. A section from Sorensen’s book (pp.46-75) is in the departmental collection. If you decide to write a term paper on thought experiments, there is much else in this book that you will find useful.

11. Sorensen considers various kinds of scepticism about thought experiments., e.g., that thought experiments cannot be as informative as real experiments (p.46). For example Franciscus Toletus has a thought experiment to show that vacuums are possible: take a jar full of hot water and cool it to way below freezing point. The contents now occupy less space, so the remainder of the container will be a void. But people contested this conclusion. Obviously, had it been possible then to do the experiment (as opposed to just thinking about it), that would have been far more satisfactory, and would have settled the dispute. Here is the dilemma as Sorensen sets it out on p.48:

If a thought experiment can be checked through public experimentation, then not actually checking leaves the results unverified, and an actual check would render the thought experiment redundant or misleading.

If a thought experiment cannot be checked through public experimentation, then its results are unverifiable.

Any experiment having results that must be either unverified, redundant, misleading, or unverifiable is without scientific value.

Therefore

No thought experiment has scientific value.

12. Hans Hahn, endorsing this conclusion, expresses the ludicrousness of getting conclusions about nature out of pure thought (see quote, p.50). An answer to this line of thinking, due to Mach, is that what we observe in nature imprints itself surreptitiously on our minds (cf. Nersessian's conception of mental models) so we know instinctively what can't happen (p.51). (So Mach is an empiricist - his position is excellently described in Sorensen, pp.54-55.) If, in the evolution of the human race, knowledge and cognitive predispositions acquired through experience by our animal ancestors gradually became hard-wired, then we might get it all free, a priori and innate. That could explain how, through thought experiments, we are able to obtain synthetic conclusions. For more on the question of why thought experiments work, see D. Gooding, in R. Giere (ed), Cognitive Models of Science and Sorensen, Chapter 4.