|July 12, 2002; August 9, 2002; November 24, 2002.
Prepared for: Christopher Hitchcock (ed.)
Contemporary Debates in the Philosophy of Science. Blackwell.
John D. Norton1
Department of History and Philosophy of Science
University of Pittsburgh
Pittsburgh PA USA 15260
The Epistemological Problem of Thought Experiments
The essential element in experimentation is the natural world. We learn about the natural world by watching what it does in some contrived circumstance. Just imagining what the world might do if we were to manipulate in this way or that would seem futile, since it omits this essential element. Yet the literature of science frequently leads us to just such imaginary experiments, conducted purely in the mind, and with considerable apparent profit. These are "thought experiments." We imagine a physicist trapped in a box in remote space, that the box is accelerated by some outside agent, and, from tracing what we imagine the physicist would see in the box, arrive at one of the fundamental physical principles Einstein used to construct his general theory of relativity. If this can be taken at face value, thought experiments perform epistemic magic. They allow us to use pure thought to find out about the world. Or at least this is dubious magic for an empiricist who believes that we can only find out about the world from our experience of the world.
Can thought experiments perform this magic? My concern in this chapter is restricted to this one question, which we can label the epistemological problem of thought experiments in the sciences:
Thought experiments are supposed to give us knowledge of the natural world. From where does this knowledge come?
I shall also restrict myself to thought experiments as they are used in the sciences, although I expect that my analysis and conclusions can be used in other contexts. My concern is not directly with the many other interesting facets of thought experiments: their effective exploitation of mental models and imagery, their power as rhetorical devices; their entanglement with prior conceptual systems; their similarity to real experiments; and so on. More precisely, I am concerned with these facets only in so far as they bear directly on the epistemological problem.
My goal in this chapter is to state and defend an account of thought experiments as ordinary argumentation that is disguised in a vivid pictorial or narrative form. This account will allow me to show that empiricism has nothing to fear from thought experiments. They perform no epistemic magic. In so far as they tell us about the world, I shall urge that thought experiments draw upon what we already know of it, either explicitly or tacitly; they then transform that knowledge by disguised argumentation. They can do nothing more epistemically than can argumentation. I will defend my account of thought experiments in Section 3 by urging that the epistemic reach of thought experiments turns out to coincide with that of argumentation and that this coincidence is best explained by the simple view that thought experiments just are arguments. Thought experiments can err—a fact to be displayed by the thought experiment - anti thought experiment pairs of Section 2. Nonetheless thought experiments can be used reliably and, I will urge in Section 4., this is only possible if they are governed by some very generalized logic. I will suggest on evolutionary considerations that their logics are most likely the familiar logics of induction and deduction, recovering the view that thought experiment is argumentation. Finally in Section 5 I will defend this argument based epistemology of thought experiments against competing accounts. I will suggest that these other accounts can offer a viable epistemology only insofar as they already incorporate the notion that thought experimentation is governed by a logic, possibly of very generalized form.
A Test for Any Epistemology of Thought Experiments
How are we to know that we have a viable epistemology of thought experiments? I propose a simple test. It is presented here as a gentle warm up exercise that the reader is asked to bear in mind as the chapter unfolds and various epistemologies are visited.
We can have cases in which one thought experiment supports a result and another thought experiment supports the negation of the same result. These I will call "thought experiment - anti thought experiment pairs." An epistemology of thought experiments must give us some account of why at least one of these fails. It is not enough for us to know by other means that one or other fails. We must be able to explain what went wrong in the failed thought experiment itself. Consider the analogous situation with real experimentation. We may be convinced that the result reported by some experiment is incorrect; it may contradict firmly held theory, for example. If we are to retain confidence in experimentation, we must at least in principle be able to explain how the experiment could produce a spurious result.2
In the following I present three thought experiments-anti thought experiment pairs that are unified by the theme of rotation.3
2.1 Is the World Spatially Finite?
Aristotle argued in On the Heavens, Book 1, Ch. 5, 272a8-21 that the universe cannot be infinite since an infinite universe cannot rotate uniformly, as he believed our universe does. In such an infinite universe, he imagined a line ACE, infinite in the direction of E, rotating with the world about the center C and asked when it would cut another infinite line BB. We can make his analysis more thought experimental by imagining that ACE is the ray indicated by a pointing hand that turns with the universe (in the clockwise direction on Figure 1.). At the 0o position shown, ACE is parallel to BB. Prior to attaining that position, ACE does not cut BB; afterwards it does. But when does it first cut BB? It is not at the 40o position, since it has already cut BB at the 20o position; and it was not at the 20o position, since it had already cut BB at the 10o position; and so on indefinitely. No position greater than 0o is the first; but ACE has not cut BB at 0o. So ACE never cuts BB, which is impossible. (It is interesting that the thought experiment does not seem to depend on the rotation of the universe; all it requires is rotation of a pointer.)
Figure 1. Is the world spatially finite?
The corresponding anti - thought experiment is ancient, most famous and due to the Pythagorean Archytas. If the universe is finite and I go to the edge: "…could I stretch my hand or my stick outside, or not? That I should not stretch it out would be absurd, but if I do stretch it out, what is outside will be either body or place…"4