Abstract
This paper presents a critical analysis of Tamar Szabó Gendler’s view of thought experiments, with the aim of developing further a constructivist epistemology of thought experiments in science. While the execution of a thought experiment cannot be reduced to standard forms of inductive and deductive inference, in the process of working though a thought experiment, a logical argument does emerge and take shape. Taking Gendler’s work as a point of departure, I argue that performing a thought experiment involves a process of self-interrogation, in which we are compelled to reflect on our pre-existing knowledge of the world. In doing so, we are forced to make judgments about what assumptions we see as relevant and how they apply to an imaginary scenario. This brings to light the extent to which certain forms of skill, beyond the ability to make valid logical inferences, are necessary to execute a thought experiment well.
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Notes
This kind of logical reconstruction has been carried out on many TEs including Galileo famous falling bodies TE (Schrenk 2004).
Gendler distinguishes between two ways in which we may take the logical reconstruction of a TE as equivalent to the execution of a TE: (a) the dispensability thesis, according to which “[a]ny good TE can be replaced without loss of demonstrative force, by a non-TE argument”, and (ii) the derivativity thesis, according to which “[t]he justificatory force of any good TE can only be explained by the fact that it can be replaced, without loss of demonstrative force, by a non-TE argument. Needless to say, Gendler rejects both theses (1998, p. 401).
These conditions in brackets are often neglected in modern presentations of the TE, but we can skip over them for the sake of the reconstruction.
Miklós Rédei has argued that this “assumption is indeed not self-evident and is in need of empirical testing” (Rédei 2003, p. 238).
For the sake of simplicity we can assume that (i) the units of speed and weight are the same, and (ii) the natural speed of a unified body is the mean of the natural speeds of each of the two bodies.
Gendler’s position is in many respects reminiscent of one we find in Lakatos’ well known work, Proofs and Refutations, in which the protagonists of the dialogue ponder the status of ‘hidden assumptions’ and ‘unconsciously held lemmas’ in the analysis of a mathematical proof (Lakatos 1976).
Here we can compare the intuitions of Tycho Brahe and Galileo on what would occur aboard a moving ship. In his Episteolarum astronomicarum Tycho claimed: “Indeed certain men think that a missile hurled upwards from a ship, if this would occur inside of the vessel, would fall to the same place if the ship is moving as if it remained motionless. They offer these theories without any reflexion for it actually happens quite differently than they suppose. In fact the swifter the ships advance, the more differences will be discovered. The same thing results from the (supposed) revolution of the earth” (Overmann 1975, p. 14). We may contrast this with Galileo’s account in the Dialogue on the Two Chief World Systems, which considers almost exactly the same scenario, although arrives at an entirely different conclusion. “So long as the motion is uniform and not fluctuating this way and that”, Galileo maintains that objects moving around in the cabin of a ship would undergo no noticeable effects in their motions: “You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still... the ship’s motion is common to all the things contained in it, and to the air also. That is why I said you should be below decks; for if this took place above in the open air, which would not follow the course of the ship, more or less noticeable differences would be seen in some of the effects noted” (Galilei [1632] 1953, pp. 186–187).
Alisa Bokulich, draws the conclusion that “(for TEs in physics) the very description of a TE requires a great many abstract symbolic expressions whose meaning and correspondence with the facts are indicated by theories” (Bokulich 2001, pp. 300–301).
For Gendler, “How one goes about individuating TEs is a question on which I will allow myself to remain neutral: Is Einstein’s clock-in-the-box TE (which assumes classical spacetime) the same TE as Bohr’s (which assumes relativistic spacetime)? ... Is the TE that I perform when I read Galileo’s text the same as the TE Galileo performed when he wrote it? Nothing of what I will go on to say will turn on how these questions—to which it seems difficult to find principled answers—are dealt with” (Gendler 2004, p. 1161 fn 9).
Here we might think of the different elaborations of the EPR TE by Einstein and Bohr, or the versions of Maxwell’s demon presented by Smoluchowski, Szillard and Brillouin, or Mach’s critical analysis of Newton’s spinning bucket TE.
One might well question whether Bohr’s assumption (of employing a relativistic energy-time relation) was relevant, given that the TE was intended to show the incompleteness of non-relativistic quantum mechanics. It is not at all obvious why certain relativistic assumptions should be relevant, or even necessary, in this context. However, my point here is not to argue for the reevaluation of Bohr’s triumph over Einstein. I merely wish to point out that judgments about the relevance of certain assumptions are indispensable for TEs.
In the years from 1911 to 1915, a number of leading physicists expressed some disagreement about precisely which aspect of relativity theory was relevant for the resolution of the paradox. While it was generally agreed that only one of the twins experienced a change in inertial reference frame, such noted physicists as Max von Laue, Max Born and Albert Einstein offered different explanations of the phenomenon (see Miller 1981, p. 261; Jammer 2006, p. 165).
It is interesting to note that Humphreys argues that TEs are not well-defined problems. But this seems too restrictive, and would exclude many cases commonly considered to be good examples of TE, such as the ladder-barn paradox. It seems rather that knowing whether or not a TE is ‘well-defined’ in the sense of containing all the necessary and sufficient conditions for its resolution is precisely one of the skills of a good thought experimenter (Humphreys 1993).
As de Regt and Dieks make clear: “It is possible to have technical proficiency in manipulating formulas and symbols in the theory, without possessing understanding” and conversely “it is possible to understand how a theory works without being able to do precise calculations with it” (De Regt and Dieks 2005, p. 151).
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Camilleri, K. Toward a constructivist epistemology of thought experiments in science. Synthese 191, 1697–1716 (2014). https://doi.org/10.1007/s11229-013-0358-1
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DOI: https://doi.org/10.1007/s11229-013-0358-1