Some Thoughts on Thought Experiments

A KANTIAN ACCOUNT?

Since I cannot find a satisfactory Kantian approach (by the way, Buzzoni’s article seems to be a terrible translation from the Italian?!), I thought I would attempt to reconstruct what I think a Kantian account of Thought Experiments (TE’s) would look like. I will not defend this account here, though I am interested in what you all take to be the strengths and weaknesses of such an approach. For my purpose here, I am bracketing the issue of whether or not TE’s are really arguments. Rather, I will try to make sense of Brown’s Platonic Perception (PP).

Kantian Modalities

TE’s are different from real experiments in the sense that they deal with what “might be” the case (possibility), or sometimes what “must be” the case (necessity), but never what “is” the case (though TE’s may very well correspond, in some way, to what is the case). Take, for example, Galileo’s TE, which purports to show the inconsistency in Aristotle’s account of falling bodies. Assuming that the speed of falling bodies in a given medium is proportionate to their weights, a stone half the size of a larger stone will fall at half the rate of the larger stone. Given this, if the smaller stone is attached to the larger, we might expect the smaller, slower stone to retard the larger, faster stone. So, if the two stones are attached, their composite will fall at a slower rate than larger stone alone. Nevertheless, if the speed of falling bodies is proportionate to their weights, then we might expect that the composite will fall faster than the larger stone by itself, since the composite of both the larger and smaller stone is undoubtedly heavier than the the larger stone alone.

Evidently, the composite cannot be both faster and slower than the larger stone alone. Aristotle’s view — that the speed of falling bodies in a given medium is proportionate to their weights — leads to a contradiction, and therefore must be rejected. This discovery corresponds the Kantian modality of necessity or apodictic knowledge, i.e. what must be the case. If we accept the assumptions in Galileo’s TE, we must conclude that Aristotle’s account of falling bodies is mistaken — for how can one and the same thing be faster and not-faster in the same instance?

The first part of Galileo’s TE appears to be uncontroversial (at least when we allow for the assumptions he employs). For Brown, a TE which is able to expose a contradiction in another theory is a paradigm case of a knock-down or “destructive” TE.

The problematic portion of Galileo’s TE, as John Norton and Rachel Cooper both point out, is what Brown calls the “constructive” aspect of the TE. In the second part of the TE, Galileo goes on to draw the conclusion that all masses fall at the same rate. This is the aspect of Galileo’s TE that Brown takes to be an instance of PP. From a Kantian standpoint, this is a clear case of dogmatism. So-called Platonic objects (or forms) are not only unintelligible, but our supposed relation to these objects is also unintelligible. Indeed, for Kant, the status of our relation to any purportedly real object is precarious at best; and, as it stands, there is an absence of any clear criteria for determining whether or not (or how) we have accessed or perceived the Platonic realm. Brown defends PP by saying that our relation to empirical objects is no less mysterious than our relation to the Platonic realm. Kant would agree with this insight — however, this only furthers the Kantian intuition that we can only to talk in terms of appearances.

Aside from the fact the Brown gives us no tools for recognizing PP, he is equally unclear about what exactly PP is. I will say more about this in the next section. For now, the important point is that Galileo need not have reached the conclusion that all bodies fall at the same rate, nor does the conclusion follow naturally for every reader who considers the TE. As Cooper puts it: “Showing that heavy bodies do not fall faster than light bodies is consistent with a multitude of alternative theories, such that red balls fall faster than balls of other colours, that square objects fall faster and so on. Brown thinks that Galileo’s success in picking the right theory can only be explained by his Platonic account. For Brown the thought experiment enables Galileo to perceive the Platonic laws that govern the movement of masses and so see that all masses fall at the same rate.” Norton also exposes the various tacit assumptions that Galileo employs in his TE.

So, we might say that the constructive aspect of Galileo’s TE corresponds to the Kantian modality of possibility. It is possible that all bodies fall at the same rate. Indeed, based on Galileo’s background assumptions, this appears to be the best explanation. At any rate, it is not the only possible explanation. Because Galileo employs certain background assumptions (e.g., that colour, shape, chemical composition, and so on, have no effect on the rate at which a mass falls), the only consistent options left are: (1) that heavy masses fall more quickly than light masses; (2) that light bodies fall more quickly than heavy bodies; or (3) that all masses fall at the same rate. Since Galileo’s reductio showed that (1) and, mutatis mutandis, (2) cannot be the case, (3) is the only option left (again, given the background assumptions). Whether or not Galileo’s TE generated this insight (which may or may not be a contingent matter of fact) does not seem to me all that important. The important point is that — on a Kantian reading at least — the constructive aspect of the TE appears to correspond only to physical or hypothetical necessity (possibility). After all, there is is no contradiction involved in saying that ‘all masses do not fall at the same rate.’ Nor does this judgment appear to be a necessary condition of human experience.

De Dicto and De Re Necessity

In the Kantian framework, there are certain first principles of physics which are absolutely or metaphysically necessary, e.g., the principle of the conservation of matter, Newton’s law of inertia, or the law of the equality of action and reaction. Kant terms these principles synthetic a priori judgments of physics. Of course, these judgments do not fit Kant’s definition of analyticity, and are therefore synthetic. They are also a priori inasmuch as they constitute the form of experience, as opposed to the content of experience. For Kant, these laws are metaphysically necessary insofar as they make experience of a certain kind possible.

Determining which laws are metaphysically necessary or only physically or hypothetically necessary is doubtless a difficult task. Rather than treading through these muddy waters, I will say why both cases are ultimately instances of logical possibility for Kant; and why Brown’s PP reveals nothing more than what logically possible.

It is clear that Kant would consider Galileo’s law that ‘all masses fall at the same rate’ as an a posteriori judgment expressing hypothetical or physical necessity. As Norton points out, there is no mysterious Platonic leap here. Our degree of belief in the conclusion of Galileo’s TE corresponds to our degree of belief in the assumption that the degree of fall of bodies depends only on their weights (which, of course, is not true in instances where the shape of the objects differ). The tacit assumptions Galileo uses are based on experience. Thus, in Kant’s framework, Galileo’s conclusion is synthetic and a posteriori (at most, physically necessary or contingently true).

Whether or not we think that Galileo’s law is physically or metaphysically necessary, it is clear that it is not necessary in a strong sense (i.e. logically necessary or necessary in all possible worlds). Brown treats PP of natural laws as analogous to PP of mathematical truths. But even if we assume that there are mathematical entities existing in some realm outside space and time (i.e. Platonic objects), these entities are in no way analogous to natural laws — which presumably exist within the bounds of space and time.

Thus Brown’s PP, from a Kantian standpoint, is no more than the perception of physically or metaphysically necessary, spatio-temporal laws of nature. Since space and time, for Kant, are transcendentally ideal and empirically real, though not (necessarily) transcendentally real, it follows that the physical laws of nature also lack the necessity that Brown is looking for. While mathematical objects may be Platonic entities insofar as they may obtain in all possible worlds, it is unclear how mathematical entities are analogous to natural laws, since the former may be considered to be non-spatial and non-temporal, while the latter depend on a spatio-temporal framework.

Anyway, I have a lot more to say about how TE’s are successful/unsuccessful; whether or not they are arguments; and whether or not they are equivalent to real experiments. Since this is getting long, I will leave you with my rushed Kantian account of TE’s. The most important point here is that the supposed PP in the Galileo TE is nothing more than the perception of physical necessity based on empirical assumptions. This is in accordance with Cooper's and Norton's accounts. Although, we might ask whether TE’s are able to reveal the forms of experience — i.e. laws which are metaphysically necessary?