The use of a specific a priori method in philosophy is often justified by remarking that the same method is also used to good effect in physics. The method in question is, of course, the use of thought experiments to refute, or to support, claims or theories. A thought experiment can be characterized as stipulating a scenario and then ‘playing it through’ in one’s head. There is much to say about thought experiments, their epistemic status, and the role they play in science, but here I will settle with making some observations about one of the most celebrated thought experiments in physics and philosophy: Galileo’s two falling bodies.
In his Dialogues Concerning Two New Sciences (Discorsi e Dimostrazioni Matematiche intorno a Due Nuove Scienze, 1638 [1954]) Galileo Galilei’s stand-in, Salviati, tries to convince his interlocutors Sagredo and Simplicio of the inconsistency of Aristotelian physics. Salviati states that even without performing any experiments it is possible to show that Aristotle is wrong in his claim that heavier bodies fall faster than lighter ones. To wit:
If […] we take two bodies whose natural speeds are different, it is clear that on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter.
Galileo 1954: 63 [107]
After Simplicio agrees with him Salviati continues:
But if this is true, and if a large stone moves with a speed of, say, eight while a smaller moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter; an effect which is contrary to your supposition. Thus you see how, from your assumption that the heavier body moves more rapidly than the lighter one, I infer that the heavier body moves more slowly.
Galileo 1954: 63 [107–108]
Here Simplicio fails to follow Salviati, and I will soon argue, is not wrong in doing so. Salviati does go on to solidify his reasoning, but the crucial trick has already been played. In any case the above is the way Galileo’s thought experiment is usually presented (Brown 2010: 1–2, Brown & Fehige 2019).
It occasionally behooves one to formalize an argument, just to see what the requisite premises are. This is one of those occasions. The form of Galileo’s argument is as follows:
- P1: Heavier objects fall faster than lighter ones. (From Aristotle)
- P2: Uniting a light object (mass m1) to a heavy one (mass m2) will slow down the heavy object.
- P3: Uniting a heavy object (mass m2) to a light one (mass m1) will speed up the light object. (Included for completeness.)
- C: So an object with mass m1 + m2 will fall slower than one with mass m2. (From P2)
- But from P1 m1 + m2 will fall faster than m2. A contradiction!
The Aristotelian is committed to P1, so in order to evade the contradiction, he will have to deny P2 and P3. Is this move available to him? It indeed is, for there is a hidden assumption at play here, one that does all the heavy lifting. In order to justify P2 and P3, one needs to argue that one can consider parts of composite objects as if they were separate. Let us look at this more closely.
Consider two cannon balls of masses m1 and m2 (m1 < m2). Now tie these together with a piece of string (of negligible mass). Then we will have a composite object of mass m1 + m2. Can cannon ball 1 (of mass m1) act as a drag for cannon ball 2? Intuitively it seems that it can, since it has the smaller mass and thus in Aristotelian physics it will fall slower and so attaching it to the heavier ball will slow the heavier ball down. I will argue that this intuition is mistaken. I will borrow a leaf from Daniel Dennett’s book (2013: 7) and turn the knobs of this intuition.
Now it seems that if the cannon balls are tied together with a piece of string, we can, in some important respect, consider their kinematic properties separately from the whole composite object. What then is the case if we glue the cannon balls together? Can we still consider their kinematic properties separately? If not, why not? Is glue different from string in some (metaphysically?) special way? If glue works the same way as string, then why not consider all objects that have parts as refuting Aristetelian physics? But of course the Aristotelian will not agree with this! If, on the other hand glue is taken to be different from string in combining objects, then surely this requires further arguments, and in lieu of them the Aristotelian can rest content.
To be explicit: the move the Aristotelian should resist (as should all of us) is the one where one willy nilly considers parts of a composite object occasionally as separate objects and occasionally as a singular object. Resisting this move removes support from P2 and P3, and at the same token the contradiction. So Simplicio made a mistake in agreeing with Salviati’s claim that “it is clear that on uniting the two, the more rapid one will be partly retarded by the slower (Galileo 1954: 63 [107]).” As we can see this was far from clear. So, at least on this occasion, Galileo did not refute Aristotle by sheer force of reason.
Now, am I saying that Aristotelian physics was in good standing after Galileo’s treatment of it? Of course not. I am merely pointing out that, unlike some over ambitious defenders of thought experiments claim (Brown 2010: 2, Brown & Fehige 2019), this particular thought experiment is far from devastating. Galileo’s greatness is in his impeccable experimentation and rigorous mathematization of physics. These, not some clever thought experiments, rang the death knell of Aristotelian physics.
So what then of thought experiments in general? It is clear that they have played a major role in the development of physics and philosophy. However I believe that their (especially epistemic) importance has been overplayed, as my analysis above shows. By all means feel free to explore your intuitions about imagined scenarios to your hearts’ content – such exploration might give rise to new hypotheses and arguments, and admittedly it can be great fun. But do not think that such methods suffice to show such hypotheses and arguments to be true. If only it were so easy!
References:
Brown, James Robert (2010). The Laboratory of the Mind, 2nd edition, New York: Routledge.
Brown, James Robert and Yiftach Fehige (2019). Thought Experiments, in The Stanford Encyclopedia of Philosophy (Winter 2019 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/win2019/entries/thought-experiment/
Dennett, Daniel C. (2013). Intuition Pumps and Other Tools for Thinking, New York: W. W. Norton & Company.
Galileo (1954). Dialogues Concerning Two New Sciences (trans. Henry Crew & Alfonso de Salvio), Norwich NY: William Andrew Publishing. (Also published in Hawking, Stephen (ed.) On the Shoulders of Giants, London: Penguin Books, 2003, 399–626.)
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