Aristotle said that heavier bodies fall faster than lighter bodies. If you were to drop a cannon ball and a musket ball from a tower then the cannon ball would hit the ground first. Galileo contradicted Aristotle’s claim using a thought experiment. Imagine that we tied together the heavier body to the lighter body and then dropped them. According to Aristotle’s theory, the compound ball is going to fall faster than either ball individually because it weighs more. But since they are tied together the musket ball would retard the speed of the cannon ball, making this compound ball fall slower than the cannonball. Intuitively, this is an absurdity. So Galileo concludes that Aristotle’s theory must be wrong.
The only possibility left was that heavier bodies fall at the same rate as lighter bodies because the opposite of Aristotle’s theory is also absurd. What is fascinating about this thought experiment is it seems to give us knowledge about the world and how bodies fall, without presenting us with any facts or new information. And yet it seems like we can come away from the act of imagining with a new piece of knowledge. The philosophical questions surrounding thought experiments is how this is possible.
If thought experiments didn’t give us knowledge then both philosophers and scientists would be out of a job. Because of this they want to say that thought experiments do give us knowledge. Nevertheless, those who accept them are divided. They argue between whether or not the knowledge is a priori or a posteriori. This is the Epistemological Puzzle of Thought Experiments. It asks: Where does this new knowledge come from?
Execution: The way the thought experiment is executed in our minds and how we come to be convinced by the conclusions of the thought experiments. John Norton says that this is a psychological issue. The other issue has to do with the Justification that thought experiments seem to provide.
Is the justification that we think we get ultimately based in experience or something else? Is the knowledge that we seem to get from some thought experiments a priori or a posteriori?
Brown on Thought Experiments
Brown thinks that at least some thought experiments are a priori. This is because he thinks that the knowledge that we get from them cannot be got from experience alone, as in the example of Galileo’s cannon ball and musket ball. He says there are Extensive Properties in thought experiments and these have to do with the matter in an object, like mass, weight, height and volume. These properties he calls additive. The opposite are Intensive properties and don’t have to do with the amount of matter in an object(s) like temperature or density. These properties are not additive.
Brown says to substitute extensive properties for weight in the original thought experiment, imagining that one ball is higher then the other, or has greater volume, then imagine how it will fall and you will derive the same contradiction in the original thought experiment. This shows that the rate at which objects fall is independent of all extensive properties. Brown says that we are not justified in believing this on the experience of the world. We have not observed objects of different mass, height, volume falling. He says we know this a priori.
How can we have a priori knowledge about the way nature works? Brown’s answer rests on what he and Norton call the Platonic View of Laws of Nature, which state that laws of nature are not just correlations or constant conjunctions between physical things, they are actually relations between universal abstract properties. They are properties that exist independently of us, outside time and space.
Ex. Ideal gas law: Gas expands when heated. According to the Platonic view, if ideal gas law is a law of nature, it is because you have the abstract universal property of being a gas, and you have the property of expanding when heated, and if this is a law of nature there is a relation of nomic necessity. Every actual gas (every physical instantiations of the abstract property) in the world does in fact expand when heated.
We can come to know laws through empirical observation, but the laws of nature do not just consist in observed correlation or physical connection. It is something more then that. Brown wants to say that we think of the laws of nature the same way we think in math—intuitively.
Norton on Thought Experiments
Norton, unlike Brown, is an empiricist, which means he thinks that all knowledge of the world comes from justification from experience and observation. He wants an account of thought experiments that is consistent with his empirical view. That is his first criterion. The second is that thought experiments must explain why some are not reliable while others are. Brown does not emphasize this point but Norton thinks it’s important. Norton thinks that while not all thought experiments have anti-thought experiments which contradict them, many do.
Ex. Imagine a helicopter that has infinitely long blade, will it fly? NO! The amount of lift that a helicopter generates is a function of the speed at which the propeller pushes down the air as well as the mass of air under the rooter. The mass of air is a function of how long the propeller is. The velocity is a function of how fast the rooter turns. In this case if you were to slow down the rooter you could generate the same amount of lift simply my lengthening the rooter.
Imagine doubling the length of the rooter. Doing this more than doubles the amount of air under it. By doing this you will have the speed that it is needed to lift the copter. You can continue doubling the length. At one point you will have an infinitely long rooter that does not need to move at all to generate lift.
This cannot be considered to be a reliable thought experiment. Thought experiments have to help us decide between them and their anti-thought experiments. To satisfy his two criteria, Norton thinks thought experiments are disguised arguments. This is a claim about both the execution and justification of thought experiments. Norton claims that all thought experiments can be reconstructed as arguments, and we are justified in accepting the conclusion of a thought experiment in so far as the argument that is built into it is a good one. All thought experiments can be reconstructed as arguments.
Norton says that these thought experiments are reduction ad absurdum. An example would be Aristotle’s view on the two balls:
1. Assumption: Heavier bodies fall faster than lighter ones.
2. Cannonball is heavier than a musketball.
3. If we combine heavier and lighter object, heavier object will speed up lighter object & lighter object will slow down heavier object.
4. If we combine the cannonball and musketball, the composite will fall slower then the cannonball.
5. The composite will be heavier than the cannonball.
6. The composite will fall faster than the cannonball.
4 & 6 contradict, so
1 must be false.
We come to be convinced of the conclusions of thought experiments because, according to Norton, we have reconstructed the argument and have seen that it is a good argument.
The challenge for the empiricist is, how we can get new empirical information from a thought experiment without putting any in? Norton says that if thought experiments are arguments, then like all arguments they take as premises knowledge or information that you already posses and they transform that knowledge. That new knowledge is implicit in that old knowledge. Therefore, if thought experiments are arguments then they are essentially doing the same thing. This is how Norton meets the first criterion.
Norton says that if thought experiments are just arguments then the obvious explanation for why some TEs are good and some are bad is that some arguments are good, and some are not. Some may have bad premises or that they draw illegitimate inferences. Others will be good because the premises are justified and the conclusions follow logically from the premises.
Norton vs. Brown
Norton says that his view explains why some TEs go awry and tells which are trustworthy and which are not. Norton thinks that Brown’s view can’t do those things. Brown says TEs go awry because our intellectual perception is fallible and sometimes wrong. Norton doesn’t consider this a good explanation, not unless Brown can tell us more about how intellectual perception works and how it fails. But Brown doesn’t seem to have any of this information, he doesn’t have a theory for how the intellectual perception works and no rules to determine when it is reliable and when it is not. So Norton believes that this is where his view is better.
Another point of disagreement: Can all thought experiments be reconstructed into arguments? And should they be? Norton is able to draw out arguments from all of Brown’s thought experiments. Brown says that this does not show much however. Just because an argument can be drawn out doesn’t mean that this is what is happening in our minds. TEs are not justified because they can be transformed into arguments. Norton argues that is it not a bizarre coincidence that all thought experiments are able to be constructed as arguments—because they are in fact arguments.
By: Steven Umbrello – Originally posted on The Leather Library Blog