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TimS comments on How to Not Lose an Argument - Less Wrong
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I can't write it better than Feyerabend. My argument about Aristotelian and Newtonian physics is a paraphrase of section 5 of his argument, starting at pg. 94, and ending at about 101.
ETA: And I looked at it again and it's missing 95-96, where some of the definitions are. If there's interest, I'll type it up, because I think it addresses the criticisms fairly well.
Ok, I have to admit that I haven't read the entire book, but only skimmed the section your mentioned -- because my time is limited, but also because, in its infinite wisdom, Google decided to exclude some of the pages.
Still, I can see that Feyerabend is talking about the same things you're talking about; but I can't see why those things matter. Yes, Aristotle had a very different model of the physical world than Newton; and yes, you can't somehow "plug in" Aristotelian physics into Newtonian mechanics and expect it to work. I agree with Feyerabend there. But you could still go the other way: you can use Newtonian mechanics, as well as what we know of Aristotle's environment, to explain why Aristotle got the results he did, and thus derive a very limited subset of the world in which Aristotle's physics sort of works. This does not entail rewriting the entirety of Newtonian mechanics in terms of Aristotelian physics or vice versa, because Aristotle was flat out wrong about some things (a lot of things, actually). Feyerabend seems to believe that this makes the two theories incommensurate, but, as I said above, by that standard the word "incommensurate" becomes synonymous with "different", which is not informative. I think that Feyerabend's standards are simply too high.
I was also rather puzzled by something that Feyerabend says on page 98, toward the bottom. He says that "impoetus" and "momentum" would give you the same value mathematically, and yet we can't treat them as equivalent, because they rest on different assumptions. They give you the same answer, though ! Isn't this what science is all about, answers ?
Let me illustrate my point in a more flowery way. Let's say that Aristotle, Newton, and Einstein all went to a country fair together, and entered the same block-pushing contest. The contestant randomly picks a stone block out of a huge pile of blocks of different sizes, and then a tireless slave will push the block down a lane (the slave is well-trained and always pushes the block with the same force). The contestant's job is to predict how far the block will slide before coming to rest. The contestant will win some amount of money based on how close his prediction was to the actual distance that the block traveled.
As far as I understand, Feyerabend is either saying that either a). Aristotle would win less money than Newton who would win less than Einstein, but we have no idea why, or that b). We can't know ahead of time who will win more money. Both options look disingenuous to me, but it's quite likely that I am misinterpreting Feyerabend's position. What do you think ?
If we imagine a test given by an Aristotelian physicist, defining impetus with the Newtonian definition of momentum would get no points (and vice versa). Feyerabend says
In other words, impetus is meant to explain, while momentum is something to be explained. The point is that it's very odd that two theories on the same subject disagree about what explains and what needs to be explained. (Imagine if one scientist proposed that cold caused ice, and the next generation of scientist proposed that ice caused cold, while making more accurate predictions). In the same way that impetus is a primary explanation for Aristotle, force is a primary explanation for Newton. And impetus and force are nothing alike. The assertion is that this type of difference is more than saying that Newton had better data than Aristotle.
In your hypothetical, I think that Feyerabend says something like (a). Perhaps "Aristotle would win less money than Newton who would win less than Einstein, but the naive scientific method cannot explain why." For some perspective, Feyerabend is opposing Ernest Nagel and logical positivism, which asserts that empirical statements are true by virtue of their correspondence with reality. If you believe Newtonian physics, the causal explanation "Impetus" doesn't correspond with any real thing (because momentum does not explain, but is to be explained). You could bit the bullet and accept that impetus is a false concept. But if you do that, then a theory based on lots of false concepts makes predictions in the block-push contest that do substantially better than chance. How can a false theory do that?
If that's what Feyerabend is saying, then he's confusing the map for the territory:
That would indeed be odd, but as I understand it, both theories are trying to explain why objects (such as stone blocks or planets) behave the way they do. Both "impetus" and "momentum" are features of the explanatory model that the scientist is putting together. Aristotle believed (according to my understanding of Feyerabend) that "impetus" was a real entity that we could reach out and touch, somehow; Newton simply used "momentum" as a shorthand for a bunch of math, and made no claim about its physical or spiritual existence. As it turns out, "impetus" (probably) does not have an independent existence, so Aristotle was wrong, but he could still make decent predictions, because the impetus's existence or lack thereof actually had no bearing on his calculations -- as long as he stuck to calculating the motion of planets or rocks. In the end, it's all about the rocks.
What is the "naive scientific method", in this case ? How is it different from the regular kind ?
No, you can't, since the existence of impetus as an independent entity is unfalsifiable (if I understand it correctly). The best you can do is say, "this impetus thing might exist or it might not, but we have no evidence that it does, so I'm going to pretend that it doesn't until some evidence shows up, which it never will, since the concept is unfalsifiable". Aristotle probably would not have said that, so that's another thing he got wrong.
The statements "ice causes cold" or "cold causes ice" are both falsifiable, I think, in which case the "ice causes cold" theory would make less accurate predictions. It might fail to account for different freezing temperatures of different materials, or for the fact that the temperature of a liquid will not decrease beyound a certain point until the entire volume of the liquid had frozen, etc.
I think that Feyerabend is mostly talking about maps, not territory. I shouldn't have said naive scientific method, because naive is unnecessarily snarky and I'm talking about a different basic philosophy of scientists than the scientific method. The basic "truth theory" of science is that we make models and by adding additional data, we can make more accurate models. But in some sense, the basic theory says that all models are "true."
That leaves the obvious question of how to define truth. "Makes accurate predictions" is one definition, but I think most scientists think that their models "describe" reality. The logical positivists tried to formalize this by saying that models (and statements in general) were true if they "corresponded" with reality. Note that this is different from falsifiability, which is basically a formal way of saying "stick your neck out." (i.e. the insight that if your theory can explain any occurrence, then it really can't explain anything) The Earth suddenly reversing the direction of its orbit would falsify impetus, momentum, relativity, and just about everything else human science knows or has ever thought it knew, but that doesn't tell us what is true.
For the logical positivist, when one says that "impetus does not have an independent existence" that means "impetus is false." There is some weirdness in a "false" theory making accurate predictions. To push on the map/territory metaphor slightly, if Columbus, Magellan, and Drake all came back with different maps of the world but all clearly got to the same places, we would be justified in thinking that there was something weird going on. Yet if you adopt the logical positivist definition of truth, that seems to be exactly what is happening. At the very least, the lesson is that we should be skeptical of the basic theory's explanation of what models are.
I really don't think so. Let's pretend that my theory says that lighter objects always fall slower than heavier ones, whereas your theory says that all objects always fall at the same rate. Logically speaking, only one of those theories could be true, seeing as they state exactly opposite things.
In addition, if I believe that the Moon is made out of green cheese, and so does everyone else; and then we get to the Moon and find a bunch of rocks but no cheese -- then my theory was false. I could make my green cheese theory as internally consistent as I wanted, but it'd still be false, because the actual external Moon is made of rocks, whereas the theory says it's made of cheese.
I prefer my truth to be simple...
What's the difference ?
Well, no, but it would tell us that lots are things we thought are true are probably false. In order to figure out what's likely to be true, we'd have to construct a bunch of new models, and test them. I don't see this as a problem; and in fact, this happens all the time -- see the orbit of Mercury, for example.
I wouldn't say that "impetus is false" (at least, not in the way that you mean), because it's actually worse than false -- it's irrelevant. There's no experiment you can run, in principle, that will tell you whether "m*v" is caused by impetus or invisible gnomes. And if you can't ever tell the difference, then why bother believing in impetus (as an actual, non-metaphorical entity) or gnomes (ditto) ? Aristotle may not have been aware of anything like Ockham Razor (I don't know whether he was or not), but that's ok. Aristotle was wrong. Scientists are allowed to be wrong, that's what science is all about (though Aristotle wasn't technically a scientist, and that's ok too).
I don't see why you'd make the logical leap from "These three explorers had different maps but got to the same place", directly to, "we must abandon the very idea of representing territory schematically on a piece of vellum", especially when you know that explorers who rely on maps tend to get lost a lot less often than explorers who just wing it. Instead of abandoning all maps altogether, maybe you should figure out what piece of information the explorers were missing, so that you could make better maps in the future.
Is it really your position that no experiment can tell whether something is a cause or an effect? That sounds like an assertion that the statement "gravity is a cause of motion, not an effect" is not meaningful.
I'd like truth to be simple. For practical purposes, it is simple. But "simple" truth doesn't stand up to rigorous examination, in much the same way that a "simple" definition of infinity doesn't work.
Sorry, no, that wasn't what I meant. As far as I understand -- and my understanding might be incorrect -- Aristotle believed that moving objects are imbued with this substance called "impetus", which, according to Aristotle, is what imparts motion to these objects. He could calculate the magnitude of impetus as "m*v", but he also proposed that impetus (which, according to Aristotle, does exist) is undetectable by any material means, other than the motion of the objects.
In a way, we can imagine two possible universes:
Is there any way to tell, in principle, whether you are currently living in Universe 1 or Universe 2 ? If the answer is "no", then it doesn't matter whether impetus is a cause or an effect, because it is utterly irrelevant.
Contrast this with your "ice causes cold vs cold causes ice" scenario. In this case, ice and cold are both physically measurable, and we can devise a series of experiments to discover which causes which (or whether some other model is closer to the truth).
I would argue that if your rigorous examination cannot explain your simple, useful, and demonstrably effective notion of truth, then the problem is with your examination, not your notion of truth.
What is a "simple" definition of infinity, and how does it differ from the regular kind ? As far as I understand, infinity is a useful mathematical concept that does not directly translate into any scientific model, but, as usual, I could be wrong.
I don't think an Aristotelian physicist would say that impetus is "otherwise undetectable" any more than a modern physicist would say "gravity causes objects to move, but is otherwise undetectable."
There are lots of statements that we desire to assign a truth value to that a much more complicated than the number of sheep in the meadow. Kant described a metaphysical model that was not susceptible to empirical verification (that's a feature of metaphysical models generally). When we say the model is true (or false), what do we mean? If you want to abandon metaphysics, then what does it mean to say something like "qualia have property X" is true?
Is it your position that all truths are "scientific" truths? Does that mean that non-empirical assertions can't be labelled true (or false)?
I mentioned infinities an an example of an unintuitive truth, in order to argue by analogy that the intuitiveness of EY's "definition" of truth does not show that the definition is complete. Folk mathematics would assert something like "All infinities are the same size" and that's just not true.
Fair enough, but then, how would an Aristotelian physicist propose to detect impetus, if not by observing the motion of objects ? I'm pretty sure I'm missing the answer to this part, so I genuinely want to know.
The modern physicist doesn't have to answer this question, because he treats gravity as a useful abstraction in his model. The Aristotelian physicist, on the other hand, believes that impetus is a real thing that actually exists and is causing objects to move. And if the answer is, "you can only detect impetus by observing the motion of objects and using the formula m*v", then it becomes trivially easy to answer your original question, "how can you explain the fact that Aristotelian physics and Newtonian mechanics make the same predictions despite being so different". The answer then becomes, "because both of them describe the motion of objects in the same way, one of them just as this extra bit that doesn't really change much". As I said though, I may be missing a piece of the puzzle.
I personally think that qualia, along with free will, are philosophical red herrings, so I'm not terribly interested in their properties. That sounds like a topic for a separate argument, though...
I would say that statements such as "2+2=4" and "if all men are mortal, and Socrates is a man, then Socrates is mortal" are either true by definition, or derive logically from statements that are true by definition. There's nothing wrong with that, obviously, but scientific truth is a bit different, since in science, you are not free to pick any axioms you want -- instead, the physical universe does that for you.
That said, I'm not sure how your question relates to our main topic: the incommensurability of scientific truths, specifically.
That is similar to my take on this.