I was trying to be precise to avoid the appearance of a naive claim like “purpose is an objective property of things,” which is clearly false.
Ah, yes, agreed.
The Aristotle / Newton comparison is meant to be evidence for the hypothesis of incommensurability of scientific theories.
I think I might be misunderstanding what the word “incommensurability” means. I thought that it meant, “the performance of theory A cannot be compared with the performance of theory B”, but in case of Aristotle/Newton/Einstein, we can definitely rank the performance (in the order I listed, in fact). Aristotle’s Laws of Motion are more or less (ok, closer to the “less” side perhaps, but still) useful, as long as you’re dealing with solid objects on Earth. Their predictive power isn’t great, but it’s not zero. Newton’s Laws are much more powerful, and relativity is so powerful that it’s overkill in many cases (f.ex. if you’re trying to accurately lob a rock with a trebuchet). Each set of laws was devised to explain the best evidence that was available at the time; I see nothing incommesurate about that. But, again, it’s possible that I’m using the word incorrectly.
because theories of everything that are not scientific (i.e. moral theories) are definitely incommensurable.
I am not convinced that they are. In fact—again, assuming I’m using the word correctly—how can theories be incommesurable and yet falsifiable ? And if a theory is not falsifiable, it’s not very useful, IMO (nor is it a theory, technically).
As I use incommensurability, I mean that the basic concepts in one theory cannot be made to correspond with the basic concepts of another theory.
At bottom, Aristotelian physics says that what needs to be explained is motion. In contrast, Newtonian physics says that what needs to be explained is acceleration. I assert that there is no way to import principles for explaining motion into a theory that exists to explain acceleration. In other words, Aristotelian physics is not a simpler and more naive form of Newtonian physics. You can produce a post-hoc explanation of the differences like your invocation of the limits of observable evidence (but see this discussion). I find post-hoc explanation unsatisfying because scientists talk as if they can ex ante predict (1) what sorts of new evidence science needs to improve and (2) what the “revolutionary” new theories will look like. And yet that doesn’t seem to be true historically.
And if a theory is not falsifiable, it’s not very useful, IMO (nor is it a theory, technically).
There is some unfortunate equivocation in the the word theory (“Theory of Gravity” vs. “Utilitarianism: A Moral theory”). But something like Freudian thought is unified(-ish) and coherent(-ish). What is wrong with referencing “Freudian theory”? That doesn’t reject Popper’s assertion that Freudian thought isn’t a scientific theory (because Freudian thought isn’t falsifiable). On falsifiability more generally, I’m not sure what it means to ask whether utilitarianism (or any moral theory) is falsifiable.
At bottom, Aristotelian physics says that what needs to be explained is motion. In contrast, Newtonian physics says that what needs to be explained is acceleration. I assert that there is no way to import principles for explaining motion into a theory that exists to explain acceleration.
What about “V = a * t” ? That said, AFAIK “at bottom” Newton didn’t really want to explain acceleration, or motion, or any abstract concept like that; he wanted to know why the planets appear at certain places in the sky at certain times, and not others—but he could pinpoint the position of a planet much better than Aristotle could.
And I think we can, in fact, correspond Newtonian concepts to Aristotelian ones, if only by pointing out which parts Aristotle missed—which would allow us to map one theory to the other. For example, we (or Archimedes, even) could talk about density and displacement, and use it to explain the parts that Aristotle got right (most rocks sink in water) as well as the parts he got wrong (actually some porous rocks can float).
What is wrong with referencing “Freudian theory”?
Nothing really, it’s just that most people around here, AFAIK, mean something like “a scientific, falsifiable, well-tested theory” when they use the word.
That doesn’t reject Popper’s assertion that Freudian thought isn’t a scientific theory (because it isn’t falsifiable).
If it’s unfalsifiable, what good is it ? Isn’t that the same as saying, “it has no explanatory power” and “it lacks any application to anything” ?
On falsifiability more generally, I’m not sure what it means to ask whether utilitarianism (or any moral theory) is falsifiable.
I see utilitarianism as more of a recipe (or an algorithm) than a theory, so it doesn’t need to be falsifiable per se.
For theories to be commensurate, you need to be able to move all the interesting insights of each theory into the other and still have the same insight. Sure, Aristotle and Newton seemed to agree on the definition of velocity and acceleration. But there’s no way to state “An object in motion will tend to stay in motion” as a conclusion of Aristotelian physics because the caveats Aristotle would want to insert would totally change the meaning. (As an aside, I’m making a point about the theories, not the scientists. Boyi might find Newton’s motivation interesting, but I’m trying to limit the focus to the theories themselves).
The point about moral “theory” is sufficiently distinct that I hope you’ll forgive my desire to move it elsewhere just to make this conversation easier to follow.
For theories to be commensurate, you need to be able to move all the interesting insights of each theory into the other and still have the same insight.
In this case, I don’t think I fully understand what you mean by “insights” being “the same”. Any two scientific theories will make different models of reality, by definition; if they didn’t, they’d be the same theory. So, if you go the extreme route, you could say that all theories are incommensurate by definition, but this interpretation would be trivial, since it’d be the same as saying, “different theories are different”.
I agree that there’s “no way to state ‘An object in motion will tend to stay in motion’ as a conclusion of Aristotelian physics”, but that’s because Aristotelian physics is less correct than Newtonian mechanics. But there is a way to partially map Newtonian mechanics to Aristotelian physics, by restricting our observations to a very specific set of circumstances (relatively heavy objects, an atmosphere, the surface of Greece, etc.). Similarly, we can map relativity to Newtonian mechanics (relatively heavy objects, slow speeds, etc.). It seems odd to say that these theories are totally incommensurate, while still being able to perform this kind of mapping.
In fact, we perform this kind of reduction every day, even in practical settings. When I want to drive from point A to point B, Google Maps tells me that the Earth is flat, and I implicitly believe that the Earth is flat. But if I want to fly to China, I have to discard this assumption and go with the round-Earth model. I see nothing philosophically troubling about that—why use an expensive scalpel when a cheap mallet works just as well ?
Boyi might find Newton’s motivation interesting, but I’m trying to limit the focus to the theories themselves
I was trying to make a point that scientific theories are not just about moving abstract concepts around; their whole purpose is to make predictions about our observations. This is what differentiates them from pure philosophy, and this is also what makes it possible to compare one theory to another and rank them according to correctness and predictive power—because we have an external standard by which to judge them.
The point about moral “theory” is sufficiently distinct that I hope you’ll forgive my desire to move it elsewhere just to make this conversation easier to follow.
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 ?
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 ?
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
. . . the impetus is supposed to be something that pushes the body along, the momentum is the result rather than the cause of [the body’s] motion
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?
In other words, impetus is meant to explain, while momentum is something to be explained.
If that’s what Feyerabend is saying, then he’s confusing the map for the territory:
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.
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.
Perhaps “Aristotle would win less money than Newton who would win less than Einstein, but the naive scientific method cannot explain why.”
What is the “naive scientific method”, in this case ? How is it different from the regular kind ?
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.
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.
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
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.
But in some sense, the basic theory says that all models are “true.”
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.
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.
What’s the difference ?
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.
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.
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.
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).
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… At the very least, the lesson is that we should be skeptical of the basic theory’s explanation of what models are.
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.
There’s no experiment you can run, in principle, that will tell you whether “m*v” is caused by impetus.
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.
Is it really your position that no experiment can tell whether something is a cause or an effect?
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:
Universe 1: Impetus imparts motion to objects but is otherwise undetectable; we can estimate its effects as “m*v”.
Universe 2: There’s no such thing as “impetus”, though m*v is a useful feature of our model.
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).
But “simple” truth doesn’t stand up to rigorous examination,
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.
in much the same way that a “simple” definition of infinity doesn’t work.
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.
Impetus imparts motion to objects but is otherwise undetectable
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.”
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.
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?
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.
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.
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.”
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.
If you want to abandon metaphysics, then what does it mean to say something like “qualia have property X” is true?
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...
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? … Is it your position that all truths are “scientific” truths?
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.
The modern physicist doesn’t have to answer this question, because he treats gravity as a useful abstraction in his model.
A while ago, I said to Boyi that the best of post-modern thought gets co-opted into more mainstream thought. If you think gravity is only a useful abstraction, not “a real thing that actually exists and is causing objects to move,” then you are already much, much closer to Feyerabend than to the logical positivists. As a sociological fact, I assert that most scientists (especially in the “hard” sciences) take a position closer to “gravity is a real thing” than “gravity is a useful abstraction” (if not for gravity in particular, than for whatever fundamental explanatory objects they assert).
The incommensurability of scientific models (I shouldn’t have said truths) is the assertion that an earlier scientific model is not necessarily a simpler version of a later scientific model. I’ve made the best case that I can about Aristotle vs. Newton. The lesson is to be suspicious of the “truth” of scientific models. Because I think most scientists want to say something stronger about the model than “makes more accurate predictions.”
If you think gravity is only a useful abstraction, not “a real thing that actually exists and is causing objects to move,” then you are already much, much closer to Feyerabend than to the logical positivists. As a sociological fact, I assert that most scientists (especially in the “hard” sciences) take a position closer to “gravity is a real thing” than “gravity is a useful abstraction
Isn’t that the whole point of (for example) the search for the Higgs Boson ? Gravity is an abstraction, and we’re trying to refine the abstraction by discovering what is causing the real phenomenon that we observe. Of course, that discovery will not represent the world as it really, truly is, either; but at least it’ll be a bit closer than just “GMm / r^2”. I think there’s a big difference between the scientific concept of an abstraction, which refers to a simplified and incomplete model of reality; and the post-modern concept, which treats every abstraction as just another narrative that is socially constructed and does not relate to any external phenomena.
The incommensurability of scientific models (I shouldn’t have said truths) is the assertion that an earlier scientific model is not necessarily a simpler version of a later scientific model
If this is all you’re saying, then I can fully endorse this statement—but then, as I said before, it basically boils down to saying, “some earlier scientific models were pretty much wrong”. This statement is true, but not very interesting.
Because I think most scientists want to say something stronger about the model than “makes more accurate predictions.”
Like what ? Isn’t that the entire point of the model, to make predictions ?
Let me use another analogy. At one point, people believed that all swans were white; in fact, the very term “black swan” is an idiom meaning “something that is completely unexpected, contradicts most of what we know, and is likely disastrous”. Of course, today we know that black swans do exist.
So, let’s say that I, having never seen a black swan, believe that all swans are white. You believe that some swans are black. Our two models of the world are incommensurate; logically, only one of them can be true. And yet, if I have seen plenty of white swans, but never a black one, I’d be perfectly justified in believing that my model is (probably) true (until you show me some evidence to the contrary). Do you think this means that we should be “suspicious” of the entire notion of predicting the color of the next swan one might come across ?
Let me use another analogy. At one point, people believed that all swans were white; in fact, the very term “black swan” is an idiom meaning “something that is completely unexpected, contradicts most of what we know, and is likely disastrous”. Of course, today we know that black swans do exist.
So, let’s say that I, having never seen a black swan, believe that all swans are white. You believe that some swans are black. Our two models of the world are incommensurate; logically, only one of them can be true. And yet, if I have seen plenty of white swans, but never a black one, I’d be perfectly justified in believing that my model is (probably) true (until you show me some evidence to the contrary). Do you think this means that we should be “suspicious” of the entire notion of predicting the color of the next swan one might come across ?
You are conflating theory conflict with theory commensurability. The fact that theories make different predictions does not prove that the theories are incommensurable. For example, the white-swan theory predicted that there were no black swans, while the black-swan predicted that some black swans existed. But both theories mean the SAME thing by swan, so they are commensurable theories.
In addition, making similar predictions does not mean that theories are commensurable. I think there was a time when epicycle theory and heliocentric theory made similar predictions of planetary motion. Notwithstanding this agreement, there is no way to translate the concepts of Ptolemaic astronomy into heliocentric astronomy, which is what I mean when I say incommensurable.
In reading this discussion of Feyerabend, it seems like I’m defending a position that Feyerabend did not actually endorse. As you say:
I think there’s a big difference between the scientific concept of an abstraction, which refers to a simplified and incomplete model of reality; and the post-modern concept, which treats every abstraction as just another narrative that is socially constructed and does not relate to any external phenomena.
According to that discussion, Feyerabend is fully post-modern as you describe it. (This was the position Boyi was articulating, and I think we agree that it has trouble explaining the success of science). I’m trying to defend a philosophy of science that “treats every abstraction as a narrative that is socially constructed, but does (somehow) relate to external phenomena.”
Isn’t that the entire point of the model, to make predictions ?
Eliezer’s essay that you linked implies that one purpose of science is to know true facts about the world. Gravity isn’t an abstraction of the (hypothetical) Higgs bosom. It’s a property of the particle (or whatever it is-I’m not up on the physics). I’m articulating a position in which we don’t know certain kinds of facts (i.e. models do not “correspond” to reality), but are nonetheless able to make accurate predictions.
You are conflating theory conflict with theory commensurability. The fact that theories make different predictions does not prove that the theories are incommensurable.
Technically, you’re right; my swan example wasn’t fully analogous. I could still argue that one theory meant “swan” to be “a bird that is exclusively white”, whereas the other theory allows swans to be white or black, and thus the two theories do mean different things by the word “swan”… but I don’t know if you or Feyerabend would agree; nor do I think that it’s terribly important.
What’s more important is that I disagree with you (and possibly Feyerabend) regarding what theories are. As far as I understand, you believe that scientific models utilize “concepts” in order to make predictions; these concepts are the primary feature of the model, with predictions being a side-effect (though a very important and useful one, speaking both practically and philosophically). I, on the other hand, would say that it is the concepts that are secondary, and that a scientific model’s main feature is the predictions it makes.
If this is true, then as long as your model makes accurate predictions, you are justified in believing that its concepts are also true. Thus, if your epicycle model allows you to predict the motion of planets with reasonable accuracy, you’re justified in believing that planets move in epicycles. But as soon as some better measurements come along, your predictions will start failing, and you’d be forced to get yourself some new concepts.
In other words, the concepts are not a statement about how the world really, truly works; but only about how it works to the best of your knowledge. Once you get better knowledge, you are forced to get better concepts; and once you do that, you can go back, look at your old concepts, and say, “ok, I can see why I came up with those, because I’d need to know X in order to see that they’re wrong, and we’d just built the X-supercollider last year”.
Thus, I see no philosophical problem with having two scientific models that use different concepts, yet arrive at similar predictions. They are simply two local maxima in our utility function that describes our understanding of the world; and, since we’re not omniscient, neither of them are 100% true. When the maxima are sufficiently close, you can even use a simpler model (f.ex., “the world is flat”) in place of the other (f.ex., “the world is round”), if you’re willing to deal with the marginally increased errors in your predictions (f.ex., lobbing that giant boulder 1cm to the side of its intended target).
Gravity isn’t an abstraction of the (hypothetical) Higgs bosom. It’s a property of the particle (or whatever it is-I’m not up on the physics).
Right, but what’s a “particle” ? In reality, there (probably) aren’t any “particles” at all, there are just waves—except that the waves aren’t exactly real, either, and instead there are “amplitude flows”, except those are a model too… and so on. It is still possible that all of these things are just local maxima, and that in reality the world is a giant computer simulation, or something. For now, our models work quite well, but that doesn’t mean that they are somehow directly tied to actual particles (or waves, etc.) that actually exist. Photons don’t care about what’s in our heads.
If you ask Alice the Engineer what scientific theories do, I think she would say that scientific theories “describe the world” and “make predictions.” Without getting into relative importance, I think she’d say that a theory that couldn’t both describe and predict would be a failure of science. If that’s not what she would say today, I’m fairly confident that her counterpart from 1901 would say that.
I think Feyerabend has a devastating critique of the ability of scientific theories to describe. And the difference is huge. If you follow Feyerabend, you can’t say “Light is both a particle and a wave.” The best you can do is say “Our most accurate theory treats light as both a particle and a wave” and forbid the inference that “the world resembles the theory in any rigorous way.”
It seems like your response is to remove “descriptiveness” from the definition of science, then say that Feyerabend doesn’t have any interesting critique of science as properly defined. But your new definition of science is the one that post-modernism says is best. More importantly, you can’t go back to Alice and say “Look, I’ve driven off the post-modernists with no losses” because she’ll respond by asking about science’s ability to describe the world and cite The Simple Truth at you.
If you ask actual practicing scientists (researchers, doctors, engineers, etc), I assert that they would agree with Alice, if forced to take a position (ignoring for the moment why we’d ever want to force them to think about this theoretical issue). And regardless of the penetration of post-modern theory of science into modern folk philosophy, the overwhelming majority scientists throughout history have asserted the position I’ve ascribed to Alice.
It seems like your response is to remove “descriptiveness” from the definition of science, then say that Feyerabend doesn’t have any interesting critique of science as properly defined.
My intent wasn’t to remove “descriptiveness”, but to remove both certainty and absolute precision. Thus, instead of saying, “planets move in epicycles”, we can only say, “to the best of our knowledge, planets move in something closely resembling epicycles (but we’re not sure of that, and in reality planets don’t move in neat little epicycles because they’re not perfectly round, etc.)”. This may seem like a minor difference, but IMO the difference is huge: instead of treating the features of your model—the “concepts”—as primary, they are now entirely dependent on your observations.
This is what I was trying to show with my (admittedly flawed) swan analogy. I see no problem with two theories making similar predictions yet explaining them using different models, because in the end it’s the predictions that are important. If you are unable to make measurements that are precise enough to tell one model from another, you might as well go with a simpler model just by using Occam’s Razor. This doesn’t mean that your simpler model must be 100% accurate; it just means that it’s much likely to be much closer to the way the world really works than other models.
Thus, there’s no real need to explain why two different theories make similar predictions; the explanation is, “this isn’t a question about theories or true reality, it’s a question about us and our models”, and the answer is, “our model was wrong because we couldn’t make precise enough measurements, but it was still closer to reality than all other models at the time; and BTW, our current model isn’t perfect either, but we think it’s close”.
This approach is different, I think, from your approach of treating the features of the model (the “concepts”) as primary. If you do that, and if you assume that the world must look exactly like your model in order for its predictions to work, then you do have a problem with explaining how more or less correct predictions can arise from incorrect models. But this is a way to look at science that goes too far into the Platonic realm, IMO.
Since I accept theory incommesurability, I don’t believe that closer to reality is a useful thing to say about scientific theories. I’m not even sure what it could mean. Specifically, the statement “precise enough measurements” doesn’t explain or cause me to expect the thing you seem to mean by closer to reality, which sounds to me a lot like what Alice means by “descriptiveness.”
Since I accept theory incommesurability, I don’t believe that closer to reality is a useful thing to say about scientific theories.
I’m confused. Can’t one construct a counterexample?
For consideration, F=ma performs much worse under scrutiny than F=ma*e, where e is the number of elephants in the room plus one, even though the latter is usually accurate.
What exactly is an epicycle supposed to translate into in a heliocentric theory?
You evaluate both theories in terms of predictive power, and then compare the two.
Ah, I see what you and Feyerabend are doing there: commensurability is supposed to allow some translation between the internal parts of the theories. I don’t see why that should be necessary, or why that would be called ‘commensurability’. Ordinarily, to say 2 things are commensurable merely requires that they are comparable by some common standard.
Since I accept theory incommesurability, I don’t believe that closer to reality is a useful thing to say about scientific theories. I’m not even sure what it could mean. … I’m asserting that “makes better predictions != closer to reality”.
But in your example, Alice the Engineer and her hypothetical scientist friends say that
a theory that couldn’t both describe and predict would be a failure of science.
So, it sounds like you disagree with Alice and the scientists, then ? But if so, are you not removing “descriptiveness” from scientific theories, just as you accused me of doing ?
But perhaps, by “makes better predictions != closer to reality”, you only meant “makes better predictions probably == closer to reality, but not certainly” ? I could agree with that.
I think I could also agree with you that, if one accepts theory incommesurability, then it probably wouldn’t make sense to talk about theories being (probably) closer to reality (assuming it exists). But I don’t accept theory incommesurability, so at best we’re at an impasse.
If, on the other hand, one assumes that there probably exists an external reality that influences our senses in some way, however indirect (and which we can influence in return with our bodies), then IMO commensurabilty follows more or less naturally.
Since our understanding of this reality is not (and can probably never be) perfect, we can treat the sum total of all of our scientific models as a sort of cost function, which measures the projected difference between our models and things as they truly are (thus, our models still describe things, but imperfectly). By carrying out experiments and updating our theories we are trying to minimize this cost function. It’s entirely likely that we’d get stuck in some local minima for a while; hence the theories that make similar predictions but describe reality differently.
I take it you disagree with some of this, so which, if any, of my assumptions do you find objectionable ?
Reality probably exists (this seems to be non-controversial)
Reality affects our senses (which are part of it, after all) and we can affect it in turn by moving things around (ditto).
We can create what we think of as models of reality in our heads, however imperfect or wildly incorrect they might be.
Since our models imply predictions, it is possible for us to estimate the difference between our models of reality and the actual thing, by carrying out experiments and comparing the results we get to the expected results.
In trying to minimize this difference, we can get stuck in local minima.
Some other hidden assumption that I have forgotten to list here.
I’m sorry if I wasn’t clear about Alice, who is intended to represent a school of thought in philosophy of science called logical positivism.
I think you were advocating a position similar to her position, especially when you were saying that A Simple Truth was a sufficient theory of what truth is. Further, I agree that the adjustment that Alice should make to her theory is to abandon what I’ve called descriptiveness. Thus, I still think you are closer to Alice than to Feyerabend as long as you think scientific theories get “closer to reality” in some meaningful way.
As I understand it, theory incommesurability should be understood as an empirical theory, much the same way that academic historical theories are empirical theories.
Theories change.
I’m pretty sure Alice agrees.
Some theory changes are radical (i.e. involve incommensurability)
I think this is true, as a historical matter. A geocentric theory (epicycles) was replaced by a heliocentric theory. There’s no reasonable way to translate rotating circles on top of other rotating circles embedded in the sky (epicycles) into anything in the Copernican/Keplerian planets-elliptically-orbit-the-Sun theory. I don’t think Alice rejects this either. I expect she explains that Science became non-empirical for a extended period of time, probably based on influence/co-option by non-empirical entities like the Catholic Church. But when Science was restored to its proper function by the return of empiricism, the geocentric nonsense was flushed away. There was no reason to expect that geocentrism would translate into heliocentrism because geocentrism was not sufficiently based on observation. (I’m not sure if this story is historically correct, but that’s Alice’s problem, not mine).
All significant theory changes were radical theory changes. Alice obviously doesn’t agree. If impetus != momentum, this is evidence in support of this proposition. Likewise, if impetus = momentum, this is evidence against the proposition. If the proposition is true, I think you are right when you say:
if one accepts theory incommesurability, then it probably wouldn’t make sense to talk about theories being (probably) closer to reality.
But I don’t think that requires one to reject the concept of reality.
I think you were advocating a position similar to her position, especially when you were saying that A Simple Truth was a sufficient theory of what truth is.
I don’t think that A Simple Truth advocates a theory per se; I see it as more of call to reject complex and convoluted philosophical truth theories, in favor of actually doing science (and engineering).
theory incommesurability should be understood as an empirical theory
As far as I understand from your arguments so far, the notions of empiricism and incommensurability are incommensurable.
There’s no reasonable way to translate rotating circles on top of other rotating circles embedded in the sky (epicycles) into anything in the Copernican/Keplerian planets-elliptically-orbit-the-Sun theory.
No, but you could probably go the other way. Given both theories, you could calculate the minimum magnitude of the experimental error required in order for them to become indistinguishable. If your instruments are less precise than that, then you may as well use epicycles (Occam’s Razor aside).
I expect she explains that Science became non-empirical for a extended period of time, probably based on influence/co-option by non-empirical entities like the Catholic Church.
I don’t think this is accurate, historically speaking. Yes, the influence of the Catholic Church was quite harmful to science, but they didn’t invent geocentrism. In fact, geocentrism is quite empirical. If you’re a sage living in ancient Babylon, you can very easily look up and see the Sun moving around the (flat) Earth. Given the available evidence, you’d be fully justified in concluding that geocentrism is true. You’d be wrong, as we now know, but it’s ok to be wrong sometimes (see what I said earlier about local minima).
All significant theory changes were radical theory changes.
This sounds like a tautology to me.
If impetus != momentum, this is evidence in support of this proposition. Likewise, if impetus = momentum, …
Sorry, I must have missed a sentence: what is the “this” you’re referring to, when you say “this is evidence” ? As for impetus and momentum, they’re quite different concepts, so you can’t equate them. Impetus is a sort of elan vital of motion, whereas Newton’s momentum (if I understand it correctly) is just an explanation of how objects move. Either impetus exists (in the same way that elan vital was thought to exist), or it doesn’t; there aren’t any other options. Today, we believe that impetus does not exist, but there’s still a small chance that it does; if we ever discover any evidence of it, we’ll update our beliefs.
But I don’t think that requires one to reject the concept of reality.
As far as I understand from your arguments, you are rejecting the notion that scientific theories describe reality in any way; and, due to your belief in incommensurability, you believe that the fact that some theories allow us to develop what seems to be an understanding of the world (*), to be somewhat of a mystery. Does this accurately describe your position ? If so, I don’t see what accepting “a concept of reality” would buy you, since reality is (due to incommensurability) unknowable.
I agree with you that, given that incommensurability is true, your position makes sense. But I still don’t see why I should accept that incommensurability is true. From your arguments, it almost sounds like you require scientists to be omniscient: you see any significant mistake in our scientific understanding of the world as an insurmountable barrier to understanding. But I still don’t understand why. All people make mistakes all the time, not just scientists.
At one point, I personally thought that driving from my house to work takes about 30 minutes. But then I found a shortcut through a corporate parking lot, which shaved the time down to about 25 minutes. My two maps of the world were certainly incompatible: one contained the shortcut, the other did not; and the routes were very different. Does this mean that the two maps are incommensurate, and that we must therefore reject the very notion of them describing the actual terrain in any way ? Why can’t we just say, “Bugmaster was wrong because he didn’t have enough data” ?
(*) Seeing as I’m typing these words using a device powered by our understanding of quantum mechanics, etc.
IIRC, even Feynman refused to answer to whether electrons, or even the interior of a brick, are real, saying that they are useful concepts in our description of the world and that’s all that matters.
That’s not quite what he was saying. Full quote (emphasis mine):
When I sat with the philosophers I listened to them discuss very seriously a book called Process and Reality by Whitehead. They were using words in a funny way, and I couldn’t quite understand what they were saying. Now I didn’t want to interrupt them in their own conversation and keep asking them to explain something, and on the few occasions that I did, they’d try to explain it to me, but I still didn’t get it. Finally they invited me to come to their seminar.
They had a seminar that was like a class. It had been meeting once a week to discuss a new chapter out of Process and Reality — some guy would give a report on it and then there would be a discussion. I went to this seminar promising myself to keep my mouth shut, reminding myself that I didn’t know anything about the subject, and I was going there just to watch.
What happened there was typical — so typical that it was unbelievable, but true. First of all, I sat there without saying anything, which is almost unbelievable, but also true. A student gave a report on the chapter to be studied that week. In it Whitehead kept using the words ‘essential object’ in a particular technical way that presumably he had defined, but that I didn’t understand.
After some discussion as to what ‘essential object’ meant, the professor leading the seminar said something meant to clarify things and drew something that looked like lightning bolts on the blackboard. ‘Mr. Feynman,’ he said, ‘would you say an electron is an “essential object?”’
Well, now I was in trouble. I admitted that I hadn’t read the book, so I had no idea of what Whitehead meant by the phrase; I had only come to watch. ‘But,’ I said, ’I’ll try to answer the professor’s question if you will first answer a question from me, so I can have a better idea of what “essential object” means. Is a brick an essential object?
What I had intended to do was to find out whether they thought theoretical constructs were essential objects. The electron is a theory that we use; it is so useful in understanding the way nature works that we can almost call it real. I wanted to make the idea of a theory clear by analogy. In the case of the brick, my next question was going to be, ‘What about the inside of the brick?’ — and I would then point out that no one has ever seen the inside of a brick. Every time you break the brick, you only see the surface. That the brick has an inside is a simple theory which helps us to understand things better. The theory of electrons is analogous. So I began by asking, ‘Is a brick an essential object?’
Then the answers came out. One man stood up and said, ‘A brick is an individual, specific brick. That is what Whitehead means by an essential object.’ Another man said, ‘No, it isn’t the individual brick that is an essential object; it’s the general character that all bricks have in common — their ‘brickiness’ — that is the essential object.’
Another guy got up and said, ’No, it’s not in the bricks themselves. ‘Essential object’ means the idea in the mind that you get when you think of bricks.’
Another guy got up, and another, and I tell you I have never heard such ingenious different ways of looking at a brick before. And, just like it should in all stories about philosophers, it ended up in complete chaos. In all their previous discussions they hadn’t even asked themselves whether such a simple object as a brick, much less an electron, is an ‘essential object’.
Ah, yes, agreed.
I think I might be misunderstanding what the word “incommensurability” means. I thought that it meant, “the performance of theory A cannot be compared with the performance of theory B”, but in case of Aristotle/Newton/Einstein, we can definitely rank the performance (in the order I listed, in fact). Aristotle’s Laws of Motion are more or less (ok, closer to the “less” side perhaps, but still) useful, as long as you’re dealing with solid objects on Earth. Their predictive power isn’t great, but it’s not zero. Newton’s Laws are much more powerful, and relativity is so powerful that it’s overkill in many cases (f.ex. if you’re trying to accurately lob a rock with a trebuchet). Each set of laws was devised to explain the best evidence that was available at the time; I see nothing incommesurate about that. But, again, it’s possible that I’m using the word incorrectly.
I am not convinced that they are. In fact—again, assuming I’m using the word correctly—how can theories be incommesurable and yet falsifiable ? And if a theory is not falsifiable, it’s not very useful, IMO (nor is it a theory, technically).
As I use incommensurability, I mean that the basic concepts in one theory cannot be made to correspond with the basic concepts of another theory.
At bottom, Aristotelian physics says that what needs to be explained is motion. In contrast, Newtonian physics says that what needs to be explained is acceleration. I assert that there is no way to import principles for explaining motion into a theory that exists to explain acceleration. In other words, Aristotelian physics is not a simpler and more naive form of Newtonian physics. You can produce a post-hoc explanation of the differences like your invocation of the limits of observable evidence (but see this discussion). I find post-hoc explanation unsatisfying because scientists talk as if they can ex ante predict (1) what sorts of new evidence science needs to improve and (2) what the “revolutionary” new theories will look like. And yet that doesn’t seem to be true historically.
There is some unfortunate equivocation in the the word theory (“Theory of Gravity” vs. “Utilitarianism: A Moral theory”). But something like Freudian thought is unified(-ish) and coherent(-ish). What is wrong with referencing “Freudian theory”? That doesn’t reject Popper’s assertion that Freudian thought isn’t a scientific theory (because Freudian thought isn’t falsifiable). On falsifiability more generally, I’m not sure what it means to ask whether utilitarianism (or any moral theory) is falsifiable.
What about “V = a * t” ? That said, AFAIK “at bottom” Newton didn’t really want to explain acceleration, or motion, or any abstract concept like that; he wanted to know why the planets appear at certain places in the sky at certain times, and not others—but he could pinpoint the position of a planet much better than Aristotle could.
And I think we can, in fact, correspond Newtonian concepts to Aristotelian ones, if only by pointing out which parts Aristotle missed—which would allow us to map one theory to the other. For example, we (or Archimedes, even) could talk about density and displacement, and use it to explain the parts that Aristotle got right (most rocks sink in water) as well as the parts he got wrong (actually some porous rocks can float).
Nothing really, it’s just that most people around here, AFAIK, mean something like “a scientific, falsifiable, well-tested theory” when they use the word.
If it’s unfalsifiable, what good is it ? Isn’t that the same as saying, “it has no explanatory power” and “it lacks any application to anything” ?
I see utilitarianism as more of a recipe (or an algorithm) than a theory, so it doesn’t need to be falsifiable per se.
For theories to be commensurate, you need to be able to move all the interesting insights of each theory into the other and still have the same insight. Sure, Aristotle and Newton seemed to agree on the definition of velocity and acceleration. But there’s no way to state “An object in motion will tend to stay in motion” as a conclusion of Aristotelian physics because the caveats Aristotle would want to insert would totally change the meaning.
(As an aside, I’m making a point about the theories, not the scientists. Boyi might find Newton’s motivation interesting, but I’m trying to limit the focus to the theories themselves).
The point about moral “theory” is sufficiently distinct that I hope you’ll forgive my desire to move it elsewhere just to make this conversation easier to follow.
In this case, I don’t think I fully understand what you mean by “insights” being “the same”. Any two scientific theories will make different models of reality, by definition; if they didn’t, they’d be the same theory. So, if you go the extreme route, you could say that all theories are incommensurate by definition, but this interpretation would be trivial, since it’d be the same as saying, “different theories are different”.
I agree that there’s “no way to state ‘An object in motion will tend to stay in motion’ as a conclusion of Aristotelian physics”, but that’s because Aristotelian physics is less correct than Newtonian mechanics. But there is a way to partially map Newtonian mechanics to Aristotelian physics, by restricting our observations to a very specific set of circumstances (relatively heavy objects, an atmosphere, the surface of Greece, etc.). Similarly, we can map relativity to Newtonian mechanics (relatively heavy objects, slow speeds, etc.). It seems odd to say that these theories are totally incommensurate, while still being able to perform this kind of mapping.
In fact, we perform this kind of reduction every day, even in practical settings. When I want to drive from point A to point B, Google Maps tells me that the Earth is flat, and I implicitly believe that the Earth is flat. But if I want to fly to China, I have to discard this assumption and go with the round-Earth model. I see nothing philosophically troubling about that—why use an expensive scalpel when a cheap mallet works just as well ?
I was trying to make a point that scientific theories are not just about moving abstract concepts around; their whole purpose is to make predictions about our observations. This is what differentiates them from pure philosophy, and this is also what makes it possible to compare one theory to another and rank them according to correctness and predictive power—because we have an external standard by which to judge them.
Yeah, that’s a good move, no objections here.
But not too heavy...
Haha, yes, very important detail, that :-)
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:
Universe 1: Impetus imparts motion to objects but is otherwise undetectable; we can estimate its effects as “m*v”.
Universe 2: There’s no such thing as “impetus”, though m*v is a useful feature of our model.
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.
A while ago, I said to Boyi that the best of post-modern thought gets co-opted into more mainstream thought. If you think gravity is only a useful abstraction, not “a real thing that actually exists and is causing objects to move,” then you are already much, much closer to Feyerabend than to the logical positivists. As a sociological fact, I assert that most scientists (especially in the “hard” sciences) take a position closer to “gravity is a real thing” than “gravity is a useful abstraction” (if not for gravity in particular, than for whatever fundamental explanatory objects they assert).
The incommensurability of scientific models (I shouldn’t have said truths) is the assertion that an earlier scientific model is not necessarily a simpler version of a later scientific model. I’ve made the best case that I can about Aristotle vs. Newton. The lesson is to be suspicious of the “truth” of scientific models. Because I think most scientists want to say something stronger about the model than “makes more accurate predictions.”
Isn’t that the whole point of (for example) the search for the Higgs Boson ? Gravity is an abstraction, and we’re trying to refine the abstraction by discovering what is causing the real phenomenon that we observe. Of course, that discovery will not represent the world as it really, truly is, either; but at least it’ll be a bit closer than just “GMm / r^2”. I think there’s a big difference between the scientific concept of an abstraction, which refers to a simplified and incomplete model of reality; and the post-modern concept, which treats every abstraction as just another narrative that is socially constructed and does not relate to any external phenomena.
If this is all you’re saying, then I can fully endorse this statement—but then, as I said before, it basically boils down to saying, “some earlier scientific models were pretty much wrong”. This statement is true, but not very interesting.
Like what ? Isn’t that the entire point of the model, to make predictions ?
Let me use another analogy. At one point, people believed that all swans were white; in fact, the very term “black swan” is an idiom meaning “something that is completely unexpected, contradicts most of what we know, and is likely disastrous”. Of course, today we know that black swans do exist.
So, let’s say that I, having never seen a black swan, believe that all swans are white. You believe that some swans are black. Our two models of the world are incommensurate; logically, only one of them can be true. And yet, if I have seen plenty of white swans, but never a black one, I’d be perfectly justified in believing that my model is (probably) true (until you show me some evidence to the contrary). Do you think this means that we should be “suspicious” of the entire notion of predicting the color of the next swan one might come across ?
You are conflating theory conflict with theory commensurability. The fact that theories make different predictions does not prove that the theories are incommensurable. For example, the white-swan theory predicted that there were no black swans, while the black-swan predicted that some black swans existed. But both theories mean the SAME thing by swan, so they are commensurable theories.
In addition, making similar predictions does not mean that theories are commensurable. I think there was a time when epicycle theory and heliocentric theory made similar predictions of planetary motion. Notwithstanding this agreement, there is no way to translate the concepts of Ptolemaic astronomy into heliocentric astronomy, which is what I mean when I say incommensurable.
In reading this discussion of Feyerabend, it seems like I’m defending a position that Feyerabend did not actually endorse. As you say:
According to that discussion, Feyerabend is fully post-modern as you describe it. (This was the position Boyi was articulating, and I think we agree that it has trouble explaining the success of science). I’m trying to defend a philosophy of science that “treats every abstraction as a narrative that is socially constructed, but does (somehow) relate to external phenomena.”
Eliezer’s essay that you linked implies that one purpose of science is to know true facts about the world. Gravity isn’t an abstraction of the (hypothetical) Higgs bosom. It’s a property of the particle (or whatever it is-I’m not up on the physics). I’m articulating a position in which we don’t know certain kinds of facts (i.e. models do not “correspond” to reality), but are nonetheless able to make accurate predictions.
Technically, you’re right; my swan example wasn’t fully analogous. I could still argue that one theory meant “swan” to be “a bird that is exclusively white”, whereas the other theory allows swans to be white or black, and thus the two theories do mean different things by the word “swan”… but I don’t know if you or Feyerabend would agree; nor do I think that it’s terribly important.
What’s more important is that I disagree with you (and possibly Feyerabend) regarding what theories are. As far as I understand, you believe that scientific models utilize “concepts” in order to make predictions; these concepts are the primary feature of the model, with predictions being a side-effect (though a very important and useful one, speaking both practically and philosophically). I, on the other hand, would say that it is the concepts that are secondary, and that a scientific model’s main feature is the predictions it makes.
If this is true, then as long as your model makes accurate predictions, you are justified in believing that its concepts are also true. Thus, if your epicycle model allows you to predict the motion of planets with reasonable accuracy, you’re justified in believing that planets move in epicycles. But as soon as some better measurements come along, your predictions will start failing, and you’d be forced to get yourself some new concepts.
In other words, the concepts are not a statement about how the world really, truly works; but only about how it works to the best of your knowledge. Once you get better knowledge, you are forced to get better concepts; and once you do that, you can go back, look at your old concepts, and say, “ok, I can see why I came up with those, because I’d need to know X in order to see that they’re wrong, and we’d just built the X-supercollider last year”.
Thus, I see no philosophical problem with having two scientific models that use different concepts, yet arrive at similar predictions. They are simply two local maxima in our utility function that describes our understanding of the world; and, since we’re not omniscient, neither of them are 100% true. When the maxima are sufficiently close, you can even use a simpler model (f.ex., “the world is flat”) in place of the other (f.ex., “the world is round”), if you’re willing to deal with the marginally increased errors in your predictions (f.ex., lobbing that giant boulder 1cm to the side of its intended target).
Right, but what’s a “particle” ? In reality, there (probably) aren’t any “particles” at all, there are just waves—except that the waves aren’t exactly real, either, and instead there are “amplitude flows”, except those are a model too… and so on. It is still possible that all of these things are just local maxima, and that in reality the world is a giant computer simulation, or something. For now, our models work quite well, but that doesn’t mean that they are somehow directly tied to actual particles (or waves, etc.) that actually exist. Photons don’t care about what’s in our heads.
If you ask Alice the Engineer what scientific theories do, I think she would say that scientific theories “describe the world” and “make predictions.” Without getting into relative importance, I think she’d say that a theory that couldn’t both describe and predict would be a failure of science. If that’s not what she would say today, I’m fairly confident that her counterpart from 1901 would say that.
I think Feyerabend has a devastating critique of the ability of scientific theories to describe. And the difference is huge. If you follow Feyerabend, you can’t say “Light is both a particle and a wave.” The best you can do is say “Our most accurate theory treats light as both a particle and a wave” and forbid the inference that “the world resembles the theory in any rigorous way.”
It seems like your response is to remove “descriptiveness” from the definition of science, then say that Feyerabend doesn’t have any interesting critique of science as properly defined. But your new definition of science is the one that post-modernism says is best. More importantly, you can’t go back to Alice and say “Look, I’ve driven off the post-modernists with no losses” because she’ll respond by asking about science’s ability to describe the world and cite The Simple Truth at you.
If you ask actual practicing scientists (researchers, doctors, engineers, etc), I assert that they would agree with Alice, if forced to take a position (ignoring for the moment why we’d ever want to force them to think about this theoretical issue). And regardless of the penetration of post-modern theory of science into modern folk philosophy, the overwhelming majority scientists throughout history have asserted the position I’ve ascribed to Alice.
My intent wasn’t to remove “descriptiveness”, but to remove both certainty and absolute precision. Thus, instead of saying, “planets move in epicycles”, we can only say, “to the best of our knowledge, planets move in something closely resembling epicycles (but we’re not sure of that, and in reality planets don’t move in neat little epicycles because they’re not perfectly round, etc.)”. This may seem like a minor difference, but IMO the difference is huge: instead of treating the features of your model—the “concepts”—as primary, they are now entirely dependent on your observations.
This is what I was trying to show with my (admittedly flawed) swan analogy. I see no problem with two theories making similar predictions yet explaining them using different models, because in the end it’s the predictions that are important. If you are unable to make measurements that are precise enough to tell one model from another, you might as well go with a simpler model just by using Occam’s Razor. This doesn’t mean that your simpler model must be 100% accurate; it just means that it’s much likely to be much closer to the way the world really works than other models.
Thus, there’s no real need to explain why two different theories make similar predictions; the explanation is, “this isn’t a question about theories or true reality, it’s a question about us and our models”, and the answer is, “our model was wrong because we couldn’t make precise enough measurements, but it was still closer to reality than all other models at the time; and BTW, our current model isn’t perfect either, but we think it’s close”.
This approach is different, I think, from your approach of treating the features of the model (the “concepts”) as primary. If you do that, and if you assume that the world must look exactly like your model in order for its predictions to work, then you do have a problem with explaining how more or less correct predictions can arise from incorrect models. But this is a way to look at science that goes too far into the Platonic realm, IMO.
Since I accept theory incommesurability, I don’t believe that closer to reality is a useful thing to say about scientific theories. I’m not even sure what it could mean. Specifically, the statement “precise enough measurements” doesn’t explain or cause me to expect the thing you seem to mean by closer to reality, which sounds to me a lot like what Alice means by “descriptiveness.”
I’m confused. Can’t one construct a counterexample?
For consideration,
F=maperforms much worse under scrutiny thanF=ma*e, whereeis the number of elephants in the room plus one, even though the latter is usually accurate.I’m asserting that makes better predictions != closer to reality.
F= ma(elephants+1) clearly makes worse predictions. That’s a good and sufficient reason to reject it.
A longer explanation of what I think is at stake is here.
If you can reject it because it makes worse predictions, doesn’t that make the theories commensurable, regardless of how they relate to reality?
Not at all. What exactly is an epicycle supposed to translate into in a heliocentric theory?
You evaluate both theories in terms of predictive power, and then compare the two.
Ah, I see what you and Feyerabend are doing there: commensurability is supposed to allow some translation between the internal parts of the theories. I don’t see why that should be necessary, or why that would be called ‘commensurability’. Ordinarily, to say 2 things are commensurable merely requires that they are comparable by some common standard.
Ok I am kind of confused now. At first, you say:
But in your example, Alice the Engineer and her hypothetical scientist friends say that
So, it sounds like you disagree with Alice and the scientists, then ? But if so, are you not removing “descriptiveness” from scientific theories, just as you accused me of doing ?
But perhaps, by “makes better predictions != closer to reality”, you only meant “makes better predictions probably == closer to reality, but not certainly” ? I could agree with that.
I think I could also agree with you that, if one accepts theory incommesurability, then it probably wouldn’t make sense to talk about theories being (probably) closer to reality (assuming it exists). But I don’t accept theory incommesurability, so at best we’re at an impasse.
If, on the other hand, one assumes that there probably exists an external reality that influences our senses in some way, however indirect (and which we can influence in return with our bodies), then IMO commensurabilty follows more or less naturally.
Since our understanding of this reality is not (and can probably never be) perfect, we can treat the sum total of all of our scientific models as a sort of cost function, which measures the projected difference between our models and things as they truly are (thus, our models still describe things, but imperfectly). By carrying out experiments and updating our theories we are trying to minimize this cost function. It’s entirely likely that we’d get stuck in some local minima for a while; hence the theories that make similar predictions but describe reality differently.
I take it you disagree with some of this, so which, if any, of my assumptions do you find objectionable ?
Reality probably exists (this seems to be non-controversial)
Reality affects our senses (which are part of it, after all) and we can affect it in turn by moving things around (ditto).
We can create what we think of as models of reality in our heads, however imperfect or wildly incorrect they might be.
Since our models imply predictions, it is possible for us to estimate the difference between our models of reality and the actual thing, by carrying out experiments and comparing the results we get to the expected results.
In trying to minimize this difference, we can get stuck in local minima.
Some other hidden assumption that I have forgotten to list here.
I’m sorry if I wasn’t clear about Alice, who is intended to represent a school of thought in philosophy of science called logical positivism.
I think you were advocating a position similar to her position, especially when you were saying that A Simple Truth was a sufficient theory of what truth is. Further, I agree that the adjustment that Alice should make to her theory is to abandon what I’ve called descriptiveness. Thus, I still think you are closer to Alice than to Feyerabend as long as you think scientific theories get “closer to reality” in some meaningful way.
As I understand it, theory incommesurability should be understood as an empirical theory, much the same way that academic historical theories are empirical theories.
Theories change.
I’m pretty sure Alice agrees.
Some theory changes are radical (i.e. involve incommensurability)
I think this is true, as a historical matter. A geocentric theory (epicycles) was replaced by a heliocentric theory. There’s no reasonable way to translate rotating circles on top of other rotating circles embedded in the sky (epicycles) into anything in the Copernican/Keplerian planets-elliptically-orbit-the-Sun theory.
I don’t think Alice rejects this either. I expect she explains that Science became non-empirical for a extended period of time, probably based on influence/co-option by non-empirical entities like the Catholic Church. But when Science was restored to its proper function by the return of empiricism, the geocentric nonsense was flushed away. There was no reason to expect that geocentrism would translate into heliocentrism because geocentrism was not sufficiently based on observation. (I’m not sure if this story is historically correct, but that’s Alice’s problem, not mine).
All significant theory changes were radical theory changes.
Alice obviously doesn’t agree. If impetus != momentum, this is evidence in support of this proposition. Likewise, if impetus = momentum, this is evidence against the proposition. If the proposition is true, I think you are right when you say:
But I don’t think that requires one to reject the concept of reality.
I don’t think that A Simple Truth advocates a theory per se; I see it as more of call to reject complex and convoluted philosophical truth theories, in favor of actually doing science (and engineering).
As far as I understand from your arguments so far, the notions of empiricism and incommensurability are incommensurable.
No, but you could probably go the other way. Given both theories, you could calculate the minimum magnitude of the experimental error required in order for them to become indistinguishable. If your instruments are less precise than that, then you may as well use epicycles (Occam’s Razor aside).
I don’t think this is accurate, historically speaking. Yes, the influence of the Catholic Church was quite harmful to science, but they didn’t invent geocentrism. In fact, geocentrism is quite empirical. If you’re a sage living in ancient Babylon, you can very easily look up and see the Sun moving around the (flat) Earth. Given the available evidence, you’d be fully justified in concluding that geocentrism is true. You’d be wrong, as we now know, but it’s ok to be wrong sometimes (see what I said earlier about local minima).
This sounds like a tautology to me.
Sorry, I must have missed a sentence: what is the “this” you’re referring to, when you say “this is evidence” ? As for impetus and momentum, they’re quite different concepts, so you can’t equate them. Impetus is a sort of elan vital of motion, whereas Newton’s momentum (if I understand it correctly) is just an explanation of how objects move. Either impetus exists (in the same way that elan vital was thought to exist), or it doesn’t; there aren’t any other options. Today, we believe that impetus does not exist, but there’s still a small chance that it does; if we ever discover any evidence of it, we’ll update our beliefs.
As far as I understand from your arguments, you are rejecting the notion that scientific theories describe reality in any way; and, due to your belief in incommensurability, you believe that the fact that some theories allow us to develop what seems to be an understanding of the world (*), to be somewhat of a mystery. Does this accurately describe your position ? If so, I don’t see what accepting “a concept of reality” would buy you, since reality is (due to incommensurability) unknowable.
I agree with you that, given that incommensurability is true, your position makes sense. But I still don’t see why I should accept that incommensurability is true. From your arguments, it almost sounds like you require scientists to be omniscient: you see any significant mistake in our scientific understanding of the world as an insurmountable barrier to understanding. But I still don’t understand why. All people make mistakes all the time, not just scientists.
At one point, I personally thought that driving from my house to work takes about 30 minutes. But then I found a shortcut through a corporate parking lot, which shaved the time down to about 25 minutes. My two maps of the world were certainly incompatible: one contained the shortcut, the other did not; and the routes were very different. Does this mean that the two maps are incommensurate, and that we must therefore reject the very notion of them describing the actual terrain in any way ? Why can’t we just say, “Bugmaster was wrong because he didn’t have enough data” ?
(*) Seeing as I’m typing these words using a device powered by our understanding of quantum mechanics, etc.
IIRC, even Feynman refused to answer to whether electrons, or even the interior of a brick, are real, saying that they are useful concepts in our description of the world and that’s all that matters.
That’s not quite what he was saying. Full quote (emphasis mine):
That is similar to my take on this.