I wrote that elegance has no epistemic virtues, citing the apparent failure of supersymmetry and my wish to see an end to the invocation of elegance as a dimension along which (linguistic) theories should, or even can, be evaluated.
Josh responded with a vote of confidence for elegance in syntax. In doing so, Josh says that I am ”hoping that ‘elegance’ will go away as a desideratum of Linguistic theory. Or, maybe not go away, but be relegated to lesser importance. Or … actually, it’s a little hard to tell exactly what he [Noah] means – which is always the case when you’re essentially arguing for a re-weighting of things, but won’t specify what weighting you’re after.”
I thought it was clear what I meant when I wrote that “I don’t see how elegance can possibly matter when evaluating a theory’s claim to constitute knowledge” and that “I hope that the (apparent) failure of the undoubtedly very elegant theory of Supersymmetry will make it more obvious to physicists and non-physicists alike that elegance isn’t scientifically valuable.”
So, just to clarify, to the extent that I’m arguing for a re-weighting of evaluative dimensions, I want the dimension of elegance to have zero weight. I want elegance to go away as a desideratum in scientific theory evaluation. And I’m unconvinced by Josh’s argument to the contrary.
Josh and I both agree that notions like simplicity are, in principle, useful when comparing two theories all else being equal. Josh describes the general approach outlined by the authors of Understanding Minimalism (Hornstein, et al.) this way:
First you look at the data and come up with a theory that explains the facts. Once you’re broadly satisfied with your theory, you refine it and hope that the process of refinement increases your understanding.“Explanatoriness” – which Noah correctly asserts is epistemologically prior to the others – must be satisfied before you get to the other criteria, which are really criteria for refining a theory. Elegance, parsimony, etc. are parasitic on having first explained something. I really don’t see any ground for objection: that seems to me to be exactly the right way to look at these things.
To further clarify my position, I believe that there are a number of evaluative dimensions that are epistemologically prior to dimensions like simplicity. I mentioned a few in my first post on this issue: explanatory scope, predictive accuracy, consistency with ‘neighboring’ theories, and the generation of surprising predictions. There are almost certainly others. But even if we restrict ourselves to Hornstein, et al.’s explanitoriness, the argument for elegance falls flat.
Josh is correct to point out that I’m concerned that all else won’t be equal. It’s plausible to me that P-and-P and Minimalism differ with respect to one or more of these dimensions. If they do, this would preclude the need to invoke elegance in comparing the two approaches. But where I’m just concerned that all else won’t be equal (and, frankly, I don’t know enough about the relevant syntactic facts or the two theories to be anything more than concerned), Josh explicitly states that all else is not equal, writing that:
[T]he authors [of Understanding Minimalism] believe that the Principles and Parameters Theory is in a stage of development where things have been more or less adequately explained, and we’re now ready to expand our understanding of the explanation by paring down the theory. Interestingly, I don’t agree with that assessment. I think Minimalism is actually the approach that should have been taken from the get-go, and that in addition to being a better theory across the latter-day criteria, it’s also much more explanatory than Government and Binding ever was. Government and Binding made the wrong generalizations, and precisely because in those days people were simply stating observations gussied up in theoretical jargon. Social sciences should start with Minimalist-style approaches, actually. And in any case, the empirical coverage of Government and Binding Theory was actually pretty poor, and there is no reason to believe that we were in a stage where the existing theory was ready for wholesale refinement on that basis.
I’m willing to defer to Josh with respect to the relative explanatory scope of the two theories. But even if I agreed with Hornstein, et al., that P-and-P satisfactorily explained the relevant syntactic facts, it’s not obvious to me that, per Josh’s description of exactly the right way to build syntactic theories, refinements along the dimensions of simplicity, elegance, and naturalness will leave the epistemologically prior desiderata satisfied. Josh says that Minimalism is a better explanatory theory, but it’s easy to imagine that simplifying a good explanatory theory could reduce that theory’s explanatory scope, its predictive accuracy, its consistency with other theories, etc…, which, to belabor the point, obviates the need to invoke elegance or simplicity.
Finally, even if P-and-P and Minimalism are on equal primary epistemic footing, and even if refining P-and-P to build Minimalism hasn’t changed this fact, it’s still not clear to me that elegance can do any epistemic work for us, because it’s still not clear to me just what elegance is. Josh takes a stab at defining it:
I see people use “elegant” mostly in situations where two/multiple things which there is no reason to believe are connected can be made to seem or shown to be connected in a convincing way. Call it the “two birds with one stone” principle. So, an “elegant” move in Chess is usually when someone is facing two unconnected lines of attack, and to the casual observer it looks like dealing with one will expose a weakness in dealing with the other, and the player nevertheless manages to make a single move that puts him in a position of strength to deal with both lines simultaneously. An “elegant” solution to a math problem is similar. We’re faced with something that looks complicated, and it looks like we’ll have to go through many steps to simplify one part of the problem before dealing with another. An “elegant” solution in that case manages to simplify both parts of the problem simultaneously. An elegant solution to a crime novel is when a series of events which seem unrelated and are in any case confusing are shown not only to be connected, but in a simple way. “Elegance” usually plays on the unexpected, seeing things that are not immediately obvious, and in a way that connects things that did not seem connected before.
To the extent people share that impression of what “elegance” is, it is obvious what it has to do with “a theory’s claim to constitute knowledge.” In fact, it is central to explanation. If two (or more) things which seem to be unrelated and lack explanations can be shown to be related in a convincing way, then knowledge has been advanced. Of course, this is, as mentioned above, parasitic on “explanatoriness.” If the theory is elegant but fails to correspond to reality, then it’s worthless. “Elegance” does nothing to make a useless theory useful. But this is why the authors insisted that different desiderata acquire different levels of importance at different stages of theory development. You must absolutely start with a theory that explains things, and elegance, parsimony, simplicity and naturalness be damned. Once you have a basic explanation, you refine that explanation by trying to make it more elegant, parsimonious, simple and natural. To the extent that elegance finds unexpected connections between parts of the theory, it cannot fail to advance knowledge.
If multiple phenomena lack explanations at time t and an elegant theory explains them and convinces us that they’re connected at time t + 1, it’s not the elegance of the theory that’s doing the work, it’s the explanation.
In Josh’s chess example, it’s the effectiveness of the move that matters to the outcome of the game, not it’s elegance or beauty. In the crime novel example, elegance is a mixture of explanation and simplicity. And in the math example, it seems to be functioning entirely as a synonym of simplicity.
As I wrote in my earlier post, I don’t doubt that elegance is pleasing to the beholder. But if we’ve already got all the explanitoriness we want – and that’s a big if, as discussed above - elegance just isn’t giving us anything scientifically valuable.
We seem to be talking past each other. No, “elegance” shouldn’t outrank anything that has to do with the epistemological value of a theory, but to evaluate two theories with similar coverage, we will prefer the more elegant theory. That is not just because it’s more aesthetically satisfying, but because the fact of finding a unifying explanation is a good clue we’re tapping into some underlying truth. It doesn’t guarantee it, no, and the final evaluation has to be empirical, yes, but come on. If you have two theories that cover the same facts, and one of them presents a more unified explanation, you’re inclined to pursue that theory rather than the other. It’s not solid evidence, but it is prima facie evidence, and in any case looking for elegance is a good exercise in theory refinement. I’ll admit that I haven’t done anything but skim the Hornstein et al introduction recently, but I don’t remember them asserting that elegance had any epistemological value either. More to the point, you haven’t quoted them saying any such thing (and I, meanwhile, have quoted them saying things that at least suggest they understand the difference). I think this might be more effective if you could find someone who has unambiguously argued that elegance is on equal epistemological footing with things like predictive power. I’m certain I haven’t done that, and I don’t think Hornstein has done that either.
I’m happy for you, Hornstein, and everyone else to grant that elegance doesn’t have any epistemological value, since that’s been my position all along.
That said, when you say things like ‘to evaluate two theories with similar coverage, we will prefer the more elegant theory. That is not just because it’s more aesthetically satisfying, but because the fact of finding a unifying explanation is a good clue we’re tapping into some underlying truth’ and ‘If you have two theories that cover the same facts, and one of them presents a more unified explanation, you’re inclined to pursue that theory rather than the other. It’s not solid evidence, but it is prima facie evidence,…’ it sounds an awful lot like you’re making claims about the epistemic virtues of elegance.
Or, rather, I would argue that you’re making claims about the epistemic virtues of simplicity, which we’ve already agreed only comes into play if all else is equal. And, as discussed above, with respect to P-and-P vs. Minimalism, it’s not at all clear that all else is equal.
I haven’t said anywhere that anyone is arguing for elegance being on equal epistemic footing with things like explanatory scope, predictive accuracy, or the like. In fact, I stated explicitly above that you and I agree that, e.g., simplicity is useful only as a ‘second tier’ evaluative dimension.
Even if elegance can be useful in choosing between two equally explanatory theories, and even if elegance is distinct from simplicity, if Hornstein, et al., want to argue that Minimalism is preferable to P-and-P because it’s more elegant, the burden is on them to show that P-and-P and Minimalism are, in fact, equally explanatory (and, I would argue, that the two are equal with respect to predictive accuracy, consistency with other theories, and any number of other desiderata that are epistemically prior to elegance and its ilk).
Maybe they’ve done so, but I note, again, you have stated explicitly that these two theories are not equally explanatory, which makes me think either that the case for equal explanitoriness hasn’t been made at all or that it hasn’t been made all that convincingly.
Saying that the two theories are not equally explanatory is irrelevant to the argument about elegance, though – that’s just a side-argument about some of the justifications for Minimalism. If Hornstein et al believe in those justifications, then they’re in a position to be using elegance as a theory evaluation criterion. I’m not – but not because it isn’t a relevant factor. I’m not because I don’t think GB was all that convincing to begin with.
Fair enough, but the phrase “prima facie” is in there to do the work of assuring you that I’m not making any real claims to epistemic virtues. “Prima facie” evidence is good enough to get the government interested in a suspect, but it’s not admissible in the proof of the crime. That’s sort of how I think about elegance. It’s enough to convince me that there is probably something there, but it’s still a long way from proving the case. I wouldn’t choose a theory simply because it is elegant, and (more importantly) I wouldn’t rule out a theory for lack of elegance, but I would use elegance to choose between theories of similar explanatory power – and especially in domains like Syntax where my claims are not immediately testable anyway.
I was thinking about this some more, and I remembered a discussion in one of Larry Laudan’s books or papers about how it is that new theories ever even get developed. Laudan (along with other philosophers of science, I’m sure) distinguishes between belief-worthy and pursuit-worthy theories. Elegance is maybe a good candidate for pursuit-worthiness, with epistemic criteria like explanitoriness doing the heavy lifting with respect to belief-worthiness. Correct me if I’m wrong, but this seems to be consistent with Minimalism emerging out of the older, more thoroughly developed GB/P-and-P theory of syntax, at least for folks like Hornstein (i.e., people who, unlike you, take P-and-P to be explanatorily satisfactory).
That’s a good distinction. So OK, what I should have said is that elegance contributes to pursuit-worthiness. And yes, it’s consistent with Minimalism emerging out of GB. But I’m not sure it’s a totally accurate characterization of what Hornstein et al think they’re doing with Minimalism. They think of Minimalism as a reworking of GB consciously undertaken with the hope of yielding new insights. That is, you take a P and P framework, mix in some new-but-currently-unjustified assumptions (namely “language is something like perfect,” or however Chomsky phrases that), and see how far you get with those new assumptions. So, it’s an odd way of doing science, but then Syntax is an odd science (definitely one of the least “sciency” of the soft sciences; it’s damn close to Philosophy). In any case, elegance plays a more prominent role in this exercise than it does in most theoretical endeavors because to the extent that the original hypothesis is true, the theory that describes it will be elegant.
It was to disassociate myself from this kind of thinking that I added that last bit about GB and Minimalism being equally explanatory. I think Hornstein et al would say that Minimalism is currently less explanatory than GB, but since it is showing promise we expect it to eventually be more explanatory. I would personally say that GB was never all that explanatory, and that there are independent reasons to do Minimalism. That’s probably the subject of a whole nother blog post, but the cliff’s notes version is that I think when you’re dealing with something as empirically slippery as Syntax, it’s more important to get your (assumptions about first) principles in order first than it is with other sciences just because your assumptions will invariably color how you interpret your findings, and there’s really no way to test them. So, you have to spend more time than you normally would making sure that what you’re peddling seems right, and more time than you normally would making sure that you’re not unnecessarily multiplying entities. In Physics, that can come out in the tests. In Syntax, it never will. The only way to eliminate unnecessary assumptions is by thinking through it like a philosopher. So, I think Minimalism was always the better starting point, and I find it much more convincing than GB. GB covers more data, but I don’t think it really accounts for it in a lot of cases – like OT in Phonology, it’s better as a data classification system than as a real explanation for anything. So, GB was useful for laying out what we’d observed, but I have trouble thinking of it as a theory. So, to me, Minimalism isn’t really about chasing elegance in the hopes that it pans out and that language turns out to be “something like perfect,” it’s more about enforcing on ourselves the kind of discipline that data would enforce in Physics, but will not in Syntax. So, I guess I have a kind of inverted version of it: Minimalism will start out maximally elegant and get less so as we go along. Although, this descent into messiness will not be linear, and from time to time we may discover connections that bring us closer to the original elegance, and in such cases I would take that as prima facie evidence that the proposal was on the right track.