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.