Leonard Finkelman writes:
Say hello to Dimetrodon grandis:
Dimetrodon would be perfect evidence for intelligent design, provided that the intelligent designer is Descartes’ evil demon. The animal seems to exist for the purpose of confusing learners and frustrating the learned.
One of Dimetrodon's more frustrating aspects is also its most obvious. Look at that sail: what's up with that? Despite finding a few similar structures in modern animals, everything about the sail--its function, its evolutionary origins, and even its appearance--remains mysterious. Recent research suggests that even the little that we thought we had figured out might be wrong (Rega et al 2012). In fact, I think that our errors about biological sails run even deeper--not only do we probably have them empirically wrong, we also have them conceptually wrong.
This is Spinosaurus aegyptiacus, a dinosaur that simply is not helping:
There are obvious similarities between Dimetrodon and Spinosaurus. Of course there are! As Nelson Goodman argued: there are infinitely many ways for any two objects to be similar. Most similarities are entirely trivial. To wit: both had skeletons less than 1000m long and both had skeletons less than 1000.1m long. What makes Dimetrodon a frustrating animal and Spinosaurus an unhelpful point of comparison is that the less trivial similarities between them can be misleading. The two share a number of seemingly reptilian similarities, but Spinosaurus is classified as a reptile whereas Dimetrodon is not. Systematists consider the reptilian similarities to be (relatively) trivial and the dissimilarities between the animals' temporal fenestrae to be (relatively) substantive.
I'm burying the lede, of course: what about the sails? Like many philosophers I'm more gadfly than human, and so I'm tempted to respond, "There's no such thing as a sail!" But that would be disingenuous. Of course there is such a thing! Sails are not only a thing; they're a fascinating thing! It's just that when I admit that there is such a thing as a sail, I'm not talking about something biological. 
Substantiveness and triviality are relativistic concerns in the life sciences. Similarities between the maxillae of Dimetrodon and Spinosaurus will be important to a researcher studying (say) biomechanics, but a paleontologist trying to reconstruct evolutionary history will find that similarity less compelling. We might therefore ask which similarities between the animals are more or less trivial, and we'd answer that question by asking the relevant researchers which similarities matter to their work.
But some similarities shouldn't matter to any life scientist at all: they are purely trivial. For example, the fact that both animals are represented by toys stored in my parents' basement doesn't have any effect whatsoever on the work done by any biomechanist or paleontologist. We might therefore ask which similarities between the animals are purely trivial. This question--in the biological context, the problem of trait individuation--is difficult to answer in part because a purely trivial similarity is nevertheless a real similarity between organisms. Dimetrodon and Spinosaurus really do share toy representation in my parents' basement. Whereas that similarity obviously shouldn't matter to any life scientist, it isn't always clear which similarities should matter to some researcher.
Philosophers face the same problem in a broader context. I can rattle off a list of things that pop into my head: the toes on my left foot, the quadrilateral figure formed by the relative positions in time and space of this blog's primary authors, and Planet X. One thing that's really common to all those objects is that I just listed them all. Peter Geach termed this kind of purely trivial similarity a "mere-Cambridge property," and it is the kind of similarity that isn't important to anyone (except, presumably, for pedants in Cambridge). David Lewis argued that the difference between mere-Cambridge properties and nontrivial similarities is that nontrivial similarities make a real causal difference in the world at large (Lewis 1986).  The problem in distinguishing mere-Cambridge properties from nontrivial similarities is--well, it's a pretty big problem. Nevertheless, we can assume that at least some similarities between objects are nontrivial.
I don't want to argue that the sail, common to Dimetrodon and Spinosaurus, is a mere-Cambridge property. I do want to argue that the sail is not a biological trait.
Brian Epstein (2015) recently introduced a distinction between grounding and anchoring similarities between objects. I think that a distinction along those lines is useful here. As I understand it, a nontrivial similarity is grounded by the theory that defines the similarity's functionality whereas a nontrivial similarity may be anchored in a theory in which the similarity plays an explanatory role. In other words: grounding theories define a nontrivial similarity and anchoring theories determine how and why the defined similarity explains a phenomenon of interest.
The maxilla, for example, is a nontrivial similarity both grounded by and anchored in theories of anatomy. An organism's maxilla is a biological trait of the organism insofar as the similarity the organism shares with other organisms bearing maxillae is a similarity grounded by the life science. By contrast, mass is a nontrivial similarity grounded by theories of physics, but potentially anchored in (say) biomechanical theories. I would call mass a nontrivial property, but not a biological trait, because the similarity shared between an organism and other objects of the same mass is a similarity grounded by physics, even if it can be anchored in biological theories. 
So what, if anything, is a sail? Let's assume that the sail is a similarity between Dimetrodon and Spinosaurus. The similarity is probably shared with other animals, too. But which ones? Are the relevantly similar animals sailfish:
Or sailfin lizards:
The term "sail" is ambiguous. What's similar between Dimetrodon and Spinosaurus might be a rounded protrusion raised above and parallel to an animal's spine, in which case a sail is a similarity shared with sailfish and sailfin lizards, but not buffalo. But "sail" might also refer more specifically to a protrusion created by an elongation of a vertebrate's neural spines, in which case Dimetrodon and Spinosaurus are similar to the sailfin lizards, but not to sailfish or to buffalo. A third possibility is that "sail" might refer to the collection of elongated neural spines themselves, in which case Dimetrodon and Spinosaurus are similar to the sailfin lizards and buffalo, but not to the sailfish.
Whatever a sail may be, it's a similarity shared between around two dozen known vertebrate genera. My ultimate justification for denying that the sail is a biological trait lies in the fact that these genera are a mixture of extant and extinct ones. If we grant that all of these genera share this nontrivial similarity, then the sail is a similarity that cannot be grounded by any single biological theory.
Biological traits are normally categorized as either homologous--structurally similar--or analogous--structurally different, but functionally similar--but the similarity shared between Dimetrodon and Spinosaurus is neither. One of the reasons that the sail is so fascinating is that there seems to be so much diversity in the use, construction, and origin of sails.
The functions of any sails found in extinct genera are difficult to ascertain. We have seemingly equal reason to believe that Spinosaurus sails might have served a thermoregulatory function or a display function or a bioenergentic function. There are certainly structural differences between the neural spines of Spinosaurus and Dimetrodon that suggest a functional difference between their sails. Considering Dimetrodon alone, Rega et al (2012) argue that the sail might have split the structural and functional differences between modern sailfin lizard displays and buffalo humps. Nevertheless, these functional differences don't count against the nontrivial similarity evidently shared between these animals.
Philosophers of biology working in Evo-Devo have recently picked up on the concept of evolvability as a means to explain similar biological traits that are either structurally or functionally diverse (Love 2014). The sail would be evolvable if its evolution in Dimetrodon and Spinosaurus could be explained by some common developmental mechanism--for example, a change in the timing of some genetic switch that contributes to the elongation of neural spines. But it seems unlikely that the sail is a nontrivial similarity grounded by a single Evo-Devo account. Perhaps the structural differences between Dimetrodon and Spinosaurus neural spines could be explained away by idiosyncracies of the animals' genomes, but it seems more difficult to explain why some common cause would yield a single hump in Dimetrodon's sail and two humps in Spinosaurus sails. And it seems even less likely that a common developmental cause of Dimetrodon and Spinosaurus sails could adequately account for the sail of Edaphosaurus, given the presence of novel cross-bar structures on neural spines in the latter genus:
I'm willing to grant that a single theory in some life science might someday account for the nontrivial similarities between Dimetrodon and Spinosaurus and Edaphosaurus and Morelladon and sailfin lizards.  Nevertheless, there is no guarantee of any such development. The reason that the recognition of a nontrivial similarity between those extinct and extant genera defeats the grounding of sails by the life sciences is that, given the paucity of data on the structures found in extinct genera, there remains a possibility that no single biological or paleontological theory will ever account for the conspicuous similarity shared by those genera. Nevertheless, it is the case that the similarity shared by the genera remains nontrivial. 
What, then, grounds the nontrivial similarity between Dimetrodon and Spinosaurus? What functionality do the sails of those genera share if not a biological function? That functionality might be grounded by physics (perhaps aero- or hydrodynamics) or psychology (humans seem to be predisposed to recognize sails as a distinctive or novel feature). I'll admit that I'm not sure. In any event, there should be some means of grounding the similarity even if attempts to ground it in biology fail, because sails do not seem to be a mere-Cambridge property.
In summary: sails are a nontrivial similarity shared by a number of extinct and extant genera, including Dimetrodon and Spinosaurus; nontrivial similarity are grounded by theories that are biological or by theories outside of biology; since the similarity between Dimetrodon and Spinosaurus is not grounded by biology, then it must be grounded elsewhere. I suspect that this consequence, whereby apparently biological traits cannot be grounded biologically, follows particularly as a result of recognizing a poorly-understood similarity between extinct taxa and extant ones. Given that the apparent trait's functionality may vary between what we observe now and how animals functioned in the past, and given that the similarity is nevertheless nontrivial, it follows that biological history and function are insufficient to account for the similarity.
Perhaps the easiest solution is to abandon belief in sails altogether: perhaps Descartes' demon really has been engaged in a (strangely elaborate and specific) deception all along. This thing that we've been struggling to understand--the sails that have cropped up repeatedly throughout evolutionary history--may be nothing more than illusions, tricks of our perceptual light. But I tend to think not. To endorse that view--to set the sail away--would entail losing a real and wonderful feature of the world's past and present. 
 Like I said: gadfly.
 Lewis' main point here is that functionality in some sense causes the non-triviality of properties. Other metaphysicists differ in assigning an order of causation here. While I do agree with Lewis--on this and other related points--I don't think that my argument would have to change much if we assume a different account of nontrivial properties. All that matters is that properties make some functional difference.
 Thanks to our very own Adrian for explaining this to me (despite my reflexive groaning at the sound of the word "grounding"), and apologies to Dr. Epstein if the stated view misrepresents the one he originally elaborated in the context of social science studies.
 I'll even exclude sailfish and buffalo here if that suits your tastes--no accounting for those, either!--but my point would remain the same (and it would certainly be strengthened by their inclusion!).
 One might argue that the similarity could be grounded by multiple theories in the life sciences, in which case the sail would still be a biological trait; however, I think this suggestion equivocates grounding and anchoring. For example: we might say that there is some bioenergetic similarity between the sails of Spinosaurus and buffalo humps, and a developmental similarity between the sails of Dimetrodon and Spinosaurus, but no bioenergetic similarity between Dimetrodon and the buffalo. We might also say that all three have some sail in common. But if we make that last claim, then we're helping ourselves to some definition of "sail" that isn't shared between biological theories. The biological theories are therefore anchoring use of the term "sail," but they aren't grounding it. In the end, it's the grounding theory that does the definitional work, and I don't think that theory can be biological in the case of sails.
 Thanks again to Adrian for some helpful commentary on this post!
Epstein, B. (2015). The Ant Trap: Rebuilding the Foundations of the Social Sciences. Oxford University Press.
Lewis, D. (1986). On the Plurality of Worlds. Oxford: Blackwell.
Love, A. C. (Ed.). (2014). Conceptual change in biology: scientific and philosophical perspectives on evolution and development. Springer.
Rega, E. A., Noriega, K., Sumida, S. S., Huttenlocker, A., Lee, A., & Kennedy, B. (2012). Healed fractures in the neural spines of an associated skeleton of Dimetrodon: implications for dorsal sail morphology and function. Fieldiana Life and Earth Sciences, 104-111.