In a recent post on this blog, Thomas Graf addresses the derivationalism vs. representationalism debate---sparked (Thomas' post, that is) by my remarks in the comments section of this post.
Thomas notes, among other things, that literally any derivational formalism can be recast representationally. For example, one could take the set of licit derivational operations in the former model, and turn them into representational well-formedness conditions on adjacent pairs of syntactic trees in an ordered sequence. (Each tree in this ordered sequence corresponds, informally, to an intermediate derivational step in the former model.) As best I can tell, this translatability of any derivational formalism into representational terms is not even debatable; I certainly wouldn't argue this point.
Here's where things start to fray, though:
So why is one inherently derivational, and the other one is not? [...] The difference is only in our interpretation of these [formal devices]. But judging a technical device by our interpretation of it is rather peculiar because, in general, there's no bounds on how one may interpret some formal piece of machinery.I agree wholeheartedly with the last part---namely, that when discussing the interpretation(s) that can be assigned to a particular formalism, one is usually dealing not with what can be proven, but with what is plausible, reasonable, or even just conceivable. And this means that one brushes up against matters of opinion, personal preference, and, dare I say, scientific taste. To make matters worse, we linguists---myself obviously included---are not always as terminologically hygienic as we should be in making sure to avoid the "proven"-style lingo when addressing these matters.
But at the risk of attributing to Thomas sentiments that he may not hold, I read this passage as a suggestion that we should therefore avoid entirely the question of how we interpret our formalisms, and instead stick to the formalisms themselves. On this, I could not disagree more. Obviously, it would be more straightforward if things weren't so darn murky; but in my view, the point at which we stop caring about how we interpret these formalisms is the point at which we stop being cognitive scientists, and instead become something more like mathematicians [in the broad sense, the way a graph-theorist can be thought of as a mathematician]. To put it another way: as a linguist, I am not interested in formalisms qua formalisms; I am interested in them as idealized versions of computations in the mind. Consequently, I am fundamentally interested only in those formalisms for which there exists at least one plausible cognitive interpretation.
This means that it is entirely possible that two formalisms X and Y would be mathematically equivalent---let's say X and Y are identical in both their weak and strong generative capacities---and yet only one of them would be considered a plausible linguistic theory.
Moving to a specific example, I see no reasonable cognitive interpretation for the "ordered n-tuple of representations" formalism, and thus---speaking only for myself here---I consider it largely irrelevant to linguistics (at least until someone can show me a reasonable cognitive interpretation of it).
And this brings us back to the derivationalism vs. representationalism issue. I have stated, in the remarks linked to above, that I find the "generate-and-filter" grammatical architecture to be bankrupt, and that I was disheartened that Chomsky seems to be veering in that direction (yet again). How can that be squared with the aforementioned, not-even-debatable translatability of derivationalism to representationalism? Simple. The only generate-and-filter architecture that I find cognitively plausible---and with this, I think Chomsky would concur---is one in which syntax (what Chomsky would call the "computational system") does the generating, and the interfaces (LF/PF) do the filtering. Alas, this system simply doesn't get the facts right; I won't rehash the argument here, but it boils down to the fact that---contrary to Chomsky's own claims---the obligatoriness of syntactic agreement cannot be reduced to anything the interfaces should be paying attention to (interpretability/uninterpretability or particular interpretations on the LF side, overtness/non-overtness or particular phonological content on the PF side). So, since the only cognitively plausible generate-and-filter system doesn't work, I consider the generate-and-filter architecture to be bankrupt.
Is this an "I have never baked a good cake so there are no good cakes" argument? I'm not sure. Bankruptcy is temporary (just ask Donald Trump!), and as I said above, I'm willing to have my mind changed if someone gives me a working generate-and-filter architecture that has at least one plausible cognitive interpretation. But until such time, forgive me if I shop for cakes at the bakery, a.k.a. the derivationalism store ;-)