It is very much in vogue today to assume that features in the lexicon can freely vary along two dimensions: interpretability and value (Pesetsky and Torrego 2007). This gives us four possible forms of syntactic features shown below.
(1) The typology of Formal Features
But the stipulation that we tossed aside wasn’t really a stipulation, but an empirical observation. Consider the sentence below.
(2) She likes her.
This sentence displays three instances of inflection: nominative case on she, subject argeement on likes and accusative case on her. Let’s make the fairly standard and well-founded assumptions that these inflections are the phonetic realizations of formal features and that these features receive no semantic interpretation. It’s obvious that the features have values, but not obvious where the values come from. We could say that all features enter the syntax valued and uninterpretable feaures must be checked, but let’s not do that. Rather, let’s say that uninterpretable features have no inherent values and must receive their values from valued features. Thus we have arrived at the “stipulation” that P&T dispensed with, largely based on evidence and reason. Since Chomsky’s interpretability/valuation bidirectional seems less like a stipulation and more like an empirical hypothesis, P&T would require further evidence to overturn it and expand the logical space of features. While P&T and, others who follow them, show that the expansion of the feature typology can lead to greater empirical coverage, they do not, to my knowledge, give evidence of the two new feature types (uF:val, and iF:__). I would argue that when you add more primitives to a theory, you will almost always expand its empirical coverage. In fact, If you were to propose removing primitives from a theory, you would likely be met with cries of “We need that for X!”
So where are the uF:val's, and iF:__'s?
Bošković (2011) proposes that grammatical gender on nominals is an example of a uF:val, because it is lexically determined (and therefore valued) and has no semantic interpretation (and therefore uninterpretable). As Bošković (2011) notes: ". . . the fact that ‘table’ is feminine in French and masculine in [Serbo-Croatian] doesn't lead to a difference in the interpretation of the noun in these languages." This conclusion, however, is slightly rash. While grammatical gender does not seem to add to the propositional content of a sentence, it may have other semantic effects. As Boroditsky, Schmidt, and Phillips (2003) show, speakers of a language with grammatical gender tend to unconsciously impose a gender on an object based on the grammatical gender of the nount that denotes it. Without accepting the conclusions that Boroditsky, et al. draw from this data, we still cannot ignore it, which means that Bošković has not found uF:val's yet.
More problematic still are the interpretable unvalued features. Again, I can think of no examples of them, likely because I don’t know how to distinguish them from iF:val's. Both would have morphophonological information and semantic information, but that information on iF:__'s would be determined contextually. It’s hard to imagine why a learner would choose the unvalued version with its additional stipulation of context dependence. What’s more, a theory that includes iF:__'s seems to predict the possibility of a single head bearing all sorts of iF:__'s. Why don’t we have a language whose interpretable features are all on one head?
Why do verbs not have interpretable unvalued φ, tense, aspect, mood, force, etc. features that are valued by uninterpretable counterparts on D, Infl, C, etc.? We could do our best to introduce constraints on our grammar that would preclude these, but we would then have to justify those constraints, which seems like a long way to go to allow for a theoretical device that isn’t even fully justified.
I'll admit that I was once quite enamoured of this approach to linguistic theory, the What-if-we-relax-this-constraint approach, because it always allows for new and interesting devices to play with. I've come to the realization, though, that we ought to be much more resistant to relaxing constraints on our theories. We ought to demand incontrovertible evidence for every new device in our theory. So I ask again:
Where are the uF:val's, and iF:__'s?