In recent comments Veno has put one part of the SFP view very succinctly and clearly:
"In other words, phonology (as an aspect of the mind/brain) treats features (and other units of phonological representation) as arbitrary symbols. From the point of view of phonology, then, features are substance-free units. This, of course, does not mean that features are not related to phonetic substance, and such a conceptualization of features does not preclude the construction of a neurobiologically plausible interface theory (even spelled out in Marr’s terms)."
So I think we need to unpack what "arbitrary symbols" means here. To put my cards on the table, when I read "arbitrary" I think of two things: the use of arbitrary in mathematics (meaning "anything meeting the definition") and Saussure's arbitrariness of the sign. My worry is that this view tends to exclude an important middle, the existence of abstraction -- distinct, but non-arbitrary relationships between levels of representation, call it hidden substance (because it's useful and partly veridical). And I think such non-arbitrary relationships of abstraction play an important role in sensory systems, and constitute the "substance" (or "substantive relationship") between adjacent levels of representation (being veridical and useful). So what we're going to uncover in this blog post are a few instances of "hidden substance". A word of warning -- this post might not make for light bedtime reading. On the other hand, it might be very soporific.
Let's start with a simple example of a non-arbitrary system, the unary numeral system, or tally marks. In this system for the natural numbers, 0 is the empty string, 1 = "|", 2 = "||", 3 = "|||" and so on. This is a non-arbitrary system because "more is more": larger numbers are represented with larger representations (larger numbers correspond to larger data structures). And addition in this system is concatenation, which then automatically (and non-arbitrarily) preserves important properties like being associative and commutative. So this isn't purely Saussurean as the representations have hidden substance (or partial substance if you prefer). Onomatopoeia (sound-symbolism) is another kind of in-between case, and it might be helpful at least as an analog in understanding the point here, namely that there's still some substance (veridicality and usefulness) but it has been partly obscured by the mapping (but this analogy is imperfect, and I really don't want to discuss theories of sound-symbolism here). It is also obscured by the fact that many other mappings are much more arbitrary (e.g. Roman numerals). Perhaps another way to think about this idea would be to say that arbitariness can be put on a scale of how much of the system is done via lookup tables, and how much of the system is done by general laws of combination (see Gallistel and King 1999).
Sensory systems, even mechano- and chemo-transducers, tend to do a similar kind of abstraction in lawfully transmitting some relationships. But admittedly those cases are not nearly as clean as the unary numerals toy example. For example, the conversion done by the rod cells in the retina also abides by "more is more" -- within the operational limits more photons received means more activity. (At the low end the limit reaches down to a single photon, at the high end, the rods reach saturation pretty quickly, leaving the rods relatively less to do for humans in the modern built world.)
I think the intended use of arbitrary in Veno's quote is for something like "substitutable, interchangeable in the functions, operations and/or relations". This is also what I take to be the point of the dogs-cats argument, which is in Bridget's article that she mentioned in response to our first post. Here's Bridget quoting Daniel Currie Hall, channeling Alec Marantz.
"The phonological component does not need to know whether the features it is manipulating refer to gestures or to sounds, just as the syntactic component does not need to know whether the words it is manipulating refer to dogs or to cats; it only needs to know that the features define segments and classes of segments. The phonetic component does not need to be told whether the features refer to gestures or to sounds, because it is itself the mechanism by which the features are converted into both gestures and sounds. So it does not matter whether a feature at the interface is called [peripheral], [grave], or [low F2], because the phonological component cannot differentiate among these alternatives, and the phonetic component will realize any one of them as all three." (p 206)
I have a couple of comments about this argument. First, I think that the appropriate comparison for phonology is semantics, not syntax, because it is semantics that connects to the CI interface. That is, the question is whether the difference between dog() and cat() is semantically substantive, not if they are syntactically distinct. But the argument is presented in various places ranging across both semantics and syntax. And to be clear, I think this observation about cats and dogs is correct about both syntax and semantics. That is, interchanging cat() for dog() doesn't affect the nature of the syntactic or semantic computations, though it might eventually end up in different truth values for particular instances (e.g. dog(laika) vs cat(laika)). (And this is not an endorsement on my part of truth-value-oriented semantics, see Pietroski, but it will do for this discussion.)
The issue I have with the argument is simply that the range of semantic examples (cats vs dogs) is too narrow to reveal the hidden semantic substance. These cases both have the same type, (e,t)
So let's try to translate the free-substitution-within-types idea into the proposed EFP
Free substitutability is certainly a situation "devoutly to be wished", even when restricted to items of the same type, but I'm afraid we will still fall a little short of this ideal. Why? Because there are the dreadful "special cases", meaning more examples of hidden substance. In the EFP model, the # and % events are special cases, which means that they aren't fully interchangeable with other (ordinary) events. An automatic consequence of their special status is that the precedence relations involving # and % are not fully interchangeable with other precedence relations either. And furthermore that there are no features that apply to # and % events. (I.e. [spread]e for e = # isn't a thing, though see this exchange between Lass and Morris Halle.) One way of thinking about this is that # and % are "purely formal", but that again highlights that the difference is one of substance -- either the special events don't have any (which seems not quite right), or they have weird, special properties that are preserved across the interface ("beginning/end of form").
This is similar in some respects to math cases where certain Abelian groups are extended to form fields. In those cases we need to "special case" the identity element over addition (0) to say that it does not have a multiplicative inverse (i.e. 0 has no reciprocal, or you can't divide by 0). I think in general we are so used to these special cases that we often fail to even notice them. So let me point out a very general source of special cases. In a recursive definition, the special cases will be the base cases (= stopping cases), like "end of string" or 0. Are there any additional special cases for events, features or precedence beyond the ones just noted? Unfortunately, we suspect that there are some more. Again, the minimalist program qua program is to try to keep the special cases to a minimum, not to declare them all out-of-bounds a priori.
To bring this post to another bumper-sticker conclusion, the hidden substance cases show that arbitrary ≠ systematic ≠ substance-free. We need to keep these notions separate, because they interact in interesting ways in complex, modular systems like language.