Monday, April 9, 2018

Arbitrary, or dogs and cats

Bill Idsardi

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). The important question is not about dogs and cats but about dogs and some item with a different type, like all which has type ((e,t), ((e,t),t)). Is the difference between dogs and all important within the semantic computation? The answer would seem to be yes -- that's the whole point of having a type system. And consequently, the difference between dogs and all is again a kind of hidden substance, only now between the CI notions DOG and ALL that map to dogs and all. That is, the difference between DOG and ALL in the CI system maps to a type difference in the semantics between (e,t) and ((e,t), ((e,t),t)). Consequently we should restrict the notion of free substitution to substitution between items of the same type. For me, this interchangeability notion is not a question of being "substance-free" (although one might say that the calculations are substance-agnostic, adapting Thomas Graf's use of "content-agnostic" from his reply to Norbert's post), rather the idea seems more closely related to the notion of systematicity (Fodor and Pylyshyn 1988, Aizawa 2003).

So let's try to translate the free-substitution-within-types idea into the proposed EFP structure to try to find cases of hidden substance. The resulting claim, which we largely agree with, would say that all events are freely interchangeable with other events without affecting the nature of the computation, all features are interchangeable with other features, and all precedence relations are interchangeable with other precedence relations. Not, importantly, that there are no differences between events and features and precedence relations, which all have different type signatures (in a "truth-value" phonology they would be (e), (e,t) and (e,(e,t)) respectively). So, we'll say a little boldly, type differences indicate hidden substantive differences. But having hidden substance isn't being "substance free" though it does make it harder to spot.

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.


  1. What would a strong substance-free view say about feature combinations - should they all be equally available? What if some combinations are illicit – does this in itself suggest some substance, or is this a ‘late-filter’ case with the illicit combination being ruled out at a later stage, e.g., due to impossibility to execute corresponding motor commands?

    1. Hi Nina! Yes, that's definitely one part of it. To the degree that we can find useful work for the seemingly-illicit combinations (like [high, low]) to do, this suggests that the computations within the phonological system are divorced from the (ultimate) interface conditions. That is, things that would be illicit if they reached the interface can do interesting work within the phonology proper. (We have a couple of these that we'll post in a week or so.) And maybe then such things are simply "cleaned up" at the interface (that part is less clear to me).

    2. Not clear about your "to the degree that..." clause. The availability of "seemingly illicit" (i.e. to us with our intuitive "understanding" of what these feature combinations mean or transduce to) comes for free by construction with a strong SFP; it doesn't matter whether or not they get used for anything. As you say, though, if they "do work" in the phonology, then whatever it is they eventually map/are transduced to probably doesn't look like what we would normally expect.

    3. Hi again Fred. I think what I going for will become clearer once I put the examples up, sorry to keep people in suspense about that. If the "seeming illicit" cases are never used in interesting ways in the phonology (e.g. in deriving different behaviors) then it's not logically impossible that they're in the phonology nevertheless, it's just that we wouldn't have positive evidence that they are there. And I want to try to predict and find positive evidence whenever I can. I want to see the bold predictions confirmed, not just to see them fail to be disconfirmed. (And I do think this is a bold prediction of SFP.)

  2. '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"'

    This is a big semiotic pet peeve of mine: what you are describing here is not something non-arbitrary; you're describing MOTIVATED signs. A sign is motivated if there is a predictable mapping of signifiers to signified based on a system. But the whole system and every pair of signifier and signified in it is still arbitrary.

    Graphically arbitrarines is about the horizontal line here:

    signifier <----> signified

    What you're describing is a vertical relationship among signifiers parallel to the vertical relationship among signifieds:

    | <----> 1

    || <----> 2

    ||| <----> 3

    The two sides of the arrow parallel each others in a motivated way, but every horizontal line is arbitrary.

    So your case is not an in-between case. The arbitrariness of the sign is just a fact of how signs work, it's not violable.

    1. Hi Max. I'm not sure that the term "motivated" is that much better than the term "non-arbitrary" here. But I'm open to other terminological suggestions, perhaps "systematic". Because, as you say it's the presence of a *system* that's important here, which means (at least for me) that isn't "arbitrary" in the way that word is used in mathematics. In fact, it seems likely that any infinite mapping has to at some point become "non-arbitrary", "motivated", "systematic" or "combinatorial" after a finite number of special cases have been dealt with.

    2. "Motivated" is just more general than "systematic", because there are also loose ways that a sign can be motivated. E.g. Leach's 1970 analysis of the semiotics of street lights in which the sign yellow<->slow down is motivate by the fact that yellow is between red an green, and slowing down is between stopping and going normally. This is motivation, but not quite systematic.

      Indeed arbitrariness of the sign is not the sense of arbitrariness used in mathematics. A sign is arbitrary if the connection has nothing to do with its two parts. In dog<-->DOG there is nothing in dog that connects it to DOG and nothing in DOG that connects it to dog. If you have a system you can derive, say "black dog"<-->BLACK DOG from the signs dog<>DOG and black<>BLACK (and the long chain of rules of syntax an semantics that connect these forms to the the interpretation), but there is still nothing in "black dog" or BLACK DOG connecting them, hence they are arbitrary. Arbitrary in the sense that the signifier could have stood for anything, and the signified could have had any form, and thus the pairing is merely a chance occurrence from the point of view of the sign.

      This is probably taking us further afield than needed. The main question here can be rephrased without dragging ourselves into talking about semiotics: how much should the systematicity of phonology (the formal facts of the data-structure) recapitulate the systematicity of phonetics (the raw structural facts of bodily organization)? The SFP answer is not at all, but you have some convincing cases in mind where you think phonology does recapitulate bodily organization.

  3. Thank you Bill for another interesting and stimulating post.

    I don’t think that Saussure’s intended conception of the arbitrariness of the sign is applicable to phonological features (although I do believe that Saussure’s aphorism about langue should be extended to phonology: phonology is “form, not substance” (cf. “La langue est une forme et non une substance”; Saussure 1916/1964: 169). If a feature were granted an equivalent of S’s arbitrariness, then I guess that would mean that that feature could in principle be realized by any possible human articulation, similarly to how the concept/signified DOG could in principle be assigned to any possible signifier. For example, in that case it should be possible that a [+ROUND] feature gets realized as a lowering of the velum. But that does not seem possible.

    Instead, in the above quote, I actually did intend to equate arbitrary and substance-free (i.e., void of any consideration of phonetic substance), but I wrote an important caveat: “from the point of view of phonology”. From the perspective of the computational part of phonology features are treated arbitrarily (without reference to how they are/can be/should be externalized), but, crucially, from the perspective of the phonetic implementation system (PIS) features are not treated arbitrarily. It is because of how features get interpreted by the PIS at the phonology-phonetics interface that [+ROUND] cannot ever be realized as a lowering of the velum. This is exactly why it is not contradictory to regard features as substance-free and substantive at the same time; it is a matter of perspective (phonology vs. phonetic implementation, respectively). Thus, while it is certainly true that “distinct, but non-arbitrary relationships between levels of representation”, which Bill aptly calls “hidden substance”, “play an important role in sensory systems”, they do not seem to play any role in phonological computation (i.e., they are not available to rules). In my opinion, this sort of arbitrariness does in principle lead to substitutability, but there are of course some bounds: For example, in rule, a feature cannot be substituted with, say, a tone. Substitutability probably works only between elements of the same class, and this class has to be explicitly defined. (Perhaps, then, # and % are not of the same class as other units with which they enter into precedence relations, and are therefore not freely substitutable.)

    In brief, here’s a bumper-sticker that I’d gladly stick to my car:

    Feature --------(arbitrary)--------- Rule

    1. Typo correction: "in rule" --> "in a rule".

    2. Thanks Veno. I think we're approaching some convergence here. I hope that the "substitutability within type" idea has some traction for people. Eventually we'll get to some interesting cases for rule types, when we get there I'll be very interested in what you think. In a week or two probably.

  4. Let me just toss out a quotation from Brian Cantwell Smith, On the Origin of Objects

    Because formal symbol manipulation is usually defined as “manipulation of symbols
    independent of their interpretation,” some people believe that the formal symbol manipulation
    construal of computation does not rest on a theory of semantics. But that is simply
    an elementary, though apparently very common, conceptual mistake.
    Symbols must have a semantics—i.e., have an actual interpretation, be interpretable,
    whatever—in order for there to be something substantive for their formal manipulation
    to proceed independently of.

  5. Your blog post on the arbitrariness of cats and dogs is both amusing and relatable for pet owners. It's like a slice of daily life with our furry friends. And for those looking to pamper their pets, perhaps they can find some fantastic deals using a "7now promo code" for pet supplies and treats. Thanks for the delightful read!