Saturday, April 6, 2019


Chabot 2019:

"The notion that phonetic realizations of phonological objects function in an arbitrary fashion is counterintuitive at best, confounding at worst. However, order is restored to both phonology and phonetics if a modular theory of mind (Fodor 1983) is considered. In a modular framework, cognition is viewed as work carried out by a series of modules, each of which uses its own vocabulary and transmits inputs and outputs to other modules via interfaces known as transducers (Pylyshyn 1984; Reiss 2007), and the relationship between phonetics and phonology must be arbitrary. This formalizes the intuition that phonology deals in the discrete while phonetics deals in the continuous. A phonological object is an abstract cognitive unit composed of features or elements, with a phonetic realization that is a physical manifestation of that object located in time and space, which is composed of articulatory and perceptual cues." [italics in original, boldface added here]

The implication seems to be that any relation between discrete and continuous systems is "arbitrary". However, there are non-arbitrary mappings between discrete and continuous systems. The best known is almost certainly the relationship between the integers (ℤ) and the reals (ℝ). There is a homomorphism (and only one) from ℤ into ℝ, and it is the obvious one that preserves addition (and lots of other stuff). Call this H. That is, H maps {... -1, 0, 1 ...}  in ℤ to {... -1.0, 0.0, 1.0 ...} in ℝ (using the C conventions for ints and floats). Using + for addition over ℤ and +. for addition over ℝ, then H also takes + to +. (that is, we need to say what the group operation in each case is, this is important when thinking about symmetry groups for example). So now it is true that for all i, j in ℤ H(i + j) = H(i) +. H(j).

However, mapping from ℝ onto ℤ (quantization, Q) is a much trickier business. One obvious technique is to map the elements of ℝ to the nearest integer (i.e. to round them off). But this is not a homomorphism because there are cases where for some r, s in ℝ, Q(r +. s) ≠ Q(r) + Q(s), for example Q(1.6 +. 1.6) = Q(3.2) = 3, but Q(1.6) + Q(1.6) = 2 + 2 = 4. So the preservation of addition from ℝ to ℤ is only partial.


Chabot A 2019. What’s wrong with being a rhotic?. Glossa, 4(1), 38. DOI:


  1. Hi Bill, I still have to read up on your previous posts, but one thing about the arbitrariness of the relationship between the categories belonging to two different modules. I know of two ways intermodular communication is conceived of: computational and lexical translation. The former is argued for by Jackendoff over the years (translation rules in 1987, correspondence rules in 1997, interface processors in 2002). The latter is list-based, i.e. a dictionary of the form alpha> where x and alpha belong to two distinct vocabularies. This is what we know from the morpho-syntax - phonology interface, i.e. Vocabulary insertion.
    The difference between computational and list-based translation is crucial (the former is a modular monster since it provides for a (translational) module that understands several vocabularies), but that's an aside here. What I want to say is that both define translation as arbitrary. Jackendoff has always defended his all-powerful computational translation against the critique of overgeneration (Jackendoff 1997: 40). Hence any input category can be related to any output category and its reverse. An arbitrary relationship.
    List-based translation also has arbitrariness in-built: that's the very definition of a dictionary (and undisputed for Vocabulary Insertion: there is no reason why, say, "past tense" corresponds to -ed).
    Hence your argument is correct: the contimuum-discrete transition does not necessarily entail arbitrariness (although I'm not sure math can be transposed into the cognitive/biological system without precaution). But all models of intermodular communication I know of entail arbitrariness. Maybe I'm missing an interface theory that allows for non-arbitrary translation?
    For the time being my conclusion is that if you buy modularity you also have to buy arbitrariness in intermodular communication.

    Jackendoff, Ray. 1987. Consciousness and the computational mind. Cambridge, Mass.: MIT Press.
    Jackendoff, Ray. 1997. The Architecture of the Language Faculty. Cambridge, Massachusetts: MIT Press.
    Jackendoff, Ray. 2002. Foundations of Language. Brain, Meaning, Grammar, Evolution. Oxford: Oxford University Press.

    1. Thanks Tobias.

      Indeed, we disagree at this point: "if you buy modularity you also have to buy arbitrariness in intermodular communication."

      There are many examples in sensation and perception of lawful (non-arbitrary) intermodular communication. So intermodular communication does not imply arbitrary mappings. See, for example, any case of -otopic motor or sensory organization, such as retinotopy, tonotopy, somatotopy ( ).

      The lexicon isn't like this, which is why it's special.

  2. ...the machine has interpreted some of my earlier post as html code...

    "a dictionary of the form alpha> where x and alpha belong to two distinct vocabularies."

    "a dictionary of the form |x ↔ alpha| where x and alpha belong to two distinct vocabularies.

  3. Hi Bill, I think this is fair extrapolation of my position. That is, whenever an object that exists outside of the mind as a continuous and gradient physical phenomenon – light, odor, sound, linguistic sound, and so on (I am tempted to say any real-world object but I am not sure that excludes purely symbolic mathematical objects) -- has a representation as a cognitive object, that cognitive object is by nature discrete and categorical. This is in line with the position of Harnad (2005), for whom any relationship between an ``adaptive sensorimotor’’ system and the world is one of categorization.

    My argument in the rhotics paper is that at least for some phonological categories, the relationship between the phonological object and the phonetic object which instantiates it is arbitrary; that is, they do not use the same vocabulary (a voiceless velar fricative is a phonological sonorant, as in French `tRain’). If this is true for one class of phonological objects, why not for all of them?

    Now its like Russian dolls: if this is true for the phonetics/phonology relationship, why isn’t it true for all mappings between cognitive objects and their real-world referents?

    This is to argue that whenever one passes beyond the veil, by translating from gradient in the real-world to categorical in the mind, the translation process is by nature arbitrary since those categories don't exist in the mind except as representations created therein -- that is they are entirely detached from their real-world correlate. The blue in my mind has nothing to do (physically) with the light-waves that I perceive as blue.

    This brings to mind the study by Blakemore & Cooper (1970). Upon birth, kittens are placed into cylinders with only vertical or horizontal lines. When they come out six-months later, they can only see vertical or horizontal lines respectively – the lines to which they had no exposure seem to be effectively invisible. That is, they aren’t born with those lines in their minds, or even the ability to perceive those lines – it is exposure to the stimuli that gives rise to them in the mind.

    Another less cruel and more recent example: Ma et al. (2019) showed that when mice are gifted the ability to see in infra-red mechanically via modified retinas, they are perfectly happy to go about using the new information; surely mice do not have innate infra-red detecting brain cells. That is, their cognitive system, which has never been under any evolutionary pressure to adapt to anything but the normal mammalian visible-light spectrum, has no problem making a new category for a heretofore unexperienced kind of stimuli. The bottleneck in perception isn’t cognitive, it is mechanical.

    1. Thanks Alex.

      We disagree at this point, "entirely detached from their real-world correlate". I would say instead that they are "somewhat detached" because they preserve various important properties (but not all).

      As to the atrophy of certain kinds of visual features in V1 of cats, yes there is a "use it or lose it" aspect to neural organization and a critical period for the activation (not learning) of visual features. The actual findings are much more complex, however, with various types of recovery possible, see Voss, P. (2013). Sensitive and critical periods in visual sensory deprivation. Frontiers in Psychology, 4, 664 for a more recent review. A large portion of this work is on ocular dominance.

      Actually, nothing that exciting is happening with the mice. The nanoparticles remap infrared wavelengths into the visible spectrum, "the nanoparticles absorb light with longer – infrared – wavelengths and convert it into shorter wave light that retinal cells can detect. This converted light peaks at a wavelength of 535 nanometres, so the mice see infrared light as green." So nothing really changes for the mouse visual system, it's just like putting on night vision goggles. The cool new thing here is the nanoparticles. Frankly, the Brainport device is a better example, but, as I've already said, I'm sure that the remappings are severely limited.

    2. To underscore this point, a striking example is provided by the study of neural plasticity in deaf cats by Lomber and colleagues (Lomber et al., 2010). This study showed that deaf cats show functional enhancement for motion detection and object localization that was eliminated when particular areas of auditory cortex were temporarily deactivated. Plasticity was functionally constrained; the relevant auditory areas that provided perceptual enhancement for visual motion detection and localization are normally involved in auditory motion detection and localization in hearing cats.

      Thus the sensory-perceptual mapping isn't arbitrary at all, even in cases of cross-modal plasticity.

    3. Or rather, the mapping is only partially arbitrary, as Bill has emphasized.

    4. Thanks William! I do remember when Steve Lomber came to UMD to give a talk on this. The pictures of Steve with the cats with the tiny refrigeration units on their heads was great.

  4. Arbitrariness is hard to see, because we live in the mind and not the real-world. 

    The biological brain may not be so arbitrary, it is also an object located in space and time – mind is not. So there are geographic ‘maps’ of sensory perceptions, for vision, for smell, for taste; at least relative to the perceiver. But a module is not a part of brain (although it is obviously derived from brain) but rather a part of mind. Fodor has always said he does not intend for modules to be associated with precise geographic regions of the brain.

    I am not sure I am clear on why lawful communication has to be non-arbitrary. Arbitrariness, to me, means not of like kind with its real-world referent. So regarding lawfulness, the communication is lawful to whom? To the modules, right? So, regarding the McGurk effect, timing can be encoded differently in various modules, but it has to be quasimorphic across modules. But does the encoding of time have to be quasimorphic with ‘real time?’ Does such a thing exist? It seems that communication between modules can operate in a fixed, lawful manner, while still being in an arbitrary relationship to the real world.

    All that to say, I don't pretend to have as strong a grasp on the cognitive side – for me this is a learning experience – but I don’t think the translation between pure mathematical objects work the same way as physical phenomenon/cognitive representations. Blue is what my mind says it is, the smell of honeysuckle in Virginia in June is what my mind says it is, a speech sound is what my mind says it is.

    Blakemore, Colin & Grahame F. Cooper. 1970. Development of the Brain depends on the Visual Environment. Nature, 228, 477-478.

    Harnad, Stevan. 2005. To cognize is to categorize: Cognition is categorization. In Henri Cohen & Claire Lefebvre (eds.), Handbook of categorization in cognitive science, 19–43. Amsterdam: Elsevier.

    Ma, Yuqian et al. 2019. Mammalian Near-Infrared Image Vision through Injectable and Self-Powered Retinal Nanoantennae. Cell, published online February 28, 2019; doi: 10.1016/j.cell.2019.01.038

    1. I think we differ at this point, "Arbitrariness, to me, means not of like kind with its real-world referent." My word for "not of like kind" is "different", and I agree that the entities in the mind/brain are different from their real world counterparts. The mind/brain has representations of the "distal layout" in Fodor's terms.

      The meaning of arbitrary is "based on random choice or personal whim, rather than any reason or system" (from Google) and so "arbitrary" is opposed to "systematic". Sensory perception is partially systematic, and so it is not completely arbitrary.

      And I agree that mathematical objects are special too, but that doesn't mean that mathematical concepts are not useful in studying perception and cognition. A quick look at psychometrics and psychonomics shows that there is a lot to be learned this way.

    2. Hi Bill,

      You know I hadn’t thought about the mice in terms of night-vision googles. I have gone back and forth about being excited about that study and being less excited. I do think it is exciting though because it means that a nervous system with less meta-analytic functions (I presume, forgive me) than our own can take that new kind of input. It’s just ersatz green-light on the retina, but it still corresponds to a stimulus out of the range of normal mammalian perception.

      What I would like to do is plug something like the Ampullae of Lorenzini into the occipital lobe and see if sense could be made from that input. Perhaps that is a bridge too far and some specialized brain hardware has to be present for a whole different kind of stimulus, perhaps the brain could make categories for it and all would be well.

      As for the meaning of arbitrary, there is the mathematical meaning: `any, out of all that are possible.’ I think in linguistics it has often been meant to be non-iconic. This is what I mean when I use the word arbitrary.

      This discussion has inspired me to take a dive into the Gallistel and King volume, which I have had on hand but not spent time with. I want to thank you again for taking the time to read the paper and engage with it.

  5. I’ve been following this discussion with interest, but it seems to me that it is not taking sign language sufficiently seriously. I thought sign language phonologists like Sandler had shown that sign language phonology is very much like auditory phonology in terms of the behavior and organization of distinctive features (e.g., Sandler 1989), with the important exception of newly emergent sign languages (Sandler et al. 2011, Sandler 2014).

    If that is correct, then either the features of sign language phonology are homologous with the features of spoken phonology, as in Morén 2003, and consistent with Idsardi’s “partial veridicality”, or they are not, as in Blaho 2008 who argues for radical substance freedom.

    Any tighter connection between a universal inventory of phonological features and phonetic substance leads to a contradiction: it would have to presume that sign language phonology is learned without the benefit of that substance-laden inventory, which would show that the substance-laden inventory isn’t needed for the learning of a phonology, which pulls the rug out from under the arguments for a substance-laden inventory.

    The examples from mice and cats show something about the flexibility or not of the visual system in interpreted ocular input, which is not nearly as impressive as the example of sign language phonology. I'm similarly not impressed with the brainport example, if I understand it correctly, since sighted infants have lots of practice comparing haptic to visual experience of objects, so it doesn’t seem impressive that you can tell what shape something has by feeling its silhouette on your tongue.

    Sign language shows us something much cooler than these examples, and something which suggests that whatever “partial veridicality” there is must be very weak at best, doesn’t it? It seems to me that sign language shows that the burden of proof is on the substance-laden side to show that the universal features are doing some work.


    Blaho, S. 2008. The Syntax of Phonology: A radically substance-free approach. PhD dissertation, University of Tromsø. Available at

    Morén, B. 2003. The Parallel Structures Model of Feature Geometry. In J. Brugman and A. Riehl, (eds.). Working Papers of the Cornell Phonetics Laboratory, vol. 15. Ithaca, New York. pp. 194-270.

    Sandler, W. 1989. Phonological Representation of the Sign: Linearity and Nonlinearity in American Sign Language. Providence: Foris.

    Sandler, W. 2014. Where do features come from? Evidence from sign language. Nordlyd 41.2: 183-212. Available at

    Sandler, W., M. Aronoff, C. Padden, and I. Meir. 2011. The gradual emergence of phonological form in a new language. NLLT 29: 503-543.

    1. Thanks Peter.

      I'll say more at GLOW next month about what I think the relations between sign and spoken languages are, and (perhaps surprisingly for people following this thread) I think they share almost all major abstract properties.

      I believe that the basis for comparison is that both systems can be modeled with very similar algebras. For spoken language this includes events (= abstract points in time), features (= monadic properties of events), and precedence (= a dyadic temporal relation over events), yielding an (E,F,P) structure.

      Sign languages are different from spoken languages in that they add additional (egocentric) spatial relations that spoken languages lack, such as spatial symmetry (temporal symmetry -- palindromes -- are not a property of spoken language phonologies), giving an (E,F,P,S) structure where events are now points in spacetime rather than just in time. The inclusion of spatial relations certainly makes the sign language algebra distinct from the spoken language one, but there is a quasimorphism between them as long as you disregard space.

      But I also think that the sign language primitives (in all of the events, features, precedence, spatial relations) have substance (partial veridicality) based in the motor primitives for the upper body and the perceptual relations provided by the visual system.

      In short, you can have similar abstract algebraic structures while still maintaining partial verdicality in the definitions for the primitive elements, monadic properties and dyadic relations in the system. (And I freely acknowledge that my view on this is heavily influenced by Paul Pietroski's work on semantics.)

    2. On spoken and signed languages sharing most abstract properties, I thought that was the consensus among sign languages phonologists -- Here’s Sandler 2014: 93f:
      “Indeed, certain abstract organizing principles underlying all phonology regardless of modality have been implicated by many sign language researchers. Examples, some of them seen in the previous discussion, include features (Liddell and Johnson 1989; Sandler 1989, 1996a; syllables and other aspects of word-level prosodic structure (Sandler 1989, 1993a, 1999; Perlmutter 1992; Wilbur 1993; Brentari 1998); sequential segments (Liddell 1984; Sandler 1989); autosegmental associations (Liddell 1984; Sandler 1989, 1990); feature geometry (Sandler 1987, 1989); underspecification (Sandler 1987, 1989; Corina 1993; Brentari 1998); headedness and binarity (van der Hulst 1993). In her book, The Phonological Mind, Berent (2013) argues that while phonology adapts to the properties of the human production and perceptual systems, it is also characterized by organizational properties that can’t be explained on that basis alone, and suggests that such properties are innate and characterize sign languages as well. Krämer (2012) goes so far as to propose phonological features that are abstract enough to be shared with other levels of linguistic form such as event structure (e.g., telic/atelic), as well as with sign languages.”

      So what I meant by "weak" partial veridicality would be like Krämer's suggestion referred to by Sandler: features which are so abstract that they can underlie both systems.

      Now I understand you to be saying something different: namely, that spoken language features are partially veridical with one set of innate features, and signed language features are partially veridical to another set of innate features ("based in the motor primitives of the upper body and the perceptual relations provided by the visual system").

      So then there is an innate set F of abstract features that natural language features are partially veridical with, but F is not specific to language and two languages might be based on completely disjoint subsets of F -- is that right? It seems like this might be such a weak notion of innate features that even people who reject innate features would be comfortable with it.

      Sandler, W. 2014. Where do features come from? Evidence from sign language. Nordlyd 41.2: 183-212. Open Access:

    3. No, that's not quite what I have in mind. I would say that the features are specific to language, and provide the memory system links between the action and perception systems. This is the position taken in Poeppel et al 2008 and Idsardi & Poeppel 2012, and for a concrete proposal for a set of spoken language features, see Avery & Idsardi 1999. The individual features can be "deactivated" during language development, and they are also subject to parameter turning (in Kuhl's sense). Of course, there's more than just this to phonological development, as constellations of features coordinated in (space)time can also be "tuned" as a group (Jackendoff's "preassembled units as shortcuts").

      As to the "completely disjoint" question, my answer to this is no. Both systems contain events as primitive objects (= abstract points in (space)time), both systems restrict features to be monadic predicates of events, and both systems employ a dyadic relation of precedence. Sign languages differ in adding further dyadic spatial predicates that spoken languages do not have. This seems like quite a bit of stuff to build in.

      In my opinion, in order to appreciate how much built-in stuff this is, you have to look at "phonology-adjacent" systems, including the differential abilities of various songbird species, see Lawson et al 2018.

      Avery, P., & Idsardi, W. J. (2001). Laryngeal dimensions, completion and enhancement. In T. A. Hall (Ed.), Distinctive Feature Theory (pp. 41–70). Berlin: Mouton de Gryter.

      Lawson, S. L., Fishbein, A. R., Prior, N. H., Ball, G. F., & Dooling, R. J. (2018). Relative salience of syllable structure and syllable order in zebra finch song. Animal Cognition, 21(4), 467–480.

      Poeppel, D., Idsardi, W. J., & van Wassenhove, V. (2008). Speech perception at the interface of neurobiology and linguistics. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 363(1493), 1071–1086.

      Poeppel, D., & Idsardi, W. J. (2011). Recognizing words from speech: the perception-action-memory loop. In M. G. Gaskell & P. Zwitserlood (Eds.), Lexical Representation: A Multidisciplinary Approach. (pp. 171–196). Berlin: Mouton de Gruyter.

    4. Sorry, some of the references in the text are incorrect. It should be Avery & Idsardi 2001, and Poeppel & Idsardi 2011.

    5. Not to rehash too much from the sign phonology discussion in Bill's Fodor post (and because I'll also give my two cents at GLOW), but there are some subtle representational points here.

      Peter: On spoken and signed languages sharing most abstract properties, I thought that was the consensus among sign languages phonologists

      What sign phonologists agree on is the need to study sign on its own terms, and let the properties emerge. Connections between speech and sign depend on the right level of abstraction. Another Wendy paper, "The Challenge of Sign Language Phonology", lays out the trickiness of this.

      Bill: both systems restrict features to be monadic predicates of events

      I agree but the sense of "events" is key, and, I assume, distinct from Steven Bird's sense. In my view, it's the relations that give the notion of space and time, which aren't inherent of the events themselves. Sign languages have autosegmental structure too, for example (this is the received view these days). We might wanna say having linear and nonlinear relations is a feature of both sign and speech, but it's hard to claim that in the one case it's a "spatial" relation and in another a "temporal" one.

      Here's another kicker sign phonologists agree on: signs are "adapted systems". The standard argument goes: If humans evolved for language in general without respect to modality, we should find hearing communities that just happen to use sign language instead of spoken language, and we don't. This means that the question of "what is shared between speech and sign" misses the forest for the trees. Instead we can ask, "how do the cognitive faculties of phonology exploit the visual modality when reorganizing into another modality?" This means there will necessarily be representational and computational tradeoffs. As Bill knows, I'll push for model theory as a great way to distill phonology to discuss these issues.

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