26 February 2011

Abstraction as Work, Universals as Artifacts

Filed under: Culture, Ktismata, Language, Psychology — ktismatics @ 6:32 am

In Aronofsky’s film Pi, Max is looking for the patterns that underlie the surface details. For Max, the stock market is like the game of Go is like the Torah is like the cream swirling in his coffee: all of them are built up from the same sort of deep structure; all of them iteratively change states through the movement of the same deep process. So too with Max’s understanding of his own mind: underlying any particular configuration of thoughts or any sequential train of thought there are the same deep structures and processes. And so, inevitably for Max, the mind is like the stock market is like Go etc. etc. — the same deep structures, the same deep processes. The world and the mind both embody the same abstract universals. Ultimately for Max, those abstract universals are the voice of God.

According to Chomsky, underlying the wide variety of human languages, with their idiosyncratic rules for word order and conjugation and possessives and so on, there is a universal grammar, a common set of deep structures and processes for forming meaningful utterances by which all languages operate. Per Chomsky, the reason that any human child can learn any human language is that human brains are hard-wired with a set of deep structures that map onto the universal grammar. Language and mind both embody the same abstract universals.

Tomasello disagrees with Chomsky. Tomasello acknowledges that is possible to arrive at an abstract understanding of language by which all specific languages can be compared with one another. However, this linguistic “universal grammar” is best understood as an abstract cultural artifact constructed by linguists. Children learn to understand and to speak from the bottom up, through repeated exposure to specific words, phrases, and sequences. Kids soon learn that language functions as a communication tool: linguistic symbols function as metaphors for specific situations in the world to which the speaker wants to draw the listener’s attention. Only gradually do children build up a more abstract understanding of their own language, enabling them to construct intentional, meaningful, complex, grammatically correct utterances on the fly.

To be sure, humans are uniquely capable of forming categories and abstractions, as well as of making the sorts of comparisons across categories by which symbols and metaphors operate. But the content of the categories and abstractions and metaphors that humans construct don’t necessarily precede or underlie the work that humans perform in constructing them. Chomsky’s universal grammar might do useful work in the sense that it describes many common features shared by all languages. But it works in a way not unlike (excuse the metaphorical thinking) a hammer or an algorithm for doing long division or a general schema for going to restaurants. Each is a multi-purpose cultural artifact useful for performing intentional actions in a variety of specific situations. Just because a hammer works for breaking nutshells and putting nails into boards and pounding veal for scallopini doesn’t mean that all humans have the structure of hammers prewired into their brains, or that nutshells and nails and veal all share the same underlying structure in the world. The hammer is a cultural artifact, invented and incrementally improved upon by generations of humans in order to perform various specific tasks that involve the same abstract general operation of pounding.

It’s conceivable that the movement from concrete to abstract, from specific to universal, reflects not a dawning awareness of a fundamental “universal grammar” that has always underlain all the surface diversity in human minds and cultures, but rather an incremental and progressive movement in human culture toward some future state of abstract universality waiting for us out there at the end of history.  If I were more philosophically literate I might be able to draw an analogy to Kant and Hegel here. What seems more likely is that generalized abstractions are thought up, passed on to others, and improved upon to the extent that they enable humans to do specific kinds of work in specific situations. As the nature of the work changes, so do the workers’ tools. Universal grammar has proven itself a useful tool for working linguists. As linguistic work gets more complicated, linguists incrementally modify the universal grammar tool. If it’s useful to them, they invent altogether new linguistic tools and teach one another how to use them.



  1. Hi, John! I think the hammer metaphor really captures something important about the whole “universal grammar” debate. A couple of additional thoughts:

    Any specific hammer reflects both the world (i.e., the veal it was designed to tenderize, the rock that it was designed to chip) and the body (the hand it was designed to be grasped by). In other words, the deep or universal structure of a hammer is a form determined to a large extent by the constraints of the body and the thing-to-be-pounded. I think language as a cultural artifact works the same way. It gives us the sense of having a deep, universal structure because in terms of its constrained form, it has to reflect both the structure of the world (the things and events being talked about) and the structure of the brain. Just as it is absurd to think about a hammer that doesn’t fit our hands, it’s absurd to think about a language that doesn’t fit the way our brains categorize, generalize and symbolize the world.

    Your post got me thinking about the aptness of the hammer as a metaphor in general. As an analogy, it’s proved to be a very useful “tool”, and I wonder why that is. I heard somewhere that linguists show a decided preference for violent acts (people whacking each other with things) in their example sentences. I know Langacker uses the hammer several times when he’s describing radial vs. central categories.

    Maybe it’s the simple nature of the “bridge” that hammers provide between the human and the things-in-themselves world. It’s a little bit of us, and a little bit of that which we are unable to touch (or pulverize, as the case may be) directly. If that’s the case, I think Harman was right to “elevate” Heidegger’s tool analysis to an ontological level.


    Comment by Asher Kay — 26 February 2011 @ 7:54 am

  2. Hey Asher. That’s funny about linguists using violent acts in their examples. Maybe linguists tend to being aggressive, or more likely passive-aggressive. Hitting is probably the most universal action that an “agent” can perform on a “client.” It’s a useful action in evaluating how and when kids learn to use grammatically correct sentences. E.g., “The boy hit the wall” and “The wall hit the boy” are grammatically equivalent, but it’s been shown empirically that little kids learn to use the former earlier than the latter. Such findings suggest that it’s not just achieving mastery of universal grammar that leads to linguistic competence. Specific repeated experience in relevant communicative context is developmentally crucial. Similarly, little kids have an easier time performing the various permutations of “X hit Y” than of, say, “X smote Y,” even when they’ve learned that “smote” means the same thing as “hit.”

    I agree that language has to bridge the brain and the world, and also the society of language-users. There has to be some sort of compatibility or complementarity between these three kinds of entities. Those compatibilities clearly aren’t at the surface level; e.g., the word “hammer” looks nothing like the object to which the word applies (or at least it doesn’t look like the one I’ve got), and a brain looks nothing like the collectivity of all people who speak English (thank God). I think that language does more closely correspond structurally to the world it describes than, say, a hammer corresponds structurally to nails, nuts, and pieces of veal. I.e., language functions as a tool not just by pointing at things and processes and relationships happening in the world, but by representing them symbolically. Similarly, a human brain seems to represent the world neurologically as perceptual categories and behavioral scripts and remembered objects/events and so on. So I think there does have to be some sort of correspondence between linguistic grammar, “the grammar of the world,” and “the grammar of the brain.” These correspondences must happen not at a surface level but in deeper structure. But there is no reason to assert that world, language, and brain map precisely one-to-one-to-one with each other. A language-user, for example, isn’t just describing the world to a listener; he is also conveying subjective intent and attitude and emphasis, while also framing the utterance in a way that the listener can understand the communicative meaning and connotations. So too a human brain’s cognitive structures have to conform with the unique capabilities and limitations of the human sensory apparatus, within the context of an organism better equipped evolutionarily to survive in the world than to achieve an objective understanding of the world. It’s these mismatches between world, language, and brains that open up the possibility of learning more than we know intuitively.


    Comment by ktismatics — 26 February 2011 @ 11:34 am

  3. It’s conceivable that the movement from concrete to abstract, from specific to universal, reflects not a dawning awareness of a fundamental “universal grammar” that has always underlain all the surface diversity in human minds and cultures, but rather an incremental and progressive movement in human culture toward some future state of abstract universality waiting for us out there at the end of history.

    I do not think that the universality of the underlying shall be understood as an ideal sameness that is somehow transcendental and may be unveiled in an apocalyptic event. Of course PI, the movie, speculates on something like this and the metaphysics of the TOE, popular among physicists, is also alike. Instead it more resembles the introduction of coordinates in algebra or a meta-grammar like BNF whose articulations are grammars. Universality is encoded in the neural parser-generator, and it doesn’t shine through other than as specific grammars which are sentences in a meta-grammar which is also a formal language but much simpler, actually, than any specific language.

    I don’t even think this is too far fetched given that context free grammars are equivalent to finite automatons which are basic cybernetic entities which can be represented as directed cyclic graphs or neural networks. So syntax may not be that much of a problem and one gets it almost for free. Semantics and communication of content based on syntactical structures is a different problem entirely.


    Comment by Kay — 14 April 2011 @ 5:49 am

  4. I think I’m following your ideas here, Kay. The geometric space described by a graph, and the assignment of coordinates within that space via algebraic equations, is an abstract scheme by which virtually anything that can be quantified can also be represented in a similar way. But this isn’t to say that, e.g., the speed with which falling objects accelerate and the box office receipts for the top 50 movies of 2010 both manifest some shared “deep structure,” either in the world of falling objects and elections or in the heads of people who interact with them. The universality of the algebra and geometry of the abstract graph is, as you say, much simpler than anything actually represented by means of this universal schema.

    The algebraic geometry is an abstract cultural artifact that imposes a common structure on otherwise-disparate kinds of things that had previously traced independent paths through the world and through minds. But these graphable things don’t just spontaneously conform to the graphical structure; they must be transformed — quantified, scaled, standardized. Structure and content mutually shape each other. Take music. Presumably the first graph invented in the Western world was the musical staff, where the x-axis is time and the y-axis is pitch. But there’s no reason to assert that every human who sings has an implicit version of musical annotation built into the brain. The formal annotation itself underwent historical refinement; e.g., the time-distinctions between eighth notes, quarter notes, and so on were added later. This standard annotation works particularly well with an 8-tone scale, regular rhythms, and note durations increase by a factor of two. This abstract annotation scheme makes it possible to represent a march and a waltz and a dirge all within the same structure. At the same time, I suspect that the practice of Western music gradually adapted itself to this standard annotation; i.e., human musical practice has adapted to the structure, which in turn has been adapted in order to conform better to practice. And the graphing system doesn’t even work all that well in other kinds of musical traditions: 12-tone, varying note durations, and so on. Its universality is still culturally constrained.

    This sort of thing probably plays out in language. The sorts of universal grammatical structures I learn as a native English speaker is similar but not identical to the universals of, say, the Japanese language. Language speakers and the grammatical structures are mutually evolving cultural artifacts. Sure, all humans share some common innate linguistic capabilities, running on a common neural architecture, capable of almost machine-like iterative refinement via interaction with the world and other language speakers. But each human grows up speaking some specific language. And sure, it’s possible to create an abstract representation of language in general, covering English, Japanese, and all the rest. But that abstract universal grammar would be at such an abstract and simplified level as to be virtually useless to any person actually trying to speak/understand any particular human language.


    Comment by ktismatics — 14 April 2011 @ 11:48 am

    • The algebraic geometry is an abstract cultural artifact that imposes a common structure on otherwise-disparate kinds of things that had previously traced independent paths through the world and through minds.

      Yes, equality is artificial. I do think that’s the whole point of mathematics, showing that unequal things are equal: by means of reduction / applying some transformation which respects a prescribed equality or symmetry. The representation continuously changes whereas the underlying is preserved. Mathematics has no respect for the significant or a particular manifestation.

      On the other hand a physicist can argue that equality is for real, that nature in fact preserves quantities like energy. It is essentially mathematical in the above sense. Nature produces differences while preserving some specific equality: Max numerical invariant, he found through computer wizardry. This assertion is “interesting” and strong, fragile and rigid enough to be possibly wrong.

      In contrast there is also boring and robust universality: grammars are articulations of meta-grammars, differential equations can be used to model this and that, set theory is used to describe a wide range of mathematical objects etc. They fall on the side of conceptual evolution and while being important and attracting lots of attention, they should be given a different status than the particular and falsifiable universality which brings us in touch with the essence of nature. This might also explain the little disappointment with Meillassoux’s book. The interesting correlation is that between us and nature in the medium of mathematics which is shared by both. It is a specific correlation not some shallow universality like the “necessity of contingency”.

      I’m not quite sure on which side Chomsky’s universality falls. It seems to be an empirical hypothesis but at the same time it can be retracted to a shallow meta-grammar assertion which reflects the conceptual evolution of which Chomsky was a major driver.


      Comment by Kay — 17 April 2011 @ 1:54 am

  5. The trajectory of a hawk capturing a sparrow midflight can be described in mathematical equations, and the accuracy of these equations can be iteratively tweaked based on empirical observation of hawks. Does this mean that the hawk’s eye-wing-talon coordination really is intrinsically mathematical? It has to mean at least that the mathematics describes or represents or predicts the reality of the hawk. But math is an abstraction, a cultural artifact, even a kind of language. If I say “the hawk caught the sparrow midflight,” that statement could accurately convey the reality of a particular situation even though the particular words of that statement bear no similarity whatever to the hawk or the sparrow. Maybe this way of thinking about math and language keeps us in “The Correlation.” Still, I don’t think anyone expects science to be the same thing as the world it describes — the map that covers the territory so to speak. But if both the hawk’s neuromuscular system and the scientist’s equations prove to be two different means for achieving the same end, then there would seem to be some correlation between science and the reality it describes, no?

    Arguably Chomsky never provided a strong empirical basis for his universal grammar assertions. One would expect that, if human brains contain a “linguistic organ” that prestructures utterances according to universal grammatical categories, then all actual human languages would share a common set of grammatical structures. Empirically this isn’t so. Again, all languages can be made to fit into a higher-order theoretical abstraction, but it’s not the way actual humans learn their actual languages. If it were, then a child who learns to use a particular grammatical construction in one case should be expected to attain rapid mastery of this construction in all other cases. It doesn’t happen that way. It’s more a matter of familiarity and practice with individual cases building up toward the abstractions, rather than intuitively deducing right linguistic practice through spontaneous exercise of the language organ.


    Comment by ktismatics — 17 April 2011 @ 2:30 pm

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