Frames /sing


Savant Rule Following, What Shape is a Number?

A Short Film on Daniel Tammet, mathematical Savant.

Philosophical Bloggist Anderson Brown, would like to tell us that the calculations of Autistic Savants are somehow the rule-following equivalent of digestion. We may use rules to describe what is happening, just as we can use rules to describe what is happening in our stomachs, but because these calculations are somehow not “out in public” they are not what he calls “literal” rule-following.

There is some problem with this notion of a rule-following distinction, a favorite of those of the Wittgensteinan bent. Somehow Real rule-following must be categorically distinguished from only seeming rule-following (central I believe to Wittgenstein’s Private Language argument). First, is the idea of intentionality, which regards choice. Anderson would like to make the intentionality of persons the vector of their status as literal rule-followers. But there is a problem with this, since Wittgenstein himself, at least to some degree, actually takes choice (intentionality) out of what “rule following” is:

 “How am I able to obey a rule?” If this is in not a question about causes, then it is about the justification of for my following a rule in the way I do.  If I have exhausted the justifications, I have reached bedrock, and my spade is turned. Then I am inclined to say: “This is simply what I do” (PI §217).

When I obey a rule, I do not choose. I obey the rule blindly (PI §219). 
So to separate out “real” rule following under an index of choice alone, is difficult. Indeed, we are all following rules to some degree involuntarily. Just because “our spade is turned” does not mean that we, or Daniel Tammet has fallen into the world of strictly “causes” (as opposed to “reasons”, an important Wittgensteinian distinction).
Secondly, I have difficulty with Anderson’s idea that:
“Actual rule-following is done by persons, out in the world. Thus the savant is “rule-following” (computing with his brain), but he is not rule-following (thinking with his “mind’).”
Somehow savants seem to be denied, in such a conclusion, the status of being “real persons”, doing things “out in the world” here, that they are not “thinking”. I don’t know what, for instance, such doing out in the world would consist of. I would say that f I am doing calculations in my head, I indeed am rule-following, even though I am not “out in the world”, whether a Wittgensteinian would allow me that official distinction. A Wittgensteinian may like to tell me that whatever is going on in my head when I add 124 and 28 together may appear to be “rule-following”, but isn’t really rule-following until it is checked by others. For, afterall, I may be halucinating the answer to be correct (leaving aside the logical potential that those checking my answer might be halucinating the answer they think is correct).
I can certainly see the intersubjective aspect of creating a ballast for what is correct or incorrect, but rule-following cannot be broken up merely into the shadowy realm of internal, black-box, pseudo rule-following (in the “characteristic accompaniments” theatre of the mind), and “actual” rule-following which ONLY occurs “in public”. This is too sharp a categorical distinction, I would say, and misses some important aspects of how rule-following works. 
The ballast lies in two places, in a differential. Daniel Tammet the mathematical savant indeed is, I would say, rule-following when he tells you what shape the number 1012 is (this is not the equivalent of digestion). When he tells us that he knows what the answer is because the answer is a certain shape, this is not absolutely different than saying that I know where the town is, because the sign has just pointed me to it. Wittgenstein makes the very good point that these ARE different. What pops into my mind, functions more like a cause, than a reason. But there is a depositional orientation to causes that makes up our experience of intentionality. Tammet does not involuntarily blurt out the answer when a certain shape pops into his head. He evaluates it. He can in fact sculpt it in clay. He looks to it. In this way Wittgensteinian causes can be act like reasons (and reasons can be like causes: see Donald Davidson). This aspectual nature of orientation to own’s own metal events, the way that we can take an orientation to them, epistemically, is the counter-ballast to the public knowing which makes our knowledge intersubjective. One can justify, in part, to one’s self, without such justification being simply “buying several copies of the morning newspaper”.  Because it is not done “out in the world” does not make Tammet’s calculation the rule-following equivalent of “digestion”, as much as Wittgensteinians may like to by-definition, make them so.

3 responses to “Savant Rule Following, What Shape is a Number?

  1. Anderson Brown May 22, 2008 at 12:03 pm

    My PhD dissertation was about mental states in non-human (non-linguistic) animals. At that time, I appealed to evidence from ethology (from seed-hoarding chickadees to Savage-Rumbaugh’s bonobos) to argue that animals had mental content just as humans did. Now I continue to think that human and non-human brains must work in the same way, but I’m not sure about mental representations. It seems to me that if there is even the possibility that the intentional/representational model of mind is flawed, we need to get to the bottom of that. That is why I am intrigued by Wittgenstein. For me the issue is motivated mostly by metaphysics (perhaps neither Kevin nor Wittgenstein would agree). Semantic properties seem to me to be impossible (this applies to both mind and language). This is the appeal (to me) of my behavioristic/anthropological interpretation of W. Maybe Descartes had it right: he thought that dream images, for example, were in themselves irrefutable proof of mental content: self-evident. Certainly the intuition that we have mental images is powerful. For myself, I don’t know: I feel that this is an ongoing investigation, for me. I do know that W. wasn’t unaware of the phenomenal argument for content, so I find Descartes’ position of simply plunking dream images down as “proof” to be obtuse. Meanwhile, a humbler point of contention with Kevin is that whatever the case may be here (content or no), his special cases do not add anything to the argument of the person who simply points to calculating and to mental images as proof of content. A concession to Kevin: certainly conscious rule-following emerges somehow from “rule-following,” such that there can be no clear demarcation: to insist that they were essentially different would amount to a kind of mind-body dualism, I think. Anderson Brown

  2. kvond May 22, 2008 at 6:21 pm


    It depends what one means by “content”. It is a tricky word, much abused, both in terms of criteria and attribution. There is of course “propositional content” which in the case of animals would be very difficult to establish in any form other than attributive and explanatory, 3rd person description.

    I too am interested in metaphysics (apart from Wittgenstein’s anti-metaphysical project), so perhaps we share some ground. The problem comes in playing the “content” game. Some would have it that the senses bring “content” to our mind, (this to my ear is ridiculous). I believe that much of this problem is dissolved by Davidson’s critique of the “Very Idea of A Conceptual Scheme” the idea that there is some sort of framework, which then gets filled in with “content”. Once we let go of the scheme/content assumption, much that is efficacious gets into play.

    For Wittgenstein the issue comes down to “justification”, that is, the appeal to criteria which grounds our public discourse over matters. He wants such ground to be ENTIRELY public, that is, there is no such thing (as a matter of logic), as private justification (we pass for him here, into the realm of causes). Much can be said for this view. At times such an idea strikes one as silly as having a monetary currency which only you exchange with yourself.

    But such analogies are misleading. One can use mental events as PART of a justification process to oneself, without collapsing into a completely causal world, without seeming like one is buying only newspapers of the same printing. One is not “proving” such and such to be the case, but one certainly is orienting oneself towards one’s own mental events such that confirmation from others is not the SOLE determiner of sense. One experiences sense, and does so by taking a view towards one’s own mental states.

    Daniel Tammet, for instance, might do his calculations in an entirely pragmatic circumstance, but one devoid of the correction from others. He might be building a tree house in a way that needs precise mathematical measure. What confirms to someone like Daniel that the calculation is right is two things, his process of arriving at it (that is, he understands the relationships between spatial manifestations of numbers, as his mind is able to manipulate them), and that they WORK, in the world. There is no need for a public tribunal of whether he got the calculation right.

    Now, how far one can go in this solitary, self-justifying process may be fairly limited, for our conceptions of ourselves is based in large measure upon our intersubjective knowledge of others (Wittgenstein got that part right). Limited, but not logically impossible. It is not solely as a point of logic that self-justifying procedures are empty ritual acts in which no gear turns any other gear, because indeed criteria following, even in the private sense, has one corrective measure, and that is real world consequences.

    Your suspicion that it is metaphysics which might lead one down away from Wittgenstein’s Private Language Argument I think is correct (though one need not be a metaphysician to embrace its critique). It is the metaphysical assumption that we live in one world (monism), and that even our criteria are caused by our interaction with that world, if only in the form of beliefs held. Wittgenstein explanation via language game would not even get off the ground, if not for this cohesive metaphysical assumption. Wittgenstein’s ultimate categorization of cause and reason experiences a double fold, for reasons, (for instance mental predicate attributions, such as beliefs, or fears, or desires), must be understood themselves, as causes of intentional behavior: He was afraid of bees, so he ran home. And in addition, these beliefs, fears, etc., but also be read as caused by the world, in order for the whole explanatory apparatus to fit into a rational view of the world and action in it.

    The reason/cause distinction certainly does well to separate out public criteria from the experience of mental events, but an orientation towards those mental events (interpretations of belief or disbelief, for instance), regularly make up our own, individual, justification for sense making in the world. That is, what is merely a “cause” in Wittgenstein’s reason/cause distinction, can be treated as reason, to some effect. And conversely, what is a reason (an explanatory attribution of mental predicates), can be consideration a cause.

    This interlacing is the very thing that give substance to the epistemic nature of mental events, without breaking the chain to public intersubjectivity. It is rather, at the very least, once language has been learned, though criteria-sharing does help make up and structure subjectivity, subjectivity itself has the capacity to comment back upon the intersubjectivity which helps make it up. It can “feedback”, so to speak.

    By restricting your burden of “proof” to “content” I believe you are missing out the gradated nature of what thinking entails. What is the “content” of Daniel Tammet’s thoughts as he calculates to immense numbers, watching their shapes interact? It is a misplaced question. This does not mean that he is not using criteria, that he is not making judgments, that he is not “thinking”. The mistake really is to assume, for the benefit of philosophical discourse, which for the most part wants to have firmly boundaried, well-defined, quanta of descriptions (so that its logics and science-like actions can take hold), that “content” is the signpost of thought, or even criteria use.

    What was the “content” of Mozart’s mind, when composing Piano Sonata #14? Can we not strictly say? If we, or even he, could not specify the “content”, does this mean that he was not using criteria? Does this mean that he was merely operating in a world causes, without reasons? Could Mozart only have composed his sonata if others were there to confirm that he truly was making music, and not merely suffering under the impression that he was? Does this mean that his mind was not “thinking” but only seeming to think? Just because Mozart could not PROVE that he was making music, and not just noise, and if no one had ever heard that one sonata, does not mean that the composition of the music itself would not have real, cognitive, meaningful and orienting effects, for Mozart, and Mozart alone.

  3. kvond May 22, 2008 at 6:40 pm


    One more note that occurs to me. (And thank you for your excellent comments), when you say:

    “certainly conscious rule-following emerges somehow from “rule-following,” such that there can be no clear demarcation: to insist that they were essentially different would amount to a kind of mind-body dualism, I think.”

    what comes to mind is Rorty’s comment, when he made his final turn towards objectivity, that the Mind/Body distinction, really is a Person/Thing distinction. As a aspect of personhood (that is, the measure by which we respect and identify with another entity’s reports one the world), there is both a categorical, conceptual binary (that is a person, that is not) often ideological or political (that is a citizen, that is not), or (that is a human being, and that is not); but there is also the gradated pragmatism of epistemologically reading the world through others, in which intentionality plays a major role discerning effects. Here, there is no duality of kind, but only the degrees to which others can inform us about the world we share, through their states of experience (so manifested). To try to isolate “thought” and “criteria” works well in the first sort of categorization, that between person/thing, citizen/non-citizen, human/non-human. In such a realm, Wittgenstein’s Private Language argument works perfectly well, (as does “thought content”). What is a reason and what is a cause seems to divide itself up fairly neatly. But in the gradated view of person/thing, it is circumstances and benefits, which guide the distinction. A person afflicted with Alzheimer’s suddenly can become much more like a “thing” in how it/he/she can inform us about the world. And a barely cognitive “thing” (perhaps a fly, or a worm), can suddenly have person-like status in what it informs. Intentionality is shot through the entire description, the degree to which the actions of a person or object can report something about the world, and as such, be reporting about their own states of experience, which color one way or another that report.

    Importantly, our connectivity to others (persons and things) is what is at stake when we seek to establish the criteria for what is “mind” and what is not. And for me, any notion of “content” must fall to the circumstantial conditions of epistemic readings.

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