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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.

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