Rule-Following, Dispositionalism, and Functionalism

In “Kripke and Functionalism” (Episode 61), Buechner describes how Kripke’s criticism of the dispositionalist response to the ‘rule-following paradox,’ found in Wittgenstein’s Philosophical Investigations,can be generalized as a criticism of functionalist accounts of mental states, the thesis that mental states are abstract computational states realized in physical objects, like a brain. Here, I’d like to give a sketch of the rule-following paradox, the dispositionalist response, and Kripke’s criticism in Wittgenstein on Rules and Private Language, in order to give you a clearer idea of the criticism of functionalism Buechner points to.  (For those following along at home, the crux of the rule-following paradox can be found in §§185-202 of the Investigations; Kripke’s (articulation of what he takes to be Wittgenstein’s) criticism of the dispositionalist response can be found on pages 22-35 of Wittgenstein on Rules and Private Language.)

Imagine that you are trying to teach a young student to count by twos. You start her off by writing on a piece of paper, ‘2, 4, 6, 8, 10…’, tell her to continue the series, and walk off for a bit to work with another student. Looking over her sheet when you return, you notice that something has gone wrong— when the student gets to 1000, her worksheet looks like this: ‘998, 1000, 1004, 1008….’ ‘No, no, no! Why did you do that?’ you say in exasperation. ‘You were supposed to go on like you were before.’ ‘I am, just like you told me!’ your student responds curtly.

Now, it seems clear that something has gone wrong here: you were trying to teach your student to apply the ‘+2’ function, so she should have proceeded ‘1000, 1002, 1004….’ But the student’s behavior is perfectly compatible with applying some function: add 2 for values less than 1000, 4 for values equal to or greater than 1000. (Indeed, it’s compatible with an infinite number of functions!) The question we are confronted in the rule-following paradox is: what fact of the matter determines that the student is following your instruction by writing ‘1002’ after ‘1000,’ rather than ‘1004?’ What makes the one, and not the other, a correct application of the rule you intended her to follow?

(The rule-following paradox emerges because Wittgenstein demonstrates that the justifications the philosopher would typically appeal to are, in fact, inadequate; yet we’re still inclined to say that the student has applied the ‘+2’ function—the rule you instructed her to apply— incorrectly. Here I won’t go through all the different solutions Wittgenstein undermines, nor (the many readings of) Wittgenstein’s ultimate resolution of the paradox—we’ll just focus on the dispositionalist response, and why it’s inadequate on Kripke’s reading of Wittgenstein.)

You may be inclined to respond impatiently: ‘I meant for the student to write ‘1002’ after ‘1000’ when I told her to continue the series! I already knew, at that time, that this was the right answer, not 1004.’ Rightly so— but you don’t mean that you thought ‘write ‘1002’ after you write ‘1000,’’ when you gave your student the instruction. And even if you happened to think of that particular application of the ‘+2’ function, there are an infinite number of applications of the function—you clearly didn’t think of all of them at once (see PI §187).

Here’s where the dispositionalist response comes in. When you say that you meant for the student to write ‘1002’ after ‘1000,’ the dispositionalist takes you to really mean something like:

(Dis) “If I had been asked what number [the student] should write after 1000, I would have replied ‘1002.’” (PI §187)

Even though you hadn’t actually thought ‘write ‘1002’ after ‘1000’’ when you told the student to continue the series, you were disposed to have that thought. You would have given it if you had been prompted—it just so happened that you weren’t prompted. Because you know how to apply the ‘+2’ function (you are the teacher, after all), your disposition counts as a fact of the matter that settles the dispute with your student: ‘If I were continuing the series as I instructed you to, I would have written ‘1002’ after ‘1000’—you aren’t doing what I told you.’

Kripke reads out of Wittgenstein a series of related criticisms of this response: my dispositions are finite, but there are an infinite number of applications of the ‘+2’ function; I don’t discover what rule I meant for the student to apply, but the dispositionalist account makes it seem this way. But one criticism in particular intersects neatly with the criticism of functionalism Buechner describes. According to (Dis), you have a disposition to write ‘1002’ after ‘1000,’ and this disposition is the fact of the matter that determines what the student should have written, if she were to follow your instructions. Surely (Dis) captures one way you might respond when asked to apply the ‘+2’ function to 1000, but it isn’t the only one! Perhaps Billy Eichner, dollar in hand, bursts into your classroom at the moment you give the instruction, demanding ‘Apply the ‘+2’ function to 1000!’ Caught off-guard, it isn’t implausible to imagine that you might respond ‘1004.’ Or, try actually rotely applying the ‘+2’ function from 0 to 2000—the sheer boredom of the task may cause you to skip right from 1000 to 1004. (If these examples don’t grab you, you’ll surely acknowledge that we sometimes misapply slightly more complex arithmetic rules, like subtracting two digit numbers from three digit numbers.)

The point is that you have a whole set of different dispositions about applying the ‘+2’ function to 1000—some of these are dispositions to reply with ‘1002,’ some with ‘1004,’ maybe some with other numbers entirely. The dispositionalist might reply: ‘Sure, you’ve got a bunch of different dispositions in weird circumstances, but normally you’d say ‘1002.’’ She might revise (Dis) this way:

(Dis*) If I had been asked, under normal circumstances, what number the student should write after 1000, I would have replied ‘1002.’

With the ‘under normal circumstances’ clause, the dispositionalist is trying to rule out mistaken dispositions, so that the only dispositions that count are those in which you reply with ‘1002.’ Kripke has an incisive criticism of this response:

“No doubt a disposition to give the true sum in response to each addition problem is part of my ‘competence’, if by this we mean simply that such an answer accords with the rule I intended, or if we mean that, if all my dispositions to make mistakes were removed, I would give the correct answer…. But a disposition to make a mistake is simply a disposition to give an answer other than the one that accords with the function I meant. To presuppose this concept in the present discussion is of course viciously circular” (Wittgenstein on Rules and Private Language, 30).

If the purpose of the ‘under normal circumstances’ clause is to rule out mistaken dispositions, then we already need to have determined which dispositions count as mistaken, and which count as correct. But the whole point of the dispositionalist response to the rule-following paradox was to use my disposition, as someone competent in applying the ‘+2’ function, to determine what the correct application of your instruction was (what rule you intended for her to follow). With (Dis*), we need something other than the disposition itself to tell us what count as ‘normal circumstances.’ So the dispositionalist is stuck between the untenable options of (Dis), which puts the disposition to follow 1000 with 1002 on par with the disposition to follow 1000 with 1004, or (Dis*), which presupposes that 1002 is the correct response to applying the ‘+2’ function to 1000. Either way, dispositions aren’t equipped to explain why your student should have written ‘1002’ instead of ‘1004.’

To conclude, let me gesture briefly towards the connection Buechner draws with Kripke’s criticism of functionalism. The basic idea of functionalism is that we can characterize mental states as abstract computational states realized by physical objects. A very crude functional analysis of belief might look like this:

Input —> Belief —> Output

For example:

Perception of coffee cup on the counter & Call by barista: “Latte for Phil” —> Belief that there is a latte on the counter —> Take cup & Belief that the barista has moved onto the order after mine.

The problem is that, just like I have many different dispositions when asked to apply the ‘+2’ function to 1000, there are many different beliefs that can go with these inputs and outputs: maybe I don’t believe that there’s a latte in that cup, since the barista has messed up my order before, but I’m in a rush. Or maybe I believe that an arch-nemesis has switched out my latte for a poisonous beverage without my noticing.

The goal here is to get the functionalist to say: ‘Sure, I guess those weird beliefs could stand in relation to these inputs and outputs (or vice versa), but under normal circumstances, the belief that stands in these relations is the belief that there is a latte on the counter.’ Once we get the functionalist to appeal to ‘normal circumstances,’ she ends up in the same position as the dispositionalist: how do we determine what counts as normal circumstances, without already assuming that the belief at play is that there is a latte on the counter? But the functional analysis is supposed to determine what belief is at play—it’s the one that stands in relation to the specified inputs and outputs. So appealing to ‘normal circumstances’ undercuts the functionalist, just like the dispositionalist.

Questions about the rule-following paradox, the dispositionalist response, or Kripke’s criticisms of dispositionalism and functionalism? Feel free to post them below!

Phil Yaure






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