The grammar of "in accord with the rules"
Sunday, April 24, 2005
The rule following paradox is generally presented in relation to the sort of infinite regress described in the central part of PI §201:
[...] in the course of our argument we give one interpretation after another; as if each one contented us at least for a moment, until we thought of yet another standing behind it.
For example, Kripke describes such a situation when he makes his skeptic challenge our intuitive notion of the addition procedure by having him interpret not only "plus" as "quus" but also "count" as "quount", "independent" as "quindependent", and so on(1). Wittgenstein's works also contain a number of references to similar situations. For example, while investigating the meaning of the words "to read" and "to derive" (PI §156-178) several possible interpretations are proposed. But none are found to be fully satisfactory and secure, leading to the seemingly desperate "But does this mean that the word 'to derive' has no meaning, since the meaning seems to disintegrate as we follow it up?" (PI §163). Also, there is the case of the pupil learning to follow the "+n" rule (PI §185-187): when he writes '1004' after '1000', it is said that this behavior may still be considered correct under the "+2" rule provided it is interpreted as "Add 2 up to 1000, 4 up to 2000, 6 up to 3000, and so on" (PI §185).
We have seen, in the description of the order-processing example, that attempting to answer the question "is the system in accord with the specification?" gives rise to just this sort of infinite regress. As the "four possible answers" section shows, it appears that any possible system behavior can be made out to be compliant with any specification. The parallel with the rule-following paradox is readily apparent:
This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule. The answer was: if everything can be made out to accord with the rule, then it can also be made out to conflict with it. And so there would be neither accord nor conflict here. (PI §201)
But the order-processing example also shows that not all certainties vanish in such circumstances. What was at stake during the meeting was the determination of whom was to blame. Which means that everyone recognizes that something is wrong with the system. At no point did anyone doubt whether the system was in accord or not with the rules of the company; everyone knew it was not. Let (Qa) and (Qb) be the two following questions :
(Qa) Is the system in accord with the rules?
(Qb) Is the system in accord with the specification?
(Qa) never raises any doubt. Everyone involved would readily assert that the proper answer to it is "no". For (Qb), it is a different matter. As we have seen, it gives rise to an infinite regress of the rule-following type. Why is there such a difference between (Qa) and (Qb)?
One way to answer this question is to point, as Wittgenstein often does, to the importance of practice. To emphasize this we may note that, in the example, the mistake in the calculation of internal invoices is discovered during the acceptance tests phases; that is to say, when the behavior of the system is compared with the pre-existing invoice processing procedure of the company: its practices regarding invoices. During the coding phase of the project, no one knew for sure whether the system would be judged to have the correct behavior. It is only during the tests, i.e. when the system is used in actual cases that we discover whether it accords with the rules or not. As Wittgenstein says:
What this shows is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call 'obeying the rule' and 'going against it' in actual cases. (PI §201)
This is clearly the way out of his own paradox that Wittgenstein intends to point to. It turns out that, under the name of "tests", MIS professionals have adopted a practice which fits in very well with this principle.
However, I believe there is more to say than just to emphasize the importance of practice, and that cases like the order-processing example provide an opportunity to realize it. Let us focus on sentence (Qa) and ask ourselves how "grammar" (in the sense Wittgenstein uses this word) would allow us to split it into sub-components. There are at least two possible ways to do that, which we will label (Qa-1) and (Qa-2) :
(Qa-1) Is / the system / in accord with the rules?
(Qa-2) Is / the system / in accord with / the rules?
These two versions lead to two different interpretations of (Qa) which can be represented using a predicate-like notation:
(Qa-1) in-accord-with-the-rules( the system )?
(Qa-2) in-accord-with( the system, the rules )?
Which of the two possibilities is the right one? Grammar, in the ordinary sense, cannot help us since it clearly allows both (plus some others). But, keeping in mind the kind of difficulties we met with (Qb), we may wonder whether (Qa-2) is really allowed by the "depth grammar" of our language. If it was, we would be allowed to substitute "the specification" for "the rules", in (Qa), and the sentence (Qb) thus obtained should not be so different. But, as we have seen, (Qb) gives rises to an infinite regress and therefore appears to be beyond the boundaries of what our language allows. Or, more accurately, the boundaries of the kind of language game being played in the kind of setting described in the order-processing example.
Of course, there is still another way to put this, which is to say that the word "the rules" does not refer to an object, when used in sentences like (Qa); just as the word "five" does not refer to an object in the sentence "five red apples" of the §1 of the Philosophical Investigations(2). According to the "surface" grammar of our language, the word "the rules" is a noun and so could very well refer to an object (or a collection thereof), just as the word "apple" does. Guided by this similarity, we find it quite natural to put "the specification", a word which does refer to a document (i.e. an object), in the place previously occupied by "the rules" and end up with (Qb). But this is a dead end, as the infinite regress shows.
According to this interpretation, the main outcome of the rule-following paradox is to make it difficult to be a realist about rules. It is not, however, skeptical in the least. As the last part of the §201 suggests, and as the fact that no one doubts that the system violates the company's rules illustrates, there is a perfectly valid and uncontroversial use of the phrase "in accord with the rules".