From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

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The primary object of this paper is to draw out Wittgenstein's thought that understanding of a rule does not transcend the explanations that can be given of it. I call this Wittgensteinian thought an "anti-realist premise". There is a skeptical argument, common to readings of Wittgenstein's rule following remarks as an anti-realist argument, that is read to contain this thought as a premise. A further skeptical argument, drawing on private language considerations as they apply to rule following, interestingly serves as support for this premise. It is argued in closing that, despite initial appearances to the contrary, this does not make Wittgenstein's primary skeptical argument in the rule following remarks, anti-realist as it may be, circular.

Consider the following remarks:

But if a person has not yet got the concepts, I shall teach him to use the words by means of examples and by practice. - And when I do this I do not communicate less to him than I know myself. (PI 208)

"But then doesn't our understanding reach beyond all the examples?" - A very queer expression, and a quite natural one! -
    But is that all? Isn't there a deeper explanation; or mustn't at least the understanding of the explanation be deeper? - Well, have I myself a deeper understanding? Have I got more than I give in the explanation? - But then, whence the feeling that I have got more? (PI 209)

"But do you really explain to the other person what you yourself understand? Don't you get him to guess the essential thing? You give him examples, - but he has to guess their drift, to guess your intention." - Every explanation which I can give myself I give to him too. (PI 210)

There is a thought concerning understanding and explanation conveyed in the above remarks (and elsewhere) which is as follows:

AR

There is not more to my understanding of a rule than what I can convey in its formulation or instructions.

But often times, we do understand more than we can convey. For instance, when we have a word at the tip of our tongues - we have an understanding of what we want to say but are just missing the appropriate word. Or when we are ill or fatigued and just not up to conveying what we understand. And so, let us admit that Wittgenstein is making a principled point to which these considerations of circumstance do not apply:

AR*

There is not more to my understanding of a rule than it is possible for me to convey in its formulation or instructions.

However, since the formulation and instructions for a rule are public goods (they are commonly available to the linguistic community), they provide a limit on what can be understood in general in that linguistic community. In other words, Wittgenstein's remarks apply generally; he is making a comment about understanding and not simply individual understanding. Hence we can say:

AR**

There is not more to be understood of a rule than it is possible (for us) to convey in its formulation and instructions.

That is to say, understanding a rule does not involve more than understanding what can be given in an explanation of the rule. I am taking formulation and instructions to be equivalent to explanation (for explanation is in terms of providing formulation and instructions), and moreover, both as exhaustive of whatever can be communicated of a rule in conveying an understanding of the rule.¹ The exegetical basis for AR** is not simply the remarks given above (and similar remarks not given) but further, the place it fills in the skeptical argument which shows that such a premise is needed.²

The skeptical argument of the rule following remarks, in brief, proceeds as follows. Consider a rule for the development of a number series (say +2). Any formulation, set of instructions, or in short, any explanation we give for the rule do not determine the application of the rule for every place; they do not determine how the rule is to be followed at every step (cf. PI 185). Consequently, an indefinite number of courses of action, often exclusive of each other, are in accord with the instructions for the rule but are not correct to the rule as intended (for they vary at places or steps not covered explicitly by the instructions). This is to say that the rule can be interpreted in an indefinite number of ways; however, in saying this we are saying that the instructions given for following the rule can be interpreted in an indefinite number of ways. Interpretation, it is important to note, as it is used here just means that the instructions license an indefinite number of courses of action and thus, if we follow the rule according to a particular course of action we are in effect choosing an interpretation of the instructions (i.e., for the instructions to be open to interpretation just means that there are an indefinite number of courses of action each equally in accord with the letter of the instructions).

The skeptical argument may summarily be presented as follows:

• If following the formulation and instructions available for a rule requires interpretation of the formulation and instructions,
• and there is nothing else to go by in following a rule but the formulation and instructions available (i.e., AR**, there is no understanding of something else that could guide us),
• then we are left unable to follow the rule because we are without means to choose which, among an indefinite number of courses of action that are in accord with the formulations and instructions available, is the correct course of action to pursue in order to follow the rule correctly (i.e., as intended).

Recall, the first conjunct in the antecedent follows from the point that any set of instructions cannot account for the application of a rule at every step. Hence, there are an indefinite number of courses of action that are in accord with the instructions, and thus, following the instructions requires interpretation (i.e., picking a course of action as the correct way to follow the rule is to interpret the instructions according to the course of action picked). The second conjunct in the antecedent, as noted above, is the anti-realist premise: there is no more understanding to be had than that which can be gathered from the formulation and instructions for following a rule.

If the first conjunct is accepted, acceptance of the anti-realist premise leads to a skeptical paradox. Wittgenstein accepts the second conjunct, and therefore, to avoid the skeptical conclusion, he must reject the first. And this is just what he claims for himself (cf. PI 201 and also PI 198). Appropriately, we may view the skeptical argument, as presented herein, as used by Wittgenstein to argue against the first conjunct (by pain of paradox).

Rather than pursue the anti-realist consequences of this premise, and the skeptical argument in general, I will elucidate the support for this premise in private language considerations as they are found in the rule following remarks and, in general, discuss the connections between the anti-realist premise and these private language considerations. Let us stipulate that understanding that outreaches explanation be called "intuition". The primary reason for choosing this word, despite its philosophical baggage, is that this is the term that Wittgenstein (as will be discussed below) uses in the rule following remarks for explanation-transcendent understanding.

PC

If AR** is not true of our understanding of a rule, then our understanding is necessarily private.

To explain, the means of conveying understanding in AR** (formulations, instructions, etc.) are, ex hypothesi, exhaustive of public means of conveying understanding; they are meant to include whatever can be communicated of a rule by way of explanation. Thus, if AR** does not apply to our understanding, then our understanding is necessarily private for, by the definition of AR**, it is not possible for us to convey our understanding through public linguistic means.

Where AR** does not hold, our understanding is necessarily private, and therefore private language considerations can be brought to bear. PI 202 makes a case that there cannot be private rule following (and hence, that there cannot be an understanding of a rule that is private). "And to think one is obeying a rule is not to obey a rule. Hence it is not possible to obey a rule 'privately': otherwise thinking one was obeying a rule would be the same thing as obeying it." (PI 202) To explain, there can be no private rule following because the private rule follower cannot make the distinction between following the rule and thinking he was following it. It is taken that rule following requires that we be able to make this distinction. The upshot is that since intuition is private (by PC and the denial of AR**), intuition is not a candidate for being followed. Hence, intuition is not a source of understanding that can guide us in following a rule.

In sum, as a consequence of the above private language consideration, AR** is a necessary condition of rule following (i.e., there cannot be an understanding of a rule that cannot be explained or conveyed through public means, e.g., formulations and instructions). And so, intuition, or whatever we are to call that understanding that outreaches the understanding that can be gained through explanation, cannot be a source of understanding of a rule (and neither can anything else of which AR** does not hold).

The exegetical case for the above argument is as follows. Wittgenstein, in arguing against intuition in rule following, by which as noted above, he names understanding that is explanation transcendent, adopts private language argument considerations. He says,

So it must have been intuition that removed this doubt? [regarding which is the correct interpretation of a rule for the development of a series] - If intuition is an inner voice - how do I know how I am to obey it? And how do I know that it doesn't mislead me? For if it can guide me right, it can also guide me wrong.
    ((Intuition an unnecessary shuffle.)) (PI 213)

Wittgenstein's argument against the role of intuition in rule following is essentially a private language argument consideration: he says that intuition could guide us wrongly just as much rightly without our being able to tell. This is a private language argument consideration (as it applies to private rule following) because it implies that if we were to claim that intuition was guiding us correctly, we would have no basis for this other than its seeming so (for it is denied that we could know that it was doing so). This confirms the reading I am giving in that it shows that private language considerations are being applied to the appeal for intuition in rule following. Also, it should be borne in mind that in arguing against intuition as such, Wittgenstein is arguing against explanation transcendent understanding. The exegetical case is strong that the "something essential" that is grasped but not conveyed by the explanation of a rule is likened to and called 'intuition'.³ And so, Wittgenstein's remark supports the point that where AR** does not apply, we are face with an understanding that is private, and hence, susceptible to private language considerations.

In the remaining paragraphs of this paper, I will discuss some of consequences of the above considerations. Specifically, I will focus on the apparent circularity of the above line of argument. Given that the rule following remarks putatively provide an argument against a realist construal of rules, the above line of argument shows that integral to this case is an anti-realist premise itself supported by private language considerations. Any realist regarding rules may thus claim that the argument against him in the rule following remarks begs the question. Alternatively stated, in support of the anti-realist premise, a premise in a commonly albeit divisively regarded skeptical argument, is another skeptical argument. This latter skeptical argument relies on the point that intuition cannot be followed, and this basically for skeptical reasons (for we would not know how to follow it correctly). But then, we may ask, what is the support for this point (is there another skeptical argument, we may ask sarcastically). It seems that Wittgenstein takes this point as somewhat self-evident, broadly for verificationist reasons (i.e., that we have no independent correctness criterion to determine whether we are following an intuition correctly - all we have is our own authority that we are following it correctly). But, as noted, there is a circularity in this strategy: in support of an anti-realist premise is brought an argument with verificationist presumptions.

This is true, but on Wittgenstein's behalf it is argued that the circularity does not come full circle. There is an important disanalogy between the two skeptical lines of argument. With regard to the first skeptical argument, Wittgenstein admits that rule following is still possible: if all we are given is an explanation, or formula and set of instructions, for how a rule is to be followed, we may be unable to follow the rule for reason of being unable to choose among an indefinite number of courses of action equally correct to the instructions and formula given. Wittgenstein accepts this but adds that form of life considerations, which involve being engaged in a custom which serves to determine how the rule in question is to be followed given the alternatives available, serve to dispel skeptical doubts; they are to enable us to follow a rule without need of interpretation. The latter skeptical argument, for Wittgenstein, is not to be mitigated. Intuition is not a candidate for being followed at all. Specifically, and it is important to note, the disanalogy here is of a public/private asymmetry. The first skeptical argument need not imply that we are unable to follow rules because considerations of publicity (e.g., there being a custom for how such a rule is to be followed, in which we are trained) enable us to follow rules without facing skeptical doubt in most cases. The latter skeptical argument, however, notes that rule following in terms of following intuition (or whatever we term understanding that is explanation transcendent) takes place strictly in a private domain. Consequently, custom, forms of life, public agreement, etc., have no role in this type of alleged rule following. There is no public bearing or custom regarding how intuition is to be followed for intuition is a strictly private affair. And so, we may conclude that the apparent circularity of the argument portrayed above is certainly not vicious for the public/private asymmetry of the two cases.

In conclusion then, we may say that in Wittgenstein's rule following remarks are to be found two skeptical arguments, the latter, drawing on private language considerations, serves to support a premise in the former skeptical argument. This strategy, for reasons discussed above, does not prove circular given a public/private asymmetry in the two arguments.

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