The Origins of the So-Called ‘Rule-Following Paradox’
The Origins of the So-Called ‘Rule-Following Paradox’


The notion of ‘rule-following’ is already important in the Tractatus. There it characterizes ‘thought’ as the activity of following rules of projection. In MS 109-110 (1930-31), especially, Wittgenstein goes back to the discussion of the nature of Satz and thought. Its result is a version of some aspects of the so-called ‘rule-following paradox’ as presented in the Philosophical Investigations (PI). In those manuscripts, there is neither a solution for the ‘paradox’, nor a clear answer to the question of how the problem arises. Nevertheless, there are important indications of what could count as such an answer for Wittgenstein in line with the new method that he seems to be developing there.

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    The notion of ‘rule-following’ is already important in the Tractatus. There it characterizes ‘thought’ as the activity of following rules of projection. In MS 109-110 (1930-31), especially, Wittgenstein goes back to the discussion of the nature of Satz and thought. Its result is a version of some aspects of the so-called ‘rule-following paradox’ as presented in the Philosophical Investigations (PI). In those manuscripts, there is neither a solution for the ‘paradox’, nor a clear answer to the question of how the problem arises. Nevertheless, there are important indications of what could count as such an answer for Wittgenstein in line with the new method that he seems to be developing there.

    1. Background: The Tractatus

    What is a thought? In 3.5 Wittgenstein says that “a propositional sign, applied and thought out, is the thought”. So the applied sign explains what a thought is. In order, then, to explain what a thought is, we need to be clear about what it means to apply signs. In 3.11 Wittgenstein gives us a further hint concerning the activity of applying signs:

    We use the perceptible sign of a proposition (spoken or written, etc.) as a projection of a possible situation.
    The method of projection is to think of the sense of the proposition.

    If the thought is the used propositional sign and to think is the method of projection, to get clear about what thinking is for Wittgenstein in the Tractatus, we need to understand in what projecting signs consists. The simplest case of projection is the projection of an image of a plane figure onto a parallel plane (projection plane) at an incidence of 90 degrees. Those are the rules of this projection. As a result, the ratios of the figure to be projected are preserved in the projection plane and the figures are similar. With such rules, we can easily recognize what the original figure is by means of the result of the projection. We can, nevertheless, change those rules and create different kinds of projection. If we change the incidence angle or do not require the parallel planes, the result of the projection will be figures that differ from the figures that we start with. With an incidence angle of 110 degrees, for instance, we would not know immediately which are the figures that were used as the starting point. We could only tell what the figures were if we knew the rules of projection used.

    Different from the depiction of a real landscape, which presents the elements as they appear in the combination seen in the landscape, the projected signs of a proposition don’t look like the described situation and its elements. But if we know the rules used to describe the situation, we can recognize how the propositional signs depict what is described. Thus the notion of thought explains how the proposition is a picture of what it describes by means of the notion of projection.

    In 4.0141, Wittgenstein gives an example of a projection:

    There is a general rule by means of which the musician can obtain the symphony from the score, and which makes it possible to derive the symphony from the groove on the gramophone record, and, using the first rule, to derive the score again… And that rule is the law of projection which projects the symphony into the language of musical notation. It is the rule for translating this language into the language of gramophone records.

    To project a propositional sign – to think the sense of a proposition – we need general rules of projection: rules that interpret the signs and relate them in a certain way. What are those rules? We need two kinds of rules to represent facts by means of signs: a general rule of correlation and a general rule of articulation. We can think, for instance, that a match on a box of matches represents the fact that Jack is at home. In this case, we could say that the match would designate Jack while the box would designate Jack’s home (here we have a correlation rule) – see 4.0312. But since any object or word can stand for any object (as long as we use the given object or word in such a function), we need more to make clear what we are representing. We can also say that names don’t have an autonomous meaning, for they have meaning only once a rule of articulation is in place (see context principle in 3.3). We need a rule that articulates the objects used as signs in a way that is similar to the articulation of objects in the situation that we want to project. We can say, for instance, that a rule prescribes that the position of the signs expresses the relation between the objects that we want to represent.

    Thus, rules of projection express under which conditions a proposition is true; they determine, therefore, the sense of a proposition. To think the sense of a proposition is, therefore, to apply rules of projection. Thus, following rules of projection is what essentially characterizes thinking given that a “thought is a proposition with sense” (Tractatus 4).

    2. MS 109-110

    In MS 109-110, Wittgenstein systematically goes back to the question of thought and rules. But now he investigates some difficulties involving those notions1: “Does the depiction (das Abbilden) consist in acting according to a rule? But how is this rule given? – How am I conscious of the rule? What is its expression?” (MS 109, p. 71 – all translations of MS are mine).

    Those questions point to what one may take as an important problem. The question “What is the expression of the rule?” has a simple answer: the action of depicting or of following the rule of depiction is the expression of the rule. This seems to imply that the depiction consists in acting according to a rule. But to act according to a rule, then, we need a formulation of the rule as a standard for our action. In other words, the rule seems to be given to us when we act.

    Suppose that a general rule is given. One can, nonetheless, apply the rule only if he understands its application. Suppose, for instance, that someone should translate a sentence from one language into another. He is given the set of sentences to be translated and a dictionary, which is the set of rules of translation:
    One could say then: But it is not enough to give him both things; you have also to tell him how to use them as well. But in this way a new plan would be created, which would need an explanation as much as the first one. (MS 109, p. 82).

    The rules of translation, as it were, cannot do the work by themselves, for they also need to be explained. But once the rules in the dictionary are explained, the words used to explain the rules may also need an explanation. As if any interpretation hanged “in the air along with what it interprets” (PI §198). This would, then, imply an infinite regress.

    Wittgenstein’s conclusion is not, nevertheless, that this shows that we cannot follow rules. On the contrary, for him, there must be something wrong going on:

    …I don’t need another model that shows me how /the depiction goes and, therefore/ how the first model has to be used, for otherwise I would need a model to show me the use/application of the second and so on ad infinitum. That is, another model is of no use for me, I have to act at some point without a model. (MS 109, p. 86)

    This certainly doesn’t explain why we don’t need a different interpretation to follow the rule or how to stop the presumed regress. It simply suggests that the need of a new model will not arise. As a matter of fact, we act without interpreting at some point. Immediately after the passage quoted above, Wittgenstein introduces the seeds of what could be thought as a new paradoxical situation:

    One could also say this: a drawing is not a plan because someone once – accidentally – walked in such a way that his path corresponded to the plan, but rather because he followed the plan according to a definite rule. Incidentally, otherwise each path would correspond to the plan (according to some rule) (MS 109, p. 86-7; see also p. 281 for a similar situation involving rules of grammar).

    This is similar to what Wittgenstein says in PI §198: “whatever I do is, in some interpretation, in accord with the rule”. Something is needed, so it seems, to fix the rule, i.e., to determine which is the rule that is followed. If something does not fix the rule that expresses the correspondence of plan and action, we cannot be sure if someone is not simply accidentally in accord with a rule instead of following it. Now, the danger is the complete trivialization of rules, for each action is in accord with some rule.

    Is Wittgenstein discovering the ‘paradox’ of PI §201 in MS 109? Wittgenstein, I take it, is rehearsing thoughts concerning the nature of thought and rules, which have their ancestor in the remarks on thought and projection of the Tractatus. I think that the only discovery that he makes is the discovery that one can come to believe that there is a problem concerning rules. The discovery that Wittgenstein wants to make (and this is why he rehearses thoughts on rule-following) is the one concerning how one could be led into thinking that rules cannot be followed; for instance, why one requires that to follow a command he needs always to interpret the signs used in the command (which can lead to an infinite regress).

    This kind of discovery is, actually, the point of his investigation. In a remark that immediately precedes the ones I cited above, he says: “(The method of philosophizing is to make yourself crazy, and to cure the craziness again)” (MS 109, p. 84). “To make yourself crazy” is to get into philosophical thinking. Wittgenstein rehearses philosophical thoughts in order to see when things go wrong. Those thoughts are “good only because they show the illness of the conception” (MS 110, p. 248) and bring into light how to solve (or dissolve) philosophical confusions: “the cure is the pointing out of the misleading picture…” (MS 110, p. 248).

    In the manuscripts of 1930-31, Wittgenstein sees that what he has to locate are false analogies that lead to philosophical puzzlement. To be led by false analogies into mistakes and being unable to get rid of its predicaments is, for Wittgenstein, “the morbus philosophicus” (MS110, p.87). As the following passage shows, Wittgenstein is himself not clear about the misleading analogies and still in the middle of a predicament concerning rule-following at the time he writes MS109-10:

    But what we certainly want is to make clear the grammar of the expression ‘the command is followed’.’
    Well, then how do I know that I followed the command?’
    (I cannot find the central grammatical mistake on which all those problems rest). (MS 110, p. 95).

    It is very important to see that Wittgenstein is not clear about how to explain the mistake in those trains of thought, or how to make clear how the sources of mistake work in the train of thought. He points to some of those sources in the manuscripts. He mentions, for instance, the following misleading ideas: that the meaning of a word is a representation in MS110, p. 230, that thoughts accompany sentences on p. 231 and that understanding is a state on p. 236. So we have already in MS110 some of the themes discussed in PI. Nevertheless, they are not treated systematically yet. On the other hand, Wittgenstein is sure about where he has to find a solution for the problems, namely, in mistakes underlying their formulation. It is the very train of thought that leads to the problem and seems to support it where things go wrong. Therefore:

    One of the most important tasks is to express all false trains of thought in such a characteristic way that the reader says ‘yes, I meant it in exactly this way’. To portray the physiognomy of each error (MS 110, p.230).

    ‘To portray the physiognomy’ of an error means thinking the thoughts that lead to the error and finding the source of the train of thoughts that leads us to the formulation of the problem (see PI §§39 and 40). Wittgenstein rehearses philosophical reasoning to find where it goes wrong and for himself to see where his philosophical inclinations lead him. After his own exercise, he wants to present this process with its errors in front of the reader in order for the reader to see himself, as it were, in a mirror. In PI those rehearsals come back in the voice of interlocutors who express philosophical inclinations. (The reason, then, why those voices seem so convincing is that the author of the book went through them himself -- as if through the “morbus philosophicus” --, but came back to tell the story).

    Thus, even in its early version, the rule-following remarks are not intended as a paradox at all. So it speaks against Kripe’s reading (Kripke 1982). Also, manuscripts 109-10 develop a method of philosophizing that consists in tracking philosophical problems to their origin in order for the reader to see his own mistakes. This method is invented, so it seems, in MS 109-10 and it will be constantly present in Wittgenstein’s later philosophy. Another point to be mentioned is that discussions on the ‘rule-following paradox’ are present in Wittgenstein’s work before his work on PI around 1944; i.e., when Wittgenstein introduces the sequence on the ‘paradox’ in the rule-following sections of PI around 1944, he is simply bringing it back to where it belongs.


    1. Kripke, Saul 1982. Wittgenstein on Rules and Private Language. Cambridge, Massachusetts: Harvard University Press.
    2. Wittgenstein, Ludwig 2001 Philosophical Investigations. G.E.M. Anscombe (tr.), 3rd edition. Blackwell.
    3. Wittgenstein, Ludwig, Tractatus Logico-Philosophicus 2004. Brian McGuiness and David Pears (tr.) London and New York: Routledge.
    4. Wittgenstein, Ludwig, Manuscripts 105-113 2001b. Michael Nedo (ed.). Wiener Ausgabe, Band 1-5, Frankfurt a. M.: Zweitausendeins.
    The major difficulty that underlies Wittgenstein’s thoughts is the characterization of the relation among different kinds of Sätze (commands, expressions of desire, expectation, etc), their rules of projection and facts (facts that make Sätze true, correspond to expectations, satisfy the expression of desire, etc.). I think that Wittgenstein’s interest in these difficulties is connected with his reading and dislike of Russell’s Analysis of Mind. In the manuscripts between 1929-32 there are several references to the “causal theory of meaning” of that book (for instance MS 107, p. 107, MS108, p.180 & 254, MS 109 74 & 198) as well as criticisms of Russell’s explanation of the nature of desire (see especially MS107, p. 290 & MS 109, p. 28).
    Mauro Engelmann. Date: XML TEI markup by WAB (Rune J. Falch, Heinz W. Krüger, Alois Pichler, Deirdre C.P. Smith) 2011-13. Last change 18.12.2013.
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