Notes on Following a Rule

Wittgenstein argues that no action could be identified as following a rule. This is because any action can be made to correspond with a myriad number of different rules. To demonstrate this point, he uses two examples.

First Example

The first example is of two people playing a game involving a series of numbers. Person A writes down the series, while person B tries to find a sequence in the series. The series is made up of the numbers 1, 5, 11, 19, and 29. In this scenario, B could try the formula ‘an = n2 + ni’ after A had written the number 19, with the next number A writes down confirming his hypothesis. However, he could just as much ask himself ‘what are the series of differences?’ before writing the series 4, 6, 8, 10 down. Here, we can apply two methods for guessing the sequence in the series: the first method for guessing the rule of the sequence, is the formula ‘an = n2 + ni’ while the second method for finding the rule of the sequence is finding the series of differences within the sequence.

Second Example

The second example that Wittgenstein uses is that of two people belonging to a tribe who are unacquainted with games, sitting down and going through all the different moves of a chess game. Though the moves are in fact random and without intentional accordance to the rules of chess, we would think the two tribesmen are playing a game of chess by categorising their actions as following certain rules. Wittgenstein then asks us to imagine if the game of chess was translated into certain rules, e.g. yells, the stamping of feat, etc. If the yells and movements were translatable into chess moves, would we be inclined to say they were playing a game?


Wittgenstein’s main point is to highlight how an action, random or systematic, can be made to correspond with multiple rules. This is problematic however, as since rules are absolute in their application i.e. either we follow the rule or we don’t, and rules have a tendency to conflict with other rules, Wittgenstein argues that the rules ascribed to an action will necessarily conflict with each other. Therefore, actions can accord with rules, but because rules conflict with each other, actions cannot be determined by rules.

Kripke – Sceptical Solution

Saul Kripke argues that Wittgenstein offers us a solution to the paradox. For Kripke, the main problem the paradox entails is not if we are right or not, but rather if we have a justification for following a rule. Kripke argues that we should not look for the ‘entities’ or ‘facts’ which correspond to numerical assertions, rather that we should look at where and when we make utterances involving numerals and the usage we gain by making them in specific situations. Kripke argues we do not follow rules in isolation but are influenced by our different mental states, which fool us into thinking we are following a rule. He uses the illustration of both a young child and a person under the influence of drugs as examples of people who think they are following rules, even though they’re actions are random.

Grocer Example

Kripke imagines he goes to a grocer and hands him a note saying ‘five red apples’. The grocer hands over the apples to him, reciting each numeral by heart until he reaches the fifth apple. Kripke argues that in this situation, the customer expects for the grocer to act like he does and not according to some bizarre non-standard rule. Although the grocer may make mistakes or be dishonest in the computation, the customer none the less attributes to him an ability to grasp the concept of addition and does not expect him to behave bizarrely. It is this entrustment of people’s ability to follow the same rules as we do, which is at the basis of Kripke’s solution.  It becomes a communal game of trust/distrust, whereby individuals whose behaviour does not follow such expectations are distrusted in their ability to follow the rule in future cases.

McDowell – Straight Solution

In contrast to Kripke, John McDowell offers a different solution to the paradox. McDowell’s interpretation of Wittgenstein argues that our reasoning ability is simply spoiled by a misunderstanding, and that the right response to the paradox is not to accept it but to correct the misunderstanding that it is based on. To correct a misunderstanding, we need to make sure that the rule cannot be reinterpreted ad infinitum. Grasping a rule for McDowell must come from arriving at an interpretation, yet the interpretation must not be susceptible to the movement of thought. The interpretation that cannot be reinterpreted must solely join, the original instructions for following the rule and how one goes about following the rule.

Shared Command of Language

McDowell argues that obeying a rule is a practice, if we find that there is a way of grasping a rule which is not an interpretation. A problem arises however: how can an action be a blind reaction to a situation (avoiding Scylla) and be a case of following a rule (avoiding Charybdis)? McDowell argues that the answer is for the rule follower to belong to or to be following a custom, practice or institution. This is a similarity he shares with Kripke. However, although the ends are the same, the means they use to get to the conclusion are different. McDowell believes that Kripke and other anti-realists, argue that a people sharing a language is constituted by correct responses in their dispositions to linguistic behaviour, which they do without referring to the terms of the contents of their utterances. In other words, focusing on how rules are being used rather than the instructions embedded in the rule. McDowell, meanwhile thinks we come to this conclusion by finding content which cannot be interpreted. McDowell argues against the communal expectations as proposed by Kripe and others, arguing that it devolves into a collection of individuals whom we have no convincing reason to consider transparent to one and other in our expectations. If the verbal behaviour of an isolated individual is obscure, how would it be different with several people with matching regularities? Instead, McDowell argues that a shared command equips us to know each other meanings without needing to arrive at that knowledge via the trial and error of interpretation. This is because for McDowell, we are already on the same wave-length as them. So we do not need to arrive at knowledge via an interpretation that can be reinterpreted ad infinitum. McDowell argues that a linguistic community is not bound by externals (facts accessible to all), but by a capacity for a meeting of minds whereby both parties hold the same grasp of the thing in question. This can be seen with McDowell’s rejection of the notion of training necessarily leading us to understanding another person’s mind. He argues that Wittgenstein sometimes discusses the phenomena of being able to grasp the principle of a series or a meaning, in a instant or flash.

Millikan – Naturalist Solution

To understand what it is to follow a rule, we must first understand what conditions allow us to follow rules in the first place. For Ruth Garrett Millikan, what causes rule-following to exist is what she terms biological purpose. This roughly refers to biological functions e.g. heart movements, blinking, etc., which exist in accordance to evolutionary design. She uses the example of hoverflies to explain the naturalist solution to following a rule: Male hoverflies, when they react to a certain stimuli, will dart off in a certain direction. This function occurs as a mating mechanism, in which a hoverfly attempts to catch a female. The hoverfly, does not consciously calculate a rule by doing this but follows it anyway. The hoverfly follows the rule, because of certain biological conditions being prompted by certain stimuli. If a condition is met, the biological mechanisms within the hoverfly will make it act in accordance with a rule. Male hoverflies who are injured and blind may have no disposition to follow the rule. They may also follow the rule mistakenly i.e. chasing a bird or midges. Following a rule has nothing to do with fitting all past instances of activity, but rather depends upon meeting the criteria for a particular material state of being. This both includes how it is internally (is it sick, is it blind, etc.) and externally (how hard is the wind blowing, how far is the object, etc.). The particular rule depends on variables, not on constants. If conditions change within the environment or the body, this may affect our ability to follow a rule.