§185

In §185 Wittgenstein returns to the example from §143 - the language game of A issuing orders to B and B then writing down a series/continuing a series according to a rule.

In sections §§143-184 Wittgenstein clarified the grammar of 'understand'. He raised the question: how can it be that what we understand/grasp in an instant (the meaning of an expression) is its use (which is extended in time)? - This could be understood as a rhetorical question meant as an attack on the claim that meaning is use. Wittgenstein said in those passages that it was a mistake to think that understanding an expression was a mental state from which correct use flowed. Understanding is not a mental state. Unlike mental states it lacks genuine duration.

Now, in §185 he commences a discussion concerning what counts as accord with a rule and what counts as following a rule. His discussing of rule-following parallels his discussion of meaning and understanding from earlier. An explanation of meaning is a kind of rule (it sets a standard of correctness) and a criterion for understanding an expression is correct application. Being able to give a correct explanation of the meaning of a word is also a criterion for understanding it. However, it seems clear that someone might satisfy one criterion but not the other (they might give a correct explanation of meaning and yet go on to use the word in question incorrectly). What are we to say about this?

Similar to the kind of case just mentioned is someone stating a formula (a kind of rule - parallel to an explanation of meaning - both give a standard of correctness and can be used to justify/criticise actions) and someone applying the formula (which parallels someone using a word correctly or incorrectly). So his discussion of rule-following bears upon his discussion of meaning and use.

In §185 the pupil (B) is asked to continue the series '+2' from 1000 upwards. B has previously demonstrated the ability to add 2 to numbers below 1000. B continues the series '1000, 1004, 1008, 1012'. When challenged about this ('you should have added 2!') B says 'I did add 2. - I went on in the same way.' What can we say to B to convince them that they did not go on in the same way? It seems that repeating what has already been said in the course of instructing B would be pointless. They think that they've gone on in the same way despite having had that training. Does the rule 'add 2' determine a correct way to go on in every instance? - It seems that Wittgenstein wants to say 'yes'. 'x + 2 = y' would count as a formula which determines a number, y, for a given value of x according to §189. What Wittgenstein wants to do is to clear up any confusion surrounding what this (the formula determining a value in each case) might amount to.

Some have found in these passages (§185 onwards) a sceptical argument leading to the paradoxical conclusion that "no course of action could be determined by a rule, because every course of action can be made out to accord with the rule" (§201) i.e. Kripke. - It could be that B interpreted '+2' to mean 'add 2 up to 1000, then add 4 up to 2000, and add 6 up to 3000 and so on'. Is there anything in the rule '+ 2' that rules out this way of interpreting it? A could respond by saying that the correct way to interpret the rule was the way that he (A) meant it. But did A, when giving the rule mean that B should write '1002' after '1000'? - This kind of sceptical concern is examined by Wittgenstein but it isn't clear that what Wittgenstein does is to raise sceptical worries and then proffer a sceptical solution. More likely, I think, is that Wittgenstein wants to expose nonsense and dissolve philosophical problems rather than offer a traditional/Humean solution to them.

Question:  Would this be another way of posing the sceptical problem? -- Given that continuing the series '1002, 1004, 1006, 1008' and '1004, 1008, 1012, 1016' are both possible ways of interpreting '+2' how are we to decide which is the correct way of continuing the series?