This lecture is about a skeptical problem developed by Kripke according to his reading of Wittgenstein. Students will be able to identify the skeptical problem, learn about dispositionalism and the normativity thesis of meaning, and explore a possible solution to the skeptical problem. Recommended reading: From On Rules and Private Language (1982), Saul Kripke in The Philosophy of Language Edition 6 by Martinich and Sosa. For the full course, visit https://www.udemy.com/philosophy-of-language/

1. Introduction
In this lecture, we’re going to look at a skeptical problem that Kripke develops according to his reading of Wittgenstein. This skeptical problem raises doubts about whether anyone can mean anything when using the terms of his language. To give an example, if I use the term ‘plus’ in mathematics, I mean the rule of addition by my use of the term ‘plus’; however, if Kripke’s Wittgenstein is right, then there’s no such thing as my meaning addition by ‘plus’. Similarly, there’s no such thing as my meaning anything by my use of any term. This is troubling and we need to confront this problem with care.
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Suppose Jones is a mathematician and he’s only added numbers that do not go beyond say 5,000,000. So, he’s added 4,500,000 to 300,000 before, but no numbers beyond 5,000,000. Since Jones is a finite being and there are infinitely many numbers, surely we can find some really large number that Jones never went beyond when adding two numbers.
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Let us define a rule, called quaddition, which is just like addition except that when any of the two numbers are 5,000,000 or higher the result of the operation is 5. We can denote quaddition by a circled plus sign.
m⊕n=൜ 푚+푛,푖푓 푚,푛<5,000,0005,표푡ℎ푒푟푤푖푠푒
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If we look at all of Jones’ past uses of the term ‘plus’, it appears that he was just using addition. For example, he once uttered ‘50 plus 2 is 52’ and ‘4,500,000 plus 4 is 4,500,004’. So he could have meant addition by ‘plus’; and his meaning addition by ‘plus’ accords with all of his actual uses of ‘plus’. However, he could have meant quaddition instead. Since he never added two numbers that were greater than or equal to 5 million, we can’t distinguish between his meaning addition and his meaning quaddition. His meaning quaddition also accords with his actual uses of ‘plus’. We might not know whether he meant addition or quaddition, just by observing his past uses of ‘plus’. Is there anything that determines

2. whether he meant addition or quaddition? Is there anything that makes it true that Jones meant addition by ‘plus’? Forget about whether we can know if Jones means addition by ‘plus’. The question before us is whether there is any metaphysical fact which makes it the case that Jones means addition by ‘plus’.
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What do we mean by a metaphysical fact which makes it the case that Jones means addition by ‘plus’? To illustrate, consider this example: we can ask whether there is any fact which makes it the case that rubbing alcohol is flammable. The candidate fact could be that rubbing alcohol has a certain chemical composition, or the candidate fact could be that if rubbing alcohol were to be put in contact with fire it would catch on fire. In the case of Jones meaning addition by ‘plus’, the candidate fact might be something about Jones’ mental state or it might be something about his behavioral inclinations.
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Consider the assertion ‘Jones means addition by ‘plus’’. The question is whether there is any fact which makes the assertion true. This fact should settle the issue of which rule Jones means by ‘plus’-- whether Jones means addition or quaddition. Kripke’s Wittgenstein thinks that there is no fact which makes the assertion true.
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Here is what I take the skeptical argument to be:
The Skeptical Argument
P1) If there is a fact which makes the assertion true, then that fact is the unique fact which accords with Jones’ actual uses of the term ‘plus’.
P2) There is no unique fact which accords with Jones’ actual uses of the term ‘plus’.
C1) There is no fact which makes the assertion true.
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According to Kripke’s Wittgenstein, P2 is true because both addition and quaddition accord with Jones’ actual uses of the term ‘plus’. Jones has used ‘plus’ for numbers less than 5 million only. There is no unique rule which accords with Jones’ actual uses of the term ‘plus’. I agree with P2.

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However, the problematic premise is P1. It seems to me that Jones does mean addition by ‘plus’ and that there is a fact which makes this assertion about Jones true, even though there is no unique fact which accords with Jones’ actual uses of the term ‘plus’. What could the fact be that makes the assertion about Jones true? Here is a proposal: the fact which makes the assertion about Jones true is the fact that Jones means addition by ‘plus’. We can rely on Tarski’s truth schema.
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According to Tarski’s truth schema, the assertion ‘p’ is true just in case p. For example, the assertion ‘snow is white’ is true just in case snow is white. So, analogously, the assertion ‘Jones means addition by ‘plus’’ is true just in case Jones means addition by ‘plus’. We’ll call this the Tarskian solution.
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Another way to be suspicious of P1 is to accept the dispositionalist theory. Perhaps Jones could mean to use addition by ‘plus’ as opposed to quaddition. We can ask what Jones would have done if asked to apply ‘plus’ to 4 million and 5 million. If he gave 9 million as the answer, then he meant addition; but if he gave 5 as the answer, then he meant quaddition. This is the dispositionalist response. We say that Jones is disposed to answer addition questions by giving the sums of the two numbers. Dispositions are what make the assertion about Jones meaning addition true. Jones has the disposition to answer each potential addition problem with the sum of the two numbers.
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One problem with a dispositionalist theory is that it doesn’t satisfy the normativity thesis of meaning. The normativity thesis of meaning says that any candidate fact that makes it the case that Jones means addition by ‘plus’ must explain why Jones ought to respond to addition problems with sums. Just because Jones is disposed to answer correctly doesn’t explain why he ought to answer a certain way. For example, Jones may be disposed to respond to ‘’4 million plus 5 million’ with ‘9 million’ but this doesn’t

4. explain why he ought to respond with ‘9 million’. This seems like a plausible objection to dispositionalism.
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The normativity thesis of meaning appears to threaten the Tarskian solution as well. Recall that the Tarskian solution is the proposal that the fact which makes the assertion ‘Jones means addition by ‘plus’’ true is the fact that Jones means addition by ‘plus’. Does the fact that Jones means addition by ‘plus’ explain why he ought to give addition responses? I think it does. If Jones means addition by ‘plus’ and this entails responding to addition questions with sums, then Jones ought to respond to addition problems with sums. One ought to use ‘plus’ in the way one means to use ‘plus’. This normativity constraint seems to be a requirement of rationality. Jones could respond to addition problems with quaddition answers; but, in such cases, Jones would not be doing what he ought to do.
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Let me formulate the argument that the Tarskian solution does satisfy the normativity thesis of meaning.
P1) If Jones means addition by ‘plus’, then responding to addition questions with sums is required in order for Jones’ responses to be mathematically correct.
P2) If responding to addition questions with sums is required in order for Jones’ responses to be mathematically correct, then Jones ought to respond to addition problems with sums.
C1) If Jones means addition by ‘plus’, then Jones ought to respond to addition problems with sums. [P1 & P2]
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Note that the conclusion C1 is just what we need in order to show that the fact that Jones means addition by ‘plus’ explains why he ought to give addition responses. Let’s look at the premises of this argument.
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5. First, consider P1. This is fairly uncontroversial. If Jones means addition by ‘plus’, then given the problem ‘What is 500 plus 2?’ Jones is required to answer ‘502’ in order for Jones’ response to be mathematically correct.
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P2 is the crucial normative premise. It is an instance of a more general principle--that one ought to respond to factual questions correctly. Of course, one might want to deliberately mislead and give the wrong answer. However, assuming there is no such overriding desire or intention, there is a general expectation that one answer factual questions correctly.
We’ve shown that if Jones means addition by ‘plus’ then Jones ought to respond to addition problems with sums. So the fact that Jones means addition by ‘plus’ does explain why he ought to give addition responses.
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Conclusion
In this lecture, we’ve looked at the skeptical argument and have shown that it fails. We’ve seen that dispositionalism fails to satisfy the normativity thesis of meaning, and we’ve provided a Tarskian solution to the skeptical problem that meets the normativity thesis of meaning.