I'm writing a paper for a graduate "course" on skepticism, my first paper for a philosophy class in over a decade. (I say "course," because it is independent study: I have not been to any classes, and I have only met with the professor once, at which time we agreed on the topic of the paper without discussing anything of philosophical substance.) The assigned topic is "meaning skepticism." Here's a work-in-progress draft (sans references). Comments, criticism and questions are welcome, as always. I will probably add a bit at the end about Kripkenstein's "skeptical solution."

Two Problems with

Kripkenstein's Argument for

Meaning Skepticism

According to Saul Kripke, Wittgenstein produced “a new form of philosophical skepticism,” which I shall call meaning skepticism. Kripke does not give it this or any other name, though some commentators refer to it as rule skepticism. This may be justified by the fact that Wittgenstein frames the problem in terms of a paradox about following rules. Kripke quotes such a passage by way of introducing the problem: “This was our paradox: no course of action could be determined by a rule, because any course of action can be made out to accord with the rule.” However, while “rule skepticism” might be an apt name for Wittgenstein’s dilemma, it does not clearly fit the matter of Kripke’s concern. Kripke’s focus is entirely on meaning, or, more specifically, about intended meaning.

Though Kripke does not say so, he might not be surprised to have it pointed out that his focus differs from Wittgenstein’s. As Kripke acknowledges, he makes alterations to Wittgenstein’s argument, and not always in ways Wittgenstein would accept. In his own words, Kripke’s text “should be thought of as expounding neither ‘Wittgenstein’s’ argument nor ‘Kripke’s’: rather Wittgenstein’s argument as it struck Kripke, as it presented a problem for him.” Since the skeptical argument is not directly attributable to either Kripke or Wittgenstein, it is conventional to refer to it as “Kripke’s Wittgenstien” or even “Kripkenstein.” I will refer to it as “KW.”

KW’s skeptical position is that there are no facts about what people mean by their use of particular expressions. To put it another way, there are no conditions which could make attributions of meaning true or false. Consider the following example: A person says “68 plus 57 is 125.” If they are using “plus” to indicate addition, then “125” is the correct answer. However, KW says, there is no justification for claiming that they mean plus, and not quus. Quus is a function of Kripke’s own invention, and it goes as follows: x quus y = x plus y, if x,y < 57, else x quus y = 5. Since there is no fact about whether or not a person uses “plus” to mean plus and not quus, there is no fact about whether or not their calculation is correct. If they mean quus, then they should say “68 plus 57 is 5,” not “68 plus 57 is 125.” The skeptical position is that nothing justifies one answer as opposed to the other.

Note that the position is not that there are no rules as such. Nor is the position that there are facts about intended meaning, but only that we cannot know them. Rather, KW says there are no facts about what rule a person intends to follow by their use of a particular expression. KW’s skepticism is ontological, not epistemological, an it is about intended meaning, not rules. It is skepticism about the existence of facts which determine what people intend to mean with the use of linguistic expressions.

KW begins by describing a certain picture of what it means to grasp a rule:

I, like almost all English speakers, use the word ‘plus’ and the symbol ‘+’ to denote a well-known mathematical function, addition. The function is defined for all pairs of positive integers. By means of my external symbolic representation and my internal representation, I ‘grasp’ the rule for addition. One point is crucial to my ‘grasp’ of this rule. Although I myself have computed only finitely many sums in the past, the rule determines my answer for indefinitely many new sums that I have never previously considered. This is the whole point of the notion that in learning to add I grasp a rule: my past intentions regarding addition determine a unique answer for indefinitely many new cases in the future.

There is something wrong with this picture. First, let me emphasize the key points here: We grasp rules only via internal and external representations. Second, when we learn how to follow a rule, our intentions determine how we should answer certain sorts of questions which we have never before considered. When we successfully follow a rule, we intend to follow the same rule we learned in the past, and it is that rule which determines the answer we should give. Thus, to follow a rule is, in some sense, to do just the same as one has done before. The problem, then, is how we could ever suppose that a person has followed a rule for the first time. If, in order to follow a rule, you must intend to follow the same rule you had intended to follow in the past, then a person could never follow a rule for the first time. Nobody could ever learn how to follow a rule.

It might be supposed that a person can only follow a rule if they have learned to apply a particular mental representation. KW suggests as much by focusing on the need for mental representations. However, this runs into the same difficulty. The application of the representation must be learned, and this must entail yet another 'grasping' of yet another rule. The picture of grasping a rule, as presented, invites an infinite regress. It seems evident that we cannot stipulate that a person can only correctly follow a rule if they intend to follow the same rule they intended to follow in the past. I shall return to this point shortly. For now, let is see what KW does with this picture of ‘grasping a rule.’

Given the assumption that we have finite minds, KW supposes that there are numbers greater than any of the numbers we have added in our history of using “plus” and “+.” For example, we can imagine a person who has learned how to add but has only added numbers less than 57. We can even imagine that we are such a person, and that we have never solved “68 + 57.” While 57 is a rather low number, the point is a general one. It does not matter what numbers we choose as our example, so long as it is accepted that some numbers are greater than any we have added in the past.

Having established a framework for talking about rules, KW sets the stage for his skeptical challenge. Again, say in our entire history we have only added numbers less than 57. We are then asked to calculate “68 + 57.” We respond with “125.” Assuming “68”, “57” and “+” mean 68, 57 and plus, respectively, “125” is the arithmetically correct answer. However, KW identifies another sense in which this answer might be correct: in addition to the arithmetical sense, according to which 125 is the sum of 57 and 68, there is also the meta-linguistic sense, in which the term “plus” denotes the same function it was intended to denote in the past, such that, if I had been asked “What is 68 plus 57?” in the past, I would have applied the same rule then as I applied in the present case.

For the answer “125” to be correct, it is not enough that I mean plus by “plus” in the present. I must also have intended to mean plus by “plus” in the past. According to KW, my present meaning requires conformity with my past intentions. To correctly answer the question, I must not only provide the arithmetically proper result, but I must also use the language in the way I had previously intended.

This is precisely the point I find problematic. It is unreasonable—in fact, illogical—to suppose that I can only give the correct answer to a question if I intend to use my words in the same way I intended to use them in the past. As I shall now show, this weakens the force of KW’s skeptical challenge.

The meaning skeptic asks us to reveal the fact which constitutes our prior intention to mean plus by “plus” and thereby determines how we should respond to “68 + 57.” For example, asks the skeptic, how do we know that in the past, when we used “plus,” we did not mean quus? KW admits that the likelihood of anyone having ever meant quus by “plus” is extremely low, but it is not a priori inconceivable. We might imagine, he says, that we are currently experiencing an altered mental state (due to temporary insanity or a drug-induced hallucination, say) which prevents us from remembering how we used “plus” in the past. While we think we have always used "plus" to indicate addition, we actually used it to indicate quaddition.

There is no such fact, says KW. Therefore, there is no fact about our past intention. As a result, there is no fact of the matter about whether or not we are following the same rule in the present that we followed in the past. Since our ability to follow a rule was based on our ability to follow the same rule we followed in the past, we can no longer claim to have any ability to follow any rules. We cannot claim that we are following any rules at all when we use the term "plus." To put it another way, there is no fact of the matter about what we presently mean by "plus."

As I have suggested already, there need not be any fact about our past usage of an expression in order for there to be a fact about our present use of an expression. There need not be any past usage at all. Therefore, even if KW is right in claiming that there is no fact about our past intended meaning, it does not follow that there is no fact about our present intended meaning. Still, we might wonder, if there are no facts about our past meaning, how could there be any facts about our present meaning?

Before we let ourselves get distracted by that question, another question must be addressed: Can KW consistently maintain that there are no facts about our past meaning? I think the answer is "no."

Kripke notes that Wittgenstein does not distinguish between past and present intended meanings. He thinks his introduction of the past/present distinction is an improvement over Wittgenstein, whose own formulation Kripke believes is too confusing. In fact, Kripke says, if we do not distinguish between past and present intended meanings, the skeptical argument cannot be formulated at all. Any doubt about our present usage would have to be made by appeal to our present usage, and would thus be inconsistent. A person cannot coherently doubt what they mean by a term while they are using it. But, KW says, we can doubt our past use of a term without such difficulty: “if I use language at all, I cannot doubt coherently that ‘plus,’ as I now use it, denotes plus! Perhaps I cannot (at least at this stage) doubt this about my present usage. But I can doubt that my past usage of ‘plus’ denoted plus. The previous remarks – about a frenzy and LSD – should make this quite clear.”

Yet, a related difficulty does arise and it confounds KW’s argument. Consider how KW’s skeptic operates: A person is asked how they know they meant plus, and not quus, in the past. They say that they remember learning that ‘plus’ denotes a rule that is applied in the same way for all positive integers, so it could not have been quus. KW responds: How do you know that when you used “positive integers” in the past, you did not mean positive integers less than 57? Perhaps we answer that we remember learning that “positive integers” refers to an infinite set of numbers, but the skeptic continues: How do you know you used “infinite” to mean infinite? The skeptical challenge, then, is to ground our use of expressions to denote rules without appealing to more expressions denoting those same rules. To answer the skeptic, we must get outside of our language. We must show facts which connect our words to the rules they purport to express. KW says no such facts exist. That is the skeptical position.

My concern at present is not with the skeptical position, but with KW’s argument. Again, KW says no facts exist which determine what we meant by “plus” in the past. However, KW does not consistently maintain this position. Recall that KW appeals to ideas about insane frenzies and drug-induced hallucinations to cast doubt on the integrity of our pedagogical histories. KW does not ultimately want to suppose that there is anything wrong with our memories. If the skeptical position were based on appeals to psychological dysfunction, it could only be regarded as an epistemological form of skepticism: While there may have been facts about how we learned to use certain expressions, we cannot know them, because our memories are not reliable. Yet, KW does not draw an epistemological conclusion. KW explicitly denies that our inability to show facts about what we meant in the past are the result of any psychological or mental limitations: “nothing in my mental history or past behavior – not even what an omniscient God would know – could establish whether I meant plus or quus.” The appeal to frenzies and LSD is “a dramatic device” which is only meant to show that our past usage might not be the same as our present usage. It is not meant to show that we are psychologically limited in our access to the relevant facts.

This does not work. KW’s argument relies on there being an unobserved change in usage between our past and present utterances of “plus,” such that our present usage no longer conforms to the rule we had originally learned. Whether it was through drugs, insanity, or some less suspicious means, we no longer mean by “plus” what we once meant. This is a change in our mental — our intentional — history. Thus, KW is explicitly relying on facts about our past usage of the term “plus.” If there is some fact about my mental history, such that it marks a shift in my usage of the term “plus,” then there is some fact about what I meant by “plus” in the past. KW thus both appeals to and denies that there are facts about our past usage of expressions. As a result, KW’s argument is inconsistent and cannot sustain meaning skepticism.

I suppose any attempt to formulate meaning skepticism will run into such a problem. We cannot doubt that we mean anything by our present expressions, nor can we doubt that we mean one thing as oppose to another. Indeed, we cannot claim that meaning skepticism is true, because if it were, nobody could intend to use "meaning skepticism" to denote meaning skepticism. Meaning skepticism does not appear to be a coherent philosophical position. It is no wonder that KW's argument is invalid and rests on a faulty picture of 'grasping a rule.'

Nevertheless, KW has challenged us to identify what facts comprise our intending to follow one rule rather than another. While KW’s skeptical position does not appear to constitute a direct threat to notions of intended meaning, it does invite closer inspection of the phenomena of rule-following and intentionality.


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