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Notre Dame Philosophical ReviewsThis is a superb book. . . . Taking Wittgenstein at his word, as Fogelin has done, is a far, far deeper thing than taking him at face value.
— Anat Biletzki
Taking Wittgenstein at His Word is an experiment in reading organized around a central question: What kind of interpretation of Wittgenstein's later philosophy emerges if we adhere strictly to his claims that he is not in the business of presenting and defending philosophical theses and that his only aim is to expose persistent conceptual misunderstandings that lead to deep philosophical perplexities? Robert Fogelin draws out the therapeutic aspects of Wittgenstein's later work by closely examining his account of...
Taking Wittgenstein at His Word is an experiment in reading organized around a central question: What kind of interpretation of Wittgenstein's later philosophy emerges if we adhere strictly to his claims that he is not in the business of presenting and defending philosophical theses and that his only aim is to expose persistent conceptual misunderstandings that lead to deep philosophical perplexities? Robert Fogelin draws out the therapeutic aspects of Wittgenstein's later work by closely examining his account of rule-following and how he applies the idea in the philosophy of mathematics.
The first of the book's two parts focuses on rule-following, Wittgenstein's "paradox of interpretation," and his naturalistic response to this paradox, all of which are persistent and crucial features of his later philosophy. Fogelin offers a corrective to the frequent misunderstanding that the paradox of interpretation is a paradox about meaning, and he emphasizes the importance of Wittgenstein's often undervalued appeals to natural responses. The second half of the book examines how Wittgenstein applies his reflections on rule-following to the status of mathematical propositions, proofs, and objects, leading to remarkable, demystifying results.
Taking Wittgenstein at His Word shows that what Wittgenstein claims to be doing and what he actually does are much closer than is often recognized. In doing so, the book underscores fundamental—but frequently underappreciated—insights about Wittgenstein's later philosophy.
"[Taking Wittgenstein at His Word] is a thought-provoking study that gives those interested in Wittgenstein much to ponder. For that reason, I feel I can confidently recommend TWHW, both to those just beginning to explore Wittgenstein's work and to serious scholars."—Joshua McNutt, Dialogue
I want to regard man here as an animal; as a primitive being to which one grants instinct but not ratiocination. (OC 475)
The Paradox of Interpretation
Readers of Philosophical Investigations are familiar with the story of the child being taught to produce the series of even numbers starting with 2. She starts out well enough, writing down 2, 4, 6, 8. However, when asked to pick up the series at 1000, she writes down 1000, 1004, 1008, 1012 (PI 183). Told that she is no longer following the instructions we gave her-no longer doing the same thing-she replies that she is, perhaps saying, "Look, see for yourself!" The rub is this: Whatever she writes down, there will be some interpretation of the instructions we gave her-indeed, endlessly many interpretations-such that she has acted in conformity with the rule, and endlessly many interpretations such that she has not. Hence we arrive at what Wittgenstein calls a paradox:
PI 201. This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule. The answer was: if everything can be made out to accord with the rule, then it can also be made out to conflict with it. And so there would be neither accord nor conflict here.
Saul Kripke opens his second chapter of Wittgenstein on Rules and Private Language citing this passage. Then, after a detailed discussion intended to show the force of the paradox, he begins his third chapter with an account of what he thinks Wittgenstein (not the Janus-figure Kripkenstein) is trying to establish.
The skeptical argument, then, remains unanswered. There can be no such thing as meaning anything by any word. Each new application we make is a leap in the dark; any present intention could be interpreted so as to accord with anything we may choose to do. So there can be neither accord, nor conflict. This is what Wittgenstein said in PI 201. (Kripke 1982, p. 55)
Contrary to Kripke's claim, in PI 201 Wittgenstein does not say that his paradox shows that there can be no such thing as meaning anything by any word. He does not say this anywhere else. This is what he says instead:
PI 201. It can be seen that there is a misunderstanding here from the mere fact that in the course of our argument we give one interpretation after another; as if each one contented us at least for a moment, until we thought of yet another standing behind it. What this shows is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call "obeying the rule" and "going against it" in actual cases.
Here, Wittgenstein (rather uncharacteristically) is perfectly straightforward in explaining the point he is trying to make. What the paradox shows, he says, "is that there is a way of grasping a rule that is not an interpretation." Surprisingly-actually, incredibly-Kripke never cites this passage in Wittgenstein on Rules and Private Language and thus misses what I take to be the central moral of Wittgenstein's paradox: Rule-following cannot be made determinate-or, by extension, meanings cannot be fixed-through interpretation alone.
Wittgenstein has no brief against rule-following, and no brief against meaning either. He does not think that either rule-following or meaning is inherently paradoxical. His target is a certain account of rule-following (or account of meaning) that, he shows, leads to a paradox. We might call it the interpretational account. To fix this firmly in mind, from now on I will talk about Wittgenstein's paradox of interpretation. The paradox is this: If we hold that following a rule always involves acting in conformity with an interpretation, then whatever we do will count as both following the rule and not following the rule. Can't this matter be resolved by declaring what interpretation we are acting under? This will not help, for it simply reinstates the paradox of interpretation: Whatever we say about our intended interpretation will also admit of various interpretations. No interpretation can stop this regress; none has a built-in immunity to further interpretation. There are, we might say, no self-interpreting interpretations.
Just as Wittgenstein is not a skeptic concerning meaning, he has no axe to grind concerning interpretations either-provided, that is, that they are understood as a special kind of activity that takes place within language and not as something that lies at its foundation. I take it this is what Wittgenstein has in mind when he says, "We ought to restrict the term 'interpretation' to the substitution of one expression of the rule for another" (PI 201). If someone does not act appropriately when instructions are expressed one way, it may help to express them differently. Wittgenstein is not opposed to interpretations understood this way. What he does oppose is the claim (or assumption, or inclination to think) that every meaningful application of a term involves an act of interpretation. Taking him at his word encourages us to see what else Wittgenstein says about the role of interpretation in fixing meaning. What we discover is that the paradox of interpretation is not narrowly tied to Wittgenstein's concerns with private rule-following and the possibility of a private language. The paradox of interpretation is, instead, a recurrent and central feature throughout Wittgenstein's later philosophy. A case can be made for saying that it was part of the original complex of commitments that gave Wittgenstein's later philosophy its characteristic physiognomy. Such a claim is worth showing.
As far as I have been able to discover, the paradox of interpretation makes its first appearance early in Philosophical Grammar, a compilation of notes written by Wittgenstein during the years 1932-34. Wittgenstein imagines someone being ordered to square the integers, beginning with 1.
It seems to us as if by understanding the order we add something to it, something that fills the gap between command and execution. So that if someone said "You understand it, don't you, so it is not incomplete" we could reply "Yes, I understand it, but only because I add something to it, namely the interpretation."-But what makes you give just this interpretation? Is it the order? In that case it was already unambiguous, since it demanded this interpretation. Or did you attach the interpretation arbitrarily? In that case what you understood was not the command, but only what you made of it.
(While thinking philosophically we see problems in places where there are none. It is for philosophy to show that there are no problems.)
But an interpretation is something that is given in signs. It is this interpretation as opposed to a different one (running differently). So if one were to say "Any sentence still stands in need of an interpretation" that would mean: no sentence can be understood without a rider.
Of course sometimes I do interpret signs, give signs an interpretation; but that does not happen every time I understand a sign. (If someone asks me "What time is it?" there is no inner process of laborious interpretation; I simply react to what I see and hear. If someone whips out a knife at me, I do not say "I interpret that as a threat"). (PG I 9)
Though Wittgenstein does not use the term "paradox," the paradox of interpretation is already in place in this work from the early 1930s. The parenthetical remark in the center of this passage indicates that Wittgenstein's therapeutic program of dissolving philosophical problems is also in place.
The closing sentences of the passage from Philosophical Grammar anticipate what I now call Wittgenstein's defactoist response to the paradox-our next topic.
A Defactoist Account of Rule-Following
If Wittgenstein rejects the interpretational account of rule-following, what kind of account of rule-following does he put in its place? More specifically, how does he avoid the paradox that confronts the interpretational account? In Wittgenstein, I assumed that Wittgenstein was confronted with a genuine paradox and held, alluding to Hume's Enquiry Concerning Human Understanding, that he offers only a skeptical solution to his paradox.
Hume proceeded in the following way: After arguing in section 4 of the Enquiry that it is not possible to provide a rational grounding for inductive inferences, he turns to the task of describing how, despite the lack of a rational grounding, human beings do, after all, form beliefs on the basis of experience. This descriptive activity does not answer the skeptical challenge raised in section 4. Hume did not intend it to. It is in this sense that I took-and still take-Hume's solution to be a skeptical solution. In calling Wittgenstein's response to his paradox a skeptical solution, I was clearly suggesting that Wittgenstein also despaired of solving his paradox and had no other choice but to fall back on a descriptive activity.
I now think this comparison is in some ways right and in some ways wrong. For Hume, the skeptical argument concerning induction is unanswerable. There is no way of rationally ruling out the possibility that the course of nature might change, so we will forever make our inductive inferences under an irremovable threat. For Hume, the Humean predicament is a human predicament. In contrast, I now think that Wittgenstein does not hold that the paradox of rule-following is unavoidably thrust upon us as something we will have to learn to live with. To put the matter more strongly, for Wittgenstein there is no "paradox" of rule-following. The thought that it is paradoxical is the product of a misconception, namely, the misconception that rule-following is always grounded in (or implicitly contains) acts of interpretation.
Even if Hume sees himself confronted with an unanswerable challenge and Wittgenstein does not, in the tales they tell both of them demote the intellect to a subservient status. Both, to put it quaintly, ground our intellectual capacities in our animal natures. Hume in his Enquiry Concerning Human Understanding puts it this way:
Experimental reasoning itself, which we possess in common with beasts, and on which the whole conduct of life depends, is nothing but a species of instinct or mechanical power, that acts in us unknown to ourselves; and in its chief operations, is not directed by any such relations or comparisons of ideas, as are the proper objects of our intellectual faculties. (Enquiry, section 9; Hume 1999, p. 168)
Speaking more specifically about language, Wittgenstein expresses a parallel commitment in these words:
OC 475. I want to regard man here as an animal; as a primitive being to which one grants instinct but not ratiocination. As a creature in a primitive state. Any logic good enough for a primitive means of communication needs no apology from us. Language did not emerge from some kind of ratiocination.
Both Hume and Wittgenstein stress the importance of primitive natural responses shaped through training and other forms of conditioning. This is ground-floor for both. For Hume, going any deeper in exploring the operations of the human understanding is beyond our intellectual capacities. For Wittgenstein, it is an illusion to suppose that there has to be something deeper, even if hidden, that could provide such an explanation. This is an important difference-one that I did not formerly appreciate sufficiently. Still, important similarities remain, as we shall see in examining Wittgenstein's detailed remarks on rule-following.
The Communitarian versus the Defactoist Account of Rule-Following
How, precisely, does Wittgenstein give an account of rule-following that avoids the difficulties found in the interpretational account? An answer is sketched in PI 198-a section of central importance for understanding Wittgenstein's account of rule-following, and one, I think, that has often been misunderstood. It begins with a statement of the paradox of interpretation:
PI 198. "But how can a rule show me what I have to do at this point? Whatever I do is, on some interpretation, in accord with the rule."-That is not what we ought to say, but rather: any interpretation still hangs in the air along with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning.
Then Wittgenstein has an interlocutor intervene, asking a perfectly natural question:
"Then can whatever I do be brought into accord with the rule?"
Speaking in his own voice, Wittgenstein responds:
Let me ask this: what has the expression of a rule-say a sign-post-got to do with my actions? What sort of connexion is there here? Well, perhaps this one: I have been trained to react to this sign in a particular way, and now I do so react to it.
Wittgenstein speaks for the interlocutor and raises a further objection:
But that is only to give a causal connexion; to tell how it has come about that we now go by the sign-post; not what this going-by-the-sign really consists in.
On the contrary; I have further indicated that a person goes by a sign-post only in so far as there exists a regular use of sign-posts, a custom.
For reasons I do not understand, the closing sentence, with its reference to custom, seems to cloud the minds of many commentators with respect to the references to training that precede it. It also induces a subsequent blindness to the frequent references to training that will follow. Although there is overwhelming textual support-passage after passage-for assigning a central role to natural responses and training in Wittgenstein's account of rule-following, many commentators assign relatively little importance to them and have instead taken a quite different approach, maintaining that Wittgenstein attempts to deal with this paradox by invoking some form of communitarianism.
The communitarian response to the paradox can be implemented in various ways. Broadly speaking, it goes something like this. The community provides what an isolated speaker cannot provide: an independent standard for determining whether a rule has been followed correctly or not. This can be spelled out in various ways. We might insist that an individual interpret the rule as members of the community interpret it, or at least insist that the individual's action conform to the rule as the community interprets it. It is, however, hard to see how such a maneuver will get us out of our difficulties, for the paradox of interpretation breaks out anew, now at the community level. Whatever the members of the community do, or say they are doing, under some interpretations of their rules their actions will conform to them, and under others they will not. Wittgenstein's claim that "there is a way of grasping a rule which is not an interpretation" is not restricted in its scope. It applies to individuals and communities alike. Applied to communities of language users, the moral to the paradox of interpretation is that there must be a way for the community to grasp a rule that is not an interpretation-communal or otherwise. As we shall see, communitarianism does have an important role to play in Wittgenstein's understanding of rule-following, but it does not, by itself, provide the remedy for the paradox of interpretation.
Excerpted from TAKING WITTGENSTEIN AT HIS WORD by Robert J. Fogelin Copyright © 2009 by Princeton University Press. Excerpted by permission.
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Conventions for Citations and Abbreviations xvii
Introduction: Respecting the Text 1
PART I: RULE-FOLLOWING AND THE CONCEIVABILITY OF A PRIVATE LANGUAGE 13
Chapter One: On Following a Rule 15
Chapter Two: The Conceivability of a Private Language 56
PART II: WITTGENSTEIN ON THE PHILOSOPHY OF MATHEMATICS 79
Chapter Three: The Status of Mathematical Expressions 83
Chapter Four: Wittgenstein on the Mysteries of Mathematics 116
Chapter Five: Wittgenstein on Logical Consistency 139
Posted January 25, 2010
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