The problems arising through a misinterpretation of our forms of language have the character of depth. They are deep disquietudes; their roots are as deep in us as the forms of our language and their significance is as great as the importance of our language.—Let us ask ourselves: why do we feel a grammatical joke to be deep? (And that is what the depth of philosophy is.)
(Wittgenstein 1958, 111)
The logician and mathematician, Reverend Charles Dodgson, better known by his pseudonym, Lewis Carroll, is famous for his linguistic humor. In Alice’s Adventures in Wonderland, the Duck inquires in vain for the referent of “it” in the Mouse’s lecture: “Stigand, the patriotic archbishop of Canterbury, found it advisable . . . to go with Edgar Atheling. . . . ” The Duck assumes the “it” should be something particular such as a frog or a worm. But the Mouse is using “it” as a dummy pronoun; it is inserted to appease a grammatical hunger for an object term. If David Hume is correct, Descartes may be like the Duck when searching for the referent of “I” in “I think, therefore, I exist.”
Dodgson’s whimsy carried over to his recreational mathematics. Interestingly, he believed these riddles could serve the serious purpose of spiritual protection. In his introduction to Pillow Problems, he writes, “There are sceptical thoughts, which seem for the moment to uproot the firmest faith: there are blasphemous thoughts, which dart unbidden into the most reverent souls; there are unholy thoughts, which torture, with their hateful presence, the fancy that would fain be pure. Against all these real mental work is a most helpful ally.” The puzzles should be challenging but not too difficult. Veterans of sensory deprivation chambers recommend that you pass the time by posing intellectual challenges: reciting the alphabet backwards, listing all the prime numbers less than a hundred, etc. They caution that the problem must be definitely soluble. If you have the misfortune of picking a question that you cannot answer, you will not be able to switch the topic. You will come to hate the question but will not be able to stop thinking about it.
Paradoxes parasitized the attention of Bertrand Russell’s protégé, Ludwig Wittgenstein. Wittgenstein (1889-1951) was repulsed by philosophers who had actually grown fond of the Eternal Questions. He philosophizes only in the hope of ending his compulsion to answer.
When Leo Tolstoy was a boy, his older brother challenged him to stand in the corner until he stopped thinking about a white bear. The more little Leo tried to stop thinking about a white bear, the more he thought about it. He only stopped thinking about the white bear when he became distracted. People who are plagued by obsessional thoughts cannot simply decide not to think those thoughts. Relief comes involuntarily. At best, the obsessive thinker can cultivate a lapse of attention by altering his circumstances.
Wittgenstein distracted himself by watching American movies, preferably westerns. He would sit in the front row eating pot pies, completely engrossed. He also read detective stories (as do many philosophers—perhaps out of a hunger for resolution). However, such diversions only supplied a few hours of relief to Wittgenstein. His only sustained period of peace came after the publication of his Tractatus in 1921. Thinking that he had exposed all philosophical problems as violations of an ideal grammar, he retired from philosophy to become an elementary school teacher in the remote Austrian village of Trattenbach.
Eventually Wittgenstein became persuaded that this ideal language was itself delusory and so restlessly returned to Cambridge University in 1929. In the following decade, he pieced together “ordinary language philosophy.” With much self-recrimination, Wittgenstein renounced his earlier demand that grammar meet the a priori requirements of logic. Instead of trying to think of how language must operate, he resolved to observe how speakers actually behave. From this anthropological perspective, a natural language such as English resembles London—a living, growing city with ancient roots. There are modern sections laid out neatly in grids. But many other neighborhoods sprawl haphazardly. London cannot be defined in a day. It is a motley of overlapping institutions. All of the useful generalizations must be hedged and local. Paradoxes arise when we overextend analogies, when we lift expressions out of context, and when we disengage patterns of discourse from their practical (and impractical) purposes.
According to Wittgenstein, most paradoxes can be nipped in the bud by bringing words back into their natural settings, by studying how they are taught to children, and by noting the role they in play in larger practices. To avoid being overwhelmed by complexity, he also considers simplified language games. But these artificial specimens should not be treated as ideals that ordinary language imperfectly approximates. We easily slip on the ice of idealization. We steady our thinking by constantly returning to the rough ground.
In some circumstances, we may find that the rules of language really lead to a contradiction. Russell and Frege treated contradictions as crises. But Wittgenstein compared news of a contradiction to the discovery that a game has a loophole that would guarantee a trivial victory. If there is trouble, we may close the loophole on an ad hoc basis. If people do not actually exploit the loophole, then no repair is needed. We can live with some paradoxes. Perhaps some of them, such as the problem of freewill, will occasionally trouble us in a practical way. After all, we must sometimes judge hard cases involving addiction, compulsion, and duress. But the appropriate reaction is to make small adjustments. We should not replace the arthritis of common-sense with the prosthesis of metaphysics.
Sextus Empiricus tried to end philosophical inquiry by any means available, rational or irrational. If there were a safe antiphilosophy pill, Sextus would have prescribed it. Wittgenstein opposes noncognitive cures. He thinks that freedom from philosophical worries must proceed through insights into how language sets traps for us.
The meaning of names seems especially simple. When Abraham Lincoln uttered “Fido” the word’s meaning was its bearer: Lincoln’s floppy-eared, rough-coated, yellowish dog of uncertain ancestry. In Plato’s dialogues, Socrates naively extends the “Fido”/Fido model to terms such as “courage,” “knowledge,” and “good.” Since there are no mundane bearers of these words, Socrates infers that there must be transcendental bearers: the forms of courage, knowledge, and goodness. This subliming of the language leads to a cluster of problems about universals. Can a universal exist without instances? Must each pair of universals be related by a higher universal? How can material beings know anything about these abstract entities?
Wittgenstein maintains that if we look at how we actually use words, we see there is often no feature that is common and peculiar to all uses. In the case of “game,” there is only a network of overlapping similarities—a family resemblance. Thus, the Socratic demand for definition rests on the false presupposition that there is some common thread binding all uses of a term.
The “Fido”/Fido model also lurks behind key paradoxes in the philosophy of the mind. We presuppose that words such as “headache” have bearers. Since the bearer cannot be physical, we infer there is a mental bearer. On the one hand, this nonphysical entity seems elusive because it is not open to public view. Hence, there is no independent check on whether it is present. On the other hand, pain seems like the easiest thing to know. The sufferer of a headache cannot falsely believe he has a headache. And if he has a headache, he cannot fail to notice it. For pain, to be is to be perceived. This private realm of entities is easily seen as the best known realm for the person who hosts them. Thus, it becomes tempting to view the mental realm as the foundation of all other knowledge. The mental realms of other people are unavailable to your inspection, hence you seem particularly ill suited to judge whether others have the same sort of ideas as you do or even whether they have such ideas at all. The external world as a whole looks like something we must audaciously infer on the basis of our own ideas. At bottom, what you know best are your own ideas. At bottom, what you are really talking about are ideas that you are having or might have. Since these ideas are necessarily your ideas and ones about which you cannot be mistaken, each of us is really speaking a private language. Communication is impossible because our languages do not have any words or sentences that mean the same thing. We can neither agree nor disagree with each other.
Wittgenstein argues that a private language is impossible. A rule that only you can follow is a rule that cannot sustain the contrast between obeying the rule and violating the rule. If there is no way to get it wrong, there is no way to get it right. Private rule is a contradiction in terms. Private languages must be defined with private rules. Therefore, there can be no private languages.
Wittgenstein also challenges the assumption that “pain” refers to anything. He suggests that “I have headache” does not report a headache; it expresses pain like a groan. Instead of clutching your forehead in misery, you substitute a piece of verbal behavior. “The paradox disappears only if we make a radical break with the idea that language always functions in one way, always serves the same purpose; to convey thoughts—which may be about houses, pains, good and evil, or anything else you please.” (1958, 304) Wittgenstein encourages the development of alternatives to his avowal theory of “pain.” Wittgenstein’s point is not to substitute a philosophical theory with another philosophical theory. He does not trace philosophy’s problems merely to the choice of false premises. Wittgenstein thinks the real problem is that we feel compelled to choose premises.
The Scottish writer Robert Louis Stevenson was fond of a little girl who complained about being born on Christmas Day. Instead of receiving presents on two days of the year, she only received them on one. In his will, Stevenson bequeathed the girl his own birthday. He appended the following clause: “If, however, she fails to use this bequest properly, all rights shall pass to the President of the United States.”
Stevenson’s “bequest” shows that a birthday is not a possession that can be transferred. This moral resembles philosophical remarks about limits. A philosopher who is faced with the problem of other minds remarks, “I cannot feel your pain.” It is helpful to compare the deep privacy of pain to the shallow privacy of birthdays.
Wittgenstein “once said that a serious and good philosophical work could be written that would consist entirely of jokes (without being facetious). Another time he said that a philosophical treatise might contain nothing but questions (without answers).” (Malcolm 1958, 29) In his Philosophical Investigations, Wittgenstein often blends jokes and questions:
Why can’t a dog simulate pain? Is he too honest?
Why can’t my right hand give my left hand money?
Why does it sound queer to say: “For a second he felt deep grief?” (Only because it so seldom happens?)
(1958, 250, 268, II, i)
Anthony Kenny, a methodical Wittgenstein scholar, reports that Philosophical Investigations contains 784 questions; 110 are answered and 70 of these answers are meant to be wrong.
Wittgenstein says his aim is “to teach you to pass from a piece of disguised nonsense to something that is patent nonsense.” (1958, 464) For instance, one might compare “Where does an idea go after it has been thought?” with “Where does a flame go after it goes out?.” Since jokes and riddles are succinct, acknowledged cases of patent nonsense, they are handy candidates for these logical analogies.
Other “ordinary language philosophers” tried to defuse philosophical problems by drawing analogies with manifest linguistic absurdities. Gilbert Ryle’s The Concept of Mind frequently accuses René Descartes of committing “category mistakes.”
A man would be thought to be making a poor joke who said that three things are not rising, namely, the tide, hopes, and the average age of death. It would be just as good or bad a joke to say that there exist prime numbers and Wednesdays and public opinions and navies; or that there exist both bodies and minds.
(1949, 23)
Wittgenstein thought similar limits are revealed by philosophical remarks such as “The colors green and blue cannot be in the same place simultaneously.”
Ordinary language philosophy is an abridged descendant of common-sense philosophy. Contrary to the expectations of Thomas Reid, several common-sense beliefs have been overturned by post-eighteenth-century physics. Principles that hold for medium-size objects in familiar conditions break down at the scales studied by astronomers and microphysicists. To avoid encroaching on science, ordinary language philosophers only retain the linguistic aspect of Reid’s philosophy. They restrict themselves to making remarks about how language operates. As native speakers of English, they have mastered its rules and can judge whether sentences are part of English. Sadly, we do not have direct access to the rules we are employing. We must infer the rules from data about which sentences belong to English. Statements of the rules of language are analytic. They are not remarks about the world. This explains why philosophy can be done from the armchair. Philosophy, like mathematics, is an a priori field.
In practice, ordinary language philosophers exploited empirical clues as to what the rules might be. We know that English cannot be composed of infinitely many independent rules because that would make the language unlearnable. Wittgenstein frequently appeals to functions of language when suggesting how conventions are organized. But this “peeking” is much like the informal testing geometers employ to guide their conjectures. The statements themselves are a priori even if we actually used an a posteriori mode of investigation. (What matters is that the statement could have been learned without experience.)
When we use language properly, our problems are well structured: there is always an answer even if it turns out that we cannot learn the answer. With philosophical questions, we fall into dazzled confusion as to what would even count as an answer. This sentiment dates back to Wittgenstein’s Tractatus period:
Most of the propositions and questions to be found in philosophical works are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only establish that they are nonsensical. Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language.
(They belong to the same class as the question whether the good is more or less identical than the beautiful.)
And it is not surprising that the deepest problems are in fact not problems at all.
(1969a, 4.003)
There are no answers to philosophical questions because there really are no such questions; there are merely pseudoproblems that masquerade as questions. A field makes progress only by answering questions, so philosophical progress is impossible. (“The riddle does not exist. If a question can be put at all, then it can also be answered.”) At best, one can dissolve philosophical problems by showing how they arise from misunderstandings of how our language works.
The later Wittgenstein never presents a definitive resolution of a paradox. He only hints and sketches, encouraging others to think for themselves. His followers did attempt to dissolve a paradox that Jean Paul Sartre popularized in the 1950s: Is self-deception possible? I suspect the ordinary language philosophers targeted this paradox partly out of envy and resentment. While the British philosophers were dismissed by bored book reviewers as “verbosophers,” the French existentialists were lionized as beacons of culture. Sartre, Simone de Beauvoir, Albert Camus, André Malraux were celebrities. Like the Stoics, they offered an integrated vision of reality and the human condition. They honored character traits that give rise to philosophy. The existentialists met their public halfway by presenting their views in literature and plays. The cloistered Wittgensteinians were just curing each other.
In Being and Nothingness, Sartre observes that self-deception seems to be an all-too-common phenomenon. Yet, there is a compelling objection to its very possibility. To be a deceiver, one must not believe the deception, but the victim must believe the deception. Since it is impossible to both believe and not believe the deception, self-deception is impossible.
One popular way to disarm the contradiction is to divide the self into parts, homunculi, and say one homunculus is deceiving another homunculus. The danger of an infinite regress becomes apparent when we ask whether homunculi can themselves be self-deceived. Answering no is ad hoc: any creature that is sophisticated enough to deceive others is sophisticated enough to apply the same trick to itself. If the homunculi can deceive themselves, then we must postulate subhomunculi, and sub-subhomunculi, and so on.
Perhaps a metaphysical psychologist would welcome the implication that each self is composed of infinitely many selves. Wittgensteinians would recoil. Instead of postulating an infinite hierarchy of subselves, ordinary language philosophers trace the difficulty to misleading surface grammar. The statement “King George IV deceived himself into believing that he fought at Waterloo” looks like it uses “deceive” in the same sense as “King George IV deceived Princess Caroline of Brunswick into believing he fought at Waterloo.” But the Wittgensteinians denied that the “deceive” in self-deception is used in the same sense as the “deceive” in other-deception. They compared “deceive yourself” to “invite yourself,” “defeat yourself,” and “teach yourself.” You invite yourself to a party if you attend without an invitation. When you defeat yourself, you are not both victor and vanquished; you are just the main reason why someone else defeated you. We can feign a paradox for “Abraham Lincoln was self-taught” by modeling self-teaching on the teaching of others: As teacher, Lincoln knows the lesson. As student, Lincoln does not know the lesson. Therefore, Lincoln both knows and does not know the lesson!
Any puzzlement generated by this sophistry rests on a determination to model self-teaching on other-teaching. We should instead approach reflexive expressions with respect for the idiosyncrasies of language. Yes, reflexive expressions do suggest that they all have the logical form “a bears relation R to itself.” But no, this surface grammar sometimes masks a very different depth grammar. In particular, “ . . . we say when ‘Jones deceives himself about P’ is true, it is true that Jones believes P under belief-adverse circumstances, e. g., circumstances such that the evidence Jones has does not warrant belief in P.” (Canfield and Gustavson 1962, 32) This paraphrase “self-deception” aims to condense a “cloud of philosophy into a drop of grammar.”
As a byproduct of linguistic therapy, we may learn how language works. But this incidental progress in linguistics is not philosophical progress. Helpful philosophy is like medicine. The physician only offers the patient relief from a bad thing. He may make discoveries of scientific interest along the way, but these advances are not the aim of medicine. When the philosopher unties a conceptual knot, there is no positive philosophical residue.
Wittgenstein contrasts the way children learn to recite the alphabet with the way they learn to recite numerals: “There are two ways of using the expression ‘and so on’. If I say, ‘The alphabet is A, B, C, D, and so on’, then ‘and so on’ is an abbreviation. But if I say, ‘The cardinals are 1, 2, 3, 4, and so on’, then it is not.” (1976, 170-71) A child learns the alphabet by memorizing a complete list. If you give him the letters up to G, you cannot expect him to extrapolate to H, I, J, K. In contrast, a child cannot learn an endless list of number words by rote. He must learn to continue on his own.
How did you manage to master the rule for extending numerical sequences endlessly? Even simple continuations require adding. How did you learn “plus”? Saul Kripke (1982) credits Wittgenstein with the discovery of a skeptical paradox about rule following. Suppose you have never computed 68 + 57 before. You answer 125, confident that this corresponds to your past usage of “plus.” A skeptic questions your certainty: perhaps your past usage requires that the answer be 5. After all, there are indefinitely many rules that could have yielded your past results. How do you know which rule you intended?
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.
(1958, 201)
Kripke says Wittgenstein solves the paradox by denying that rule following involves self-interpretation. Instead, we are just trained to use words. Our mastery of a rule is a matter of being inducted into a linguistic practice.
Many philosophers think Kripke is perverting the aim of Wittgenstein’s therapy. Wittgenstein had no interest in discovering new paradoxes. He only wanted to eliminate old ones. If Wittgenstein were right about paradoxes being pseudoproblems, then it should not be possible to solve them.
However, Wittgenstein regularly relapses into the kind of philosophizing he renounces. He is not immune to the charm exerted by an answer “which sets the whole mind in a whirl, and gives the pleasant feeling of paradox.” (1976, 16) Like a fellow alcoholic, Wittgenstein identifies with Cantor when he giddily concludes that there are infinitely many infinitely large numbers. Wittgenstein thinks Cantor invented the transfinite numbers while under the influence of an alluring interpretation of “1, 2, 3, 4, . . . . ” He speculates that “The dots introduce a certain picture: of numbers trailing off into the distance too far for one to see. And a great deal is achieved if we use a different sign. Suppose that instead of dots we write, then ‘1, 2, 3, 4, Δ’ is less misleading.” (1976, 170) Dr. Seuss’s On Beyond Zebra opens with a young boy proudly writing on a blackboard. Conrad Cornelius o’Donald o’Dell, has demonstrated his exhaustive knowledge of the alphabet: A is for Ape, B is for Bear, . . . and Z is for Zebra. An older boy compliments Conrad. He breezily concedes to young Conrad that most people stop with Z. But his alphabet continues beyond Z. The extra letters let him spell new things. The older boy thus introduces Conrad to an otherwise inaccessible realm of exotic creatures. For instance, the Q-ish letter quan is for the vertically symmetric Quandary who lives on a shelf.
In a hole in the ocean alone by himself
And he worries, each day, from the dawn’s early light
And he worries, just worries, far into the night.
He just stands there and worries. He simply can’t stop . . .
Is his top-side bottom? Or bottom-side top?
The tour given to Conrad would put Wittgenstein in mind of other never-never lands.
Wittgenstein insists that he does not wish to replace one philosophical theory with another. But he frequently does just that. He advances, albeit guardedly, the use theory of meaning, the avowal theory of pain, the doctrine of family resemblance, etc. Despite poking fun at the philosopher’s preoccupation with limits and impossibility results, Wittgenstein is known for his refutation of private languages, for treating the limits of language as the limits of thought, and for his skepticism about infinity. And despite his denigration of paradoxes, he cannot stop inventing puzzles about infinity and rule following.
Wittgenstein “once remarked that the only work of Moore’s that greatly impressed him was his discovery of the peculiar kind of nonsense involved in such a sentence as ‘It is raining but I don’t believe it.’” (Malcolm 1958, 56) Is this a slight against the founder of analytic philosophy? Or is it the confession of a paradox addict?
Wittgenstein’s runaway rumination brings to mind a passage from Paradise Lost. John Milton is describing hell as a varied terrain in which some fallen angels fight, others mournfully sing, and yet
Others apart sat on a hill retired,
In thoughts more elevate, and reasoned high
Of Providence, Foreknowledge, Will, and Fate—
Fixed fate, free will, foreknowledge absolute—
And found no end, in wandering mazes lost. (II, 557-61)
The poor devils on the hill are tormented by the futility of their inquiry but cannot control their inquisitiveness. The more they think about why they must not think, the more deeply they wear the grooves of thought.