Aporias, Webs, and Passages:

Doubt as an Opportunity to Learn

Nicholas C. Burbules

Department of Educational Policy Studies

University of Illinois, Urbana/Champaign

Published in Curriculum Inquiry Vol. 30 No. 2 (2000)

I would like to begin this essay with the experience of getting lost on the World Wide Web. The basic hypertextual design of the Web allows for different texts, including multimedia materials, to be linked together in an enormous network of criss-cross references. Designers of specific Web pages include links that lead a user beyond the confines of their material, into other pages, which in turn are linked to other pages. Following these associations with a "click" on each link, one can quickly travel far from one’s starting point — and despite improved navigational devices that provide a record of where one has traveled and allow one to move backward as well as forward through a chain of links, all travelers on the Web have experienced the disorientation of finding themselves in a strange location, in-between the familiar and the unknown, and wondering "Where am I?" "Why am I here?" "What does this mean?"

The key element underlying this network of choices is the link. A link represents a decision by the designer to associate texts or text segments A and B. This association has both semantic (metaphorical) significance and represents a navigational path. Movement along this path represents a decision by the user to leave the known content of the page on the screen to an unknown page whose content may edify, surprise, offend, or confuse. A link can be viewed, on one level, as a simple transition, a bridge, a means of connection; but on a deeper level it represents a way of associating elements that inevitably affects how one understands them. It is a method of semiological transformation; the elements are not only joined, but changed in the process (for example, by a decision to link a page about rock music with a page about teenage drug use).

Any two things can be linked, including a raven and a writing desk; but what the link means can be a deep puzzle — a puzzle not only of conceptual ambiguity but also of confused location, since with the passage comes both an associative connection and movement within the labyrinth of the Web. A great many assumptions may be incorporated into each link, and these assumptions are almost entirely implicit — all the user knows is that the designer chose to make a connection; but why it was made, or what sense the user is to make of the connection, is often up to the user to figure out. This sense of being "lost" is an aporia: a problem of having arrived in an unfamiliar location, and a riddle of uncertain signification.

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The concept of aporia is most familiar from Plato’s dialogue, the Meno. In that dialogue, Socrates undertakes to teach a slave a lesson in geometry, which involves figuring out the area of a square. As an essential part of that proof, Socrates draws out from the slave an initial guess as to the area, and then proceeds to lead him, through a step-by-step line of argument (elenchus), to the realization that his guess must be incorrect. The slave is flustered and confused ("It’s no use, Socrates. I just don’t know"). This, says Socrates, is the moment of aporia: the moment where a misconception has been exposed, stripped away, and where a clean terrain now exists for the reconstruction of true knowledge. Socrates goes on to lead the slave, step-by-step, through an alternative proof of the area of the square, until he arrives at the correct answer.

I want to focus on this transitional stage of aporia, as Plato describes it. Several metaphors are provided, in this dialogue and others, of what aporia is like: feeling "paralyzed," "stung by a sting-ray," or "numb." Now, why should a state of conceptual puzzlement be described by such corporeal analogues? Plato does not explain this. What does it assume about learning to say that a learner must be exposed, stripped of misconceptions, before true learning can occur? Are there other ways to think about aporia — what Jacques Derrida calls this "old, worn-out Greek term...this tired word of philosophy and of logic" — in ways that might carry us through new paths of thinking about learning and understanding? Let’s begin with the etymology: a-poros means lacking a poros: a path, a passage, a way.

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When I have lost my way, I have two problems: one is not knowing how I got here; the other is not knowing where to go next. I am held up, stuck, in-between. Perhaps I keep returning to the same point again and again. Conceptually, I lack both the step-by-step algorithm that led me here, and an overall map that provides a relative sense of my location within a network of possibilities. But my confusion is not only cognitive. Aporia is an experience that affects us on many levels at once: we feel discomfort, we doubt ourselves. We may ask, "What do I do?" "What do I say?" "What’s wrong with me?" An aporia is a crisis of choice, of action and identity, and not only of belief. When I have too many choices, or no choices, I don’t have a choice; I’m stuck. I don’t know how to go on.

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How does one learn how to go on? Ludwig Wittgenstein’s discussion of rules, like his discussion of language games, covers a variety of different, but related cases. Indeed, there can be as many types of rules as there are types of games, and vice versa. Some rules, like the arithmetic algorithm he sometimes uses as an example ("add 2": 2-4-6-8...) are strict and explicit; at the opposite extreme are rules that we "make up as we go along." But all rules, he says, have some properties in common. A rule is like a sign-post; it indicates a direction, a way, a path, which must be followed.

Wittgenstein says some puzzling things here. On the one hand, he says that there is never only one way to follow a rule, and that rules do not contain within them explicit directions on how they are to be interpreted. A sign-post is both clear and yet ambiguous — pointing always requires us to make a guess about precisely what is being pointed at. On the other hand, insofar as we follow a rule, he says, we follow it "blindly." I take this to mean that once one has formed an interpretation of a rule (or even after one has made one up), one must follow it as a rule as a matter of course; otherwise it is not a rule (the same is true of being led somewhere by clicking on a web-link, following a map, or tracing a line). Hence the idea of following a rule entails both an element of obligatoriness and an element of judgment and choice: a person cannot be said to have learned a rule, or to be following it, without both. These in-between modes of thought are not easily represented by dichotomous distinctions such as "knowledge" versus "skill." The ancient Greek term metis, sometimes translated as "craft" (connoting both an artisan’s craft and the sort of craftiness demonstrated by Odysseus) represents a mode of thought more practical, more situational, than episteme. It is the craft of making one’s own way, as Odysseus made his way throughout a long, circuitous journey, and back home again. It operates within the domain of rules of thumb, general precepts, and not precise sets of directions. As Sarah Kofman puts it, "It is in effect Metis who allows us to blaze a trail, a poros, a way, to find a path through obstacles."

How does one know that another person (a student, say) has understood a rule, since how it is being interpreted is both an idiosyncratic and an inaccessible mental state? Because, Wittgenstein says, the person says "now I know how to go on," can do something in accordance with the rule, can do it in the right way (which means the socially approved way within some context, language game, or form of life). In order to do something in the "right" way, certain alternative ways of doing it must be "ruled out." In part, then, following a rule is like tracing a pattern; it must be followed more or less exactly, once one can see the line to be traced. Indeed, "rule" sometimes means "line."

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In their book, On the Line, Gilles Deleuze and Felix Guattari describe two methods of organizing information, which they liken to two types of root system: a centrally organized, hierarchical system of organization, like a root system with a central tap root and structures of diminishing significance branching off from that; and a system that is rhizomatic, spreading in all directions, with no center and no given hierarchy of importance. The World Wide Web, for example, is a rhizomatic system: it grows in all directions, allows passage along many alternate routes, with no governing set of rules for deciding which of many branching options to choose or how to organize the results one finds there. But this model of a rhizomatic "web" is of much greater importance than simply in reference to the World Wide Web: it is, more generally, a way of thinking, or a way of writing, that contains multiple lines of association; that is organized not only linearly, but laterally; that follows, not a single hierarchical outline, but a labyrinth of continually returning, criss-crossing pathways. Each particular step or link within a rhizomatic whole might be conceived as a line between two points, but the overall pattern is not linear, because there is no beginning and end to be connected.

If a link is a line, it is both a line that we follow and a line that draws us in, like a fish: the Web or ‘Net is a set of paths that we explore, but also a web or net that catches us up. We may wish for a map of this labyrinth, but this would not make things any easier, since the only complete map would need to be a replica of the web or maze, which would be as puzzling as the original. A labyrinth cannot have a complete map that is not a labyrinth itself. A map, to be useful, to help us learn how to go on, must always simplify, exclude elements. This requires the user of the map to go beyond what is in the map; to make new connections on her or his own. There is never only one way to follow a map. Someone could draw a line to show us how to get out of a particular maze (which we could then trace or follow), but this would not teach us how to cope with mazes. To learn that, we need to learn how to find our way within a labyrinth by creating a map, ourselves, as we go.

This picture of rhizomes, webs, and nets begins with the significance of the line, the relation, the link, as an object of study itself, not merely as a connection between two points. In this inversion, we do not start with the points, and then connect them; we start in-between, thinking about ways of connecting and regarding points as the nodes of intersection where lines or links come together. We make choices, but they are choices that are made from among links and pathways that we do not choose. Similarly, we may repeat lines from a play, or lines from a poem; we recite them, as givens, but we also interpret them, add something to the passages that make them our own. The lines that we follow or trace both facilitate and limit: a line in this sense is not only a connection, but also a divider, a border; just as a path facilitates going from one point to another, but also implicitly prevents or discourages a different passage.

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A passage can be many things. It can be a path or a tunnel, connecting two knowns. A connecting path or hall is often said to "communicate" between two rooms. It can be a journey, real or allegorical. A passage can be a transition, an experience of change or growth; one can undergo an arduous rite of passage. We also talk about change in terms of the passage of time. A passage can be a quotation from a scripture or a musical score; yet even when a quotation is verbatim, it is interpreted or modified within the changed context, it is never exactly the same. The use of prepositions here is significant: a passage to is different from a passage through, which is different from a passage from. Sometimes a passage connects knowns; sometimes it leads from a known to an unknown.

One can differentiate here the pattern of a constellation, which connects known elements, or givens, from the pattern of a labyrinth, which leads away from the known toward the unknown: in the latter case, we choose a path, not a destination. The example of teaching that Socrates uses in the Meno, of moving step-by-step through the logic of a geometric proof, fits the particular model of dialectic that Plato wants to endorse: The link of known steps by which the slave is led to a conclusion is linear, foredestined. It is a constellation, not a labyrinth. This is a model of teaching that does not promote exploration or inquiry; it minimizes uncertainty. Kofman distinguishes the Greek words odos (a path or road connecting knowns) and poros (a passage across a chaotic expanse, a sea-route, for example, or blazing a trail where no trail yet exists). Lacking an odos is not the same as lacking a poros. These two kinds of path or passage are important because they imply two kinds of transition out of doubt: one by progress toward a fixed answer, one by movement toward an unknown destination.

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Like a passage, a movement can be a musical sequence; it also can be a dance, a motion, a relocation. A movement can also be a political phenomenon, pursuing a prospective, but unknown future; often such political movements rely upon repeated slogans or quotations from a leader or martyr. Movement as relocation is a good way to get from point A to point B. Movement as dance is not about getting from point A to point B. The first traces a line; the second defines and explores a gestural space. Wittgenstein says that his investigation seeks "new movements in thinking," but movement concerns the body as well. When one is paralyzed one cannot move; when one is numb or dizzy one cannot tell if or where one has moved.

The progression of musical notes on a page is something we can read and analyze, seeing patterns and the relations within their movements up and down the scale; but hearing the music, playing it, or dancing to it, we feel their movement, their rhythms and relations, in a fundamentally different way. Their repetitions and variations are echoed in our motions, our bodies; we are never entirely passive listeners. We gain pleasure from them, and we are changed by the experience. Their variations become our variations.

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A variation is a repetition with a difference. Lacking either element (repetition or difference, obligatoriness or interpretation), a variation cannot be. Even a quotation, which is ostensibly verbatim, the same, is always changed by moving it from one context into another — indeed, we desire both effects, the allusion to a meaning that stays constant and is tailored to our purposes. We seem to be returning to the familiar, but with something new added each time. The quotation always says more, or less, after the movement than it did originally. With a musical variation, the familiarity of knowing that a note was previously followed with another is essential to the response of surprise or delight or interest or satisfaction we feel when the next time it is linked to something different and new. A variation or a version is always the representation of something that might be represented in a different way with equal validity and vividness.

Here, a "different way" means a different manner or style or mood; but a "way" can also be a path, a journey, a direction — and so finding a "different way" can also mean discovering, or creating, a novel organization for information. Finding one’s way means recognizing enough familiar points of reference to reconstruct a meaningful pattern out of what is unfamiliar, foreign. Recognition is both a discovery and a creation.

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Recognition is also a different way of thinking about learning in the Meno. In that dialogue, Plato says that we come to knowledge through anamnesis, which is usually translated as "recollection," a remembering of truths revealed to us in a previous life, before our birth. He says that in his teaching he is not giving the slave an answer, but drawing forth what is latently within him. This is his attempt to answer "Meno’s paradox":

Socrates here, as he does in other dialogues, changes someone else’s question into a question he wants to answer. Socrates’ version of the paradox emphasizes that one cannot look for something if one does not know what it is; in his account one either must know something perfectly and completely or one cannot know it at all. Hence he must posit an unconscious level of knowledge that is brought forth through the dialectic (another metaphor he uses for this bringing forth is midwifery). But Meno’s original question emphasizes something else: How does one recognize that something is true? What needs to be explained is that "ah-ha," that feeling that one experiences when one sees a connection that seems right. Something "clicks," one says. One recognizes it the way that one might suddenly recognize someone she or he has met before (as in the famous scene of Odysseus’s return to his household): something is familiar and yet something is also different. It is this feeling of recognition that needs explaining, not the fact of truth. One could, of course, have this experience of recognition, or rightness, with something that is not in fact true, or that might not be susceptible to determinations of "truth" either way (one’s reaction to a painting, or a piece of music, or a movement in a dance, may feel right in the same way that a proof strikes one as correct).

"Recognition" is a much more interesting philosophical question than the Platonic idea of "recollection," for it does not depend on all-or-nothing determinations of truth, but on the more varied process of seeing one thing in terms of another. One recognizes something as something; one recognizes the unfamiliar so that it becomes familiar. One re-cognizes, thinks again, thinks in a different way; and moves toward insight and understanding. There is, as Hans-Georg Gadamer reminds us, a "joy of recognition," a feeling of satisfaction in making a meaningful association (even when the particular subject of the association may be unpleasant). The answer to Meno’s paradox is not to posit a mythical prior life, but to explore what it means to think in a different way. The main burden of misconceptions is not in having false beliefs that need to be refuted and replaced with true ones; it is in thinking about a problem in the wrong way, and so not knowing how to go on. One cannot suddenly abandon one way of thinking and adopt a wholly new one — this movement requires bridges, links, which help the learner to assimilate a different vocabulary and set of assumptions. The task of the teacher is not in stripping away falsehood to clear the ground for truth, but in helping those who are lost to find their way, to make a passage, or translation, between what is foreign or puzzling and what is familiar.

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A translation is a deeply complex endeavor, much more so than our ordinary ways of thinking of it. Usually people describe translation in one of two ways: as finding a series of one-to-one equivalencies between two discourses, or of passing meaning through the mediation of some third language, or metalanguage. Both pictures are misleading. Even leaving aside questions of diverse syntax and sentence construction, simply at the level of individual words no simple equivalency across discourses is possible. The polysemic associations of denotation and connotation that each word has within the web of its own discourse simply cannot all have equivalents within the other. A link of similarity or contiguity can be established between them, but this only invites a comparison, a transfer, to see one as like the other, as in a metaphor or simile. It is only in the practice of use that one can discover if such a comparison is adequate to one’s purposes. People translate in order to communicate; something has to pass between them. Hence the success of a translation depends on the success of communication — a contextual, contingent assessment that requires being comfortable with the state of in-between.

However, a translation is not simply a transmission of meaning from one context to another: it is a kind of relation in which the elements it comprises are transformed. As Walter Benjamin explains, translation is never simply a matter of exchange or equivalency because the discourses that are translated are each changed as a result:

A successful translation involves a recognition of what the other is trying to say as well as a re-cognition of features of one’s own language.

A step beyond this is where translation is not possible, where there is a surplus of meaning that cannot be adequately communicated in another discourse. This confronts us with the limits of translation, the limits of recognition. Here it is more than a matter of moving from the familiar to the foreign, but of moving beyond the foreign to the strange. One runs up against the limits of discourse itself; what Wittgenstein says cannot be said, but only shown, or what Lyotard calls the differend: "the unstable state and instant of language wherein something which must be able to be put into phrases cannot yet be." With the strange, difference is so profound that even analogies of similarity are not possible; at such moments, one must move from the idea of a translation to the idea of an aporetic encounter — making one’s way through a labyrinth with no clear lines to follow. Uncertainty, difficulty, and discomfort in such an encounter are intrinsic. And because the failure of translation in such practical contexts of communication is related to the inability to act or coordinate action, such difficulties are moral difficulties as well. The challenge of moral responsiveness in the face of radical difference is as much a part of the feeling of aporia as are epistemic or linguistic limits. Here even the possibility of communication, let alone translation, is put at risk. We have something to say, but don’t know how to say it.

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My colleague and friend Marcia Linn has studied what students mean when they say "I don’t know." She has found, not surprisingly, that this statement does not always mean the same thing: sometimes it means "I have no idea what you are talking about," sometimes it means "I need more information to figure this out," sometimes it means "I don’t care, leave me alone."

Similarly, there are different kinds of aporia. The aporia of the Meno is an epistemic emptiness; at that moment, one knows nothing, and does not know what to think or say or do next — hence, paralysis, numbness. There is no path in sight. But a different kind of aporia is to have lost one’s way, to be confused; there are too many paths from which to choose. Different still is an aporia in which one cannot recognize a path that is already there. And yet another is an aporia in which the path is apparent, but one cannot or will not follow it (perhaps because the destination is unknown, perhaps because it is known and unpleasant).

In all of these cases, one does not know how to go on, but for very different reasons. Each requires a different sort of response by a sensitive teacher. There is no "method" here. A dialectic of reasoned argument or proof has the capacity to alleviate only some of these kinds of aporia; for others, it could make matters worse. And for some states of aporia, alleviating them in the sense of making them disappear is not the way to go at all. Perhaps the state of aporia is one to which we sometimes need to be returned; not by having a question answered but by seeing the contrast between the different versions of our understanding before and after — to recognize, rethink, our own understandings from the far end of a path we have traveled, and from which we return.

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A circle or loop can be a kind of aporia; a path that returns back upon itself. But there are different forms of this circle. One is a "vicious" circle, a circle of simple repetition and reiteration, in which the same recycles repeatedly. But another kind of circle (call it "hermeneutic") is one in which each return brings a reconsideration of the familiar from the vantage point of the novel — until the familiar becomes novel and the novel familiar, when the relations switch back again, and then again. Here the loop is a passage that represents change and growth. It is like a Möbius strip, a loop that returns one to the beginning, but with a difference, with a "twist." And this suggests one other sort of circle: the circle that cycles one around within a closed system of possibilities and which, by doing so, makes one aware of the boundaries of that system. The system’s closedness is revealed by the frequent return to the same (perhaps in either of the first two senses): but here the discovery is not primarily one concerning the associations among the elements along which one has traveled, but one that recognizes the very closedness of these possibilities, sees the boundaries of the system from the inside (one cannot be outside it). Not all fly-bottles have a way out.

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How does one see the limits of what one cannot see beyond, where there is no way out? One can travel almost infinitely within any complex network but cannot travel beyond it; every link carries one to another link but, as with space itself, the web loops back into itself. It has limits, but no edges. There are only variations upon variations; one can experience novelty, creativity, even critique within these terms — which are real, not illusory — but all paths intersect, ultimately. There is no path outside. This, too, is an a-poros: in Derrida’s words, "the aporias that appear to engage anyone who takes on the task of defining the constraints which limit philosophical discourse." But to say this is to assume that one can experience one’s self as in such a place, that one recognizes these limits, that one can say to one’s self, "I do not know how to go on." Wittgenstein says:

This means that the significance of a particular element in a web is affected by the links that join it to others and by the particular path of links that one moves through in arriving there: How one gets into an aporia affects how and whether one can get out of it. At this moment, we recognize that every link that draws one association excludes others; that every path is a passage away from some possibilities as it is toward others; that a poros is always both a way and a barrier, an opening and a closure.

With this we recognize that the most important distinction among aporias is between those of which we are aware, and those not — because every choice, every understanding, every movement is the surpassing of some limits and, simultaneously, the confirmation of others. Similarly, Derrida points out the dual, paradoxical meaning of the term "trace": as the strictly constrained following of one pattern with another line, and as a residue, an excess, that is left behind — such as Lyotard’s differend. One sometimes learns, initially, by tracing, following a pattern that has been set for one by others (as when one learns how to draw the shape of letters in the alphabet by tracing them). But when one starts using the letters to write, one is no longer tracing (though writing always leaves a trace, an excess). Similarly, one may recite the lines in a play, from memory. But the point at which one is acting — when one is able to go on — is the point at which one has gone beyond the pattern, added to and changed it, made it one’s own. The trace both facilitates and constrains, like a map that one follows.

An interesting parallel can be drawn here between how Umberto Eco describes walking through a forest, and how Michel de Certeau describes walking through a city:

Can we move beyond such limits within possibilities? Or is this a web from which there is no escape?

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I would like to return to the experience of getting lost on the World Wide Web. From what standpoint is this a problem? When can getting lost be seen instead as an opportunity for serendipity? Every navigator, every explorer, has had the experience of looking for one thing but finding something else instead; sometimes this new thing is even more useful, more interesting, more enjoyable, more important, than the thing one was looking for. There is no way to remain open to the possibility of happening upon something new if one is not prepared to accept getting lost. One is "lost" only relative to one purpose or need; sometimes being lost is an occasion for rethinking how "necessary" that imagined purpose or need actually is. We may need to be reminded of this from time to time. The experience of being lost itself teaches us something: that the associations we encounter within a web do not always make sense, are not natural or inevitable, do not explain themselves. Sometimes we learn by being returned to the same point again and again; with each return, each repetition, comes a new recognition, a changing understanding.

We also can learn from occasions to reflect on why webs are designed the way that they are, and how they might be designed differently; this both problematizes the apparent naturalness, the transparency of given associations, and begins to make explicit the processes of design so that learners can create new links, drawing lines themselves and not only tracing them. Here we learn to become familiar with complexity, and complexity’s sibling, uncertainty. Curiosity and interest, which are essential to learning, grow out of and depend upon feelings of doubt and puzzlement; they do not threaten interest, but can enhance it. Something that does not puzzle us isn’t interesting.

What Kofman calls the passage across a chaotic sea is an arduous poros; but some destinations can only be reached this way, and some lessons can only be learned by persisting in such a journey. At the margins of order and sensibility, we see "the possibility of impossibility" — where we are estranged from the familiar, confronted with differences that we cannot recognize; where we need to create our own links as we attempt to pass through. The experience of aporia can remind us of limits: our limits, the limits of our understandings, the limits of our language. We see these limits not as explicit barriers that block all movement, but as paths that lead us in some directions while also sometimes preventing us from getting to where we are trying to go. They help us to get this far, but they prevent us from getting any further. At this extremity, we encounter a deeper kind of aporia: a doubt that never goes entirely away.

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The doubt of Plato’s Meno is a transitional phase, positioned between two kinds of certainty: the certainty of strongly held misconceptions and the certainty of true knowledge. This first sense of doubt is not in itself an educational movement: it is merely the empty pause, the frozen, paralyzed instant, between two kinds of complacency. It is a moment of futility and embarrassment. It does not lead to anywhere else. Meno’s original aporia, the question about recognition, is lost in Plato’s search for criteria of epistemic certainty ("tethering" our ideas to reality so that they stay fixed and cannot run away, he says). But Meno’s question introduces a different, more puzzling, more educationally interesting, problem: How does someone recognize an answer to a question? What satisfies one’s puzzlement, makes one feel less lost?

This way of putting the problem does not focus on criteria of truth, but on one’s search, one’s purposes, one’s movement — where it begins and where it stops (or pauses). This way is more clearly a question about what one should do, and not only what one should think. This second sense of doubt is to be stymied, to be delayed, to be stuck, in-between; it is a cessation of movement, but not in the sense of paralysis, or no choices, no way out — here there are too many choices, and one does not know how to recognize the path or paths that will help one to pass through. From a teaching standpoint, this implies that the condition of doubt itself contains educational potential: that it includes questions; includes an awareness of at least some alternative ways of proceeding; includes a mixture of understanding and misunderstanding, of constructive and inhibitive ideas. These constitute potential points that can be linked to something new; they are not less-than-perfectly-true beliefs that must be simply swept away to clear the way for a recollection of the perfectly-true. The goal, from this perspective, is not to eliminate aporia, or to regard it as simply a loss, an absence; but to see within doubt the questions that make a new understanding possible.

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Teaching that begins with questions is both a moral and a pedagogical choice. A teacher teaches with questions because she or he believes that it is a better way to teach, and a better way to be a teacher. Yet to succeed at this, the questions must be real questions: questions that puzzle, confuse, and interest. Socrates’ questions, in the Meno and throughout the Platonic dialogues, are rarely authentic questions, felt questions by Socrates; they always indicate a purpose, the development of a line of elenchus, and Socrates’ professions of ignorance usually appear to the reader as quite disingenuous. This authoritarian and rather manipulative style of teaching, as illustrated in the Meno and elsewhere, can be called the "conversion" model: inducing the learner to abandon a corrupt set of beliefs, to experience the crisis of aporia, and then, with the force of revelatory discovery, to be moved into the light of truth (we see this point quite literally illustrated in Plato’s famous metaphor of the cave in the Republic). Socrates’ dialectic leads the learner into a state of aporia and undertakes to lead the learner out again.

This narrow view of teaching provides only the thinnest understanding of where questions come from, of the kinds of confusion students typically feel, and of the nature of aporia itself. By itself, it cannot support an inquiry-oriented pedagogy; it may even interfere with it.

Some general things can be said about questions:

Different kinds of questions imply different kinds of aporias. A question is the mediator between what we know and what we do not know; we need to know enough to know how to ask a question, but not know enough that the answer is interesting and important to us. A question resides in the space between knowledge and ignorance.

But how does one teach in the situation where questions do not have correct answers, where difficulty is intrinsic, where the learner is, in the deeper sense of the word, lost? Leading learners does not help them learn how to go on: it may solve the immediate problem of moving them to a particular outcome, but does not by itself provide them with the ability, or the confidence, to find their way on their own. Teachers can do more for learners, not by giving them maps, but by helping them to learn how to create maps, to draw lines and make connections themselves. This is a matter of recognizing where you are (and who you are) and how you got there. Teaching in this latter sense is not a process of conversion, but of translation: of making sufficient associations between the familiar and the foreign to allow the learner to make further associations, to find other paths, and eventually to become a translator, a path-maker, on their own.

Here we return to Wittgenstein’s point that the way in which one arrives at a point of aporia itself influences whether and how one can pass through it. This, I think, represents a crucial insight about teaching — one that Wittgenstein himself tried to heed in his university teaching and writing, so much of which was about trying to frame the right sorts of questions. Learning how to ask a good question is in one sense the central educational task, yet one that is almost never taught explicitly, and rarely taught at all. The typical sorts of questions teachers ask are questions to which the teacher already knows the answer. Learning how to ask questions is a skill of both learning and of teaching; hence this approach involves the teacher joining the learner in a process of exploration, one in which the teacher’s own questions, own doubts, will be exposed also. In order to help someone get out of an aporia, a teacher will need to understand (and help them to understand) how they got into it; this will require, in part, the teacher taking on the learner’s questions, the learner’s aporia, as her or his own. In this context, the roles of teacher and learner blur: aporia becomes a potentially shared state — "What question do I ask?" is an aporia of learning and teaching. The teacher’s task, on this view, is not simply to elicit a state of aporia in others, but to be prepared to endure that state also. Aporia in this sense is not a brief interstitial moment, but an ongoing condition that generates the questions and problems that move us to seek new understandings.

This is not to minimize the frustration and discouragement that such experiences of aporia entail. They are not simply psychological states, but bodily experiences as well; which is why we use words like discomfort and disorientation to describe them. They involve a moral as well as an epistemic element; they involve difficult choices about what to do and not only what to think — of where to move, and how to go on. They affect our senses of identity, of competence and purpose; hence teaching also requires sensitivity to the multiple ways in which people respond to the state of aporia. Sometimes these responses will not be educationally productive. But this approach to teaching also opens the possibility of learners feeling the full joy of recognition, the satisfaction of knowing how to go on without being led — and I do not see any way to experience the latter joy and satisfaction without having experienced (and moved through) the former frustration and discouragement. We need, I think, a more courageous, risky approach to teaching — a way of teaching and not a method — one that respects the educational importance of both doubt and confidence, both strangeness and familiarity, both being lost and finding a way. The teaching dialectic here is not a process of syllogistic argument leading to higher and higher truths, but an ongoing engagement with difficulty — and, in this, to embark on a path with an unknown, unknowable destination.*