Aporia

In Plato’s dialogue, the Meno, Socrates sets himself the task of teaching a slave a lesson in geometry including deducing the area of squares. Socrates’ method consists of leading the slave to guessing the area of a square and then leading him through a series of questions to the realisation that his guess was wrong. Having realised his error, the slave becomes stuck and confused and reaches a point where he can no longer answer Socrates’ questions. In the extract below (Plato, 2005, p.108) the slave has just realised the error of his answer to the question regarding the length of the sides of a square necessary in order to produce a square with an area of eight square feet:

SOCRATES: Well, what line do we get it from? Try and tell us exactly. And if you don’t want to use numbers, you can just show us. [He hands the slave his stick.] What line?

SLAVE: [He stares at the drawing.]Honest to god, Socrates, I don’t know!

SOCRATES: There, see that, Meno? You realize where he is now on the road towards remembering? At first, he didn’t know which line gave us an area of eight square feet…and he still doesn’t know now; but the point is, back then he thought he knew, and he answered as if he knew, without the slightest hesitation – he didn’t feel baffled. But now he does feel baffled; and as well as not knowing, he also doesn’t think he knows.

MENO: Yes, that’s right.

SOCRATES: So isn’t he better off now – as regards the thing he didn’t know?

MENO: Yes, I think he is.

Socrates then proceeds to lead the slave to the correct answer through a carefully constructed series of questions. The slave is only able to reach the correct answer because he realised the error of his first attempt and this moment of bemusement, confusion, or numbness  is, according to Socrates, the moment of aporia.

Nicholas Burbles (2000) identifies the aporia as “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” (Burbles, 2000, p.173). According to Burbules, there are four types of aporias:

1. the aporia of the Meno – that leaves us in numbness without a clue of how to proceed;
2. the aporia which occurs when we have lost our way and where there are too many paths to choose from;
3. the aporia in which we are unable to recognise a path that is already there;
4. finally, the aporia that occurs when we can see the path we should follow, but for whatever reason, we are unable to follow it.

It is Burbules’ assertion that the Socratic method – as demonstrated in the Meno – is manipulative. Socrates’ questions are rarely genuine and simply serve the purpose of moving the slave through a step-by-step line of reasoning (elenchus) predetermined by Socrates himself.

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. (Burbles, 2000, p.183)

So what would an inquiry-oriented pedagogy look like? According to Burbles such a pedagogy would consist in the teacher and learner asking the right kind of questions. While leading learners through an aporia via the careful use of pre-fabricated questions may move learners to a pre-determined outcome, this method in no way helps learners to be able to find their own 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 […] Teaching … 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 become a translator, a pathmaker, on their own. (p. 184)

The idea is therefore for teachers to ask questions that they don’t have the answers to. The teacher should thus expose his/her own doubts and join the students in a common journey of inquiry. Following on from Wittgenstein, Burbules argues that in order to get out of an aporia, it is first necessary to understand how one arrived at it. The role of the teacher is not only to share the state of aporia with the students, but to aid them in their understanding of how they got into it. “Aporia…is not a brief interstitial moment, but an ongoing condition that generates the questions and problems that move us to seek new understandings” (p.184).

Rancière also identifies the Socratic method as one of stultification in that Socrates interrogates in order to instruct (Rancère, 1991). Emancipatory education requires that teachers interrogate their students in the “manner of men, and not in the manner of scholars” (p.29) and this can only be carried out by a teacher who knows no more than the student; a teacher who has “never made the voyage before him”. Hence the title of his book: The Ignorant Schoolmaster.

References:

Burbules, N. (2000). Aporias, Webs, and Passages: Doubt as an Opportunity to Learn. Curriculum Inquiry , 30:2, 171-187.

Plato. (2005). Protagoras and Meno. London: Penguin.

Rancière, J. (1991). The Ignorant Schoolmaster. Stanford: Stanford University Press.

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