Meno’s Paradox

  1. A Puzzle about Definitions

    Socrates has told us he knows how to reject faulty definitions. But how does he know when he has succeeded in finding the right definition?  Meno raises an objection to the entire definitional search in the form of (what has been called) “Meno’s Paradox,” or “The Paradox of Inquiry” (Meno 80d-e).

    The argument can be shown to be sophistical, but Plato took it very seriously. This is obvious, since his response to it is to grant its central claim: that you can’t come to know something that you didn’t already know. That is, that inquiry never produces new knowledge, but only recapitulates things already known.  This leads to the famous Doctrine of Recollection.

  2. An Objection to Inquiry

    1. The argument known as “Meno’s Paradox” can be reformulated as follows:

      1. If you know what you’re looking for, inquiry is unnecessary.
      2. If you don’t know what you’re looking for, inquiry is impossible.
      3. Therefore, inquiry is either unnecessary or impossible.

    2. An implicit premise:

      Either you know what you’re looking for or you don’t know what you’re looking for.

      And this is a logical truth. Or is it? Only if “you know what you’re looking for” is used unambiguously in both disjuncts.

  3. The Ambiguity

    Suppose Tom wants to go to the party, but he doesn't know what time it begins. Furthermore, he doesn't even know anyone who does know. So he asks Bill, who doesn't know when the party begins, but he does know that Mary knows. So Bill tells Tom that Mary knows when the party begins. Now Tom knows something, too—that Mary knows when the party begins.

    So Tom knows what Mary knows (he knows that she knows when the party begins). Now consider the following argument:

    1. Tom knows what Mary knows.
    2. What Mary knows is that the party begins at 9 pm.
    3. What Mary knows = that the party begins at 9 pm.
    4. Therefore, Tom knows that the party begins at 9 pm.

    What is wrong with this argument? It commits the fallacy of equivocation.

    In (A), “what Mary knows” means what question she can answer. But in (B) and (C), “what Mary knows” means the information she can provide in answer to that question.

  4. Evaluating the Argument

    There seems to be an equivocation in “what you’re looking for”:

    1. The question you wish to answer.
    2. The answer to that question.

    Using sense (A), (2) is true, but (1) is false; using sense (B), (1) is true, but (2) is false. But there is no one sense in which both premises are true. And from the pair of true premises, (1B) and (2A), nothing follows, because of the equivocation.

    To see the ambiguity, consider the question: “Is it possible for you to know what you don’t know?”

    In one sense, the answer is “no.” You can’t both know and not know the same thing. (Pace Heraclitus.) In another sense, the answer is “yes.” You can know the questions you don’t have the answers to.

  5. How Inquiry is Possible

    So this is how inquiry is possible. You know what question you want to answer (and to which you don’t yet know the answer); you follow some appropriate procedure for answering questions of that type; and finally you come to know what you did not previously know, viz., the answer to that question.

    The argument for Meno’s Paradox is therefore flawed: it commits the fallacy of equivocation. But beyond it lies a deeper problem. And that is why Plato does not dismiss it out of hand. That is why in response to it he proposes his famous “Theory of Recollection.”

  6. The Theory of Recollection

    1. Concedes that, in some sense, inquiry is impossible. What appears to be learning something new is really recollecting something already known.

    2. This is implausible for many kinds of inquiry. E.g., empirical inquiry:

      1. Who is at the door?
      2. How many leaves are on that tree?
      3. Is the liquid in this beaker an acid?

    3. In these cases, there is a recognized method, a standard procedure, for arriving at the correct answer. So one can, indeed, come to know something one did not previously know.

    4. But what about answers to non-empirical questions? Here, there may not be a recognized method or a standard procedure for getting answers. And Socrates’ questions (“What is justice,” etc.) are questions of this type.

    5. Plato’s theory is that we already have within our souls the answers to such questions. Thus, arriving at the answers is a matter of retrieving them from within. We recognize them as correct when we confront them. (The “Aha!” erlebnis.)

  7. Plato’s demonstration of the theory

    Plato attempts to prove the doctrine of Recollection by means of his interview with the slave-boy.

    1. Note that it is non-empirical knowledge that is at issue: knowledge of a geometrical theorem. (A square whose area is twice that of a given square is the square on the diagonal of the given square.)

    2. How successful is Plato’s proof of the doctrine of recollection?

  8. The “Proof” of Recollection

    1. Call the geometrical theorem in question P. Plato assumes:

      1. At t1 it appears that the boy does not know that P.
      2. At t2 the boy knows that P.
      3. The boy does not acquire the knowledge that P during the interval between t1 and t2.

    2. Plato thinks that (2) is obviously correct, since at t2 the boy can give a proof that P. And he thinks that (3) is correct since Socrates doesn’t do any “teaching” - he only asks questions.

    3. But (2) and (3) entail that the appearance in (1) is mistaken - at t1 the boy did know that P, since he knows at t2 and didn’t acquire the knowledge in the interval between t1 and t2.

    4. Crucial assumptions by Plato:

      1. Socrates didn’t do any teaching.
      2. The only way to acquire new knowledge is to be taught it.

    5. Both assumptions are dubious:

      1. Socrates asks leading questions. He gets the boy to notice the diagonal by explicitly bringing it up himself.

      2. The disjunction - either the boy was taught that P or he already knew that P - may not be exhaustive. There may be a third alternative: reasoning. That is, deducing the (not previously noticed) consequences of what you previously knew.

  9. Interpretations of “Recollection”

    Plato certainly thinks he has proved that something is innate, that something can be known a priori. But what? There seem to be three possibilities, in order of decreasing strength:

    1. Propositions: such as the geometrical theorem P. They are literally in the soul, unnoticed, and waiting to be retrieved. According to this reading of “recollection,” propositions that can be known a priori are literally innate.

    2. Concepts: such as equality, difference, odd, even, etc. We are born with these - we do not acquire them from experience. We make use of these when we confront and organize our raw experiences. According to this reading of “recollection,” there are a priori concepts that we have prior to experience.

    3. Abilities: such as that of reasoning. We are born with the innate ability to derive the logical consequences of our beliefs. We may form our beliefs empirically, but we do not gain our ability to reason empirically. According to this reading of “recollection,” there is no innate knowledge and there are no a priori concepts. All but the most hard-boiled empiricist can accept (C).

    Plato talks as if he has established (A), but the most he establishes in the Meno is (B) or (C). But perhaps that is all he is intending to establish (cf. Vlastos article, “Anamnêsis (Recollection) in the Meno,” on e-reserve. And see esp. Meno 98a: recollection = giving an account of the reasons why.)

  10. How the Doctrine of Recollection is supposed to solve the problem of recognizing instances

    You can recognize an instance of X when you don't know what X is, in the following sense: you already know implicitly (intuitively) what X is, at least well enough to recognize instances of it. What you lack is an explicit (articulated, formulated) account of what X is.

    This seems to support (B), rather than (A). For it supposes that you have (implicitly) the concept of X even though you cannot produce the proposition that expresses the definition of X.

    In the Phaedo, Plato offers a different argument that also appears to be aiming at (B). This is the argument from imperfection, which purports to show that the imperfection of the physical world proves that we must have a priori concepts that cannot be derived from experience. Rather, the very possibility of our having experience at all requires that we already have these concepts.

    So even if “recollection” is only inference misdescribed, there is still room for Plato to argue that inference requires the use of concepts that cannot themselves be acquired empirically.

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Copyright © 2006, S. Marc Cohen