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) Menos 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 cant come to know something that you didnt already
know. That is, that inquiry never produces new knowledge, but only recapitulates
things already known. This leads to the famous Doctrine of Recollection.
An Objection to Inquiry
- The argument known as Menos Paradox can be reformulated
- If you know what youre looking for, inquiry is unnecessary.
- If you dont know what youre looking for, inquiry is
- Therefore, inquiry is either unnecessary or impossible.
- An implicit premise:
Either you know what youre looking
for or you dont know what youre looking for.
And this is a logical truth. Or is it? Only if you know what
youre looking for is used unambiguously in both disjuncts.
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:
- Tom knows what Mary knows.
- What Mary knows is that the party begins at 9 pm.
- What Mary knows = that the party begins at 9 pm.
- 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.
Evaluating the Argument
There seems to be an equivocation in what youre looking
- The question you wish to answer.
- 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 dont know?
In one sense, the answer is no. You cant both know and
not know the same thing. (Pace Heraclitus.) In another sense, the
answer is yes. You can know the questions you dont
have the answers to.
How Inquiry is Possible
So this is how inquiry is possible. You know what question you want to
answer (and to which you dont 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
The argument for Menos 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
The Theory of Recollection
- Concedes that, in some sense, inquiry is impossible. What appears to
be learning something new is really recollecting something
- This is implausible for many kinds of inquiry. E.g., empirical inquiry:
- Who is at the door?
- How many leaves are on that tree?
- Is the liquid in this beaker an acid?
- 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.
- 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.
- Platos 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.)
Platos demonstration of the theory
Plato attempts to prove the doctrine of Recollection by means of his interview
with the slave-boy.
- 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.)
- How successful is Platos proof of the doctrine of recollection?
The Proof of Recollection
- Call the geometrical theorem in question P. Plato assumes:
- At t1 it appears that the boy does not know that P.
- At t2 the boy knows that P.
- The boy does not acquire the knowledge that P during the
interval between t1 and t2.
- 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
doesnt do any teaching - he only asks questions.
- 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 didnt acquire the knowledge in the interval
between t1 and t2.
- Crucial assumptions by Plato:
- Socrates didnt do any teaching.
- The only way to acquire new knowledge is to be taught it.
- Both assumptions are dubious:
- Socrates asks leading questions. He gets the boy to notice
the diagonal by explicitly bringing it up himself.
- 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
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:
- 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.
- 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.
- 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.)
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.
Copyright © 2006, S. Marc Cohen