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Inference, Explanation, and Other Frustrations
Essays in the Philosophy of Science
University of California Press
Copyright © 1992 John Earman
All right reserved. ISBN: 0-520-07577-3
Chapter One
Thoroughly Modern Meno Clark Glymour and Kevin Kelly
Introduction
The Meno presents, and then rejects, an argument against the possibility of knowledge. The argument is given by Meno in response to Socrates' proposal to search for what it is that is virtue:
Meno: How will you look for it, Socrates, when you do not know at all what it is? How will you aim to search for something you do not know at all? If you should meet with it, how will you know that this is the thing that you did not know? Many commentators, including Aristotle in the Posterior Analytics, take Meno's point to concern the recognition of an object, and if that is the point there is a direct response: one can recognize an object without knowing all about it. But the passage can also be understood straightforwardly as a request for a discernible mark of truth, and as a cryptic argument that without such a mark it is impossible to acquire knowledge from the instances that experience provides. We will try to show that the second reading is of particular interest.
If there is no mark of truth, nothing that can be generally discerned that true and only true propositions bear, Meno's remarks represent a cryptic argument that knowledge is impossible. We will give an interpretation that makes the argument valid; under that interpretation, Meno's argument demonstrates the impossibility of a certain kind of knowledge. In what follows we will consider Meno's argument in more detail, and we will try to show that similar arguments are available for many other conceptions of knowledge. The modern Meno arguments reveal a diverse and intricate structure in the theories of knowledge and of inquiry, a structure whose exploration has just begun. While we will attempt to show that our reading of the argument fits reasonably well with Plato's text, we do not aim to argue about Plato's intent. It is enough that the traditional text can be elaborated into a systematic and challenging subject of contemporary interest.
The Meno
In one passage in the Meno, to acquire knowledge is to acquire a truth that can be given a special logical form. To acquire knowledge of virtue is to come to know an appropriate truth that states a condition, or conjunction of conditions, necessary and sufficient for any instance of virtue. Plato's Socrates will not accept lists, or disjunctive characterizations.
Socrates: I seem to be in great luck, Meno; while I am looking for one virtue, I have found you to have a whole swarm of them. But, Meno, to follow up the image of swarms, if I were asking you what is the nature of bees, and you said that they are many and of all kinds, what would you answer if I asked you: "Do you mean that they are many and varied and different from one another in so far as they are bees? Or are they no different in that regard, but in some other respect, in their beauty, for example, or their size or in some other such way?" Tell me, what would you answer if thus questioned?
Meno: I would say that they do not differ from one another in being bees.
Socrates: Suppose I went on to say: "Tell me, what is this very thing, Meno, in which they are all the same and do not differ from one another?" Would you be able to tell me?
Meno: I would.
Socrates: The same is true in the case of the virtues. Even if they are many and various, all of them have one and the same form which makes them virtues, and it is right to look to this when one is asked to make clear what virtue is. Or do you not understand what I mean?
There is something peculiarly modern about the Meno. The same rejection of disjunctive characterizations can be found in several contemporary accounts of explanation. We might say that Socrates requires that Meno produce an appropriate and true universal biconditional sentence, in which a predicate signifying 'is virtuous' flanks one side of the biconditional, and a conjunction of appropriate predicates occurs on the other side of the biconditional. Let us so say. Nothing is lost by the anachronism and, as we shall see, much is gained.
Statements of evidence also have a logical form in the Meno. Whether the topic is bees, or virtue, or geometry, the evidence Socrates considers consists of instances and non-instances of virtue, of geometric properties, or whatever the topic may be. Evidence is stated in the singular.
The task of acquiring knowledge thus assumes the following form. One is presented with, or finds, in whatever way, a series of examples and non-examples of the feature about which one is inquiring, and from these examples a true, universal biconditional without disjunctions is to be produced. In the Meno that is not enough for knowledge to have been acquired. To acquire knowledge it is insufficient to produce a truth of the required form; one must also know that one has produced a truth. What can this requirement mean?
Socrates and Meno agree in distinguishing knowledge from mere true opinion, and they agree that knowledge requires at least true opinion. Meno thinks the difference between knowledge and true opinion lies in the greater reliability of knowledge, but Socrates insists that true opinion could, by accident as it were, be as reliable as knowledge:
Meno:... But the man who has knowledge will always succeed, whereas he who has true opinion will only succeed at times.
Socrates: How do you mean? Will he who has the right opinion not always succeed, as long as his opinion is right?
Meno: That appears to be so of necessity, and it makes me wonder, Socrates, this being the case, why knowledge is prized far more highly than right opinion, and why they are different.
Socrates answers each question, after a fashion. The difference between knowledge and true opinion is in the special tie, the binding connection, between what the proposition is about and the fact of its belief. And opinions that are tied in this special way are not only reliable, they are liable to stay, and it is that which makes them especially prized:
Socrates: To acquire an untied work of Daedalus is not worth much, like acquiring a runaway slave, for it does not remain, but it is worth much if tied down, for his works are very beautiful. What am I thinking of when I say this? True opinions. For true opinions, as long as they remain, are a fine thing and all they do is good, but they are not willing to remain long, and they escape from a man's mind, so that they are not worth much until one ties them down by an account of the reason why. And that, Meno my friend, is recollection, as we previously agree. After they are tied down, in the first place they become knowledge, and then they remain in place. That is why knowledge is prized higher than correct opinion, and knowledge differs from correct opinion in being tied down.
Plato is chiefly concerned with the difference between knowledge and true opinion, and our contemporaries have followed this interest. The recent focus of epistemology has been the special intentional and causal structure required for knowing. But Meno's argument does not depend on the details of this analysis; it depends, instead, on the capacity for true opinion that the capacity to acquire knowledge implies. That is the capacity to find the truth of a question, to recognize it when found, to stick with it after it is found, and to do so whatever the truth may be.
Suppose that Socrates could meet Meno's rhetorical challenge and recognize the truth when he met it: what is it he would then be able to do? Something like the following. In each of many different imaginable (we do not say possible save in a logical sense) circumstances, in which distinct claims about virtue (or whatever) are true, upon receiving enough evidence, and considering enough hypotheses, Socrates would hit upon the right hypothesis about virtue for that possible circumstance, and would then (and only then) announce that the correct hypothesis is indeed correct. Never mind just how Socrates would be able to do this, but agree that, if he is in the actual circumstance capable of coming to know, then that capacity implies the capacity just stated. Knowledge requires the ability to come to believe the truth, to recognize when one believes the truth (and so to be able to continue to believe the truth), and to do so whatever the true state of affairs may be.
So understood, Meno's argument is valid, or at least its premises can be plausibly extended to form a valid argument for the impossibility of knowledge. The language of possible worlds is convenient for stating the argument. Fix some list of predicates V, P1,..., Pn, and consider all possible worlds (with countable domains) that assign extensions to the predicates. In some of these worlds there will be true universal biconditional sentences with V on one side and conjunctions of some of the Pi or their negations on the other side. Take pieces of evidence available from any one of these structures to be increasing conjunctions atomic or negated atomic formulas simultaneously satisfiable in the structure. Let Socrates receive an unbounded sequence of singular sentences in this vocabulary, so that the sequence, if continued, will eventually include every atomic or negated atomic formula (in the vocabulary) that is satisfiable in the structure. Let w range over worlds. With Meno, as we have read him, say that Socrates can come to know a sentence, S, of the appropriate form, true in world w, only if
(i) for every possible sequence of presentation of evidence from world w Socrates eventually announces that S is true, and
(ii) in every world, and for every sequence from that world, if there is a sentence of the appropriate form true in that world, then Socrates can eventually consider some true sentence of the appropriate form in that world, can announce that it is true in that world (while never making such an announcement of a sentence that is not true in that world), and
(iii) in every world, and for every sequence from that world, if no sentence of the appropriate form is true in the world, then Socrates refrains from announcing of any sentence of that form that it is true.
Meno's argument is now a piece of mathematics, and it is straightforward to prove that he is correct: no matter what powers we imagine Socrates to have, he cannot acquire knowledge, provided "knowledge" is understood to entail these requirements. No hypotheses about the causal conditions for knowledge defeat the argument unless they defeat the premises. Skepticism need not rest on empirical reflections about the weaknesses of the human mind. The impossibility of knowledge can be demonstrated a priori. Whatever sequence of evidence Socrates may receive that agrees with a hypothesis of the required form, there is some structure in which that evidence is true but the hypothesis is false; so that if at any point Socrates announces his conclusion, there is some imaginable circumstance in which he will be wrong.
We should note, however, that in those circumstances in which there is no truth of the required form, Socrates can eventually come to know that there is no such truth, provided he has an initial, finite list of all of the predicates that may occur in a definition. He can announce with perfect reliability the absence of any purely universal conjunctive characterizations of virtue if he has received a counterexample to every hypothesis-and if the number of predicates are finite, the number of hypotheses will be finite, and if no hypothesis of the required form is true, the counterexamples will eventually occur. If the relevant list of predicates or properties were not provided to Socrates initially, then he could not know that there is no knowledge of a subject to be had.
Weakening Knowledge
Skepticism has an ellipsis. The content of the doubt that knowledge is possible depends on the requisites for knowledge, and that is a matter over which philosophers dispute. Rather than supposing there is one true account of knowledge to be given, if only philosophers could find it, our disposition is to inquire about the possibilities. Our notion of knowing is surely vague in ways, and there is room for more than one interesting doxastic state.
About the conception of knowledge we have extracted from Meno there is no doubt as to the rightness of skepticism. No one can have that sort of knowledge. Perhaps there are other sorts that can be had. We could restrict the set of possibilities that must be considered, eliminating most of the possible worlds, and make requirements (i), (ii), and (iii) apply only to the reduced set of possibilities. We would then have a revised conception of knowledge that requires only a reduced scope, as we shall call the range of structures over which Socrates, or you or we, must succeed in order to be counted as a knower. This is a recourse to which we will have eventually to come, but let us put it aside for now, and consider instead what might otherwise be done about weakening conditions (i), (ii), and (iii).
Plato's Socrates emphasizes this difference between knowledge and mere true opinion: knowledge stays with the knower, but mere opinion, even true opinion, may flee and be replaced by falsehood or want of opinion. The evident thing to consider is the requirement that for Socrates to come to know the truth in a certain world, Socrates be able to find the truth in each possible world, and never abandon it, but not be obliged to announce that the truth has been found when it is found. Whatever the relations of cause and intention that knowledge requires, surely Meno requires too much. He requires, as we have reconstructed his argument, that we come to believe through a reliable procedure, a procedure or capacity that would, were the world different, lead to appropriately different conclusions in that circumstance. But Meno also requires that we know when the procedure has succeeded, and that seems much like demanding that we know that we know when we know. Knowing that we know is an attractive proposition, but it does not seem a prerequisite for knowledge, or if it is, then by the previous argument, knowledge is impossible. In either case, the properties of a weaker conception of knowledge deserve our study.
The idea is that Socrates comes eventually to embrace the truth and to stick with it in every case, although he does not know at what point he has succeeded: he is never sure that he will not, in the future, have to change his hypothesis. In this conception of knowledge, there is no mark of success. We must then think of Socrates as conjecturing the truth forever. Since Socrates did not live forever, nor shall we, it is better to think of Socrates as having a procedure that could be applied indefinitely, even without the living Socrates. The procedure has mathematical properties that Socrates does not.
Continues...
Excerpted from Inference, Explanation, and Other Frustrations Copyright © 1992 by John Earman. Excerpted by permission.
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