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The Dialleus

In justificationism, skepticism on 16/06/2011 at 3:34 pm

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? (Plato, Meno, 2nd ed. tr. G.M.A. Grube (Indianapolis: Hackett 1981), 13 (80d).)

In its most general form, problems take place when our conjectures run up against some sort of difficulty, some sort of wall that impedes advancement. Our intuitions are stressed during rigorous testing. That is a problem. For instance, the following argument looks like a problem…

  1. I know I have hands.
  2. If I was a brain in a vat, I would not have hands.
  3. If I do not know I am a brain in a vat, I do not know I have hands.
  4. I do no know I am not a brain in a vat.
  5. I do not know I have hands.

Here lies the beginning of the diallelus or ‘wheel’ argument. Just as one can rub a piece of gold against a touchstone to classify gold as pure or impure, we can subject scientific statements to a test to determine if they are true or false. The legitimacy of statements are determined by their pedigree or origin, and not the impossibility of doubting their truth. Otherwise, our scientific theories will always remain guesswork: after acknowledging the very possibility that you are a brain in a vat, it’s far too easy to doubt that you even have hands.

Take a definition of truth to be something like “correspondence to the facts.” The statement “grass is green” is true iff grass is in fact green, but that doesn’t tell us if grass is in fact green. A definition of truth isn’t a criterion of truth, in much the same way a definition or description of gold is not the same as rubbing a piece of gold against a touchstone. We are in need of a proper authority as a basis for our scientific knowledge: a criterion of truth, not a definition of truth.

A criterion of truth is something that provides a reason for the truth of the statement “grass is green.” The problem can then be reformulated without reference to certain-knowledge as follows:

To know whether things really are as they seem to be, we must have a procedure for distinguishing appearances that are true from appearances that are false. But to know whether our procedure is a good procedure, we have to know whether it really succeeds in distinguishing appearances that are true from appearances that are false. And we cannot know whether it does really succeed unless we already know which appearances are true and which ones are false. And so we are caught in a circle. (Rodrick Chisholm, ‘The Problem of the Criterion,’ 1982)

The problem pops up once again, but this time in reference to a proper procedure, instead of certain-knowledge.

To judge of the impressions that we receive of objects, we ought to have a judicatory instrument; To prove the reliability of this instrument we must have a demonstration; to prove the demonstration and instrument: so here we are going in a circle! Seeing that the senses cannot settle our dispute, being themselves full of uncertainty, it must be reason that is to do it; but no reason can be established without the support of another reason: so here we are running backwards to infinity! (Michael de Montaigne, “Apology for Raymond Sebond,” Essays of Michael de Montaigne, tr. and ed. Jacob Zeitlin (New York: Nopf 1935), 266.)

There are a lot of distinctions between kinds of knowledge, usually between knowledge that refers to the physical world and knowledge that refers to abstract intellectual concepts. There is a priori and a posteriori knowledge, synthetic and analytic statements, and necessary and contingent propositions. There’s a lot of complicated stuff about the differences between all these terms, but here is a good overview.

Analytic statements are true by nature of the definition of their words. For example, “all rectangles are four-sided” is an analytic statement. If you’re talking about three-sided or five-sided rectangles, you’re making a mistake in what the word means in our language. Synthetic statements, unlike analytic statements, are not true by nature of the definition of their words. For instance, the statement “Some bachelors drink beer,” while unquestionably true, is a synthetic statement.

Some analytic statements are a priori, and most synthetic statements are a posteriori. A posteriori statements are true by nature of some physical state of affairs, not as a consequence of a rule of logic. For instance, the statement “there is a dog in the bog” is a synthetic a posteriori statement, as is “there is a fox in the box”: you need to go out and find the dog in the bog or fox in the box or cat in the hat to determine its truth or falsity.

For brevity’s sake, I will call synthetic a posteriori statements “SAP” statements. We can now restate the problem of the diallelus as so:

  1. To know a SAP statement is true, we need a good procedure that distinguishes between true and false SAP statements.
  2. To distinguish between a good procedure and a bad procedure, we must know which SAP statements are true and which are false.
  3. To know a SAP statement is true …

If you’ve caught on, you’ll see that we’ve ended up in a vicious circle. For instance, in light of the tradition of Anglo-Saxon Empiricism (Hume, Mill, Berkley, etc.), which assumes the locus of authority derives from sense experience, we might say that to know a true SAP statement, one must appeal to phenomenal impressions; phenomenal impressions are known to be accurate only by knowing which SAP statements are true and which are false.

We must assume, without any reason given, that phenomenal impressions are accurate, even though phenomenal impressions are error-prone. Yet, if we’re after a foundation for our knowledge, why not just take phenomenal impressions as knowledge and toss the rest? Now we’ve got idealism, or anti-realism, or neutral monism.

In order to get out of this vicious circle or the idealist trap, we might appeal to an intellectual intuition, like the Continental Rationalist tradition (Descartes, Kant, Spinoza, etc.): there must be an a priori criterion to determine if SAP statements are true or false. How do we know that the criterion is a good criterion? There must be a meta-criterion that determines if a criterion is a good or bad criterion. How do we know that the meta-criterion is a good meta-criterion? There must be a meta-meta-criterion. How do we know that the meta-meta-criterion …?

Do not judge by appearances, but judge with right judgment.  (John 7:24)

We’ve now entered an infinite regress of criterions. Furthermore, if we choose a self-justifying criterion somewhere along this regress, then we’re no better off than before, since a self-justifying meta-criterion could be false and still be self-justifying. An a priori solution cannot work without begging the question. We must assume, without any reason given, that our intellectual intuitions are accurate, even though our intuitions are often false.

If we see knowledge as requiring a foundation of some sort, we must be either Empiricist or Continental Rationalist fideists. On the one hand, we can become antirealists; on the other (hand), we can freely engage in the most absurd kinds of metaphysics. In either case, knowledge is reduced to an act of religious faith, rather than a rational enterprise.

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