Rationality

In ‘81 Dretske wrote an article called “the Pragmatic Dimension of Knowledge,” in which he draws some interesting conclusions about the nature of knowledge.  His article is particularly useful in teaching intro kids because he illustrates his point using a number of good analogies.  His general claim is that knowledge is absolute… but what does that mean?

First he relates knowledge and justification to boiling water.  One cannot, he says, boil water better than someone else.  Either it is boiling or it isn’t – it has reached 100 degrees or it hasn’t.  One can boil water at a higher temperature than someone else, but it is still just boiling.  In the same way, one cannot know something better than someone else.  That is, if you and I both know that today is Tuesday, you cannot know it better than I.  Either we know it or we don’t – either we have sufficient justification such that our belief (that today is Tuesday) counts as knowledge or we don’t.  You might have more (or better, or different) justification than I, but you don’t thereby know it better.

He makes the same point with another anaology: pregnancy.  A woman is either pregnant or not pregnant.  One cannot be pregnant better than someone else.  One might be further along or closer to giving birth than someone else, but both are still just pregnant.

Furthermore, he says knowledge is a relationally absolute term.  It is absolute, but only relative to a context. The words “flat” and “empty” are also relationally absolute.  Something is flat when it is a surface that has no bumps.  Something is empty when it is a space that contains no things.  In this sense they are absolute.  But they are ‘relational’ because we must ask “what counts as a bump?” (in the case of flatness) and “what counts as a thing?” (in the case of emptiness).

“Texas is flat” is true when compared to Wisconsin because we count mountains as “bumps,” but it is false when compared to a mirror because we count much smaller things (say, a pebble sized irregularity) as “bumps.”  “The room is empty” might be true when we are counting people as “things,” but not true when we count chalk dust as “things.”  The room may be said to be empty even though there is a peice of chalk in it, but my pocket may not be said to be empty when there is a peice of chalk in it.

So it is with knowledge.  Dretske defines knowledge as a true belief for which the subject’s evidence eliminates all relevant alternatives.  It is absolute since one must eliminate ALL such alternatives; it is ‘relational’ because in any situation we ask “what counts as a relevant alternative?”  Here things get a bit dicey.

If I say “I know that bird is a canary,” and my justification is it is a yellow bird and all canaries are yellow, then what might be a relevant alternative?  Since goldfinches are also yellow birds, then if I cannot eliminate the possibility that the bird is a goldfinch, then I do not know it is a canary.  If I can eliminate that possibility, then perhaps I do have knowledge that it is a canary.  The point is that some alternatives are usually (or perhaps always) irrelevant – for example, the possibility that I’m in the Matrix.  If I’m in the Matrix, then what I see is not a bird (it’s a computer generated image of a bird).  But since the Matrix possibility is not relevant, I need not eliminate it in order to have knowledge.

By giving an account of knowledge as being relationally absolute, Dretske confirms our intuitions that knowledge is an all or nothing affair, but still saves us from skeptical doubt.  Or so the story goes.

I was reading through Dretske’s “Pragmatic Dimension of Knowledge” and I noticed what seems to be an inconsistency.  I thought I’d share it just because it’s rare to find anything wrong in Dretske’s work.  All of the quotes are from p.376:

1. He claims that high stakes situations do not have a greater number of relevant alternatives than do low stakes situations.  In his example, knowing the coolant level in the car is no different than knowing the coolant level in the nuclear powerplant.  He says that certainly the nuclear powerplant operators shouldn’t rely on the same device that is used in a car, but that if they do, he doesn’t “see any basis for denying that they know” that the coolant is at a safe level. They should be nervous, he says, not because they fail to know the coolant level, but because of their “uncertainty as to when they stop knowing it.”

2. When he asks whether some alternatives are just too remote to be relevant, he arrives at something like Lewis’s rule-of-belief.  Dretske writes, “I do not know exactly how to express the belief condition on knowledge, but it seems to me that anyone who believes (reasonably or not) that he might be wrong fails to meet it.”  He concludes that if the birdwatcher really believes that the Gadwall could be a Grebe (for any reason at all), then he fails to know that it is a Gadwall.

My problem is this: Based on Dretske’s claim in (2), it seems that the powerplant operator, in believing that he might be wrong, fails to know the coolant level of the powerplant.  In Dretske’s words, he would fail to meet the belief condition on knowledge.  Yet, for some reason, Dretske claims in (1) that the operator’s doubts do not prevent him from knowing the coolant level.

I guess everyone makes mistakes, but Dretske is one of those people such that when I find a problem in his work I tend to assume I made a mistake (misread, misinterpreted, or whatever).  Now I’ve thought about it for a while and I don’t see an easy way to reconcile the two points.  I would guess that Dretske would retract (1); he might explain that the powerplant operators know the coolant levels of the nuclear powerplant in the same way (with the same degree of certainty) that the auto-drivers know the coolant levels of their cars.  However, high stakes beliefs require more justification because the actions resulting from those beliefs carry greater consequences.  Knowledge is obtained when we reach optimal justification (’optimal’ meaning something like ‘enough for knowledge’, whatever that might be), but to be prepared to act based on that knowledge may require more than just optimal justification.

The idea of selective confirmation made me realize something about contrastivism. Contrastive knowledge claims are only susceptible to skeptical arguments when the contrast clause includes a contradictory element of the initial proposition P. In other words, claims of the form “S knows that P rather than not-P,” always lead to skeptical results when P is an ordinary proposition about the external world. The equivalent form “S knows that not-P rather than P,” is vulnerable in the same way, though it is less obvious.

First, it’s worth pointing out that contrastivism functions best when the contrastive elements in a knowledge claim are contraries to P. I define contraries as follows: Any two propositions that mutually entail each other’s falsity, but may both be false, are contraries. In symbolic form, A and B are contrary propositions iff the following conditions hold:

(1) A entails ~B
(2) B entails ~A
(3) (A or B) or (~A and ~B)

For example, (4) “the animal is a sheep” and (5) “the animal is a wolf” are contraries by this definition. If either one is true, the other is false – the animal cannot be both a wolf and a sheep at the same time. But (4) and (5) may both be false if, say, the animal is a bunny. In a contrastive knowledge claim, we end up with something like: (C1) “S knows that the animal is a sheep rather than a wolf.” For Schaffer this amounts to something along these lines: Given the choice between (4) and (5), subject S can truthfully answer (4) based on her evidence.

Given a knowledge claim such as (C1) that has a contrary contrast element, one cannot infer a strong skeptical hypothesis under Schaffer’s contrastive account of closure. He gives the rule “contract q,” which says that if S knows that P rather than Q1, and Q2 entails Q1, then we can infer that S knows that P rather than Q2. In the case of C1, in order to reach a skeptical k-claim, there must be some skeptical proposition that entails that “the animal is a wolf.” For example, we cannot use “the animal is a BIV-image of a wolf” as Q2 because it contradicts (and so does not entail) Q1. However, we can give a weak skeptical hypothesis for Q2: “the animal is a wolf in sheep’s clothing.” This statement works under the rule “contract q,” since “the animal is a wolf in sheep’s clothing” entails that “the animal is a wolf.” So from C1, we can make the valid inference that (C2) “S knows that the animal is a sheep rather than a wolf in sheep’s clothing.” If the wolf is sufficiently tricky, then S cannot discriminate between the disguised wolf and a real sheep, so S is clearly not in a position to know C2.

Now, let’s consider the case when the contrastive element is a contradictory to P. We need a statement of the form S knows that P rather than not-P: (C3) “S knows that the animal is a sheep rather than that it is not a sheep.” Under contrastive closure, we can give Q2 as “the animal is a BIV-image of a sheep,” which entails Q1 “that the animal is not a sheep.” From this entailment we can infer that (C4) “S knows that the animal is a sheep rather than a BIV-image of a sheep.” (C4) is obviously false since no one can know that they are not merely perceiving BIV-images (a la classical skeptical arguments).

The conclusion to be drawn is that there are precise conditions under which contrastive closure leads to the skeptical paradox. The conditions are:

P = an ordinary proposition about the external world
Q1 = a contradictory of P (some formulation of not-P)
Q2 = a strong skeptical hypothesis

From these propositions, we start with a seemingly acceptable true knowledge claim, “S knows that P rather than Q1,” and since Q2 entails Q1, we can infer via contrastive closure that, “S knows that P rather than Q2,” which is necessarily false – so we have reproduced the classical skeptical argument from closure.