CHAPTER THIRTEEN

Knowledge for Better and Worse:

The Battle with Hetherington

In a recent article Stephen Hetherington (1998) proposed a radically new theory of knowledge. Its main tenet is that propositional knowledge comes in degrees (and so we can have better or poorer knowledge of the same proposition) rather than being an all-or-nothing affair. He claims that such an approach has numerous advantages, especially in comparison with the relevant alternatives (RA) theories. Professor Hetherington’s theory is undoubtedly bold and provocative; it certainly deserves proper attention. Indeed, such an attention can only be beneficial: we will either have a better epistemic knowledge about knowledge itself, or we will be able to eliminate a relevant epistemic alternative.

Let me first briefly summarize Hetherington’s theory. He argues that propositional knowledge is a relativistic concept which comes in degrees. New pieces of information or evidence pertaining to the object of knowledge (i.e. the proposition) might increase an epistemic agent’s degree of knowledge. Consequently, even if an agent lacks some information which is connected to p, she still might know that p, though this knowledge will fall short of an absolute, or even better, knowledge of p. This approach eliminates the distinction between relevant and irrelevant alternatives. All alternatives are relevant in the sense that they all contribute (through their elimination) to an agent’s knowledge or to an increase of the knowledge she already possesses. Nevertheless, this approach is not entirely relativistic because it presupposes an absolute ordering of epistemic standards. Consequently the higher the epistemic standard your evidence satisfies, the better your knowledge is.

What are the advantages of this theory? There are at least three, according to Hetherington. First, he claims that his theory offers a new answer to the skeptic’s challenges, since it can ”reconceptualize (and defuse) traditional sceptical doubts.” Second, it is able to recognize and acknowledge the relevance of the skeptic’s position which RA theorists dismiss as insignificant. Finally, and perhaps most importantly, it is a more flexible and sophisticated theory of (empirical) knowledge by allowing for fine-grained evaluations of competing knowledge-claims.

Below, I will examine whether or not this relativistic theory can fulfill these claims. But first let me introduce the following terminology: let me retain the words, know, knowledge, known, etc. for the classical, absolutistic theories of knowledge, and denote Hetherington’s relativistic concepts as a-knows, a-knowledge, etc. Pragmatically, a can be read as a coefficient of knowledge (where a is between 0 and 1), denoting the degree of knowledge that the epistemic agent acquires. Even if we do not, or cannot, attach exact values to a, we can use it comparatively: if A a₁-knows that p while B a₂-knows it, then B knows p better than A if and only if a₂ is larger than a₁.

Several of the traditional skeptical challenges have the following formal pattern: It is known that p entails q. Consequently, if we do not, or rather cannot, know that q is not the case, then we also cannot know that p is the case. Usually p refers to some particular empirical proposition while q stands for some skeptical counter-hypothesis. If you cannot rule out the possibility that ‘you are not dreaming seeing zebras’ (or that you are not merely a brain in a vat, etc.) then you do not know that ‘this is a zebra’. RA theorists dissolve the skeptic’s argument by pointing out that q cannot be the case in any relevant alternative (while they allow it for some irrelevant alternatives). Hetherington’s dissolution is, not surprisingly now, that the skeptic fails because our ignorance about q (or ~q) entails only that epistemic agents do not know (or 1-know) that p, while they still have, or may have, a-knowledge of it. a-knowledge that p might fall short of being perfect, but it is still better, much better, than nothing. Then, admitting that the skeptic is not absolutely mistaken, he adds, in a footnote, that (1998, p. 42n7)

Consequently, if the skeptic’s D2 [you don’t know that you are not dreaming seeing zebras] is true, it seems that he does succeed to some extent. For he shows that your knowledge of seeing the zebras is poorer than you might have thought. But how poor will it therefore be? Maybe he shows only that you lack the best possible grade of such knowledge. And how worrying is that? It should not worry you at all.

Unfortunately, Hetherington does not tell us why we should not worry. Indeed, we do not know (yet) how far our knowledge is from perfection. Moreover, the skeptic will quickly point out that this answer misses the philosophical significance of skepticism. Skeptics do not usually question the fact that we possess reasonable beliefs or even practical knowledge of empirical facts. Their point is that we still do not have the knowledge, in the philosophically relevant sense, that dogmatics usually claim for us. As Descartes says about the skeptic’s hypothesis, it is a “very slight, and so to speak, a metaphysical one” (CSM.ii.25) This is the metaphysical obstacle Hetherington cannot eliminate, although skeptical doubts concern metaphysicians more than those who are engaged in practical matters.

Nonetheless, Hetherington claims that his approach, rather than the RA theorists’, does justice to the skeptics. According to Hetherington, RA theorists maintain “that there would be no epistemic advantage, were you know that you are not dreaming seeing them – beyond the fact of knowing that you are seeing zebras.” In other words, once you know that p, there is no additional advantage to be gained by knowing that ~q. The relativist theory of knowledge, on the other hand, “implies a sense in which skeptical alternatives always have some relevance for us.” Their relevance is that if we were to know that the skeptics’ alternatives do not occur, we would a-know empirical propositions with a higher a then we a-know now. In other words, the skeptics’ hypotheses determine the depth of our knowledge of empirical facts.

Hetherington’s starting point is mistaken, however. Even according to RA theorists, there is a sense in which skeptical hypotheses influence our epistemic standing. Most RA theorists, being externalists, do not assent to the KK-principle. Accordingly, they point out that although skeptical alternatives are not relevant to our knowledge of empirical facts, they are, or can be, relevant to second- or higher-order knowledge (i.e. to our knowledge of such knowledge). In other words, even though epistemic agents might know that ‘this is a zebra’, they might not know that they know it – they might lack higher-level knowledge of it. RA theorists, therefore, agree that skeptical hypotheses affect the depth of our empirical knowledge, but they define this depth differently.[1] Consequently, depth concerns our reflexive knowledge rather than the degree of our knowledge. Relativist knowledge-theorists might answer that this is still not fine-grained enough and that their theory offers a more sophisticated system of epistemic evaluation. I will return to this point later.

Referring to higher-level knowledge can explain one more thing that puzzles Hetherington. What moral, he asks, students can learn from skeptical arguments (and more broadly from epistemology), since they can only re-gain the knowledge they already possessed before. Let me mention first that I was rather surprised to learn that we actually know the existence of the external world. Once, we might recall, it was claimed the scandal of philosophy that we have no proof of it. In the last 200 years, few if any (including the Sage of Königsberg himself) have succeeded in offering a generally acceptable and convincing proof for this matter. Of course, we might a-know the existence of the external world (if it really exists) but a must be rather small in this case (so small that some would prefer to call it ‘better ignorance’ than ‘poorer knowledge’).

But let us go back to the question about the moral we can learn from skeptical arguments: Hetherington’s answer is that students can earn a deeper knowledge than they had before. But this answer is clearly mistaken. First, since we cannot eliminate the skeptic’s challenges, our knowledge will not be better or deeper according to an absolute epistemic standard. Moreover, I would argue that this is not the real gain. What this kind of study can offer is not some knowledge about the external world (anyway, courses in the sciences are far more promising for that kind of knowledge), but rather about ourselves as epistemic agents. What we learn is that our knowledge is not limitless, that we can recognize some of its (or our) limits, and that such a recognition can contribute to a deeper understanding of what we really know. Indeed, this is a lesson we can learn from Kant.

Still, there is the promise that the relativistic theory of knowledge offers a flexible approach that allows for fine-grained epistemic evaluations. If one possesses more pieces of information pertaining to p than others, then one’s knowledge is better. So, let us consider the following example: you and I are in the Zoo, looking at an animal in a pen. Since a sign on the pen says that this animal is a zebra, both of us a-know (with the same a) this fact. Furthermore, you know that zebras are horse-like, striped creatures while I know that they are grass-eating mammals (and that is all we know). Both of us have an equal amount of further information, which in some or other circumstances can be instrumental to eliminating p’s alternatives. Nonetheless, it seems that your additional evidence is better than mine. The point is that pieces of information have different levels of significance and so stipulating the value of a requires a prior ordering of the values of different pieces of information. Moreover, these values might change in different contexts, even if the proposition in question remains the same. Contextualism cannot be gotten rid of as easily as it seems. Moreover, there are many, many (probably infinitely many) facts pertaining to any proposition. Even in areas where we are expert, many facts are not known to us because they are uninteresting or insignificant and we are, of course, finite beings. Accordingly, since every new piece of information increases our (a-) knowledge, a is supposedly a rather small number. But let us take a different route here: if one believes that p, and p is in fact true, then if one has some (even a rather insufficient) reason to believe that p – and we almost always have some reason for our beliefs –, then he seems to a-know it, though a might be quite small. This, however, seems to be an extremely lenient view about knowledge. As I already indicated above, if a is really small, our epistemic position can more properly be called less (or better) ignorance, rather than less or poorer knowledge. As it seems, we can never (1-) know any (empirical) proposition, p, since there are always facts, pertaining to p, about which we have no information. There are many propositions, on the other hand, about which we are absolutely ignorant. Nice score to the skeptic!

Indeed, this whole problem takes us back to the relativistic answer to the skeptic. Once again, we can wonder, how much better or poorer our knowledge (or ignorance) is if we cannot eliminate the many-many different skeptical counter-hypotheses. It seems then, that this solution allows us to grasp rather little; we end up almost empty-handed.

I have another worry about the general aspects of this theory. Hetherington introduces an illuminating example about two scientists, A and B, who both have some knowledge of p. They have to satisfy, however – due to the social, economical circumstances of their countries – different epistemic standards. He who satisfies the higher standard has a better knowledge. Let me modify this example. Imagine that both A and B want to know whether or not p is the case. They go through many experiments and collect much data about p. Eventually, they carry out the same experiments, and they get the same data. Consequently they have the same a-knowledge of p. Nonetheless, after a while B (but not A) recognizes that there is a counter-possibility to p which is q. p and q are both possible but not simultaneously, i.e. ~?(p&q). Furthermore, the two propositions describe very similar situations, and it requires great (perhaps above-human) ability to discriminate p from q. Anyway, B, even after carrying out many experiments, cannot rule out the possibility of q (though actually p is true). Now, we can ask: who has more a-knowledge of p, A or B? According to the relativistic theory, A surely cannot have better knowledge of p.[2] But does B have a better knowledge? Certainly, he knows something that is unknown to A, which is the necessitated conditional expressing p and q’s relationship to each other. But this further piece of evidence does not contribute to his a-knowledge of p; in fact, it decreases his justification for p since this new information raises significant doubt about it. If a-knowledge is a monotonic function of justification, as Hetherington seems to suggest, then B certainly does not have better knowledge of p than A. So, A and B have the same a-knowledge of p. This is also less than convincing, since it suggests that the possibility of q does not matter at all even though we know that it, in fact, matters a great deal.

The answer to this problem is, I think, the following: recognizing the relevance of q changes the situation, or context. And the former and newer contexts are, as it seems, not comparable. This conclusion is worth generalizing: the fundamental assumption of Hetherington’s theory is that contexts or situations are always comparable and that there exists – at least in principle – an ordering of them. I agree that his approach does not require to actually present such an ordering. But my question is whether or not such an ordering is possible at all. My counter-example suggests, however, that the possibility of such an ordering is at least doubtful. Consider the following: such an ordering would require a perfect language which would be able to express the difference between any pair of possible situations. Certainly no human language has such an extraordinary capacity. This implies, at the least, that Hetherington’s theory is based on a perfect, “divine” language. His theory of knowledge, although in different ways, requires as high a standard as the skeptic’s. Both operate with the idea of omniscience. Admittedly, there is a difference between these positions: while the skeptic denies us from knowledge on the basis of his unsatisfiable standard of knowledge, the relativistic theorist just renders such a knowledge practically useless, since we are in principle unable to stipulate the level of our knowledge.

At the beginning of this chapter I anticipated two possible outcomes for my analysis. Professor Hetherington’s theory, as it seems, does not improve our epistemic knowledge about knowledge itself. Rather, if my arguments are sound, one possible epistemic alternative can be eliminated. And certainly, this is one way getting closer to know what knowledge is.