Explanatory Constraints upon the Theory of Knowledge

A potential objection to Williamson’s account of knowledge that I mentioned in a previous post turns upon the issue of whether such an account needs to provide a finite set of principles for determining whether and why individual justified beliefs constitute knowledge. JTB theories of knowledge meet this constraint by providing a set of necessary and sufficient conditions. This makes it possible both to identify cases of knowledge (in terms of whether all of the necessary conditions are met) and to say in cases where knowledge isn’t present why this is the case (for example because the subject’s belief fails to be sufficiently reliable, or because the truth condition isn’t met).

Williamson, on the other hand, holds that it is impossible to provide a set of sufficient conditions for knowledge, although his account does entail certain necessary conditions that are spelt out in terms of ‘the metaphysics of states’ (for Williamson, knowledge is semantically unanalysable, and therefore primitive). As previously described, Williamson characterises knowledge both as a mental state (whatever that term turns out to mean) and as ‘the most general factive stative attitude, that which one has to a proposition if one has any factive stative attitude to it at all’ (Williamson 2000: 34). On the face of it, this would seem to severely weaken the explanatory power of Williamson’s account since it is no longer possible to say purely with reference to terms set out within the account whether a given state constitutes knowledge or not. Consequently, Williamson appears to render the state of knowing, and the concept of knowledge, somewhat mysterious and unexplained. This in turn makes his account unsatisfying when taken as a theory of knowledge whose purpose is, by most accounts, to explain such things.

It would of course be question begging to assume that in order to provide a satisfactory explanation, the theory of knowledge must provide a set of necessary and sufficient conditions for knowledge. On the other hand, it is unclear how such a theory might provide the necessary explanatory resources through some other means. One possibility might be that the metaphysical state of knowing itself has certain characteristics that differentiates it from other mental states (e.g. belief), and that this in turn can be used to explain whether knowledge is present in individual cases. Such characteristics would not form part of the theory of knowledge per se, but rather a more general theory of mind. They may even turn out to be purely empirical in nature, and so a matter for the brain sciences, rather than a priori philosophical enquiry.

A more promising response, however, involves noting the difference between a requirement to provide a principled explanation in each individual case and providing a set of principles that explain the conditions for knowing in general. It far from clear—indeed it would be a fallacy to assume—that by rejecting the latter requirement Williamson fails to meet the former provided that there remains something to say in each individual case. This amounts to the view that there is no single exhaustive set of conditions that must be met in order for knowledge to be present, but rather a potentially infinite set of reasons why a given mental state may or may not constitute knowledge. On this view, the mistake of the traditional epistemological project is not to assume that such reasons or principles exist (they do), but that they can be codified as a (finite) set of necessary and sufficient conditions. This enables Williamson to claim that his account meets the relevant explanatory constraints upon a theory of knowledge whilst simultaneously denying that such general conditions need to be given.

The response described above has interesting parallels with other areas of philosophy, and indeed mathematics. Lucas (1995) describes the difficulty of describing a continuous curve in terms of the ‘direction’ of a line comprised of a series of points. Since such points are dimensionless, they cannot have a direction except in the mathematician’s imagination, who possesses a ‘finer level of discrimination’ than it is possible to specify algebraically. Similarly, in an argument between two individuals over the rules determining where Oxford professors should live (within 4½ miles of Carfax), there may be no finite set of principles that can be appealed to. Nevertheless, provided that one is able to adequately respond to individual challenges (“Professors of faculty x may live in Bicester”, etc.) in a way that is not entirely arbitrary, the requirement to provide a principled explanation is met even in the absence of a pre-existing set of principles.

The above example brings to mind Wittgensteinian considerations on rule following and the unanalysability of family resemblance concepts; e.g. the concept of a game. Although Williamson would probably deny that knowledge is itself a family resemblance concept, his general dialectical position is similar to that of the mathematician or professor who claims that provided one is able to adequate respond to each challenge with a principled reason, there is no need to articulate the full set of rules by which one does so in advance. Consequently, there need be no finite set of necessary and sufficient conditions for knowledge in order to meet the relevant explanatory constraints on a theory of knowledge. This in turn resolves the worry that his account renders knowledge in some way obscure or mysterious, instead asserting that the rules for determining whether or not knowledge is present and why are impossible to codify without reference to individual cases, thus resulting in a kind of epistemological particularism that is highly Wittgensteinian in character.