Knowledge and its Limits reading group: “Chapter Four: Anti-Luminosity”

This is the fourth (perhaps even the fifth) session of TEM’s summer reading group on Tim Williamson’s book Knowledge and its Limits. Below the fold you’ll find my précis of chapter four, which is entitled “Anti-Luminosity.”

4.1 TW starts by setting the context. As we saw in chapter one, TW’s main claim is that knowledge is a mental state in the most general, fundamental sense of that concept. One common way to resist such a claim is to appeal to the transparency of one’s mental states. It is commonly thought that an agent has special access to her own mental states, at least when she is attending to the question of which mental state she is in. In this way, we are commonly thought to have a cognitive home. This idea, however, seems to lead to a simple reductio of TW’s main thesis, for it is almost universally accepted that we are not always in a position to know that we know. However, if knowledge is a full-on mental state, and it is true that an attentive agent has special access to her mental states, then it follows that one does is in a position to know that she knows. In chapter four, TW attempts to show that the transparency claim is false.

4.2 In this section, TW more rigorsly defines the relevant concepts. Once again, he frames the discussion in terms of conditions that obtain or fail to obtain. If the reader has not done so already, or if the reader is unclear on the terminology, I suggest (re)reading pages 94-95. After the brief terminological interlude, he gives us (L):

(L) For every case α, if in α (condition) C obtains, then in α one is in a position to know that C obtains (95).

The conditions quantified over by (L) are those that are supposed to be transparent to the agent. The question becomes, then, which conditions are luminous? Some supposedly paradigmatic examples are pain, coldness etc.

4.3 In the third section, TW gives an argument against luminosity. He argues that ‘feeling cold’ is not luminous. His strategy is to move from (L) and a ostensibly plausible epistemic notion–which he calls reliability–to an obviously false conclusion.

The first thing he does is set up the case. Imagine that at To it is dawn, and you are freezing cold. At Tn, it is noon, and you are hot. Let To, T1….Tn be the constant set of millisecond intervals between dawn and noon. TW stipulates that you do not feel any change in temperature between any two points. Moreover, he stipulates that as the process proceeds, your confidence in whether you feel cold slowly decreases. Now, consider a time Ti, which is between To and Tn. Suppose that you are cold at Ti. By (L), you know that you feel cold at Ti. However, in order for your belief that you feel cold to be reliably based at Ti, it must be the case that you would not form the same belief in similar circumstances when you were not in fact cold. This idea supposes (R):

(R): If at time t on basis b one knows p, and at time t* close enough to t on a basis b* close enough to b one believes a proposition p* close enough to p, then p* should be true (102).

With respect to the case at hand, TW thinks that (R) entails (1i):

(1i) If in αi one knows that one feels cold, the in αi+1 one feels cold.

Now suppose feeling cold is luminous, which entails (2i):

(2i) If in αi one feels cold, then in αi one knows that one feels cold.

Suppose (3i):

(3i) In αi one feels cold.

(2i) and (3i) entail (4i):

(4i) In αi one knows that one feels cold.

(1i) and (4i) entail (3i+1)

(3i+1) In αi+1 one feels cold.

(3zero) is certainly true:

(3zero) In αo one feels cold.

However, by repeating the argument from (3i) to (3i+1) n times, you get (3n):

(3n) In αn one feels cold.

(3n) is clearly false because in αn it is noon, and you are by stipulation hot.

Reading it this way can be somewhat tricky; so, I will try to summarize it thusly: at dawn T0 you feel cold. By (L), you know you are cold. However, given (R) and (1i), you must feel cold at T1 for your belief at T0 to be reliably based. If you feel cold at T1, then by (L) you know that you feel cold at T1. Given (R) and (1i), it must be the case that you feel cold at T2 in order for your belief at T1 to be reliably based. If you repeat that line of reasoning to Tn-1, it follows from (R) that at Tn you feel cold. This is clearly false.

4.4 In this section, TW examines (in a rather opaque way) (R). First though, he makes it clear that reliability considerations apply only to outright beliefs, and not just to assigning a belief a high subjective probability. Succinctly, one beliefs a proposition p outright iff one uses it as a premise in practical reasoning. There are different degrees of outright belief, for one might only rely on a belief in practical reasoning only when the stakes are sufficiently low.

TW admits that the notion of reliability is hopelessly vague; he confronts the idea that this vagueness is insoluble and because of this we ought to reject epistemic reliabilism. He then grants that the problem is insoluble; but he does not think that this is a reason to reject the notion of reliability in our theory of knowledge. He uses arguments in chapter one regarding the impossibility of giving necessary and sufficient conditions for knowledge as evidence that even though we cannot give necessary and sufficient conditions for a concept, the concept can still be useful. He writes, “The concept is reliable need not be precise to be related to the concept knows; it need only be vague in ways that correspond to the vagueness of knows. No reason has emerged to doubt the intuitive claim that reliability is necessary for knowledge” (100). [For some reasons to doubt the intuitive claim, see this paper by Ram Neta and Guy Rohrbaugh).

With those remarks in mind, TW argues that in the proposed case, (R) supports (1i). This is because it is by stipulation that one's confidence decreases slightly throughout the process. However, since the change of temperature is imperceivable between any two points, one's confidence will only be slightly less between any two points. Thus, one's belief at Ti+1 is very similar to one's belief at Ti, albeit one has slightly less confidence at Ti+1. If one's belief at Ti is to be reliably based, then one's incredibly similar belief at Ti+1 must be true.

4.5 In section 4.5, TW addresses the similarity of his anti-luminosity argument with Sorites arguments. He admits that his argument looks similar to a Sorites argument, and that one might think that his argument fails in the same way a Sorites argument does. This section is very interesting, especially for those of us interested in the logic of vagueness. However, only one argument is important for the epistemological anti-luminosity argument, and it goes something like this:

(1) Sorites arguments fail because a word or term is too imprecise (in other words, the error is easily identified when the vague words or terms or made more precise).

(2) If TW's anti-luminosity is a Sorites argument, then a word or term is too imprecise.

(3) The vague words and terms in TW's argument are feels cold and knows.

(4) When one makes those terms precise, the argument still leads to a false conclusion.

(C) Therefore, TW's argument is not a Sorites argument.

TW argues that (4) is true because even if we sharpen feels cold or knows, (R) still makes it true that one must be cold at any preceding point after one knows one is cold.

For the remainder of 4.5, TW discusses various theories of vagueness (e.g., those that reject classical logic) and purports to show that each of them fails to deal with his argument. Again, it is very interesting, but I find it to be a diversion from the main themes of the chapter.

4.6 In this section TW conjectures as to how far the argument generalizes. He claims (albeit in a vague way) that nearly all ostensible luminous conditions are not in fact luminous, and that in each case an analogous argument to the one presented in 4.3 can be given. Although I appreciate his ambition, I find these types of sections to be frustrating. Because he merely waves his hand at the analogous arguments, he puts himself in the position of being able to claim really bold things, but not to have full responsibility if those proposals fail. Although this is rhetorically useful, I think that it is a bit philosophically dishonest. He does touch on certain issues later--so, I don't want to disparage him completely. All of this is to say that in 4.6 he makes some bold claims without giving detailed arguments for them.

4.7 In 4.7, TW briefly explores the idea that perhaps there could be some type of scientific test to confirm that one did feel cold in some case where was not in a position to know that one was cold. He thinks that such a test probably could not be created. This is because in order to create such a test, one would have to pick out the values, V, that correlate with one feeling cold. This includes the values associated with the condition that one is in a position to know that one feels cold. However, if it contains only those values, then feeling cold is luminous, which, ex hypothesi, it is not. However, if there are values that we are not in a position to know, then we cannot name such values. Thus, either feeling cold is luminous or we cannot create such a test. Since feeling cold is not luminous, we cannot create such a test.

4.8 In 4.8 TW argues that anti-luminosity has serious consequences for Michael Dummett's anti-realist theory of meaning. In short, anti-realist positions seek to explain meaning in terms of appropriateness of assertion conditions, whereas realist theories seek to explain meaning in terms of the conditions under which sentences express truths. Dummett argues that one understands the meaning of a sentence only when one knows its assertibility conditions. However, this argument would fall prey to the same problems Dummett attributes to realist theories if speakers don't have transparent access to the assertibility conditions. Thus, Dummett claims that competent speakers are in a position to know when the appropriate assertibility conditions obtain. TW claims that the argument of 4.3 generalizes to assertibility conditions. Thus, TW claims that his argument shows that Dummett's theory of meaning is either straight-forwardly false or it is plagued with the same problem attributed to the realist.

[Note: Either tonight or tomorrow I will post a critical post on the anti-luminosity argument.]

~ by Errol Lord on July 5, 2007.