Is Knowledge Composite or Prime?

In Chapter 3 of Knowledge and Its Limits, Timothy Williamson offers recombination arguments for the primeness of knowledge (and other mental states). To say that knowledge is prime is to deny that it is a composite of narrow (internal) and broad (external) conditions. Each argument begins with two cases of knowledge that are like with respect to their internal condition but different with respect to their external condition. If knowledge is composite, then recombining the internal condition of one case with the external condition of the other case will produce a third case of knowledge. Williamson needs one such recombination that fails to produce a case of knowledge to undermine the thesis that knowledge is composite. Here's Williamson:

...in [case 1] there is water on the right and gin (which looks just like water) on the left, and a brain lesion causes one visually to register only what is on the right. In [case 2] there is gin on the right and water on the left, and a brain lesion causes one visually to register only what is on the left; in the [case 3] internally like [case 1] and externally like [case 2], there is gin on the right and water on the left (as in [2]), and the brain lesion causes one visually to register only what is on the right (as in [1]). Thus, given appropriate background conditions one sees water in [1] and [2] but not in [3]. (70)

My criticism of Williamson's argument is this. It is all but clear that cases 1 and 2 are in fact cases of seeing. After all, for Williamson seeing entails knowing (Chapter 1), and he is sympathetic to the thesis that one can know only if she could not easily have gotten it wrong (Chapter 4). But it would seem that in cases 1 and 2 the subject could very easily have gotten it wrong, since she could very easily have looked at the gin when forming her water-belief. The worries here are the same for barn-beliefs in Barn County. Just as it seems strange to say that I know that there is a barn when there are fake barns in the vicinity, it seems strange to say that the subject in cases 1 and 2 knows that there is water when there is gin (indistinguishable from water) in the vicinity. Additionally, the subject in each of the two cases has a brain lesion blocking half of her visual information! One would not be remiss to pause and question the respectability of the partially disabled visual process. In sum, two worries arise. There are Ginet-Goldman style barn considerations to worry about, and there are Bon Jour-Plantinga clairvoyance-brain lesion considerations about the epistemic respectability of strange but reliable belief-forming processes. Both worries go against a claim to knowledge in cases 1 and 2. And so, if seeing entails knowing, then arguably the subjects in cases 1 and 2 fail to see. Related worries surround Williamson's other arguments. Here is Williamson arguing more directly for the primeness of knowledge.

Let [case 1] be a case in which one knows by testimony that the election was rigged; Smith tells one that the election was rigged, he is trustworthy, and one trusts him; Brown also tells one that the election was rigged, but he is not trustworthy, and one does not trust him. Let [2] be a case which differs from [1] by reversing the roles of Smith and Brown.... Now consider a case [3] internally like [1] and externally like [2]. In [1], one does not trust Brown, because one does not trust him in [1], and [3] is internally like [1]. Equally in [3], Smith is not trustworthy, because he is not trustworthy in [2], and [3] is externally like [2]. Thus, in [3], neither Smith nor Brown is both trustworthy and trusted. Consequently, in [3], one does not know that the election was rigged. Thus the condition that one knows that the election was rigged is prime. (72)

My criticism here is this. In recombining the internal condition from case 1 and the external condition from case 2, Williamson fails to include the entire external condition from case 2. Part of the external story in case 2 is that the belief in question was produced by reliable testimony. In case 3, the belief was not produced by reliable testimony. But if in case 3 the belief was not produced by reliable testimony, then Williamson has not properly recombined the cases. He has not included in case 3 the full external condition from case 2. Therefore, the recombination is incomplete.

A general criticism that I am making is that Williamson, in all of his recombination arguments, fails to include some causal or counterfactual conditions as part of the broad (external) condition of the subject in cases 1 and 2. The result is a mistaken attribution of knowledge in the first argument and an incomplete recombination in the second argument. Therefore, the question about the primeness of knowledge remains open.

The Most General Factive Mental State Operator

Last week I re-read the first chapter of Timothy Williamson's Knowledge and Its Limits. TW argues that 'knows' is the most general factive mental state operator. To be a factive mental state operator (FMSO) is to be a factive semantically unanalyzable expression that attributes a propositional attitude to a subject. The semantic unanalyzability claim is that, by definition, an FMSO is never synonymous with a complex expression whose meaning is composed of the meanings of its parts. So, for instance, 'could hear' is a FMSO. There is a reading of it such that the presumption of truth is not cancelable, as is revealed by the deviance of


(1) She could hear that the volcano was erupting, but it was not erupting.


Moreover, the meaning of 'could hear' is not composed of the meanings of 'could' and 'hear', for that would assimilate 'could hear' to something like 'it is merely possible that s heard that p', which is not factive.

Additionally, 'could hear' is further evidence that 'knows' is the most general FMSO, since 's could hear that p' implies 's knows that p'.

Let's explore the properties of other FMSOs. I want to argue that there is a more general FMSO than 'knows'.

Consider the ambiguity in each of the following expressions:

'could see that'

'could hear that'

'could feel that',


'can't believe that'

'is not happy that'

'is not surprised that'

'failed to realize that'

'is not impressed that'

'is not able to taste that'

Each of these has a factive and a non-factive reading. For instance, 'cannot believe' is factive in

(2) I cannot believe that you are smoking again,

but is not factive in

(3) I cannot believe that I don't have any beliefs.


Now the non-factive readings of the above list items are semantically decomposable. They may be paraphrased roughly as


'it is false that s believes/is happy/is surprised/realizes/is impressed/is able to taste that'

or

'it is (merely) possible that the subject s sees/hears/feels that'.



Exactly analogous remarks may be made about knowability- and ignorance-attributions. More carefully, 'could have known that' and 'does not know that' both have a factive and a non-factive reading. Let's discuss 'could have known that'. The non-factive reading, perhaps not common in ordinary English, is that it is merely possible that s knows that p. The other reading carries a presumption of truth as in 's was in a position to know that p'. Notice that the presumption of truth is not cancelable. This is demonstrated by the deviance of the following claims:


(4) Andy could have known that grandmother was ill, even though she was not ill.

and

(5) Sally was in a position to know that Andy was cheating, but he was not cheating.

The deviance of the claims suggests that the presumption of truth is semantic and not cancelable.

As with the factive readings of the items on the above list, we should expect that the factive readings of 'could have known that' and 'is not known that' are not analyzable. My hypothesis is that they are not analyzable. And I suggest that the burden is on one who thinks otherwise to show that 'could have known' is different from all of our other factive operators of the form 'could have ___ed'.

Incidentally, the non-factive readings of all of the aforementioned expressions fail to attribute a propositional attitude to a subject. They either outright deny the presence of the attitude or affirm merely its possibility of obtaining. The factive readings of the above operators, on the other hand, all attribute a propositional attitude to a subject (with the exception of 'does not know that').

According to Williamson, when a propositional attitude that p is attributed, so is a grasp of the concepts in p. Since the factive reading of 'does not know' fails to attribute grasp of meaning, we may conclude that it is not a mental state operator. A fortiori it is not an FMSO. Importantly, 'could have known' does attribute grasp of meaning. Consider,

(6) Andy doesn't understand high-energy physics, yet he could have known that there are top quarks in pp collisions.

Or

(7) Andy doesn't grasp any of the rules of Chess. He was nevertheless in a position to know that his King was about to be mated.

The oddities of (6) and (7) suggest that knowability is a mental state---that 'to s it is knowable that p' implies 's has an attitude that p'---minimally, it implies 's grasps the meaning that p'. Similar things can be said about 's failed to realize that p'. It wouldn't be a failure to realize that p, if the subject didn't have a grasp of the concepts in p.

It would seem then that 'knowable' or 'could have known' is an FMSO. The problem for Williamson's account is that 's could have known that p' does not entail 's knows that p'. Hence, 'knows' is not the most general FMSO. Instead, the entailment goes the other way. Are we to conclude that 'could have known' is the most general FMSO?