Knowledge and its Limits, Chapter 3 (part 2)
Here’s the next installment of notes on Knowledge and its Limits, Chapter 3:
3.4
Section 3.4 is devoted to arguing that prime concepts are important for “[understanding] the connection between present states and action in the non-immediate future” (80). TW gives a great example to illustrate this.
I’m thirsty; how likely am I to be drinking soon? If I’m seeing water, the answer is, of course, “very”. (Recall that Williamson showed in section 3.3 that the condition that one sees water is prime.) But if what I’m seeing is merely a mirage, then I’m not very likely to be drinking soon.
3.4 also sees TW give his take on the epistemic value problem. We seem to value knowledge more than merely true belief; why is that? TW’s answer is that knowing about others’ knowledge helps us figure out what they’re going to do. Knowledge is more stable than merely true belief; for one, it’s “less vulnerable . . . to rational undermining by future evidence” (79). Since the course of action one’s likely to take is determined in part by one’s beliefs, knowledge of knowledge is therefore more helpful than knowledge of merely true belief insofar as the prediction of action is concerned. All of this bolsters TW’s criticism of arguments for internalism that proceed via some sort of premise about the internal playing a “distinctive role in the explanation of action” (65).
3.5
In section 3.5, TW argues that prime concepts are important for another reason–they often play a crucial role in explanations that are suitably general. What does it mean to say that an explanation is suitably/appropriately general? It’s easiest to answer by saying when an explanation is not appropriately general; an explanation of why a condition obtains that appeals to the fact that some other condition obtains will fail to achieve appropriate generality when “the condition to be explained would still have obtained in the same way even if the cited condition had not obtained” (81). This motivates a comparative concept of generality; an explanation that cites a condition D to explain why condition C obtains is more general than an explanation that cites a condition E iff C is less likely to happen given that ~D obtains than given that ~E obtains. This in turn suggests a formal measure of the generality of explanations of the form ‘C obtains because D obtains’: P(C|~D).
And so we’re led to the formal work in section 3.6. I’ll skip summarizing this section or criticizing it, since Branden Fitelson does a much better job in these notes than I ever could. Everyone should take a look at those. Particularly interesting are his criticisms under the heading “Other Measures of Probabilistic Dependence.”
I had a slight problem with TW’s seeing water example. On TW’s picture, we form an intention to pursue some action, and then at some time put that intention into effect. In the seeing water/seeing a mirage case, the intention to commit an action is presumably to intend to drink. To put that intention into effect is presumably to try to drink. I think, if we are thirsty and we see a mirage we are just as likely to try to get a drink as we are if we see water.
I don’t think any of this hangs on whether time is “dense” or “action at the next instant.” It seems like we can define “the next action” in some way that doesn’t provide any explanatory value for a prime condition over the narrow part of a composite condition.
If we instead try to explain “subsequent” actions, however, then I think prime conditions do carry more explanatory weight. For instance, how likely is our next action after trying to take a drink be an action to seek out more water if we are thirsty? It seems much higher if we see the mirage than if we see water. And some of the other considerations TW goes into address my worry about the example. What do you think?
As for the rest, I think it sounds good and I’ll have to check Fitelson’s stuff about this section (I’ve only been reading some of the stuff on the site Errol linked to).
And as a totally irrelevant aside, I’m not sure that considering whether time could be “dense” seems quite right, at least if dense means what it does in math for sets (a set can be nowhere dense and still not have a “next” member for any given member, I think, at least if I’m thinking of the Cantor set correctly). Maybe dense has some other meaning here, but it seems better to just say “continuous,” or perhaps non-discrete if we continue the properties-of-sets analogy, or perhaps some form of “gunk” if we want to turn to mereology.