What follows wasn't intended as a bit of silliness as I began writing it, but I think that's what it turned out to be. It may provide amusement if not insight.
For my money, Williamson strikes his best chord in the second paragraph on page 10, beginning, "Discipline from..." — Leontiskos
Let's talk about that then. Here's the whole paragraph:
Discipline from semantics is only one kind of philosophical discipline. It is insufficient by itself for the conduct of a philosophical inquiry, and may sometimes fail to be useful, when the semantic forms of the relevant linguistic constructions are simple and obvious. But when philosophy is not disciplined by semantics, it must be disciplined by something else: syntax, logic, common sense, imaginary examples, the findings of other disciplines (mathematics, physics, biology, psychology, history, …) or the aesthetic evaluation of theories (elegance, simplicity, …). Indeed, philosophy subject to only one of those disciplines is liable to become severely distorted: several are needed simultaneously. To be ‘disciplined’ by X here is not simply to pay lip-service to X; it is to make a systematic conscious effort to conform to the deliverances of X, where such conformity is at least somewhat easier to recognize than is the answer to the original philosophical question. Of course, each form of philosophical discipline is itself contested by some philosophers. But that is no reason to produce work that is not properly disciplined by anything. It may be a reason to welcome methodological diversity in philosophy: if different groups in philosophy give different relative weights to various sources of discipline, we can compare the long-run results of the rival ways of working. Tightly constrained work has the merit that even those who reject the constraints can agree that it demonstrates their consequences. — pp 10f
There's a bit of a muddle at the beginning, because he says
(P) Discipline from semantics is by itself sufficient for the conduct of a philosophical inquiry.
is
false.
Insufficient, so something else must be needed. But then he says you need something else when the following condition holds:
(D/s-) Philosophy is not disciplined by semantics.
But the denial of (P) already guarantees that when philosophy is disciplined by semantics, it must also be disciplined by something else as well.
The condition suggested in (P) is a conjunction:
(D/s) Philosophy is disciplined by semantics.
(D/o) Philosophy is disciplined by some other field.
Then (P) is the claim that philosophy is disciplined when both (D/s) and (D/o) hold.
But that means there are two ways for (D/s-) to hold: failure of (D/s), or failure of (D/o).
Suppose (D/s-) holds because (D/s) fails: philosophy needs another source of discipline because it is missing semantics. If it happens that (D/o) holds ― so there already was another source ― you need yet another one. Which he will address:
philosophy subject to only one of those disciplines is liable to become severely distorted: several are needed simultaneously.
Only (D/s-) seems to rule out the possibility of being disciplined by a single field, so this condition can never hold.
But what about the other way for (D/s-) to hold: (D/s) holds but (D/o) fails; philosophy is disciplined by semantics but not by anything else (and so is not disciplined). Then philosophy needs to be disciplined by something else, precisely because it is not already disciplined by something else.
I think part of the problem here is that "disciplined" is being used in two different ways ― not quite two different senses. It's rather like the way we use the word "hot" in two ways: you can ask if something is hot or cold, and you can ask how hot something is (or similarly, how cold). Similarly, discipline seems to be, on the one hand, a matter of how firmly your inquiries are guided by other disciplines, and by how many; but on the other seems to be something that can be achieved, and that stands as the contrary of "undisciplined".
This is rather unfortunate. Because Williamson is a classical logic man, the language of sufficiency and necessity comes readily to hand (it's all over that paragraph), and he's inclined to piece together his thoughts in conditionals (which point one way or the other, depending). But what he wants to describe is quantitative, not an all or nothing business, so by the end of the paragraph we're relying more and more on quantifiers to round out the picture ― one is not enough, several are needed, and "not any" is right out.
But what he really seems to need is measurement:
how disciplined is this practice, to be answered by checking first
how many other disciplines are brought to bear, and then checking
how well the practice is disciplined by each. He seems to recognize this because he points out that "different groups in philosophy [might] give different relative weights to various sources of discipline," which is to say that their practice might be more or less disciplined by a given field.
The numerical model is clearly what's needed ― so why didn't we start there? Why does the model begin with "is" and "isn't", "insufficient" this and "necessary" that? Why does it sound like he wants to say "Be disciplined rather than undisciplined" when it will turn out, quite soon, that he means "Be more disciplined by more things, rather than less disciplined by fewer things"?
It's not a very interesting question, in itself, but I think there's an answer: this is a quirk of the way Williamson's mind works.
His two central pieces of work are on vagueness and knowledge. As I understand it, the work on vagueness supports the view that vague predicates do, as a matter of fact, have a sharp, definitive cutoff for when they apply and when they don't: there is a number of hairs on a man's head, having one fewer than which makes him bald. But ― and this is the curious bit ― we are unable to know what that cutoff is. I understand this was called the "margin of error" argument.
Come along to knowledge ― much of this I've actually read. There are several theses to this work, but one of them is the "luminosity" argument: knowledge is a mental state which an agent definitely is or is not in, but it is generally not luminous, meaning the agent generally cannot know whether he is in that state or not. Why not? Because the difference between being in a state of knowledge and not being in a state of knowledge is too fine for us to reliably discriminate between them. He argues for this by showing that between two states apparently easily distinguished you can interpose stages that take you gradually from one to the other, so gradually that failing to reliably discriminate each step, you cannot claim to reliably discriminate the easy cases. It's a boiling frog argument. Or a slippery slope.
It's obvious enough that the positions are related. (I don't remember clearly whether he notes the similarity in his book, but I do recall him mentioning the work on vagueness, so he probably does.)
Now what about discipline? Here again, he seems to want to stake out what we might call "realism about discipline" ― i.e., that there is a fact of the matter about whether you are or aren't ― but where he ends up is with this scale of gradations between being disciplined and undisciplined.
Now what you'd expect from his other work (I believe this paper falls between vagueness and knowledge) is that the important corollary to the discovery of this area of gradation between disciplined and undisciplined, is that we cannot know for sure where we fall on it! We may indeed be doing proper disciplined philosophy, but we cannot know it.
Well, he certainly can't say that! The whole point of the lecture is that you should
make sure you are properly disciplined, so this must be something you can do, and you must be able to know whether you are doing it or not. Otherwise, it's just "try to", which he's clearly not going to countenance.
One more little note. I think I've told this story elsewhere, but it'll have a different point now. Williamson somewhere tells the story of explaining Gettier problems to an economist, who was entirely nonplussed. "What's the big deal?" he asks. "So there are exceptions, so what? All models are wrong." Williamson reflects on this and thinks maybe the economist is onto something and that philosophers should take a stab at this model-building business. (I believe he took his own advice and collaborated with more numerical types on at least one paper.) ― So this is the odd thing: Williamson is a diehard realist of the first order, all of whose work seems to force on him a recognition of degrees and weights and multiple factors that should be considered in building a model, but either he cannot bring himself to join the Bayesian revolution
@GrahamJ has recommended to us (and where I'm inclined to land, truth be told), or his own practice already falls on the "more Bayesian" end of the scale, but he is unable to know it.