this utility is what I'd say are the sorts of we'll call them interests that the engineer and builder have to keep in mind. It can be judged to succeed or fail insofar that we have some standards of utility to judge it as successful or a failure. — Moliere

I think there's room to distinguish function from utility (or interest or value or aesthetic or ...).

A bridge (I'm just going to make this up) is a structure that enables conveyance of people or goods or vehicles across an obstacle under their own power, whether that's something you value or not. A structure can fail to enable such conveyance, whether you want it to or not, and so is not (or is no longer) a bridge.

I think it's a distinction worth calling attention to because this is exactly what people hate about analytic philosophy, and why they'd rather read Nietzsche or the Stoics or Camus.

Analytic philosophy keeps values in quarantine. When we talk about "epistemic values," or some such, that's understood to be heuristic, just shorthand for "fit to purpose," more or less. We're still not taking about "why we value knowledge" or anything like that.

And this is seen as a good thing to do by the analytic community because you ward off this sort of thing: "Your analysis is correct (or incorrect) because you share (or don't share) my values." That's a hellscape analytic philosophers want no part of, but it is embraced elsewhere, with suitable obfuscations.

That's why there is a sort of "shut up and calculate" attitude in analytic philosophy, and why Williamson is demanding that people work harder. It's why his model for a successful theoretical discipline is mathematics, which he imagines sitting in the armchair next to philosophy's.

(I can put it even more colorfully. The analytic attitude is this: Philosophy doesn't need a hero; it needs a professional.)

I'll try too:

We decide to build a bridge because we believe it would make our lives better, and the sense of "better" there is colorably an aesthetic judgement. Life with the bridge would be preferable, simply in terms of what we want our lives to be like.

That's persuasive, but we still have the problem that the bridge's capacity to improve our lives is instrumental; it has to succeed as a bridge, and can be judged to succeed or fail as a bridge, without any consideration of our motive for building it, and without considering whether we were right that the bridge would improve our lives in the way we wanted.

(Oh! Spectacular movie reference for this: Stanley Tucci's speech about his bridge in Margin Call, 2011.)

You can always take a step up like this, and examine anything by placing it in a wider context, but while you will gain new terms for evaluating the thing, you'll lose the ones you had before.

Since it's not true, and it's not good -- well, maybe it's not beautiful in the old sense of the aesthetic, but there is this broader sense of "beautiful" which is that which is judged worthy, but not on moral grounds.

Basically the judgment of values which are not-moral falls into the aesthetic. Sometimes we like to say these are "epistemic values", or some such, but even there there are are choices between which epistemic values one makes appeals to. — Moliere

Here for instance you didn't have to take the word "good" to have an exclusively moral sense, and I feel quite certain than @Count Timothy von Icarus would not. I think your use of "aesthetic" (or maybe "beautiful" in the mooted non-traditional sense) has noticeable overlap with his use of "good".

I think Williamson is only demanding that philosophical theories succeed as theories, to some recognizable degree. Whether they make our lives better or worse or give us a warm fuzzy, he's presumably going to consider a separate question.

the desire for results, success, knew knowledge -- how is that not aesthetic? — Moliere

Because it isn't?

I'm genuinely puzzled why you'd stretch the word "aesthetics" to cover, well, everything. Now if you wanted to talk about value or utility or something, you'd have an argument. But an engineer who designs a beautiful bridge has to make sure, first and separately, that what he designs will function as a bridge and it'll probably have to meet a host of other requirements before considerations of beauty come into it.

I do think philosophy can to some extent provide a service to other disciplines, fixing the leaks and bad smells. — Banno

I don't think any other discipline has asked for philosophy's help or wants it.

That's not to say that some kind of interdisciplinary business isn't possible and sometimes interesting, but no astronomer (or even social psychologist) has ever said, "Whoa, have you seen the new data? We're gonna need a philosopher."

Doing philosophy involves going back and looking again at what we have said — Banno

This is the same issue that bedeviled the other thread, that you need something to dissect. There are a lot of candidates for that; is one of them the kind of theory that Williamson thinks it is the business of philosophy to produce?

"Why not?" you'll say. "Have scalpel; will travel."

But there's a genuine question of intention here: Williamson would absolutely agree to carefully examining theories, with the goal of improving them or producing better ones, not with the expectation they'll all be left dead on the dissecting table.

Ok, lets' settle on clear knowledge... — Banno

Why do I feel like I just walked into the Meno?

Do you think that "learning" in philosophy amounts to becoming clear about what you already know? Or can philosophy provide us with knowledge we did not have before?

Do you have any impression what's happened since 2004? — Ludwig V

I really don't. That's right in SEP's wheelhouse though. I think of it primarily as a "review of recent literature" for grad students.

Wonder if anyone's ever thought of that before! — J

The emoji indicates that you know the answer is "everyone", right?

In the context of the paper, where the principal example is semantics, we could note that Williamson is going to insist that people actually try doing this analysis formally, and he has very little patience for claiming, before the work begins, that it's unnecessary or impossible.

You and I seem to agree with large portions of Williamson. — Leontiskos

I would at least say, perhaps incorrectly, that I think I get where he's coming from, and I do have considerable sympathy with the view expressed, but I also have reservations.

There honestly isn't much point in "taking his side" here or not because the paper itself, as he acknowledges, is pretty handwavy. As philosophy, it's pretty weak tea, but it might be strong medicine for philosophers.

neither side — Ludwig V

Yeah that's fair. My memory of the paper is probably colored a bit by knowing which side Williamson is on.

Here's a quick example (from Wittgenstein) of everything, I hope.

Is the standard meter rod (or whatever it's called) itself 1 meter long?

The question assumes a bivalence that turns out to be troublesome. "Obviously" and "obviously not" both spring to mind and are both defensible.

Some will be inclined to shrug off the question and say it is "by convention". But Quine argued (repeatedly and at length) that "true by convention" is actually incoherent.

So then David Lewis comes along and writes a book (cleverly titled "Convention") that gives a rigorous definition of convention in terms of game theory (complete with lemmas and theorems), and applying it to semantics, and Quine writes a preface saying Lewis has done more than any other philosopher to mount a defense of "truth by convention".

I think Williamson here says, this is how it's done. You put in the work, develop the theory as far as you can, and you'll at least have some evidence for or against, insofar as some obstacles are overcome or roadblocks to progress appear.

lowest common denominator — Leontiskos

Sometimes a grandmaster discussing a game will say something like this: "I looked at sacrificing the pawn, but I didn't see anything concrete." "Concrete" here is a magic word; it means actual variations leading to a specific advantage, not just "I'll have more piece activity," or something vague like that.

A lot of discussion of chess in the pre-engine era turns out to have been mere handwaving if not outright bullshit. Once you have a machine that cares a lot more about the concrete than vague evaluations, chess starts to look different.

I think Williamson's minimum requirement is theories that produce something concrete. Rather than "I think white stands better" versus "I think black", show me some actual variations.

That sounds fine to me, though I don't see "undemonstrated" or "unjustified" as a truth value. — Leontiskos

Intuitionistic logic is a whole thing, which we probably don't want to get into here, and to which I would not count as a reliable guide. It's part of the gossipy backstory of this paper, is all.

this comes too close for my liking to "flaw-based" resolution of a difficult issue — J

One way to read the paper is that Williamson proposes an alternative to "my theory versus your theory", namely results, success, new knowledge. Proof is in the pudding.

(For instance, skeptics of intuitionistic logic have to admit it has proved very useful for proof theory, and thus for creating automated proof checkers. That's a success.)

Then he has to come up with a plausible story about a kind of result all parties of good faith could recognize.

And you do all this so that the choice between theories or approaches is not "merely aesthetic". (@Moliere)

playing a different game — Leontiskos

My memory is that that's how this whole things started: Dummett pointed out that some philosophers seemed to be playing a game that they did not realize was rigged against them, so they tended to flounder.

The solution he proposed was to recognize when you were inclined to deny that a specific type of statement within a given domain was bivalent.

(Dummett also had no truck with more than two truth values, so for him (and I believe Williamson agrees with him about this) intuitionistic logic becomes especially attractive: the sentential operator "not" is understood as "it has not been demonstrated that ..." Hence the double negative is merely "it has not been demonstrated that it has not been demonstrated that ..." )

So, side R made the rules for the first version of the game (universal bivalence); the other side AR made a new set of rules that gave them a fair chance, but those rules were never accepted by side R (because you lose LEM).

Given Williamson's critique of (the lack of) anti-realist semantics, another title for the paper might have been "Put Up or Shut Up."

I think Williamson finds anti-realism deeply suspect, but is frustrated because its opponents are denied the opportunity to land a solid punch, if not quite a knock-out blow.

To switch to another sports metaphor, anti-realists won't step up to the plate, but hang around off to the side claiming they could easily get a hit if they wanted to.

If there were ideas definite enough to be discredited (or not) put forward, Williamson wouldn't have written this paper. Since they refuse to get in the game, as he sees it, they have discredited not their ideas but themselves.

One might think so, but this is not what happened in the realism/antirealism argument. No solution was found, no one side was shown to be discredited. So was the argument pointless? I don't think so. — Banno

Not entirely "pointless" perhaps, but Williamson is holding up the realism/anti-realism debate as an example of a philosophical debate that wasn't good enough.

And he claims that there was no resolution, or even much progress, because the anti-realist side, in particular, did not develop their theories to a sufficient extent. That is, they were never clear enough for specific arguments to take hold and produce even local, partial answers.

(He suggests that debates about truth went somewhat better and that some progress has been made.)

But nowhere here are we talking about arguments showing that people actually agree, or argument as a means of clarifying, or any of the things you said and that I was asking about. Are we just moving on?

I'll try another question: do you think that clarity tends to dissolve disagreements because it shows most disagreements to have been merely verbal? ("Just semantics" as lay people say.)

It slowly sank in that there was not one, but many questions here - that what is real in mathematics is not the same as what is real in science or as what is real in ethics. — Banno

I don't know the history here, but my memory of Dummett's paper was that he was identifying a pattern in debates across several domains in philosophy, so this would be a little odd.

So clarity may still be the end goal. — Banno

I think Williamson considers the end goal knowledge. You might not be able to know everything you want right away, but you can claim progress if you know more than you used to. And that's exactly what he says ― for instance, "we know more about truth now".

Williamson's paper argues that if we don't do better (which would include your "clarity") we'll never learn anything.

And sometimes the quarrel concerns a difference that may be sorted by a line of reasoning - an argument that dissolves an argument, as it were. — Banno

But when an argument settles a disagreement, one side agrees that the other was right. The disagreement isn't dissolved, but remedied.

Williamson is advocating explicit and clear lines of reasoning. He's doing this in order to move past the discussion being a mere quarrel. — Banno

I think there's something to that, yes. Williamson is bemoaning the lack of effort put into the realism/anti-realism debate, so it would be fair to characterize it as a kind of quarrel, and the worst kind ― the kind where people haven't developed their own positions enough for it to be clear to both sides exactly what the disagreement is and what might resolve it.

But clarity is not the end goal. One side should eventually have an argument that the other side accepts ― if not as entirely dispositive, then convincing enough that they consider their own position discredited and abandon the fight.

Clarity is a necessary condition for arguments to matter, but clarity can only resolve a disagreement if that disagreement was actually a misunderstanding.

I'm just puzzled about where the word "argument" comes into it for you, and in what sense is an argument is

working out how best to say something that we agree is the case. — Banno

Suppose we do

say the same thing in different ways — Banno

Is the point of an argument to show that?

What if the disagreement is not just about how to say what we agree on? When I say "one human perspective", I mean something very fundamental; there's still a great deal of headroom for disagreement up toward the surface of our mental lives.

Sorry, I'm just puzzled now about whether you have some general view of disagreement (which, amusingly, I don't think I share), and about, given that, why you would reach for the word "argument" at all instead of, say, "explanation" or some other word. When someone is under the mistaken impression that you disagree, the usual thing to say would be something like, "I think we're saying the same thing ― let me explain ..." I don't know how the word "argument" got in here at all, if you're talking about agreement.

the difference between an argument as convincing someone that something is the case, and an argument as working out how best to say something that we agree is the case. — Banno

Why would I need to convince you of something you agree with me about? Why would you or I bother with arguments at all?

@Moliere

Here's another element of taste ― doesn't apply to everyone.

Some people have a decided preference for the new. Sometimes this is argued for, as Dewey does: the old ideas are dead, no longer suited to our time, and we need new ideas that suit our needs. Sometimes this is argued for as "the philosophy of the future", leading the way, changing the world rather than meeting the present need.

As some people want to be in the vanguard or the avant garde, some people want to stand athwart history saying, stop. Or, if they're not interested in a fight, they want to ignore whatever foolishness people nowadays are getting up to, and stick by the tried-and-true ideas of their forefathers. Some people are naturally suspicious of the new.

As I say, not a motivator for everyone, but I think for some people very important.

Next you'll tell us there are 10 kinds of people ...

The other issue is that people very quickly learn to game metrics. — Count Timothy von Icarus

Goodhart's Law.

I am not sure about the claim that we "know much more about truth then we did decades ago," unless it is caveated for instance. — Count Timothy von Icarus

I'll have to reread if this thread continues, but my memory is that within a page it's clear what he means is the theories are more fully developed, and so brought closer to direct head-to-head comparison. There are other points in there.

Anyway, I can tell you when I read that sentence it struck me as a preposterous thing to say! Stopped me dead in my tracks. But because of his thinking about the role of theory, he means it quite literally. I don't know if it was courage, putting it this way, so removable from context, or obliviousness.

Note, however, that some of the responses to this sort of thing seem deficient. For example, simply pointing to seemingly incoherent analytic or scholastic philosophy. This doesn't say much; presumably there can be bad scholastic philosophy, bad theoretical physics, etc. — Count Timothy von Icarus

This is all very level-headed, Tim. Thanks.

I'll note that the point of Williamson's paper was very much less throwing stones at another tribe, way over there in another village, and more about throwing stones at a particular clan within his own tribe, and ― having done that ― chucking some more stones at his own tribe in general.

I'm hesitant to say this (but conscience demands it): I think it would be fair to say Williamson does this because his standards for philosophy are understood by him to be universal. (He has, elsewhere, chucked stones at the other tribe.) They needn't be. He could say, "If we are to call ourselves analytic philosophers, then we bloody well ought to act like it, and that means adhering to certain standards of rigor and discipline, which I can't believe I have to explain to you." I don't think he says that.

Now maybe that is what he's saying ― I didn't go looking for evidence in the paper either way. In the specific context, it just wouldn't matter because he was addressing his own tribe. He intended what he said to apply to them; it makes no difference if he also intended it to apply to other philosophers as well.

But it will make a difference when it comes time to debate the standards he is proposing, and the justifications he (or anyone else) is prepared to offer for those standards. I was going to say there are conditional and unconditional options, but really it's just a difference in the antecedent class: "if you want to do analytic philosophy then ..." versus "if you want to do philosophy then ..."

There is, for example, no actual philosophical work by anyone anywhere in this thread. At least on this view. Strictly speaking. — Srap Tasmaner

Did I misunderstand you here? I had understood that this was becasue of the topic, not the degree of formality...

I think I'm having trouble with the apparent juxtaposition of formal and natural languages. I understand formal language as a subclass of natural language, not as its antithesis. "A = apples" is as much a part of English as "May I introduce you to George?" The difference is in the rules around "=" that permit substitution extensionally...

Formal language is just natural language with more explicit restrictions and explanations. — Banno

I'll try this (and see what I think tomorrow).

In fields that have a perspicuous notation available (mathematics, chemistry, music, etc), the moments when a professional reaches for that notation are often the moments when he is doing (or demonstrating) the work of that field rather than talking about it. That's why they have the notation. English was already available for talking about the field. (This is not meant as an absolute, obviously.)

Philosophy doesn't really have its own notation like this, and probably cannot, but that doesn't mean there isn't still a distinction between doing the work of philosophy and just talking about it. It's just that we can't rely on differing modes of expression to identify which is which. We can do this a little ― there's logical and mathematical notation philosophers find use for, and you can draw attention to definitions or theses for which the precise wording is important (something like the house style at the SEP).

So I have not been trying to claim that real work can only be done in a more formal mode of expression, only that in other disciplines the choice of that formal mode is an indicator that we're working (or demonstrating, etc), rather than just talking about it.

He has the back-up — Leontiskos

He does, you're right, but I think this sentence

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. — Williamson, 10-11

is pie in the sky. Who's the "we" tallying the results and scoring the competition?

It’s not idealizations that are the problem. I agree that we cannot get along without them. The problem is when philosophy takes them as its starting point and adopts them as its method rather than delving beneath the facade to explicate the underlying processes. — Joshs

We're not just in agreement, then, we are brothers!

Look, I know Williamson takes a lot for granted, has a sort of philosophical ideology. My long post from yesterday, the "silliness" post, was intended at least in part as a demonstration of how he was tripping over his own tools.

In my own case, I long for the serenity I suppose he feels, the certainty about how to do things. When I had firmer ― well, any ― commitments to this or that school, this or that thinker, it was a lot easier, and I absolutely miss that.

that, in so far as it goes, is not a poor position to adopt? — Banno

I think it's clearly a pretty good idea for positions that are pretty close.

For ways of seeing and ways of setting up problems that begin very far apart, I'm not sure it's much use at all.

The obvious examples are pretty bad, and I don't want to give them the oxygen.

Do you think Russell and Wittgenstein, after 1930 -32, could have managed something like this? I'm really not sure.

what is the nature of our subjective comportment toward the world such that it makes possible the invention of abstractions which leave out the relevant and purposeful way in which we encounter the meaningful world? — Joshs

I'll just say that I am very interested in the role of ideals in our thinking, in our communication, in our lives. I tend to see them as things we construct rather than discover, and I'm curious why we do that, what role they serve (language as idealization is a crucial example, certainly), and also how we do that.

There's a bit of a sense in your post ― at least in what I quoted ― that ideals are a problem, and that their leaving stuff out is a problem, especially because they leave out what's most important. I may come to agree with you someday, but that's not really my sense of things. I guess I'm approaching them more neutrally ― idealization is a fact of human life and thought and behavior. Some clear upsides, some just as clear downsides, and something there's no reason to think we can get along without.

Perhaps it will suffice to be disciplined enough.

If you and I agree, will that do? — Banno

I think what Williamson wants is for you and I to be rigorous enough that if we disagree it is clear that we do, and, in the best case, we can agree on what would count as resolving the dispute, and, in the very best case, we agree on a way of getting there and know what it is.

Was my nephew doing philosophy? — Leontiskos

I'll take Williamson's line, not with respect to your nephew, but this question and your answer to it: is your approach here disciplined by the decades of relevant research on how children acquire concepts? It looks to me like the answer is "no". You have, it appears to me, worked out an armchair account of the rational inference that it seems to you *must* underly the process. I don't believe the relevant research supports this account.

My point that a philosophy which places natural language above formal language is more robust than a philosophy which does not — Leontiskos

I've said similar things myself, even in this thread, even recently, but at the moment the question of priority is less pressing for me than the issue of how the two are related, so that's what I've been writing about.

@Banno's position here is interesting because he is strongly committed both to the primacy of natural language and the usefulness of classical logic. The argument he often makes is that classical logic is not something you find implicit in ordinary language, as its hidden structure, say, but you can choose to conform your language use to it.

I think that view actually rhymes quite well with the description I've been trying to develop of how formal, technical language can be embedded in natural language, much as mathematical language is and must be embedded in natural language.

You have a point. I apologize for giving in to a moment of pique.

This is why Scholasticism's rigor is so much more robust than Analytic Philosophy's rigor: — Leontiskos

Please just stop doing this. No one wants to hear it.

I'll argue now for a slightly different position.

A lot of students have trouble with word problems not because they lack the needed technical mastery ― are unable to solve simple equations ― but because they are stymied by the "setting up" process. They'll say that they just don't know where to begin. There's this little story that involves numbers, but how do get that into a form that you can solve algorithmically?

(I think the issue here is a little different from the "translation" that goes on in introductory logic classes, which is mostly about understanding which words in English map to which logical constants. Not important.)

What I want to say here is that this is a problem of seeing. The question is whether you can detect the picture that the sentences of the word problem are painting and detect the part of the picture that is left blank.

One thing that's a little odd about this is that mathematical notation itself is completely superfluous, and only exists to make understanding such "pictures" easier, to make their structure graspable at a glance.

What the students who struggle lack is this mathematical perception. The real point of word problems is to develop this perception.

Now, as it happens, a great deal of philosophical writing is concerned not with technical issues per se but with changing how you see things. (Among innumerable examples, Wittgenstein is an easy one.) A great deal of work goes not into demonstrating that A is a subset of B, but in getting you to see A and B as sets at all, and particularly for getting you to see that, for the problem at hand, A and B are the relevant sets.

Now to Williamson's point: what he demands is "setting up" work that is through enough that you can reduce a "natural" question to a technical one.

I think we have to call the "setting up" work philosophy; Williamson adds a stricture on the aim of setting up, a way to compare different ways of setting up a problem, and a criterion of success or at least improvement.

So would you still have to say? — Fire Ologist

Probably.

I tried to do a bit of logical analysis of the text, but I didn't try all that hard. And I connected what I found to what I know of Williamson, but my knowledge has obvious limits. I'd call that post "quasi-philosophy," how's that?

The labeling is not all that important to me, but I don't think it's helpful to ignore the difference between what is clearly technical work and what isn't. Call it all "philosophy" if you want, but you'll still need some terminology for that obvious distinction.

I think -- and don't you? -- that this view is wrong. — J

I'll take another swing at it, and recast the question using a different analogy, instead of the mathematicians talking over dinner. (This will be something else I've talked about before, but there you go.)

If you look at a grade school math book, one with a chapter about "word problems", you'll see something like this:

Let A = the number of apples
and P = the number of pears

And from there you'll get equations that translate the conditions set out in the problem, and a demonstration of how to solve the problem once all this setup is done.

Introductory logic textbooks do something similar. In both cases, some students find it extremely difficult to do this "translation" into formal notation.

What's curious is this "Let A = ..." business. On its face, that's not ordinary English such as the problem is written in. It's also not just mathematical notation, and apparently isn't exactly math at all — what kind of "equation" could that be?!

"Let A = ..." is a sort of snapshot of the translation process. A bit of intermediate work product. Not exactly ordinary English, not exactly math, but some of the connective tissue that embeds mathematics in our lives and without which mathematics would be pointless, meaningless, and inapplicable.

There are some corollaries: the learning of mathematics is inconceivable without this intermediary "mathematical English," which is what math teachers speak most of the day, and what students speak when answering questions; similarly, the work of mathematics, the practice of mathematicians, is mostly carried on in a more developed form of this same mathematical English. No article in any mathematics journal has ever consisted entirely of notation — not to mention the fact that published proofs are not genuinely formal proofs but more like sketches or summaries of what such a thing would look like.

And so it is with philosophy.

Now, there are still differences between the three sorts of paragraphs you find in a math textbook, the English, the mathematical, and the transitional. Not all of them exactly *are* math, but all are necessary to math and for math even to be a thing.

And so I think it is with philosophy. It's not really a matter of formalism at all, but more like the distinction in a legal opinion between the actual decision, the language of which is binding on parties, and obiter dicta, which could be important to understanding the decision and complying with it, but which does not have the force of law. (Maybe I should have gone for this analogy first.)

"The Sentiment of Rationality" is one of my favorites, but not the one I was thinking of. I found what I had in mind in the next essay, "Reflex Action and Theism":

Into this debate about his existence, I will not pretend to enter. I must take up humbler ground, and limit my ambition to showing that a God, whether existent or not, is at all events the kind of being which, if he did exist, would form the most adequate possible object for minds framed like our own to conceive as lying at the root of the universe. My thesis, in other words, is this: that some outward reality of a nature defined as God's nature must be defined, is the only ultimate object that is at the same time rational and possible for the human mind's contemplation. Anything short of God is not rational, anything more than God is not possible, if the human mind be in truth the triadic structure of impression, reflection, and reaction which we at the outset allowed.

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.

Thinking well will seek out a high object of thought, and a high object of thought will attract strong thinking. — Leontiskos

@Hanover did you read the other essays in the Dover collection that has "The Will to Believe"? In one of them -- and I can't dig it out just now -- James makes a similar claim about the human mind needing an object adequate to its capacity, or something, and that object is God, the ultimate object of thought. Does that ring a bell?

Maybe that's also in the title essay, I don't remember.

Srap Tasmaner: I would say that non-Analytic philosophy does think about what is important, but it does not think well.* — Leontiskos

For the record, of course I didn't say that, even inadvertently.

Leontiskos: I would say that Analytic philosophy does think well, but not about what is important. — Leontiskos

This, on the other hand -- I'll admit I was trying to coax someone into saying exactly this. Not with any particular goal in mind, it's just that this is what people always say about philosophy in the analytic tradition, so I wanted to sort of set a place at the table for this view.