Williamson on Apriority

Here's an argument with the conclusion that there's no deep difference between cats and dogs.

The Dogs and Cats Argument. Although a distinction between cats and dogs can be drawn, it turns out on closer examination to be a superficial one; it does not cut at the biological joints. Consider, for example, a paradigmatic cat, Felix. Felix has the following properties: (i) he has four legs, fur, and a tail; (ii) he eats canned food out of a bowl; (iii) humans like to stroke his back. Now consider a paradigmatic dog, Fido. Fido has all three of these properties as well. For instance, Fido also has four legs, and fur, and a tail, and when he eats, it is often served from a can into a bowl. And humans like to stroke Fido's back, too. In these respects, Fido and Felix are almost exactly similar. Therefore, there can't possibly be any deep biological distinction between them.

I'm sure you'll agree that the dogs and cats argument is terrible. Put a pin in that and consider another argument.

In his contribution to Al Casullo and Josh Thurow's forthcoming volume, The A Priori in Philosophy, Timothy Williamson argues against the theoretical significance of the distinction between the a priori and a posteriori. The thesis of the paper is that "although a distinction between a priori and a posteriori knowledge (or justification) can be drawn, it is a superficial one, of little theoretical interest."

It's a somewhat puzzling paper, I think, because it's not at all clear how it's broad argumentative strategy is supposed to support the conclusion. Williamson does not, for instance, articulate what he takes the apriority distinction to be, then argue that it is theoretically uninteresting. Instead, he identifies certain paradigms of a priori and a posteriori knowledge, then emphasizes various similarities between them. For example, he argues that the cognitive mechanisms underwriting certain a priori judgments are similar in various respects to those that underwrite certain a posteriori judgments. Then he spends most of the rest of the paper arguing that these are not idiosyncratic features of his particular examples. But why is this supposed to be relevant?

Williamson writes:

The problem is obvious. As characterized above, the cognitive processes underlying Norman's clearly a priori knowledge of (1) and his clearly a posteriori knowledge of (2) are almost exactly similar. If so, how can there be a deep epistemological difference between them?

But I do not find this problem at all obvious. The argument at least appears to have the structure of the terrible dogs and cats argument above. The thing to say about that argument is that identifying various similarities between two things does practically nothing to show that there aren't deep differences between them. There are deep biological distinctions between cats and dogs, but they're not ones that you can find by counting their legs or examining how humans interact with them. Similarly, Williamson offers nothing at all that I can see to rule out the possibility that there is a deep distinction between the a priori and a posteriori, but it is not one that is manifest in the cognitive mechanisms underwriting these judgments. For as Williamson himself later emphasizes, there's more to epistemology than cognitive mechanisms. If apriority lives in propositional justification—which is where I think it lives—then there's just no reason to expect it to show up at this psychological level. That doesn't mean it's not a deep distinction.

That Williamson's argument needs to be treated very carefully should also be evident from the fact that prima facie, it looks like it has enough teeth to show that the distinction between knowledge and false belief is not an epistemically deep one—a conclusion that everyone, but Williamson most of all, should reject. For the cognitive processes underlying cases of knowledge are often almost exactly similar to those underlying false beliefs. Should this tempt us to ask how, then, there could be a deep epistemological difference between them? I really don't see why.

Knowledge and Modals in Consequents of Conditionals

Modals interact in a characteristic way with conditionals. Suppose it’s next Wednesday morning, and I haven’t checked the news in a while. Consider:

1. Obama probably won the election.
2. If Romney won Ohio, Obama probably won the election.

Assuming that the last time I looked at the polls, they looked roughly as they do now, (1) is true in my mouth Wednesday morning, and (2) is false. When I say (1), I say something like, ‘most of the epistemically nearest worlds are worlds in which Obama won’. When I say (2), I restrict the worlds I’m looking at: paying attention only to those worlds in which Romney won Ohio, most of the epistemically nearest of them are Obama-winning worlds. I knew going in that the winner of Ohio is likely to win overall, whichever candidate that is. (But I know it’ll probably be Obama.) So (3) is true in my mouth Wednesday morning:

3. If Romney won Ohio, Romney probably won the election.

Let’s suppose that as a matter of fact, Romney did win Ohio, contrary to my evidence. Still, since I haven’t gotten the bad news yet, my evidence still favors Obama’s having won the election. So when I say (1), it’s true. So is (3). If we look naively, this will appear puzzling. It looks like a counterexample to modus ponens, for the following are all true (not assertable by me Wednesday morning, but true):

• Romney won Ohio.
• If Romney won Ohio, Romney probably won the election.
• Obama probably won the election.

Call the inference from X and a sentence of the form "if X, Y" to Y, naive modus ponens. Naive modus ponens leads us wrong in this case.

The solution to this puzzle, of course, is that modals and conditionals interact in a subtler way than is recorded in the surface grammar of (3). The ‘probably’ modal takes wide scope; “if p, probably q” says that, restricting attention to the p worlds, q is probable. Relatedly, I can’t perform naive modus tollens on my probability conditional: Obama probably won; if Romney won, then Obama probably didn’t win; therefore, Romney didn’t win.

The same goes for ‘might’ and ‘must’. Suppose I have seen election results for every state except Ohio, and I know for certain that the winner of Ohio won the election. Then I may truly say:

4. If Romney won Ohio, Romney must have won the election.
5. If Obama won Ohio, Obama must have won the election.

It doesn’t follow from the fact that Romney did win Ohio that I’d express a truth if I said “Romney must have won the election”. Indeed, it’s false—for all I know, Obama might have won. Sentence (4) says that, of all the Romney-winning-Ohio worlds, he wins the election in them.

This is all very different from the way that conditionals interact with non-modal claims. Suppose I truly say to myself:

6. If the carpenter was here today, the picture is on the wall.

Suppose also that the carpenter was there then (the place and time where I said (6)). This entails that the picture was on the wall. Or if the picture is not on the wall, the truth of (6) entails that the carpenter wasn’t there. In other words, with non-modal consequents, you can perform naive modus ponens and modus tollens on conditionals.

Knowledge patterns with the modals. Suppose you’re trying to decide whether to trust someone. I might truly say:

7. If he’s lying, you know he’ll just deny everything later.

This can be true even though (a) he is lying, and (b) you don’t know that he’ll deny everything later. For all you know, he’s honest, and will confirm everything. Indeed, you know that you don’t know he’ll deny everything later. But you can’t reason from this known fact and (7) to the conclusion that he isn’t lying. So naive modus ponens and modus tollens are mistakes here, just as in the cases of the obvious modals like might, must, and probably.

I think this is pretty decent evidence in favor of views like mine that treat ‘knows’ as either something a lot like a modal or a literal instance of a modal. I say, broadly with David Lewis, that ‘knows p’ is an evidential quantifier: it says of a given set of worlds that one’s evidence eliminates all the not-p worlds. When it appears in the consequent of a conditional, it’s very natural to restrict the set with the antecedent. So “If X, S knows p” says, first restrict your attention only to the X worlds; S’s evidence eliminates the not-p worlds that remain.

Sider, structure, reduction, and knowledge first

This is a continuation of yesterday's post. Yesterday I identified what seemed to me to be a problem for the way that Ted Sider wanted to explain why various macro-level things are more privileged—basically, they're said to be more joint-carving. But as I said yesterday, I just don't see that they are.

I suspect, however, that one can get something quite a bit like Sider's picture here if one is willing to add a bit more structure. The prospects for a reasonable purely physical story about chemical objects and properties seem reasonable. It doesn't seem hopeless to try to give a reasonably simple definition of molecule or magnesium or valence in purely physical terms. So if we assume the (absolute) fundamentality of physics, we can run the story Sider wants for why we refer to molecules instead of molecules-or-cucumbers, or even molecules-before-2013-and-regions-of-space-afterwards, because the physical definition of molecule is significantly simpler than these more bizarre properties. (In the former case, a purely physical definition will be insanely complex, as in the case of pig; in the latter, it will still be not insanely complex, but more complex than that for molecule.)

This is basically just a way of expressing the familiar idea that chemistry somehow reduces to, or emerges from, physics. But if we buy into Ted's general ideas, we can add this: it is part of the objective structure of the world that chemical properties are related to physical properties in this way. The 'book of the world' will give us the chemical on top of the physical (and the chemical is objectively privileged over the schmemical).

Now what happens when we go up another level? It's pretty natural to suppose that cell biology relates to chemistry as chemistry does to physics. So --- and here's where the picture I'm describing departs from Ted's --- when adjudicating between which objects we refer to in our discourse about cell biology, objects with reasonably simple definitions in chemical terms --- not physical terms --- are privileged over ones that don't. We don't always go back to the most fundamental; we just go back to the more fundamental domain that is appropriate for the matter at hand. Often, but not always, the simpler definition is the more fundamental theory will correspond to the simpler definition in the ultimately fundamental theory; when it doesn't, I think we should go with the less fundamental one. (It's having a better chemical account that makes a particular referent of 'cell' the preferred one, not having a better physical account.)

The reason I'm interested in this, besides the fact that it's interesting, is that I'm leaning in this kind of a direction as a way of making sense of what the 'knowledge first' attitude is. (Yes, I'm reading metaphysics, but it's in the service of epistemology, I swear!) I understand it as a metaphysical thesis: knowledge is a more fundamental state than has been traditionally recognized. In the terms of this broad way of thinking about theorizing about the world, knowledge shows up at a more fundamental level than one might have thought.  (Compare a 'life first' theorist, who thinks that the attempt to define life in biological terms is a mistake; life's home is really at the chemical level—we need to invoke life to understand, say, combustion.) How early should knowledge appear? Presumably, people could differ about this. If you wanted to, you could think that knowledge was perfectly fundamental; knowledge is as basic as quarks or whatever. You'd oppose any kind of reduction of knowledge to anything. This doesn't sound very plausible, but you could say that if you wanted to. My suspicion is that knowledge will be an important theoretical term from the basics of intentional psychology.

Sider on joint-carving and reference

Humans refer to things sometimes. Ted Sider thinks, with David Lewis, that part of the story for why it is that we refer to some things, rather than other possible things, is that the things we refer to are more natural. This Sider understands as a matter of the primitive structure of the world. To takes one of Ted's examples, Ted's word 'pig' refers to pigs, instead of pigs-before-2011-AD-or-cows-afterwards. And he thinks that general considerations about fundamental structure can yield this intuitive result. Ted writes:

The point may be seen initially by making two strong, crude assumptions about "reasonably joint-carving". Assume first that a notion is reasonably joint-carving iff it has a reasonably simple and nondisjunctive definition in terms of the perfectly joint-carving notions, and second that the perfectly joint-carving notions are those of physics. Then surely no reasonably joint-carving relation that is to play the role of reference could relate a human population to bizarre semantic values. For the bizarre semantic values themselves have no simple basis in the physical, nor do they stand in any physically simple relations to human populations. Given any reduction that does relate us to bizarre semantic values, there is surely some other relation with a simpler basis in the physical that relates us to nonbizarre semantic values. (29)

There is considerable vagueness and imprecision in the notion of "reasonably" simply definitions Ted evokes, but I guess I agree that it's pretty plausible that one couldn't tell a "reasonably simple" story in purely physical terms of how humans are related to bizarre semantic values like pigs-before-2011-AD-or-cows-afterwards. But Ted needs more than just that fact; he needs the comparison. And I guess it just doesn't look very plausible to me that there is a "reasonably simple" definition available in purely physical terms of any of the pieces we need here. By any ordinary standards, a definition of pig --- or human! --- in purely physical terms will be rather unreasonably complex! So I worry that if this is the story about why we don't refer to pigs-before-2011-AD-or-cows-afterwards, it will generalize to show that we don't refer to pigs either. (A related problem; surely it's possible to refer to pigs-before-2011-AD-or-cows-afterwards, right?)

I think this problem persists, even given the less toy version of the theory. He continues the passage above:

The two assumptions of the previous paragraph are undoubtedly too crude, but the point is independent of them. Whether a notion is reasonably joint-carving --- enough to take part in special-science explanations --- has something to do with how it is based in the fundamental. So reference must have the right sort of basis in the fundamental if it's to be explanatory.

But it's just very difficult to say anything halfway reasonably simple about how any of this stuff arises from the fundamental. Things like pigs are just way too far removed from things like electrons. (And presumably, even electrons aren't fundamental anyway.)

More on this theme, and what I think we should say instead, tomorrow.

Sider on epistemic value and nature's joints

Ted Sider thinks that it's epistemically preferable to think in joint-carving terms; this is a way of better matching one's beliefs to the world. While something about that sounds right, I think that some of the the things he says must go too far. He writes, for example, that

[j]oint-carving thought does not have merely instrumental value. It is rather a constitutive aim of the practice of forming beliefs, as constitutive as the more commonly recognized aim of truth. (WtBotW p. 61)

I don't think this can be right. The idea of somebody forming beliefs without any kind of sensitivity or regard for whether they are true is incoherent; this is not so for someone who doesn't care whether her beliefs carve nature at the joints. Suppose one is charged with failing to carve at the joints with her beliefs, and replies flippantly --- so what? --- and maintains her previous beliefs? She might be criticizable on epistemic grounds, but her attitude is comprehensible, even if we do not approve of it. Compare the person who is charged with having false beliefs, and replies in the same way --- indifferently accepting the charge, and continuing to believe as before. This isn't just epistemically vicious; this runs counter to what it is to be a belief. In other words, a truth aim has a better claim to a constitutive connection to belief than a joint-carving aim does.

Here is another difference that should not be overlooked: some instances of non-joint-carving beliefs are absolutely correct to hold. Maybe they're not as good as their joint-carving cousins, but one needn't choose between them. You can believe that the emerald is green and that it is grue. In fact, that's exactly what you should do. And you shouldn't feel at all epistemically deficient for having the latter belief. Compare this to false beliefs: every false belief you have prevents you from having a true one.

Moore-paradoxes show a deep connection between belief and truth; there is a deep incoherence in the idea of accepting: "I believe that p, even though not-p." But there is no corresponding incoherence in "I believe that p, even though the terms in p do not carve at nature's joints."

Whatever epistemic value attaches to joint-carving, it is less central to belief than truth is.

Joint-Carving and Projectability

So this weird thing has been happening to me lately where I think about metaphysics. My current symptom is an attempted negotiation of Ted Sider's recent book, Writing the Book of the World. Ted's Big Idea is that there is objective structure to reality, and that this structure is really important for all kinds of reasons; I find the general picture a pretty attractive one, but I'm rather puzzled by some of his remarks on the applicability of structure to induction and confirmation.

Ted writes:

Which observations confirm a generalization 'all Fs are Gs'? A natural answer is the "Nicod principle": observations of Fs that are Gs confirm 'All Fs are Gs'. But suppose that an observation confirms any logical equivalent of any sentence that it confirms. Then, as Hempel pointed out, the observation of red roses confirms 'All ravens are black' (given the Nicod principle it confirms 'All nonblack things are nonravens', which is logically equivalent to 'All ravens are black'.) And as Goodman pointed out, Nicod's principle implies that observations of green emeralds before 3000 AD confirm 'All emeralds are grue' (sice green emeralds observed before 3000 AD are grue.) But anyone who believed that all emeralds are grue would expect emeralds observed after 3000 AD to be blue.
[This conclusion] can be avoided by restricting Nicod's principle in some way -- most crudely, to predicates that carve at the joints. Since 'is nonblack', 'is a nonraven', and 'grue' fail to carve at the joints, the restricted principle does not apply to generalizations containing them. In Goodman's terminology, only terms that carve at the joints are "projectable". (35)

I'm confused about this strategy. Ted says we can avoid the conclusion that nonblack nonravens confirm ravens' blackness because 'nonblack' and 'nonraven' don't carve at the natural joints. But 'nonblack' carves at exactly the same joint as 'black' does -- to push the metaphor only slightly further, it's the very same cut. So if 'nonblack' isn't joint-carving, and is therefore nonprojectable, then it looks like just the same would go for 'black', and mutatis mutandis for ravens and nonravens. So now it looks like I can't confirm that all ravens are black by observing black ravens. This isn't the result Ted wanted, surely.

So I'm worried that one of these things must be true:

1. The story quoted above about why red roses don't confirm that all ravens are black is wrong;
2. Black ravens don't confirm that all ravens are black; or 
3. The 'black' joint is natural, but the 'nonblack' joint isn't.

When I asked Carrie about this, she suggested that Ted might be intending something like (3) here. After all, she pointed out, there might be more of an objective sense in which all black things resemble each other than that in which all non-black things do. I guess the thought would be that the metaphor is breaking down here; 'joint-carving' isn't the right term. Maybe this is right, but I didn't see that Ted could go this way, since he doesn't want to take objective similarity as the most fundamental thing. He wants structure to be most fundamental, and to explain objective similarity in terms of structure.

I feel like I must be missing something obvious here, but I can't see what it is. Somebody help?

Christoph Jäger on knowledge, contextualism and assertion

Christoph Jäger argues in a recent Analysis paper that contextualism and the knowledge norm of assertion are jointly untenable. Here’s my reconstruction of Jäger’s argument. (My numbering will differ from his.) Suppose that Keith has hands and the usual epistemic access to them. Also, Keith is a contextualist. For some two contexts, C-LOW and C-HIGH,

1. In C-LOW, “Keith knows that he has hands” is true.
2. In C-HIGH, “Keith knows that he has hands” is false.
3. In C-HIGH, Keith may appropriately state his contextualist theory.
4. In C-HIGH, “Keith knows his contextualist theory” is true.
5. In C-HIGH, “Keith knows that in C-LOW, ‘Keith knows that he has hands’ is true” is true.
6. In C-HIGH, “Keith knows that he has hands” is true.

But (6) contradicts (2), so something is wrong. Jäger says that it’s either contextualism or the knowledge norm that has to go. The first two premises are standard contextualist fare. A modest closure principle is invoked in the step from (5) to (6)—but it looks fine. The move from (3) to (4) follows from Jäger's version of the knowledge norm of assertion, which I do not contest. There are two action points here: the moves to lines (3) and (5). We consider them in turn.

Why should we accept (3)? Jäger introduces the set-up thus:

Consider a conversational context in which the contextualist states his theory. Such contexts are paradigmatic epistemology or 'philosophy classroom' contexts in which sceptical hypotheses are salient and taken seriously.

This appears to me to be mere assertion; why should classroom contexts be skeptical ones? I know that David Lewis said they were, but David Lewis said a lot of silly things in that paper. This just isn’t a commitment of contextualism per se. Contextualism is a linguistic thesis, made on the basis of, among other things, facts about linguistic use. If we were really taking skepticism seriously, we would not help ourselves to such facts. Some contexts in which epistemology of this sort is being performed—this one, for instance—are not very skeptical at all.

Actually, I think, there is a deeper problem for Jäger’s claim to (3). Contextualism is a controversial theory; lots of smart people think it’s wrong. It’s a theory that I accept, but I don’t think the acceptance here is a kind of outright belief, and I don’t think my statements of contextualism are appropriately regarded as assertions—as attempts to transmit knowledge. But the kind of “appropriate stating” at issue in (3) would have to be assertions in order for a knowledge norm of the latter to put any pressure on the move to (4). It’s far from obvious that anyone in ordinary contexts (let along skeptical ones) should go around asserting that contextualism is true. (And I say this as a contextualist! I think contextualism looks like the best theory. That doesn’t make it a thing to assert in ordinary contexts.)

So there are two pretty serious problems with premise (3). Now let’s set aside those problems for the purpose of further argument, and consider line (5). The inference from (4) to (5) is supposed to follow directly from the content of the contextualist theory. Jäger writes:

[Someone denying this step] would have to argue that the contextualist can legitimately deny [(5)], i.e. deny that he knows when he asserts his theory, in CHigh, that there are low-standards contexts in which (it is true to say that) he knows that he has hands. The claim that there are such quotidian contexts, however, is a cornerstone of classical, anti-sceptical forms of contextualism.

I don’t feel the motivation here at all. Contextualism the linguistic thesis does not entail that Keith or anyone knows that he has hands; it doesn’t even entail that Keith or anyone has hands. (Obviously.) It is consistent with the truth of contextualism that you and I are brains in vats. So even if we became convinced that we could have high-standards knowledge of contextualism—say, because we have introspective access to meaning, and that access is more resistant to skeptical scenarios than perceptual knowledge—we could still abandon Jäger’s ship at the step to line (5). Sure, Keith knows-HIGH that contextualism is true; that doesn’t mean he knows-HIGH that he knows-LOW that he has hands—even granting whatever intra-context closure principle you want. We’d get that he knows-HIGH that in C-LOW, he’d be invoking a relatively weak standard if he said “I know I have hands”. It doesn’t follow that he knows whether he’d meet it.

So there are lots of ways to resist this argument.