Category Archives: Metaphysics

Here’s a paradigmatic problem of the many (Geach and Unger are the usual sources cited, but I’m not claiming this to be exactly the version they use.) Let’s take a moulting cat. There are many hairs that are neither clearly attached, nor clearly unattached to the main body of the cat. Let’s enumerate them 1—1000. Then we might consider the material objects which are the masses of cat-arranged matter that include half of the thousand hairs, and exclude to the other half. There are many ways to choose the half that’s included. So by this recipe we get many many distinct masses of cat-arranged matter, differing only over hairs. The various pieces of cat-arranged matter change their properties over time in very much the way that cats do: they are now in a sitting-shape, now in a standing-shape, now in a lapping-milk shape, now in an emitting-meows configuration. They each seem to have everything intrinsically required for being a cat.

If you’re inclined to think (and I am) that a cat is a material object identical to some piece of cat-arranged matter, then the problem of the many arises: which of the various distinct pieces of cat-arranged matters is the cat? Various answers have been suggested. Some of the most obvious (though not necessarily the most sensible) are: (i) nihilism: none of the cat-candidates are cats. (ii) brutalism: exactly one is a cat, and there is a brute fact of the matter which it is; (iii) vague cat: exactly one is a cat, and it’s a vague matter which it is; (iii) manyism: lots of the cat-candidates are cats.

(By the way, (ii) and (iii) may not be incompatible, if you’re an epistemicist about vagueness. And those who are fans of many-valued logics for vagueness should have a think about whether they can really support (iii). Consider the best candidates to be a cat, c1….c1000. Suppose these are each cats to an equal degree. Then “one of c1…c1000 is a cat” will standardly have a degree of truth equal to the disjunction=the maximum of the disjuncts=the degree of truth of “c1 is a cat”. And the degree of truth of the conjunction: “all of c1…c1000 is a cat” will standardly have a degree of truth equal to the conjunction=the minimum of the conjuncts=the degree of truth of “c1 is a cat”. So to the extent that the (determinately distinct) best candidates aren’t all cats, to exactly that extent there’s no cat among them (and since we chose the best candidates, we won’t get a higher degree of truth for “the cat is present” by including extra disjuncts. Conclusion: if you’re tempted by response (iii) to the problem of the many, you’ve got strong reason not to go for many-valued logic. [Edit (see comments): this needs qualification. I think you’ve reason not to go for many-valued logics that endorse the (fairly standard, but not undeniable) max/min treatment of disjunction/conjunction; and in which the many values are linearly arranged].)

What I’d really like to emphasize is the above leaves open the following question: Is there a super-cat-candidate, i.e. a piece of cat-arranged matter of which every other cat-candidate is a proper part? Take the Tibbles case above, and suppose that the candidates only differ over hairs. Then a potential super-cat-candidate would be the piece of matter that’s maximally generous: that includes all the 1000 not-clearly-unattached hairs. If this particular fusion isn’t genuinely a cat-candidate, then it’s open that if you arrange the cat-candidates by which is a part of which, you’ll end up with multiple maximal cat-candidates none of which is a part of the other. Perhaps they each contain 999 hairs, but differ amongst themselves which hair they don’t include.

If there is a super-cat-candidate, let’s say the problem of the many is of type-1, and if there’s no super-cat-candidate, let’s say that the problem of the many is of type-2.

My guess is that our description of cases like Tibbles leaves is simply underspecified as to whether it’s of type-1 or type-2. But I certainly don’t see any principled reason to think that the actual cases of the POM we find around us are always of type-1. There’s certainly no a priori guarantee that the sort of criterion that rules in some things as parts of a cat won’t also dismiss other things as non-parts. So for example, perhaps we can rank candidates for degrees of integration: some unintegrated parts are ok, but there’s some cut-off where an object is just too unintegrated to count as a candidate. One cat-candidate includes some borderline-attached skin cells, and is to that extent unintegrated. Another cat-candidate includes some borderline-attached teeth, and is to that extent unintegrated. But plausibly the fusion that includes both skin cells and teeth is less integrated: enough to disqualify it from being a cat-candidate. It’s hard to know how to argue the case further without going deeply into feline biology, but I hope you get the sense of why type-2 POM need to be dealt with.

Now, one response to the standard POM is to appeal to the “maximality” allegedly built into various predicates (like “rock”, “cat”, “conscious” etc): things that are duplicates of rocks, but which are surrounded by extra rocky stuff, become merely parts of rocks (and so forth). There are presumably intrinisic duplicates of rocks embedded as tiny parts at the centre of large boulders: but there’s no intuitive pressure to count them as rocks. Likewise a cat might survive after it’s limbs are destroyed by a vengeful deity, but it’s unintuitive to think of the duplicate head-and-torso part of Tibbles as itself a cat-candidate. So there’s some reasons independently of paradigmatic problem of the many scenarios to think of “cat” and “rock” etc as maximal. (For more discussion of maximality, see Ted Sider’s various papers on the topic).

If we’ve got a type-1 problem of the many, then one might think that the maximality of “cat” or “rock” or whatever gives a principled answer to our original question: the super-cat-candidate (/super-rock-candidate) is the one uniquely qualified to be the cat (/rock). For we’ve then got an explanation for why all the others, though intrinsically qualified just like cats, aren’t cats: being a cat is a maximal property, and all the rival cat-candidates are parts of the one true cat in the vicinity.

But the type-2 problem of the many really isn’t addressed by maximality as such. There’s no unique super-cat-candidate in this setup, rather a range of co-maximal ones. So maximality won’t save our bacon here.

The difference between the two cases is important when we consider other things. For example, in the light of the (fairly widely accepted) maximality of “house” and “cat” and “rock” and the like, few would say that any duplicate of a house must be a house (even setting aside extrinsicality due to social setting). But there’s an obvious fall back position, which is floating around the literature: that any duplicate of a house must be a (proper or improper) part of a house (holding fixed social setting etc). That is, any house possesses the property of being part of a house intrinsically (so long as we hold fixed social setting etc). And the same goes for cat: at least holding fixed biological origin, it’s plausible that any cat is intrinsically at least part of a cat, and any rock is intrinsically at least part of a rock.

These claims aren’t threatened by maximality. But appealing to them in a type-2 problem of the many gets us an argument directly for response (iv): manyism. For plausibly if you took a duplicate of one of the co-maximal cat candidates, T, while eliminating from the scene those bits of matter that are not part of T but are part of one of the other co-maximal cat candidates, then you get something T* that’s (determinately) a cat. And so, any duplicate of T* must be at least part of a cat. And since T is a duplicate of T*, T must be at least part of a cat. But T isn’t proper part of anything that’s even a cat-candidate. So T must itself be a cat.

So the type-2 POM is harder to resolve than the type-1 kind. Maybe some extra weakening of the properties a cat-candidate has intrinsicality are called for. Or maybe (very surprisingly) type-2 POMs never arise. But either way, more work is needed.

Does nihilism about ordinary things help us out with puzzles surrounding maximal properties and the problem of the many? It’s hard to see how.

First, maximal properties. Suppose that I have a rock. Surprisingly, there seem to be microphysical duplicates of the rock that are not themselves rocks. For suppose we have a microphysical duplicate of the rock (call it Rocky) that is surrounded by extra rocky stuff. Then, plausibly, the fusion of Rocky and the extra rocky stuff is the rock, and Rocky himself isn’t, being out-competed for rock-status by his more extensive rival. Not being shared among duplicates, being a rock isn’t intrinsic. And cases meeting this recipe can be plausibly constructed for chairs, tables, rivers, nations, human bodies, human animals and (perhaps) even human persons. Most kind-terms, in fact, look maximal and (hence) extrinsic. Sider has argued that non-sortal properties such as consciousness are likewise maximal and extrinsic.

Second, the problem of the many. In its strongest version, suppose that we have a plentitude of candidates (sums of atoms, say) more or less equally qualified to be a table, cloud, human body or whatever. Suppose further that both the sum and intersection of all these candidates isn’t itself a candidate for being the object. (This is often left out of the description of the case, but (1) there seems no reason to think that the set of candidates will always be closed under summing or intersection (2) life is more difficult–and more interesting–if these candidates aren’t around.) Which of these candidates is the table, cloud, human body or whatnot?

What puzzles me is why nihilism—rejecting the existence of tables, clouds, human bodies or whatever—should be thought to avoid any puzzles around here. It’s true that the nihilist rejects a premise in terms of which these puzzles would normally be stated. So you might imagine that the puzzles give you reason to modus tollens and reject that premise, ending up with nihilism (that’s how Unger’s original presentation of the POM went, if I recall). But that’s no good if we can state equally compelling puzzles in the nihilist’s preferred vocabulary.

Take our maximality scenario. Nihilists allow that we have, not a rock, but some things arranged rockwise. And we now conceive of a situation where those things, arranged just as they actually are, still exist (let “Rocky” be a plural term that picks them out). But in this situation, they are surrounded by more things of a qualitatively similar arrangement. Now are the things in Rocky arranged rockwise? Don’t consult intuitions at this point—“rockwise” is a term of art. The theoretical role of “rockwise” is to explain how ordinary talk is ok. If some things are in fact arranged rockwise, then ordinary talk should count them as forming a rock. So, for example, van Inwagen’s paraphrase of “that’s is a rock” would be “those things are arranged rockwise”. If we point to Rocky and say “that’s a rock”, intuitively we speak falsely (that underpins the original puzzle). But if the things that are Rocky are in fact arranged rockwise, then this would be paraphrased to something true. What we get is that “are arranged rockwise” expresses a maximal, extrinsic plural property. For a contrast case, consider “is a circle”. What replaces this by nihilist lights are plural predicates like “being arranged circularly”. But this seems to express a non-maximal, intrinsic plural property. I can’t see any very philosophically significant difference between the puzzle as transcribed into the nihilists favoured setting and the original.

Similarly, consider a bunch of (what we hitherto thought were) cloud-candidates. The nihilist says that none of these exist. Still, there are things which are arranged candidate-cloudwise. Call them the As. And there are other things—differing from the first lot—which are also arranged candidate-cloudwise. Call them the Bs. Are the A’s or the B’s arranged cloudwise? Are there some other objects, including many but not all of the As and the B’s that *are* arranged cloudwise? Again, the puzzle translates straight through: originally we had to talk about the relation between the many cloud-candidates and the single cloud; now we talk about the many pluralities which are arranged candidate-cloudwise, and how they relate to the plurality that is cloudwise arranged. The puzzle is harder to write down. But so far as I can see, it’s still there.

Pursuing the idea for a bit, suppose we decided to say that there were many distinct pluralities that are arranged cloudwise. Then “there at least two distinct clouds” would be paraphrased to a truth (that there are some xx and some yy, such that not all the xx are among the yy and vice versa, such that the xx are arranged cloudwise and the yy are arranged cloudwise). But of course it’s the unassertibility of this sort of sentence (staring at what looks to be a single fluffy body in the sky) that leads many to reject Lewis’s “many but almost one” response to the problem of the many.

I don’t think that nihilism leaves everything dialectically unchanged. It’s not so clear how many of the solutions people propose to the problem of the many can be translated into the nihilist’s setting. And more positively, some options may seem more attractive once one is a nihilist than they did taken cold. Example: once you’re going in for a mismatch between common sense ontology and what there really is, then maybe you’re more prepared for the sort of linguistic-trick reconstructions of common sense that Lewis suggests in support of his “many but almost one”. Going back to the case we considered above, let’s suppose you think that there are many extensionally distinct pluralities that are all arranged cloudwise. Then perhaps “there are two distinct clouds” should be paraphrased, not as suggested above, but as:

there are some xx and some yy, such that almost all the xx are among the yy and vice versa, such that the xx are arranged cloudwise and the yy are arranged cloudwise.

The thought here is that, given one is already buying into unobvious paraphrase to capture the real content of what’s said, maybe the costs of putting in a few extra tweaks into that paraphrase are minimal.

Caveats: notice that this isn’t to say that nihilism solves your problems, it’s to say that nihilism may make it easier to accept a response that was already on the table (Lewis’s “many but almost one” idea). And even this is sensitive to the details of how nihilism want to relate ordinary thought and talk to metaphysics: van Inwagen’s paraphrase strategy is one such proposal, and meshes quite neatly with the Lewis idea, but it’s not clear that alternatives (such as Dorr’s counterfactual version) have the same benefits. So it’s not the metaphysical component of nihilism that’s doing the work in helping accommodate the problem of the many: it’s whatever machinery the nihilist uses to justify ordinary thought and talk.

There’s one style of nihilist who might stand their ground. Call nihilists friendly if they attempt to say what’s good about ordinary thought and talk (making use of things like “rockwise”, or counterfactual paraphrases, or whatever). I’m suggesting that friendly nihilists face transcribed versions of the puzzles that everyone faces. Nihilists might though be unfriendly: prepared to say that ordinary thought and talk is largely false, but not to reconstruct some subsidiary norm which ordinary thought and talk meets. Friendly nihilism is an interesting position, I think. Unfriendly nihilism is pushing the nuclear button on all attempts to sort out paradoxes statable in ordinary language. But they have at least this virtue: the puzzles they react against don’t come back to bite them.

[Update: I’ve been sent a couple of good references for discussions of nihilism in a similar spirit. First Matt McGrath’s paper “No objects, no problem?” argues that the nihilist doesn’t escape statue/lump puzzles. Second, Karen Bennett has a forthcoming paper called “Composition, Colocation, and Metaontology” that resurrects problems for nihilists including the problem of the many (though it doesn’t now appear to be available online).]

Suppose there’s a qualitative duplicate of the actual world (It might be a world with haecceitistic differences from the actual one, but it doesn’t have to be). Call the actual world A, and its duplicate, B.

I’m conscious in world A. Call the extension at the actual world of the things which are conscious S. There are cauliflowers in world B. Call the extension at B of the things which are cauliflowers, S*. Now consider the gruesome intension cauli-consc, which has S as its extension at world A, and S* as its extension in world B (it doesn’t matter what its extension is in other worlds: maybe it applies to all and only conscious cauliflowers).

Is there a property that things have iff they are cauli-consc? So long as “property” is intended in an ultra-lightweight sense (a sense in which any old possible-worlds intension corresponds to a property) then there shouldn’t be an trouble with this.

However. Cauli-consc is a property that doesn’t supervene on the pattern of instantiation of fundamental physical properties. After all, A and B are alike in all physical respects. But they differ as to where cauli-consc is instantiated.

Cauli-consc is a property, instantiated in the actual world, that doesn’t supervene on physical properties! Does that mean that the fact that I’m cauli-consc is a “further fact about our world, over and above the physical facts” (Chalmers 1996 p.123)? That is, do we have to say that, if there are such qualitive duplicates of the actual world, then materialism is shown to be wrong by cauli-consc?

Surely not. But the interesting question is: if some properties (like cauli-consc) can fail to supervene on the physical features of the world, what is that blocks the inference from failure of supervenience on physical features of the world, to the refutation of materialism? For what principled reason is this property “bad”, such that we can safely ignore its failure to supervene?

Here’s a way to put the general worry I’m having. Supervenience physicalism is often formulated as follows (from Lewis, I believe): any physical duplicate of the actual world is a duplicate simpliciter. But if duplication is understood (again following Lewis) as the sharing of natural properties by corresponding parts, then to get a counterexample to physicalism you’d need not only to demonstrate that a certain property fails to supervene on the physical features of the world, but also that some natural property fails to supervene: otherwise you won’t get a failure of duplication among physical duplicates. The case of cauli-consc is supposed to dramatize the gap here. Sometimes it looks like you can get properties which fail to supervene, but which don’t seem to threaten materialism.

However, when you look at the failure-to-supervene arguments for dualism, you find that people stop once they take themselves to establish that a given property fails to supervene, and not, in addition, that some natural property does so (For example, Chalmers 1996 p132 assumes that it’s enough to show that the 1-intension of “consciousness” fails to supervene, without also arguing that it’s a natural property) .

Now, I think in particular cases I can see how to run the arguments to address this issue. Add as a premise that e.g. the 1-intensions of the words of our language supervene on the total qualitative character of the world, so that we’re guaranteed that if there’s a world in which “1-consciousness” is instantiated and another where it isn’t, those can’t be qualitative duplicates. If now we find a failure of 1-consciousness to supervene on physical features of the world, we’ll be able to argue for the existence of physical duplicate worlds differing over 1-consciousness, we now know can’t be qualitative duplicates. (In effect, the suggestion is that the sense in which cauli-consc is bad is exactly that it fails to supervene on the total qualitative state of the world).

That all seems reasonable to me, but it does start to add potentially deniable premises to the argument against materialism. (For example, I’m not sure it should be uncontroversial that consciousness supervenes on the total qualitative state of the world. Is it really so clear, for example, that there are no haecceitistic elements to consciousness: that a world containing me might contain a conscious being, but a qualitiative duplicate containing some other individual doesn’t?)

So I’m not sure whether the elaboration of the Zombie argument for dualism I’ve just sketched is the way Chalmers et al want to go. I’d be interested to know how they have/would respond (references welcome, as ever).

Logos are holding a meta-metaphysics conference in Barcelona in 2008. The CFP is now out: with deadline being April 1st 2008.

I went to a Logos conference back in 2005, when I was just finishing up as a graduate student. It was a great experience: Barcelona is an amazing city to be in, Logos were fantastic hosts, and the conference was full of interesting people and talks. I also had what was possibly the best meal of my life at the conference dinner. This time, the format is preread, which I’ve really enjoyed in the past.

Here’s a quick note on the “metametaphysics” stuff. Following the Boise conference on this stuff, it seemed to me that under the label “metametaphysics” go a number of interesting projects that need a bit of disentangling. Here’s three, for starters.

First, there’s the “terminological disputes” project. Consider a first-order metaphysical question like: “under what circumstances do some things make up a further thing” (van Inwagen’s special composition question). This notes the range of seemingly rival answers to the question (all the time! some of the time! never!) and asks about whether there’s any genuine disagreement between the rival views (and if so, what sort of disagreement this is). The guiding question here is: under what conditions is a metaphysical/philosophical debate merely terminological (or whatever).

Note that the question here really doesn’t look like it has much to do with metametaphysics per se, as opposed to metaphilosophy in general. Metaphysics is just a source of case studies, in the first instance. Of course, it might turn out that metaphysics turns out to be full of terminological disputes, whereas phil science or epistemology or whatever isn’t. But equally, it might turn out that metaphysics is all genuine, whereas e.g. the Gettier salt mines are full of terminological disputes.

In contrast to this, there’s the “first order metametaphysics” (set of) project(s). This’d take key notions that are often used as starting points/framework notions for metaphysical debates, and reflect philosophically upon those. E.g.: (1) The notion of naturalness as used by Lewis. Is there such a notion? If so, are their natural quantifiers and objects and modifiers as well as natural properties? Does appeal to naturalness commit one to realism about properties, or can something like Sider’s operator-view of naturalness be made to work? (2) Ontological commitment. Is Armstrong right that (at least in some cases) to endorse a sentence “A is F” is to commit oneself to F-ness, as well as to things which are F? Might the ontological commitments of our theories be far less than Quine would have us believe (as some suggest)? (3) unrestricted existential quantifier. Is there a coherent such notion? How should its semantics be given? Is such a quantifier a Tarskian logical constant?

These debates might interest you even if you have no interesting thoughts in general about how to demarcate genuine vs. terminological disputes. Thinking about this stuff looks like it can be carried out in very much first-order terms, with rival theories of a key notion (naturalness, say) proposed and evaluated. Of course, this sort of first-order examination might be a particularly interesting kind of first-order philosophy to one engaged in the terminological disputes project.

The third sort of project we might call “anti-Quine/Lewis metametaphysics”. You might think the following. In recent years, there’s been a big trend for doing metaphysics with a Realist backdrop; in particular, the way that Armstrong and Lewis invite us to do metaphysics has been very influential among the young and impressionable. A bunch of presuppositions have become entrenched, e.g. a Quinean view of ontological commitment, the appeal to naturalness etc. So, without in the first instance attacking these presuppositions, one might want to develop an alternative framework in comparable detail which allows the formulation of alternatives. One natural starting point is to go with neoCarnapian thoughts about what the right thing to say about the SCQ is (e.g. it can be answered by stipulation). That sort of line is incompatible with the sort of view on these questions that Quine and Lewis favour. What’s the backdrop relative to which it makes sense? What are the crucial Quine-Lewis assumptions that need to be given up?

Now, this sort of project differs from the first kind of project in being (a) naturally restricted to metaphysics; and (b) not committed to any sort of demarcation of terminological disputes vs. genuine disputes. It differs from the second kind of project, since, at least in the first instance, we needn’t assume that the differences between the frameworks will reduce to different attitudes to ontological commitment, or naturalness, or whatever. On the other hand, it’s attractive to look for some underlying disagreement over the nature of ontological commitment, or naturalness, or whatever, to explain how the worldviews differ. So it may well be that a project of this kind leads to an interest in the first-order metametaphysics projects.

I’m not sure that these projects form a natural philosophical kind. What does seem to be right is that investigation of one might lead to interest in the others. There’s probably a bunch more distinctions to be drawn, and the ones I’ve pointed to probably betray my own starting points. But in my experience of this stuff, you do find people getting confused about the ambition of each other’s projects, and dismissing the whole field of metametaphysics because they identify it with some one of the projects that they themselves don’t find particularly interesting, or regard as hard to make progress with. So it’d probably be helpful if someone produced an overview of the field that teased the various possible projects apart (references anyone?).