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).
Tuesday, July 24, 2007
Metametaphysics in Barcelona/some distinctions (x-post from MV)
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?).
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?).
Thursday, July 12, 2007
Williamson on vague states of affairs
In connection with the survey article mentioned below, I was reading through Tim Williamson's "Vagueness in reality". It's an interesting paper, though I find its conclusions very odd.
As I've mentioned previously, I like a way of formulating claims of metaphysical indeterminacy that's semantically similar to supervaluationism (basically, we have ontic precisifications of reality, rather than semantic sharpenings of our meanings. It's similar to ideas put forward by Ken Akiba and Elizabeth Barnes).
Williamson formulates the question of whether there is vagueness in reality, as the question of whether the following can ever be true:
(EX)(Ex)Vague[Xx]
Here X is a property-quantifier, and x an object quantifier. His answer is that the semantics force this to be false. The key observation is that, as he sets things up, the value assigned to a variable at a precisification and a variable assignment depends only on the variable assignment, and not at all on the precisification. So at all precisifications, the same value is assigned to the variable. That goes for both X and x; with the net result that if "Xx" is true relative to some precisification (at the given variable assignment) it's true at all of them. That means there cannot be a variable assignment that makes Vague[Xx] true.
You might think this is cheating. Why shouldn't variables receive different values at different precisifications (formally, it's very easy to do)? Williamson says that, if we allow this to happen, we'd end up making things like the following come out true:
(Ex)Def[Fx&~Fx']
It's crucial to the supervaluationist's explanatory programme that this come out false (it's supposed to explain why we find the sorites premise compelling). But consider a variable assignment to x which at each precisification maps x to that object which marks the F/non-F cutoff relative to that precisification. It's easy to see that on this "variable assignment", Def[Fx&Fx'] comes out true, underpinning the truth of the existential.
Again, suppose that we were taking the variable assignment to X to be a precisification-relative matter. Take some object o that intuitively is perfectly precise. Now consider the assignment to X that maps X at precisification 1 to the whole domain, and X at precisification 2 to the null set. Consider "Vague[Xx]", where o is assigned to x at every precisification, and the assignment to X is as above. The sentence will be true relative to these variable assignments, and so we have "(EX)Vague[Xx]" relative to an assignment of o to x which is supposed to "say" that o has some vague property.
Although Williamson's discussion is about the supervaluationist, the semantic point equally applies to the (pretty much isomorphic) setting that I like, and which is supposed to capture vagueness in reality. If one makes the variable assignments non-precisification relative, then trivially the quantified indeterminacy claims go false. If one makes the variable assignments precisification-relative, then it threatens to make them trivially true.
The thought I have is that the problem here is essentially one of mixing up abundant and natural properties. At least for property-quantification, we should go for the precisification-relative notion. It will indeed turn out that "(EX)Vague[Xx]" will be trivially true for every choice of X. But that's no more surprising that the analogous result in the modal case: quantifying over abundant properties, it turns out that every object (even things like numbers) have a great range of contingent properties: being such that grass is green for example. Likewise, in the vagueness case, everything has a great deal of vague properties: being such that the cat is alive, for example (or whatever else is your favourite example of ontic indeterminacy).
What we need to get a substantive notion, is to restrict these quantifiers to interesting properties. So for example, the way to ask whether o has some vague sparse property is to ask whether the following is true "(EX:Natural(X))Vague[Xx]". The extrinsically specified properties invoked above won't count.
If the question is formulated in this way, then we can't read off from the semantics whether there will be an object and a property such that it is vague whether the former has the latter. For this will turn, not on the semantics for quantifiers alone, but upon which among the variable assignments correspond to natural properties.
Something similar goes for the case of quantification over states of affairs. (ES)Vague[S] would be either vacuously true or vacuously false depending on what semantics we assign to the variables "X". But if our interest is in whether there are sparse states of affairs which are such that it is vague whether they obtain, what we should do is e.g. let the assignment of values to S be functions from precisifications to truth values, and then ask the question:
(ES:Natural(S))Vague[S].
Where a function from precisifications to truth values is "natural" if it corresponds to some relatively sparse state of affairs (e.g. there being a live cat on the mat). So long as there's a principled story about which states of affairs these are (and it's the job of metaphysics to give us that) everything works fine.
A final note. It's illuminating to think about the exactly analogous point that could be made in the modal case. If values are assigned to variables independently of the world, we'll be able to prove that the following is never true on any variable assignment:
Contingently[Xx].
Again, the extensions assigned to X and x are non-world dependent, so if "Xx" is true relative to one world, it's true at them all. Is this really an argument that there is no contingent instantiation of properties? Surely not. To capture the intended sense of the question, we have to adopt something like the tactic just suggested: first allow world-relative variable assignment, and then restrict the quantifiers to the particular instances of this that are metaphysically interesting.
As I've mentioned previously, I like a way of formulating claims of metaphysical indeterminacy that's semantically similar to supervaluationism (basically, we have ontic precisifications of reality, rather than semantic sharpenings of our meanings. It's similar to ideas put forward by Ken Akiba and Elizabeth Barnes).
Williamson formulates the question of whether there is vagueness in reality, as the question of whether the following can ever be true:
(EX)(Ex)Vague[Xx]
Here X is a property-quantifier, and x an object quantifier. His answer is that the semantics force this to be false. The key observation is that, as he sets things up, the value assigned to a variable at a precisification and a variable assignment depends only on the variable assignment, and not at all on the precisification. So at all precisifications, the same value is assigned to the variable. That goes for both X and x; with the net result that if "Xx" is true relative to some precisification (at the given variable assignment) it's true at all of them. That means there cannot be a variable assignment that makes Vague[Xx] true.
You might think this is cheating. Why shouldn't variables receive different values at different precisifications (formally, it's very easy to do)? Williamson says that, if we allow this to happen, we'd end up making things like the following come out true:
(Ex)Def[Fx&~Fx']
It's crucial to the supervaluationist's explanatory programme that this come out false (it's supposed to explain why we find the sorites premise compelling). But consider a variable assignment to x which at each precisification maps x to that object which marks the F/non-F cutoff relative to that precisification. It's easy to see that on this "variable assignment", Def[Fx&Fx'] comes out true, underpinning the truth of the existential.
Again, suppose that we were taking the variable assignment to X to be a precisification-relative matter. Take some object o that intuitively is perfectly precise. Now consider the assignment to X that maps X at precisification 1 to the whole domain, and X at precisification 2 to the null set. Consider "Vague[Xx]", where o is assigned to x at every precisification, and the assignment to X is as above. The sentence will be true relative to these variable assignments, and so we have "(EX)Vague[Xx]" relative to an assignment of o to x which is supposed to "say" that o has some vague property.
Although Williamson's discussion is about the supervaluationist, the semantic point equally applies to the (pretty much isomorphic) setting that I like, and which is supposed to capture vagueness in reality. If one makes the variable assignments non-precisification relative, then trivially the quantified indeterminacy claims go false. If one makes the variable assignments precisification-relative, then it threatens to make them trivially true.
The thought I have is that the problem here is essentially one of mixing up abundant and natural properties. At least for property-quantification, we should go for the precisification-relative notion. It will indeed turn out that "(EX)Vague[Xx]" will be trivially true for every choice of X. But that's no more surprising that the analogous result in the modal case: quantifying over abundant properties, it turns out that every object (even things like numbers) have a great range of contingent properties: being such that grass is green for example. Likewise, in the vagueness case, everything has a great deal of vague properties: being such that the cat is alive, for example (or whatever else is your favourite example of ontic indeterminacy).
What we need to get a substantive notion, is to restrict these quantifiers to interesting properties. So for example, the way to ask whether o has some vague sparse property is to ask whether the following is true "(EX:Natural(X))Vague[Xx]". The extrinsically specified properties invoked above won't count.
If the question is formulated in this way, then we can't read off from the semantics whether there will be an object and a property such that it is vague whether the former has the latter. For this will turn, not on the semantics for quantifiers alone, but upon which among the variable assignments correspond to natural properties.
Something similar goes for the case of quantification over states of affairs. (ES)Vague[S] would be either vacuously true or vacuously false depending on what semantics we assign to the variables "X". But if our interest is in whether there are sparse states of affairs which are such that it is vague whether they obtain, what we should do is e.g. let the assignment of values to S be functions from precisifications to truth values, and then ask the question:
(ES:Natural(S))Vague[S].
Where a function from precisifications to truth values is "natural" if it corresponds to some relatively sparse state of affairs (e.g. there being a live cat on the mat). So long as there's a principled story about which states of affairs these are (and it's the job of metaphysics to give us that) everything works fine.
A final note. It's illuminating to think about the exactly analogous point that could be made in the modal case. If values are assigned to variables independently of the world, we'll be able to prove that the following is never true on any variable assignment:
Contingently[Xx].
Again, the extensions assigned to X and x are non-world dependent, so if "Xx" is true relative to one world, it's true at them all. Is this really an argument that there is no contingent instantiation of properties? Surely not. To capture the intended sense of the question, we have to adopt something like the tactic just suggested: first allow world-relative variable assignment, and then restrict the quantifiers to the particular instances of this that are metaphysically interesting.
Ontic vagueness
I've been frantically working this week on a survey article on metaphysical indeterminacy and ontic vagueness. Mind bending stuff: there really is so much going on in the literature, and people are working with *very* different conceptions of the thing. Just sorting out what might be meant by the various terms "vagueness de re", "metaphysical vagueness", "ontic vagueness", "metaphysical indeterminacy" was a task (I don't think there are any stable conventions in the literature). And that's not to mention "vague objects" and the like.
I decided in the end to push a particular methodology, if only as a stalking horse to bring out the various presuppositions that other approaches will want to deny. My view is that we should think of "indefinitely" roughly parallel to the way we do "possibly". There are various disambiguations one can make: "possibly" might mean metaphysical possibility, epistemic possibility, or whatever; "indefinitely" might mean linguistic indeterminacy, epistemic unclarity, or something metaphysical. To figure out whether you should buy into metaphysical indeterminacy, you should (a) get yourself in a position to at least formulate coherently theories involving that operator (i.e. specify what its logic is); and (b) run the usual Quinean cost/benefit analysis on a case-by-case basis.
The view of metaphysical indeterminacy most opposed to this is one that would identify it strongly with vagueness de re, paradigmatically there being some object and some property such that it is indeterminate whether the former instantiates the latter (this is how Williamson seems to conceive of matters in a 2003 article). If we had some such syntactic criterion for metaphysical indeterminacy, perhaps we could formulate everything without postulating a plurality of disambiguations of "definitely". However, it seems that this de re formulation would miss out some of the most paradigmatic examples of putative metaphysical vagueness, such as the de dicto formulation: It is indeterminate whether there are exactly 29 things. (The quantifiers here to be construed unrestrictedly).
I also like to press the case against assuming that all theories of metaphysical indeterminacy must be logically revisionary (endorsing some kind of multi-valued logic). I don't think the implication works in either direction: multi-valued logics can be part of a semantic theory of indeterminacy; and some settings for thinking about metaphysical indeterminacy are fully classical.
I finish off with a brief review of the basics of Evans' argument, and the sort of arguments (like the one from Weatherson in the previous post) that might convert metaphysical vagueness of apparently unrelated forms into metaphysically vague identity arguably susceptable to Evans argument.
I decided in the end to push a particular methodology, if only as a stalking horse to bring out the various presuppositions that other approaches will want to deny. My view is that we should think of "indefinitely" roughly parallel to the way we do "possibly". There are various disambiguations one can make: "possibly" might mean metaphysical possibility, epistemic possibility, or whatever; "indefinitely" might mean linguistic indeterminacy, epistemic unclarity, or something metaphysical. To figure out whether you should buy into metaphysical indeterminacy, you should (a) get yourself in a position to at least formulate coherently theories involving that operator (i.e. specify what its logic is); and (b) run the usual Quinean cost/benefit analysis on a case-by-case basis.
The view of metaphysical indeterminacy most opposed to this is one that would identify it strongly with vagueness de re, paradigmatically there being some object and some property such that it is indeterminate whether the former instantiates the latter (this is how Williamson seems to conceive of matters in a 2003 article). If we had some such syntactic criterion for metaphysical indeterminacy, perhaps we could formulate everything without postulating a plurality of disambiguations of "definitely". However, it seems that this de re formulation would miss out some of the most paradigmatic examples of putative metaphysical vagueness, such as the de dicto formulation: It is indeterminate whether there are exactly 29 things. (The quantifiers here to be construed unrestrictedly).
I also like to press the case against assuming that all theories of metaphysical indeterminacy must be logically revisionary (endorsing some kind of multi-valued logic). I don't think the implication works in either direction: multi-valued logics can be part of a semantic theory of indeterminacy; and some settings for thinking about metaphysical indeterminacy are fully classical.
I finish off with a brief review of the basics of Evans' argument, and the sort of arguments (like the one from Weatherson in the previous post) that might convert metaphysical vagueness of apparently unrelated forms into metaphysically vague identity arguably susceptable to Evans argument.
From vague parts to vague identity
(Update: as Dan notes in the comment below, I should have clarified that the initial assumption is supposed to be that it's metaphysically vague what the parts of Kilimanjaro (Kili) are. Whether we should describe the conclusion as deriving a metaphysically vague identity is a moot point.)
I've been reading an interesting argument that Brian Weatherson gives against "vague objects" (in this case, meaning objects with vague parts) in his paper "Many many problems".
He gives two versions. The easiest one is the following. Suppose it's indeterminate whether Sparky is part of Kili, and let K+ and K- be the usual minimal variations of Kili (K+ differs from Kili only in determinately containing Sparky, K- only by determinately failing to contain Sparky).
Further, endorse the following principle (scp): if A and B coincide mereologically at all times, then they're identical. (Weatherson's other arguments weaken this assumption, but let's assume we have it, for the sake of argument).
The argument then runs as follows:
1. either Sparky is part of Kili, or she isn't. (LEM)
2. If Sparky is part of Kili, Kili coincides at all times with K+ (by definition of K+)
3. If Sparky is part of Kili, Kili=K+ (by 2, scp)
4. If Sparky is not part of Kili, Kili coincides at all times with K- (by definition of K-)
5. If Sparky is not part of Kili, Kili=K- (by 4, scp).
6. Either Kili=K+ or Kili=K- (1, 3,5).
At this point, you might think that things are fine. As my colleague Elizabeth Barnes puts it in this discussion of Weatherson's argument you might simply think at this point that only the following been established: that it is determinate that either Kili=K+ or K-: but that it is indeterminate which.
I think we might be able to get an argument for this. First our all, presumably all the premises of the above argument hold determinately. So the conclusion holds determinately. We'll use this in what follows.
Suppose that D(Kili=K+). Then it would follow that Sparky was determinately a part of Kili, contrary to our initial assumption. So ~D(Kili=K+). Likewise ~D(Kili=K-).
Can it be that they are determinately distinct? If D(~Kili=K+), then assuming that (6) holds determinately, D(Kili=K+ or Kili=K-), we can derive D(Kili=K-), which contradicts what we've already proven. So ~D(~Kili=K+) and likewise ~D(~Kili=K-).
So the upshot of the Weatherson argument, I think, is this: it is indeterminate whether Kili=K+, and indeterminate whether Kili=K-. The moral: vagueness in composition gives rise to vague identity.
Of course, there are well known arguments against vague identity. Weatherson doesn't invoke them, but once he reaches (6) he seems to think the game is up, for what look to be Evans-like reasons.
My working hypothesis at the moment, however, is that whenever we get vague identity in the sort of way just illustrated (inherited from other kinds of ontic vagueness), we can wriggle out of the Evans reasoning without significant cost. (I go through some examples of this in this forthcoming paper). The over-arching idea is that the vagueness in parthood, or whatever, can be plausibly viewed as inducing some referential indeterminacy, which would then block the abstraction steps in the Evans proof.
Since Weatherson's argument is supposed to be a general one against vague parthood, I'm at liberty to fix the case in any way I like. Here's how I choose to do so. Let's suppose that the world contains two objects, Kili and Kili*. Kili* is just like Kili, except that determinately, Kili and Kili* differ over whether they contain Sparky.
Now, think of reality as indeterminate between two ways: one in which Kili contains Sparky, the other where it doesn't. What of our terms "K+" and "K-"? Well, if Kili contains Sparky, then "K+" denotes Kili. But if it doesn't, then "K+" denotes Kili*. Mutatis Mutandis for "K-". Since it is is indeterminate which option obtains, "K+" and "K-" are referentially indeterminate, and one of the abstraction steps in the Evans proof fail.
Now, maybe it's built into Weatherson's assumptions that the "precise" objects like K+ and K- exist, and perhaps we could still cause trouble. But I'm not seeing cleanly how to get it. (Notice that you'd need more than just the axioms of mereology to secure the existence of [objects determinately denoted by] K+ and K-: Kili and Kili* alone would secure the truth that there are fusions including Sparky and fusions not including Sparky). But at this point I think I'll leave it for others to work out exactly what needs to be added...
I've been reading an interesting argument that Brian Weatherson gives against "vague objects" (in this case, meaning objects with vague parts) in his paper "Many many problems".
He gives two versions. The easiest one is the following. Suppose it's indeterminate whether Sparky is part of Kili, and let K+ and K- be the usual minimal variations of Kili (K+ differs from Kili only in determinately containing Sparky, K- only by determinately failing to contain Sparky).
Further, endorse the following principle (scp): if A and B coincide mereologically at all times, then they're identical. (Weatherson's other arguments weaken this assumption, but let's assume we have it, for the sake of argument).
The argument then runs as follows:
1. either Sparky is part of Kili, or she isn't. (LEM)
2. If Sparky is part of Kili, Kili coincides at all times with K+ (by definition of K+)
3. If Sparky is part of Kili, Kili=K+ (by 2, scp)
4. If Sparky is not part of Kili, Kili coincides at all times with K- (by definition of K-)
5. If Sparky is not part of Kili, Kili=K- (by 4, scp).
6. Either Kili=K+ or Kili=K- (1, 3,5).
At this point, you might think that things are fine. As my colleague Elizabeth Barnes puts it in this discussion of Weatherson's argument you might simply think at this point that only the following been established: that it is determinate that either Kili=K+ or K-: but that it is indeterminate which.
I think we might be able to get an argument for this. First our all, presumably all the premises of the above argument hold determinately. So the conclusion holds determinately. We'll use this in what follows.
Suppose that D(Kili=K+). Then it would follow that Sparky was determinately a part of Kili, contrary to our initial assumption. So ~D(Kili=K+). Likewise ~D(Kili=K-).
Can it be that they are determinately distinct? If D(~Kili=K+), then assuming that (6) holds determinately, D(Kili=K+ or Kili=K-), we can derive D(Kili=K-), which contradicts what we've already proven. So ~D(~Kili=K+) and likewise ~D(~Kili=K-).
So the upshot of the Weatherson argument, I think, is this: it is indeterminate whether Kili=K+, and indeterminate whether Kili=K-. The moral: vagueness in composition gives rise to vague identity.
Of course, there are well known arguments against vague identity. Weatherson doesn't invoke them, but once he reaches (6) he seems to think the game is up, for what look to be Evans-like reasons.
My working hypothesis at the moment, however, is that whenever we get vague identity in the sort of way just illustrated (inherited from other kinds of ontic vagueness), we can wriggle out of the Evans reasoning without significant cost. (I go through some examples of this in this forthcoming paper). The over-arching idea is that the vagueness in parthood, or whatever, can be plausibly viewed as inducing some referential indeterminacy, which would then block the abstraction steps in the Evans proof.
Since Weatherson's argument is supposed to be a general one against vague parthood, I'm at liberty to fix the case in any way I like. Here's how I choose to do so. Let's suppose that the world contains two objects, Kili and Kili*. Kili* is just like Kili, except that determinately, Kili and Kili* differ over whether they contain Sparky.
Now, think of reality as indeterminate between two ways: one in which Kili contains Sparky, the other where it doesn't. What of our terms "K+" and "K-"? Well, if Kili contains Sparky, then "K+" denotes Kili. But if it doesn't, then "K+" denotes Kili*. Mutatis Mutandis for "K-". Since it is is indeterminate which option obtains, "K+" and "K-" are referentially indeterminate, and one of the abstraction steps in the Evans proof fail.
Now, maybe it's built into Weatherson's assumptions that the "precise" objects like K+ and K- exist, and perhaps we could still cause trouble. But I'm not seeing cleanly how to get it. (Notice that you'd need more than just the axioms of mereology to secure the existence of [objects determinately denoted by] K+ and K-: Kili and Kili* alone would secure the truth that there are fusions including Sparky and fusions not including Sparky). But at this point I think I'll leave it for others to work out exactly what needs to be added...
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