Just a quick post to point to some hot-off-the-press developments here at Leeds (for that is where our current timeslices are located).
Leeds is advertising a new-line professorial chair in philosophy. AOS's are open, but the idea is that the appointment will be related either to areas covered by History and Philosophy of Science, or the Centre for Metaphysics and Mind.
We are also advertising a lecturership/senior lectureship position in philosophy (those grades cover everyone from PhD-ers new on the market this year to senior people). Again no AOS is specified, though philosophy of value and history of philosophy are the areas that the department states it is "keen to appoint in".
Lastly, the recent Gourmet report previews have contained pleasant reading for Leeds. We've among the big movers (upwards!) in both the overall and the local UK rankings. And the mean score has gone up significantly too, by 0.2/0.3 respectively (out of 5). No matter what you think about league tables, there's something strangely addictive about them...
Wednesday, October 25, 2006
Friday, October 20, 2006
Lowe on necessity of identity
The standard proof of the necessity of identity runs as follows:
1) For all x, necessarily x=x (Premise)2) a=b (Assumption)
3) Necessarily, a=a (From 1)
4) a has the property of being necessarily identical to a (From 3)
5) b has the property of being necessarily identical to a (From 2,4, and Leibniz’ law)
6) Necessarily, a=b (From 5)
I used to be concerned about Lowe’s objection to this proof. Lowe says (rightly) that we must be careful to distinguish between two properties: the property of being necessarily self-identical, as had by a, and the property of being necessarily identical by a, as had by a. The properties are clearly distinct: everything has the former, but only a has the latter. (3), Lowe said, is ambiguous: it could mean that everything has the property of being necessarily self-identical or it could mean that everything has the property of being necessarily identical to itself (i.e. that for all x, x has the property ‘being necessarily identical to x’). Read in the first way, (3) is uncontroversial, but then (4) doesn’t follow: all that follows is that a is necessarily self-identical and, hence, that b is necessarily self-identical. That is also uncontroversial, and a far cry from the necessity of identity. To get the claim that b is necessarily identical to a we need to get that a is necessarily identical to a, which requires the second reading of (3). But this, says Lowe, is not uncontroversial: to rule out contingent identity, we need to be given an argument for it.
Lowe is definitely right that there are two properties here. But is there any case to be made for the claim that a is necessarily self-identical but is not necessarily identical to a? I don’t think so. We can argue very simply as follows:
1) a is necessarily self-identical (Premise)
2) If is self identical then a is identical to a (Tautology)
3) Necessarily (If a is self identical then a is identical to a) (From (2))
4) Necessarily (a is self-identical) (From 1)
5) If Necessarily (a is self-identical), then Necessarily (a is identical to a) (From (3)
6) Necessarily (a is identical to a) (from (4) and (5))
7) a is necessarily identical to a (From (6))
Where could one resist that? Lowe definitely agrees with (2) because he is happy with the standard proof of the symmetry of identity, which relies on this (this is a point that
Tuesday, October 17, 2006
presentism fought the law and the law won
There’s loads of stuff I’ve got to get done today. Hence, I am procrastinating and writing more silly blog posts.
Does anyone know that content of the law against denying the Holocaust in countries like
I heard
This is a flippant point, of course; but behind it lies a more serious one: just what do laws that impose a limit on freedom of speech make illegal? If they infringe on academic freedom, that doesn’t appear to me to be a very good thing.
Friday, October 13, 2006
There are sets . . . (not really!)
I’ve been thinking a lot recently about relations of fundamentality. There are, I think, three relations here: a relation of ontological dependence that holds between entities, a relation of grounding/truth-in-virtue-of that holds between propositions, and the truth-making relation, that holds between an entity and a proposition.
One thing I am interested in is the connection between the relations. One potential connection is the following: if A makes p true and if p grounds q (i.e. if q is true in virtue of p) then A makes q true. This seems pretty plausible. If p grounds q then it doesn’t take anything more for the world to be a q-world than for it to be a p-world: so to make the world a p-world is to make it a q-world.
I’m currently intrigued by the potential of this to allow us to make sense of Fine’s distinction between what there is and what there really is. It would be nice to be allowed to make such a distinction. In particular, I’d like to be able to say that there are abstracta, but that there aren’t really any abstracta. I’d like to say that there are sets, for example, because it’s really useful to be able to talk about such things; but I’d like to deny that there are really any sets because an ontology without sets is, other things’ being equal, preferable to one with.
Now, it’s natural to think that a set is ontologically dependent on its members. Socrates’ singleton depends for its existence on Socrates, and not vice-versa. You might be tempted as well (perhaps as a consequence) to the claim that the proposition the singleton of Socrates exists is true in virtue of Socrates exists. Since Socrates is the truthmaker for Socrates exists the above principle will then imply that Socrates is the truthmaker for the singleton of Socrates exists.
First thought then: we don’t need there to actually be a singleton of Socrates. We only need Socrates, and he makes true all the truths talking about his singleton. Generalising, all we need are the ordinary concrete objects, and we get all the truths about sets for free. (Pure sets will be a bit trickier – but there are any number of stories we might tell here.) So we can secure all the truths we want – we get the benefit of talking about sets – without admitting sets into our ontology.
But that can’t be quite right. We can’t deny the existence of sets and affirm the truth of the proposition the singleton of Socrates exists. But what we can do is accept that there are sets and deny that there are really any sets. The thought is that the singleton of Socrates exists is true (and hence there are sets), and is made true by Socrates; but the singleton of Socrates really exists is not made true by Socrates; in fact, it’s not made true by anything, and so it’s false.
Armstrong says that a exists is always made true by a. I am denying that: I claim that the singleton of Socrates exists is made true not by the singleton of Socrates (since the truthmakers are what there really is, and there aren’t really any sets) but by Socrates. But I can accept a variant of the Armstrong position: that a really exists is always made true by a, which is a fundamental being.
So the thought is that we have a bunch of fundamental entities that do all our truthmaking. Some of the things they make true is that they really exist. Other things that they make true is that some non-fundamental entities exist (but not that they really exist – they don’t!). This is meant to secure all the benefits without the cost. We get the benefit of talking about sets, since all we need to secure that is that we can presuppose that sets exist – we couldn’t care less whether or not they really exist. And we secure a parsimonious ontology: since what we care about here is what there really is – what exists in reality – and sets don’t really exist.
I have no idea whether that is in line with Fine’s thinking on the distinction, but it seems to me not wholly crazy, and worthy of pursuit.
On other news, I’ve been invited to respond to
Eliminating cross-level universals
I've just come back from a CMM discussion of Lewis on Quantities (built around John Hawthorne's paper of that title).
One thing that came up was the issue of what you might call potentially "cross level" fundamental properties. These are properties that you might expect to find instantiated at the "bottommost" microphysical level, but also instantiated "further up". For example, electrons have negative charge; but so do ions. But ions are composite entities, which (from what I remember of A-level chemistry) are charged in virtue of the charges of their parts.
Clearly in some sense, electrons and ions can have the same determinate property: e.g. "charge -1". But, when giving e.g. a theory of universals, I'm wondering whether we have to say that they share the same Universal.
On Armstrong's theory of quantities, it looks to me that we won't say that the ion and the electron both instantiate the same Universal. The "charge -1" we find instantiated by the ion will be a structural universal, composed of the various charge Universals instantiated by the basic parts of the ion. The "charge -1" we find instantiated by an electron, on the other hand, looks like it'll be a basic, non-structural universal. So, it seems to me, it'll then be a challenge to Armstrong's account to say why these two universals resemble each other in a tight enough way that we apply to them the same preicate. (To avoid confusion, let's call the former "ur-charge -1" and leave "charge -1" as a predicate that applies to both ions and electrons, though not, on this view, in virtue of them instantiating the same Universal).
Let's suppose we're looking at a theory of universals (such as the one Lewis seems to contemplate at various points) which is just like Armstrong's except for ditching all the structural universals. Electrons get to instantiate the Universal "ur-charge -1". But ions, as actual-worldly complex objects, instantiate no Universals at all. Of course, again there's the challenge to spell out exactly what the conditions are under which we'll apply the predicate "charge -1" to things (roughly: when the various ur-charges instantiated by their parts "balance out"---though the details get tricksy).
What goes for charge can go for various other types of property. So we may find it useful to distinguish ur-mass 1kg (which will be a genuine basic universal) from the set of things "having mass 1kg".
A last thought. What is the relation between mass properties and ur-masses? In particular, is it the case that things can only ever have masses when their basic parts have ur-masses? I don't see any immediate reason to think so. Perhaps the actual world is one where things have mass in virtue of their parts having ur-mass. But why shouldn't we think that "having parts that have ur-masses" is but one *realization* of mass: and that at other worlds quite different ur-properties may underlie mass (say, ur-mass-densities, rather than ur-masses). That's potentially significant for discussions of modality and quantities: for two worlds that intially seem to be share the same stock of fundamental properties (spin, charge, mass, etc) may turn out to actual contain alien properties from each others point of view: if one contains ur-masses underlying the (non-fundamental) mass properties, while the other contains ur-mass-densities underlying those same properties.
(Thanks to all those at CMM for the discussion that led to this. This is x-posted at Theories n Things. And thanks to an anonymous commentator, who pointed out in an early version of this post that by "free radicals" I meant "ions"!))
One thing that came up was the issue of what you might call potentially "cross level" fundamental properties. These are properties that you might expect to find instantiated at the "bottommost" microphysical level, but also instantiated "further up". For example, electrons have negative charge; but so do ions. But ions are composite entities, which (from what I remember of A-level chemistry) are charged in virtue of the charges of their parts.
Clearly in some sense, electrons and ions can have the same determinate property: e.g. "charge -1". But, when giving e.g. a theory of universals, I'm wondering whether we have to say that they share the same Universal.
On Armstrong's theory of quantities, it looks to me that we won't say that the ion and the electron both instantiate the same Universal. The "charge -1" we find instantiated by the ion will be a structural universal, composed of the various charge Universals instantiated by the basic parts of the ion. The "charge -1" we find instantiated by an electron, on the other hand, looks like it'll be a basic, non-structural universal. So, it seems to me, it'll then be a challenge to Armstrong's account to say why these two universals resemble each other in a tight enough way that we apply to them the same preicate. (To avoid confusion, let's call the former "ur-charge -1" and leave "charge -1" as a predicate that applies to both ions and electrons, though not, on this view, in virtue of them instantiating the same Universal).
Let's suppose we're looking at a theory of universals (such as the one Lewis seems to contemplate at various points) which is just like Armstrong's except for ditching all the structural universals. Electrons get to instantiate the Universal "ur-charge -1". But ions, as actual-worldly complex objects, instantiate no Universals at all. Of course, again there's the challenge to spell out exactly what the conditions are under which we'll apply the predicate "charge -1" to things (roughly: when the various ur-charges instantiated by their parts "balance out"---though the details get tricksy).
What goes for charge can go for various other types of property. So we may find it useful to distinguish ur-mass 1kg (which will be a genuine basic universal) from the set of things "having mass 1kg".
A last thought. What is the relation between mass properties and ur-masses? In particular, is it the case that things can only ever have masses when their basic parts have ur-masses? I don't see any immediate reason to think so. Perhaps the actual world is one where things have mass in virtue of their parts having ur-mass. But why shouldn't we think that "having parts that have ur-masses" is but one *realization* of mass: and that at other worlds quite different ur-properties may underlie mass (say, ur-mass-densities, rather than ur-masses). That's potentially significant for discussions of modality and quantities: for two worlds that intially seem to be share the same stock of fundamental properties (spin, charge, mass, etc) may turn out to actual contain alien properties from each others point of view: if one contains ur-masses underlying the (non-fundamental) mass properties, while the other contains ur-mass-densities underlying those same properties.
(Thanks to all those at CMM for the discussion that led to this. This is x-posted at Theories n Things. And thanks to an anonymous commentator, who pointed out in an early version of this post that by "free radicals" I meant "ions"!))
Hawthorne on Lewis on Quantity
Just a quick reminder to metaphysicians in the Leeds area: the CMM seminar today is going to be on Hawthorne's paper "Lewis on Quantity" from his Metaphysical Essays.
A quick puzzle I'm having over Lewis-interpretation. Suppose that in the actual world, a fundamental property P is instantiated by pointy things. Can that very same fundamental property be instantiated in another world by non-pointy things?
The point is that in characterizing Humean supervenience, Lewis mentions ways it might fail e.g. there being "emergent natural properties of more-than-point sized things". He insists that, though such properties are possible, they would have to occur in worlds featuring properties "altogether alien to this world". But that wouldn't be the case if it were a contingent feature of the properties we found lying around this world, that they hold of pointy things rather than more-than-point-sized things.
Maybe the moral is that the mereological structure of the instantiators of a property is *not* a matter that can vary from world to world, for Lewis. If so, it seems a pretty strange claimed of necessity.
A quick puzzle I'm having over Lewis-interpretation. Suppose that in the actual world, a fundamental property P is instantiated by pointy things. Can that very same fundamental property be instantiated in another world by non-pointy things?
The point is that in characterizing Humean supervenience, Lewis mentions ways it might fail e.g. there being "emergent natural properties of more-than-point sized things". He insists that, though such properties are possible, they would have to occur in worlds featuring properties "altogether alien to this world". But that wouldn't be the case if it were a contingent feature of the properties we found lying around this world, that they hold of pointy things rather than more-than-point-sized things.
Maybe the moral is that the mereological structure of the instantiators of a property is *not* a matter that can vary from world to world, for Lewis. If so, it seems a pretty strange claimed of necessity.
Monday, October 09, 2006
Just me ranting . . .
Companies can be really annoying. I doubt anyone needs convincing of that, but my current gripe is rather amusing, so I’ll share it.
When I moved into my new flat I phoned Power Company (I won’t use the real name) to let them know to start my account from my move in date, and that the old occupiers had moved. After a month I duly got my first bill, addressed to me. I also got a bill addressed to ‘the occupier’, for the account of the previous occupiers. It started:
Dear occupier,
We notice you have now moved from this address: please settle your account . . . etc
I phoned Power Company to explain to them that ‘the occupier’ was an indexical, and that while it used to refer to the people who had the unpaid account, it now refers to me. I also tried to explain that ‘the occupier of flat X no longer lives in flat X’ can never express a truth, but without much success.
I thought that was the end of it until I received a letter from their solicitors (again, addressed to the occupier) demanding payment. And the funniest thing is, when I phoned them up to politely explain again, they chastised me for opening someone else’s mail! Again, I tried to explain that if you write ‘to the occupier of flat X’ on the envelope, then that is to address it to me, but they didn’t seem to be getting this.
On another totally frivolous note. I’m interested in whether particular issues of religious faith can be reconciled with science. The current hot topic here, I guess, is creationism. Some Christians appear to think they’ve got reason to hold that the Earth is only six thousand years old, and that humans were created in close to their present form. This seems straightforwardly incompatible with the scientific view that we evolved over rather a longer period. But perhaps not. Consider the eternalist/presentist debate. The eternalist thinks there is a past time with dinosaurs, the presentist thinks there is only the present time, but that it is true at the present time that there were dinosaurs nevertheless. I think the creationist should hold that there are past times only six thousand years into the past, but that it is nevertheless true that prior to this such-and-such was going on. It’s true that there were apes who would evolve into humans; but nevertheless, there are no past apes who are our ancestors. That seems like a perfectly consistent view. I wonder if I can get a grant to put this view across to US high-schools. Would that count as knowledge transfer?
Sorry this post has been a bit frivolous. That’s what we get for working in something like philosophy. Oh for the rigour and intellectual honesty of science, where they’ve just discovered that having a cup of tea can relax you. Well, no one could have told you that! – I’m glad the research money is being put to good use.
Sunday, September 03, 2006
Ontic vagueness: the shape of the debate.
(cross-posted on theories n things)
One of my projects at the moment is writing a survey article on ontic vagueness. I've been working on this stuff for a while now, but it's time to pull things together. (And writing up comments on Hugh Mellor's paper "Micro-composition" at the RIP Being conference got me puzzling about some of these issues all over again.)
One thing I'd like to achieve is to separate out different types of ontic vagueness. The "big three", for me, are vague identity, vague existence, vague instantition. But there also might be: vagueness in the parthood relation, vague locations, vague composition, vagueness in "supervening" levels (it being ontically vague whether x is bald); vagueness at the fundamental level (it being ontically vague whether that elementary particle is charged). These all seem prima facie different, to me. And (as Elizabeth Barnes told me time and again until I started listening) it's just not obvious that e.g. rejecting vague identity for Evansian reasons puts in peril any other sort of ontic vagueness, since it's not obvious that any other form of ontic vagueness requires vague identity.
[Digression: It's really not very surprising that ontic vagueness comes in many types, when you think about it. For topic T in metaphysics (theory of properties, theory of parts, theory of persistence, theory of identity, theory of location etc etc), we could in principle consider the thesis that the facts discussed by T are vague. End Digression]
Distinguish (a) the positive project of giving a theory of ontic vagueness; and (b) the negative project of defending it against its many detractors. The negative project I guess has the lion's share of the attention in the literature. I think it helps to see the issues here as a matter of (i) developing arguments against particular types of ontic vagueness (ii) arguing that this or that form of ontic vagueness entails some other one.
Regarding (i), Evans' argument is the most famous case, specifically against vague identity. But it won't do what Evans claimed it did (provide an argument against vagueness in the world per se) unless we can argue that other kinds of ontic vagueness give rise to vague identity (and Evans, of course, doesn't say anything about this). Vague existence is another point at which people are apt to stick directly. I think some of Ted Sider's recent arguments against semantically or epistemically vague existence transfer directly to the case of ontically vague existence. And we shouldn't forget the "incredulous stare" maneuver, often deployed at this point.
Given these kind of answers to (i), I think the name of the game in the second part of the negative project is to figure out exactly which forms of ontic vagueness commit one to vague existence or vague identity. So, for example, one of the things Elizabeth does in her recent analysis paper is to argue that vague instantiation entails vague existence (at least for a states-of-affairs theorist). Implicit in an argument due to Katherine Hawley are considerations seemingly showing that vague existence entails vague identity (at least if you have sets, or unrestricted mereological composition, around). (I set both of these out briefly and give references in this paper).
Again, you can think of Ted Sider's argument against vague composition as supporting the following entailment: vague composition entails vague existence. And so on and so forth.
[A side note. Generally, all these arguments will have the form:
Ontic vagueness of type 1
Substantive metaphysical principles
Therefore:
Ontic vagueness of type 2.
What this means is that these debates over ontic vagueness are potentially extemely metaphysically illuminating. For, suppose that you think that ontic vagueness of type 2 occurs, but that ontic vagueness of type 1 is impossible (say because it entails vague identity). Then, you are going to have to reject the substantive metaphysical principles that provide the bridge from one to the other. For example, if you want vague instantiation, but think vague existence is, directly or indirectly, incoherent, then you have an argument against states-of-affairs-theorists. The argument from vague existence to vague identity won't worry someone who doesn't believe in or in unrestricted mereological fusion. Hence, if cogent, it can be turned into an argument against sets and arbitrary fusions (actually, it's in that form --- as an argument against the standard set theoretic axioms --- that Katherine Hawley first presented it). And so forth.]
So that's my view on what the debate on ontic vagueness is, or should be. It has the advantage of unifying what at first glance appear to be a load of disparate discussions in the literature. It does impose a methodology that's not in keeping with much of the literature by defenders of ontic vagueness: in particular, the way I'm thinking of things, classical logic will be the last thing we give up: though non-classical logics are often the first tool reached for by defenders of ontic vagueness (notable exceptions are the modal-ish/supervaluation-ish characterizations of ontic vagueness favoured in various forms by Ken Akiba, Elizabeth Barnes and, erm, me). I'll have to be up front about this.
Still, I'd like to use the above as a way of setting up the paper. It can only be 5000 or so words long, and it has to be comprehensible to advanced undergraduates, so I may not be able to include everything, particularly if the issues allude to complex areas of metaphysics. But I'd like to have an as-exhaustive-as-possible taxonomy, of which I can extract a suitable sample for the paper. I'd be really interested in collecting any discussions of ontic vagueness that can fit into the project as I've sketched it. And I'd also be really grateful to hear about other parts of the literature that I'm in danger of missing out or ignoring if I go this route, and any comments on the strategy I'm adopting.
Some examples to get us started:
If composition is identity, then it looks like vague parthood entails vague identity. For if it's vague whether the a is part of b, then it'll be vague whether the a's are identical to b.
Indeed, if classical mereology holds, then it looks like vague parthood entails vague identity. For if it's vague whether the aa's are all and only the parts of b, then mereology will give us that that object which is the fusion of the aa's is identical to b iff the aa's are all and only the parts of b. Since the RHS here is ex hypothesi vague, the LHS will be too.
If the Wigginsean "individuation criteria" for Fs are vague, it looks like vague existence will follow when it's vague whether the conditions are met.
One of my projects at the moment is writing a survey article on ontic vagueness. I've been working on this stuff for a while now, but it's time to pull things together. (And writing up comments on Hugh Mellor's paper "Micro-composition" at the RIP Being conference got me puzzling about some of these issues all over again.)
One thing I'd like to achieve is to separate out different types of ontic vagueness. The "big three", for me, are vague identity, vague existence, vague instantition. But there also might be: vagueness in the parthood relation, vague locations, vague composition, vagueness in "supervening" levels (it being ontically vague whether x is bald); vagueness at the fundamental level (it being ontically vague whether that elementary particle is charged). These all seem prima facie different, to me. And (as Elizabeth Barnes told me time and again until I started listening) it's just not obvious that e.g. rejecting vague identity for Evansian reasons puts in peril any other sort of ontic vagueness, since it's not obvious that any other form of ontic vagueness requires vague identity.
[Digression: It's really not very surprising that ontic vagueness comes in many types, when you think about it. For topic T in metaphysics (theory of properties, theory of parts, theory of persistence, theory of identity, theory of location etc etc), we could in principle consider the thesis that the facts discussed by T are vague. End Digression]
Distinguish (a) the positive project of giving a theory of ontic vagueness; and (b) the negative project of defending it against its many detractors. The negative project I guess has the lion's share of the attention in the literature. I think it helps to see the issues here as a matter of (i) developing arguments against particular types of ontic vagueness (ii) arguing that this or that form of ontic vagueness entails some other one.
Regarding (i), Evans' argument is the most famous case, specifically against vague identity. But it won't do what Evans claimed it did (provide an argument against vagueness in the world per se) unless we can argue that other kinds of ontic vagueness give rise to vague identity (and Evans, of course, doesn't say anything about this). Vague existence is another point at which people are apt to stick directly. I think some of Ted Sider's recent arguments against semantically or epistemically vague existence transfer directly to the case of ontically vague existence. And we shouldn't forget the "incredulous stare" maneuver, often deployed at this point.
Given these kind of answers to (i), I think the name of the game in the second part of the negative project is to figure out exactly which forms of ontic vagueness commit one to vague existence or vague identity. So, for example, one of the things Elizabeth does in her recent analysis paper is to argue that vague instantiation entails vague existence (at least for a states-of-affairs theorist). Implicit in an argument due to Katherine Hawley are considerations seemingly showing that vague existence entails vague identity (at least if you have sets, or unrestricted mereological composition, around). (I set both of these out briefly and give references in this paper).
Again, you can think of Ted Sider's argument against vague composition as supporting the following entailment: vague composition entails vague existence. And so on and so forth.
[A side note. Generally, all these arguments will have the form:
Ontic vagueness of type 1
Substantive metaphysical principles
Therefore:
Ontic vagueness of type 2.
What this means is that these debates over ontic vagueness are potentially extemely metaphysically illuminating. For, suppose that you think that ontic vagueness of type 2 occurs, but that ontic vagueness of type 1 is impossible (say because it entails vague identity). Then, you are going to have to reject the substantive metaphysical principles that provide the bridge from one to the other. For example, if you want vague instantiation, but think vague existence is, directly or indirectly, incoherent, then you have an argument against states-of-affairs-theorists. The argument from vague existence to vague identity won't worry someone who doesn't believe in or in unrestricted mereological fusion. Hence, if cogent, it can be turned into an argument against sets and arbitrary fusions (actually, it's in that form --- as an argument against the standard set theoretic axioms --- that Katherine Hawley first presented it). And so forth.]
So that's my view on what the debate on ontic vagueness is, or should be. It has the advantage of unifying what at first glance appear to be a load of disparate discussions in the literature. It does impose a methodology that's not in keeping with much of the literature by defenders of ontic vagueness: in particular, the way I'm thinking of things, classical logic will be the last thing we give up: though non-classical logics are often the first tool reached for by defenders of ontic vagueness (notable exceptions are the modal-ish/supervaluation-ish characterizations of ontic vagueness favoured in various forms by Ken Akiba, Elizabeth Barnes and, erm, me). I'll have to be up front about this.
Still, I'd like to use the above as a way of setting up the paper. It can only be 5000 or so words long, and it has to be comprehensible to advanced undergraduates, so I may not be able to include everything, particularly if the issues allude to complex areas of metaphysics. But I'd like to have an as-exhaustive-as-possible taxonomy, of which I can extract a suitable sample for the paper. I'd be really interested in collecting any discussions of ontic vagueness that can fit into the project as I've sketched it. And I'd also be really grateful to hear about other parts of the literature that I'm in danger of missing out or ignoring if I go this route, and any comments on the strategy I'm adopting.
Some examples to get us started:
If composition is identity, then it looks like vague parthood entails vague identity. For if it's vague whether the a is part of b, then it'll be vague whether the a's are identical to b.
Indeed, if classical mereology holds, then it looks like vague parthood entails vague identity. For if it's vague whether the aa's are all and only the parts of b, then mereology will give us that that object which is the fusion of the aa's is identical to b iff the aa's are all and only the parts of b. Since the RHS here is ex hypothesi vague, the LHS will be too.
If the Wigginsean "individuation criteria" for Fs are vague, it looks like vague existence will follow when it's vague whether the conditions are met.
Friday, September 01, 2006
An argument for conditional excluded middle
(cross-posted from Theories n Things)
Conditional excluded middle is the following schema:
if A, then C; or if A, then not C.
It's disputed whether everyday conditionals do or should support this schema. Extant formal treatments of conditionals differ on this issue: the material conditional supports CEM; the strict conditional doesn't; Stalnaker's logic of conditionals does, Lewis's logic of conditionals doesn't.
Here's one consideration in favour of CEM (inspired by Rosen's "incompleteness puzzle" for modal fictionalism, which I was chatting to Richard Woodward about at the Lewis graduate conference that was held in Leeds yesterday).
Here's the quick version:
Fictionalisms in metaphysics should be cashed out via the indicative conditional. But if fictionalism is true about any domain, then it's true about some domain that suffers from "incompleteness" phenomena. Unless the indicative conditional in general is governed in general by CEM, then there's no way to resist the claim that we get sentences which are neither hold nor fail to hold according to the fiction. But any such "local" instance of a failure of CEM will lead to a contradiction. So the indicative conditional in general is governed by CEM
Here it is in more detail:
(A) Fictionalism is the right analysis about at least some areas of discourse.
Suppose fictionalism is the right account of blurg-talk. So there is the blurg fiction (call it B). And something like the following is true: when I appear to utter , say "blurgs exist" what I've said is correct iff according to B, "blurgs exist". A natural, though disputable, principle is the following.
(B) If fictionalism is the correct theory of blurg-talk, then the following schema holds for any sentence S within blurg-talk:
"S iff According to B, S"
(NB: read "iff" as material equivalence, in this case).
(C) The right way to understand "according to B, S" (at least in this context) is as the indicative conditional "if B, then S".
Now suppose we had a failure of CEM for an indicative conditional featuring "B" in the antecedent and a sentence of blurg-talk, S, in the consequent. Then we'd have the following:
(1) ~(B>S)&~(B>~S) (supposition)
By (C), this means we have:
(2) ~(According to B, S) & ~(According to B, ~S).
By (B), ~(According to B, S) is materially equivalent to ~S. Hence we get:
(3) ~S&~~S
Contradiction. This is a reductio of (1), so we conclude that
(intermediate conclusion):
No matter which fictionalism we're considering, CEM has no counterinstances with the relevant fiction as antecedent and a sentence of the discourse in question as consequent.
Moreover:
(D) the best explanation of (intermediate conclusion) is that CEM holds in general.
Why is this? Well, I can't think of any other reason we'd get this result. The issue is that fictions are often apparently incomplete. Anna Karenina doesn't explicitly tell us the exact population of Russia at the moment of Anna's conception. Plurality of worlds is notoriously silent on what is the upper bound for the number of objects there could possibly be. Zermelo Fraenkel set-theory doesn't prove or disprove the Generalized Continuum Hypothesis. I'm going to assume:
(E) whatever domain fictionalism is true of, it will suffer from incompleteness phenomena of the kind familiar from fictionalisms about possibilia, arithmetic etc.
Whenever we get such incompleteness phenomena, many have assumed, we get results such as the following:
~(According to AK, the population of Russia at Anna's conception is n)
&~(According to AK, the population of Russia at Anna's conception is ~n)
~(According to PW, there at most k many things in a world)
&~(According to PW, there are more than k many things in some world)
~(According to ZF, the GCH holds)
&~(According to ZF, the GCH fails to hold)
The only reason for resisting these very natural claims, especially when "According to" in the relevant cases is understood as an indicative conditional, is to endorse in those instances a general story about putative counterexamples to CEM. That's why (D) seems true to me.
(The general story is due to Stalnaker; and in the instances at hand it will say that it is indeterminate whether or not e.g. "if PW is true, then there at most k many things in the world" is true; and also indeterminate whether its negation is true (explaining why we are compelled to reject both this sentence and its negation). Familiar logics for indeterminacy allow that p and q being indeterminate is compatible with "p or q" being determinately true. So the indeterminacy of "if B, S" and "if B, ~S" is compatible with the relevant instance of CEM "if B, S or if B, ~S" holding.)
Given (A-E), then, I think inference to the best explanation gives us CEM for the indicative conditional.
[Update: I cross-posted this both at Theories and Things and Metaphysical Values. Comment threads have been active so far at both places; so those interested might want to check out both threads. (Haven't yet figured out whether this cross-posting is a good idea or not.)]
Conditional excluded middle is the following schema:
if A, then C; or if A, then not C.
It's disputed whether everyday conditionals do or should support this schema. Extant formal treatments of conditionals differ on this issue: the material conditional supports CEM; the strict conditional doesn't; Stalnaker's logic of conditionals does, Lewis's logic of conditionals doesn't.
Here's one consideration in favour of CEM (inspired by Rosen's "incompleteness puzzle" for modal fictionalism, which I was chatting to Richard Woodward about at the Lewis graduate conference that was held in Leeds yesterday).
Here's the quick version:
Fictionalisms in metaphysics should be cashed out via the indicative conditional. But if fictionalism is true about any domain, then it's true about some domain that suffers from "incompleteness" phenomena. Unless the indicative conditional in general is governed in general by CEM, then there's no way to resist the claim that we get sentences which are neither hold nor fail to hold according to the fiction. But any such "local" instance of a failure of CEM will lead to a contradiction. So the indicative conditional in general is governed by CEM
Here it is in more detail:
(A) Fictionalism is the right analysis about at least some areas of discourse.
Suppose fictionalism is the right account of blurg-talk. So there is the blurg fiction (call it B). And something like the following is true: when I appear to utter , say "blurgs exist" what I've said is correct iff according to B, "blurgs exist". A natural, though disputable, principle is the following.
(B) If fictionalism is the correct theory of blurg-talk, then the following schema holds for any sentence S within blurg-talk:
"S iff According to B, S"
(NB: read "iff" as material equivalence, in this case).
(C) The right way to understand "according to B, S" (at least in this context) is as the indicative conditional "if B, then S".
Now suppose we had a failure of CEM for an indicative conditional featuring "B" in the antecedent and a sentence of blurg-talk, S, in the consequent. Then we'd have the following:
(1) ~(B>S)&~(B>~S) (supposition)
By (C), this means we have:
(2) ~(According to B, S) & ~(According to B, ~S).
By (B), ~(According to B, S) is materially equivalent to ~S. Hence we get:
(3) ~S&~~S
Contradiction. This is a reductio of (1), so we conclude that
(intermediate conclusion):
No matter which fictionalism we're considering, CEM has no counterinstances with the relevant fiction as antecedent and a sentence of the discourse in question as consequent.
Moreover:
(D) the best explanation of (intermediate conclusion) is that CEM holds in general.
Why is this? Well, I can't think of any other reason we'd get this result. The issue is that fictions are often apparently incomplete. Anna Karenina doesn't explicitly tell us the exact population of Russia at the moment of Anna's conception. Plurality of worlds is notoriously silent on what is the upper bound for the number of objects there could possibly be. Zermelo Fraenkel set-theory doesn't prove or disprove the Generalized Continuum Hypothesis. I'm going to assume:
(E) whatever domain fictionalism is true of, it will suffer from incompleteness phenomena of the kind familiar from fictionalisms about possibilia, arithmetic etc.
Whenever we get such incompleteness phenomena, many have assumed, we get results such as the following:
~(According to AK, the population of Russia at Anna's conception is n)
&~(According to AK, the population of Russia at Anna's conception is ~n)
~(According to PW, there at most k many things in a world)
&~(According to PW, there are more than k many things in some world)
~(According to ZF, the GCH holds)
&~(According to ZF, the GCH fails to hold)
The only reason for resisting these very natural claims, especially when "According to" in the relevant cases is understood as an indicative conditional, is to endorse in those instances a general story about putative counterexamples to CEM. That's why (D) seems true to me.
(The general story is due to Stalnaker; and in the instances at hand it will say that it is indeterminate whether or not e.g. "if PW is true, then there at most k many things in the world" is true; and also indeterminate whether its negation is true (explaining why we are compelled to reject both this sentence and its negation). Familiar logics for indeterminacy allow that p and q being indeterminate is compatible with "p or q" being determinately true. So the indeterminacy of "if B, S" and "if B, ~S" is compatible with the relevant instance of CEM "if B, S or if B, ~S" holding.)
Given (A-E), then, I think inference to the best explanation gives us CEM for the indicative conditional.
[Update: I cross-posted this both at Theories and Things and Metaphysical Values. Comment threads have been active so far at both places; so those interested might want to check out both threads. (Haven't yet figured out whether this cross-posting is a good idea or not.)]
Tuesday, August 22, 2006
The necessity of identity and essentialism
Here's one argument for the necessity of identity. Assume a=b. a has the property of being essentially identical to a. By Leibniz's law, b also has this property. So in every world in which b exists, b is identical to a, so there's no world in which a and b are distinct.
Will that convince the anti-essentialist? No, because it relies on an essentialist assumption: that every thing x has the property of being essentially identical to x. (This is not the premise that every thing x has the property of being essentially self-identical, which the anti-essentialist may well grant.)
Can the necessity of identity be established without relying on essentialist assumptions? I don't think so. But there is a tradition of thinking it can be established solely by considerations concerning rigid designation. I thought this tradition had died and been buried, but it has arisen in a recent article in the Philosophical Quarterly by Sören Häggqvist. (Häggqvist, Sören, (2006), ‘Essentialism and Rigidity’, The Philosophical Quarterly 56:223, p275-283.)
He argues as follows. If ‘a’ and ‘b’ are rigid designators then they designate in every possible world that which they designate in the actual world. Since they designate the same thing in the actual world (let us suppose) they therefore designate the same thing in every possible world, and so ‘a=b’ is a necessary truth.
I don't think this argument works, and want to bury it for good. The argument moves from (1) ‘a’ and ‘b’ designate the same thing in the actual world and (2) in any world, both ‘a’ and ‘b’ designate what they designate in the actual world to (3) in any world ‘a’ and ‘b’ designate the same thing. But (3), pretty obviously, only follows from (1) and (2) if the necessity of identity is true, and so to rely on this move is just to beg the question. Suppose ‘a’ and ‘b’ actually co-designate but that there is a world, w, in which ‘a’ designates something distinct from ‘b’. Does it follow that one or other of ‘a’ and ‘b’ designate in w something that they do not designate in the actual world? Not if a and b are identical in the actual world but distinct in w. If a and b are merely contingently identical then of course the rigid designators ‘a’ and ‘b’ will not necessarily co-designate; in a world in which a and b are distinct then, since ‘a’ must still designate a and ‘b’ still designate ‘b’ in this world, ‘a’ and ‘b’ will designate distinct things in this world. And so to conclude that the rigid designators ‘a’ and ‘b’ necessarily co-designate because they actually do begs the question against the contingent-identity theorist.
Monday, August 21, 2006
Defining presentism: the real problem
At the CMM event Robbie mentions below, Jonathan Tallant discussed a problem for defining presentism. The problem didn't seem to me to problematic, since it assumed the only existential quantifiers the presentism has in her toolbox are one equivalent to 'exists now' and one equivalent to 'existed, exists now, or will exist'. Since this is patently false, that problem seems to vanish.
But there did seem to me to be a problem in the vicinity; namely, that all obvious attemtps at a definition require us to reify times.
Intuitively I can refuse to admit the existence of times and there still be an eternalism/presentism question. Two theorists should be able to have a debate concerning the nature of time and existence without quantifying over times. But I couldn't think how to define the terms without reifying times, and certainly the familiar definitions fail.
Consider 'the only time is the present time'. If there are no times, this is true. So if there can be a presentist/eternalist debate between those who don't reify times, this doesn't capture presentism.
What about 'only present things exist' (where 'exists' here is atemporal)? Nope, that won't do if there are no times. Consider two endurentists who believe that the world started with A, B and C coming into existence. Those three objects proceed to endure through some changes, and then the world ends (taking A, B and C with it of course). So nothing comes into or goes out of existence in this world. At any time it is true that only the things that are present at that time exist atemporally, since A, B and C are the only things that exist at any time, and are the only things that exist atemporally. But that doesn't mean presentism is true at this world: intuitively, there is still a debate to be had between the two endurentists as to whether presentism or eternalism is true.
Any thoughts?
But there did seem to me to be a problem in the vicinity; namely, that all obvious attemtps at a definition require us to reify times.
Intuitively I can refuse to admit the existence of times and there still be an eternalism/presentism question. Two theorists should be able to have a debate concerning the nature of time and existence without quantifying over times. But I couldn't think how to define the terms without reifying times, and certainly the familiar definitions fail.
Consider 'the only time is the present time'. If there are no times, this is true. So if there can be a presentist/eternalist debate between those who don't reify times, this doesn't capture presentism.
What about 'only present things exist' (where 'exists' here is atemporal)? Nope, that won't do if there are no times. Consider two endurentists who believe that the world started with A, B and C coming into existence. Those three objects proceed to endure through some changes, and then the world ends (taking A, B and C with it of course). So nothing comes into or goes out of existence in this world. At any time it is true that only the things that are present at that time exist atemporally, since A, B and C are the only things that exist at any time, and are the only things that exist atemporally. But that doesn't mean presentism is true at this world: intuitively, there is still a debate to be had between the two endurentists as to whether presentism or eternalism is true.
Any thoughts?
Friday, August 18, 2006
CMM event
Just a quick note to remind those in the Leeds area of today's internal workshop, featuring CMM-ers Tallant, Shalkowski, McGonigal and Keiran (and of course pertinent and witty interventions from the rest of us). Schedule:
9.30-11.00 Matthew Kieran. "Aesthetic Judgement and snobbery"
11.30-1.00 Andrew McGonigal "Truth, relativism and serial fiction"
1-2 lunch
2-3.30 Scott Shalkowski. "A Short Argument for Essentialism"
4-5.30 Jonathan Tallant "Presentism vs. Eternalism and the Problem of Tense"
6+ meal and pub.
We have a seminar room + a coffee room booked at the IDEA CETL for the day. No specific arrangements for lunch and dinner have been made, but I conjecture Opposite Café will be involved.
9.30-11.00 Matthew Kieran. "Aesthetic Judgement and snobbery"
11.30-1.00 Andrew McGonigal "Truth, relativism and serial fiction"
1-2 lunch
2-3.30 Scott Shalkowski. "A Short Argument for Essentialism"
4-5.30 Jonathan Tallant "Presentism vs. Eternalism and the Problem of Tense"
6+ meal and pub.
We have a seminar room + a coffee room booked at the IDEA CETL for the day. No specific arrangements for lunch and dinner have been made, but I conjecture Opposite Café will be involved.
Wednesday, August 16, 2006
bestriding the blogosphere...
Five posts in, and we're up at the latest Philosopher's carnival! The kids go wild for a good bit of truthmaking...
Friday, August 11, 2006
Why hold truthmaker necessitarianism?
It is orthodoxy amongst truthmaker theorists that the existence of a truthmaker necessitates the truth of that which it makes true: if a thing A is a truthmaker for the proposition that p, then there is no possible world in which A exists and p is false. Is there any good argument for this claim?
The only argument I know of for truthmaker necessitarianism is that given by David Armstrong. Armstrong says[1]:
If it is said that the truthmaker for a truth could have failed to make the truth true, then we will surely think that the alleged truthmaker was insufficient by itself and requires to be supplemented in some way. A contingently sufficient truthmaker will be true only in circumstances that obtain in this world. But then these circumstances, whatever they are, must be added to give the full truthmaker.
His thought, I take it, is this. Suppose that A makes p true but doesn’t necessitate the truth of p. In that case there are some possible worlds in which A exists and p is false: some set of circumstances in which the existence of A does not suffice for the truth of p. But then isn’t it overwhelmingly intuitive that the truthmaker for p is not simply A but rather A together with whatever makes it true that those circumstances do not in fact obtain?
Let’s spell this argument out in a little more detail, making explicit Armstrong’s implicit assumptions. A first shot is:
1) A makes p true. (Assumption)
2) The existence of A does not necessitate the truth of p. (Assumption for reductio)
3) There is a possible world in which A exists and p is false. (From 2)
4) There is a (probably highly disjunctive) proposition q which is true in exactly those worlds in which A exists and p is false. (q is the proposition that describes the circumstances in which the existence of A does not suffice for the truth of p.) (This assumption follows from the general assumption that for any set of possible worlds, there is a proposition that is true at exactly those worlds.)
5) What makes p true is A together with what makes not-q true. I.e. if not-q is made true by B, then p is made true by the sum of A and B. (Assumption)
6) p is not made true by both A and the sum of A and B. (Assumption)
7) p is not made true by A. (From 5 and 6)
8) Contradiction. (From 1 and 7)
But what right does Armstrong have for premise (6)? A proposition can have more than one truthmaker – you and I both make it true that there are humans – so there is no contradiction in holding that p is made true both by A and by the sum of A and B. I guess Armstrong’s thought is that the sum of A and B jointly necessitate the truth of p, and that if there is a necessitating truthmaker for a proposition, nothing which did not necessitate the truth of that proposition deserves to be called its truthmaker. That is, it would only be reasonable to think that p had a non-necessitating truthmaker if p had no necessitating truthmaker. (That is, I think, what is behind his comment that “the alleged truthmaker was insufficient by itself”.) That is a fairly plausible thought, so let us amend Armstrong’s argument as follows:
1) A makes p true. (Assumption)
2) The existence of A does not necessitate the truth of p. (Assumption for reductio)
3) There is a possible world in which A exists and p is false. (From 2)
4) There is a (probably highly disjunctive) proposition q which is true in exactly those worlds in which A exists and p is false. (q is the proposition that describes the circumstances in which the existence of A does not suffice for the truth of p.) (This assumption follows from the general assumption that for any set of possible worlds, there is a proposition that is true at exactly those worlds.)
5) The truth of p is necessitated by A together with what makes not-q true (call it B). A and B together are a necessitating truthmaker for p. (Assumption)
6) There is no non-necessitating truthmaker for p. (From 5)
7) Contradiction. (From 1, 2 and 6)
I used to think the best point of resistance for the denier of necessitarianism was the assumption, presupposed by premise (5), that every truth has a truthmaker. [2] If we deny that negative facts such as not-q require a truthmaker then the argument doesn’t go through. But, I thought, one who upholds truthmaker maximalism is committed, by this argument, to truthmaker necessitarianism. Now I think that is wrong. No one, maximalist or non-maximalist, should be persuaded by this argument to accept truthmaker necessitarianism.
Ask yourself first: what right does Armstrong have to premise (5)? Why should we think that A together with whatever makes it true that not-q is a necessitating truthmaker for p? The only reason I can see is as follows. q is a complete specification of the possible circumstances in which A exists and p is false. So if not-q is made true then those circumstances do not obtain. So if not-q is made true then we are in a world in which the existence of A suffices for the truth of p. So, necessarily, if both the truthmaker for not-q and A exist, then p is true.
Unfortunately, this last step is no good. It is true that every world in which not-q is true is a world in which the existence of A suffices for the truth of p. There is no possible world in which not-q is true and A exists and p is false. But it only follows that the truthmaker for not-q cannot exist in a world in which A exists and p is false if we add the assumption that the truthmaker for not-q cannot exist in a world in which not-q is false (i.e. a world in which q is true). But of course we can’t assume that, for that would simply beg the question. Our only reason for thinking that the truthmaker for not-q couldn’t exist in a world in which q is true is if truthmakers must necessitate the truth of the propositions they are truthmakers of, and that is exactly what the argument is trying to establish.
If Armstrong is to avoid begging the question he must leave it open that B, the truthmaker for not-q, can exist in a world in which q is true. That is a world in which the existence of A does not suffice for the truth of p, so we have been given no reason to rule out the possibility of worlds in which A and B both exist and p is false. So we have no reason to think that A and B together are a necessitating truthmaker for p, and hence no reason to think that A is not an adequate truthmaker for p.
To focus discussion, let us consider a particular account of truthmakers according to which a truthmaker for p need not necessitate the truth of p: Josh Parsons’ theory that the truthmaker for p is that which is intrinsically such that p.[3] Since an object needn’t have its intrinsic properties essentially, Parsons denies necessitarianism. A can make p true and exist in worlds in which p is false provided that, in each of those worlds, A differs intrinsically from how it actually is.
How should Parsons respond to Armstrong’s argument? Well, what should Parsons think the truthmaker for not-q is? q is the proposition that describes exactly the circumstances in which A exists and p is false. What are those circumstances on Parsons’ theory? They are the circumstances in which A differs intrinsically from how it actually exists. So not-q is the proposition that is true exactly when A is as it actually is intrinsically. So what makes this true? That which is intrinsically such that A has the intrinsic properties it actually has – namely, A.
So for Parsons, A is the truthmaker for not-q. What makes it true that we are not in the circumstances in which A can exist and p be false is just the truthmaker for p. A can exist in worlds in which not-q is false, of course – the existence of A does not necessitate that A is intrinsically as it actually is. But that is no objection; it is part of the theory that the existence of the truthmaker need not necessitate the truth of that which it makes true. All that is required is that in the worlds in which A exists and not-q is false, A differs intrinsically from how it actually is. And that is obviously guaranteed: A cannot be as it actually is intrinsically and q be true, since q just is the proposition that A differs intrinsically from how it actually is.
It is clear then that Armstrong’s argument has no pull against someone who accepts a theory like Parsons’. The argument only works if the truthmaker for not-q must be a necessitating truthmaker, but to assume this would beg the question.
[1] D.M. Armstrong, A World of States of Affairs,
[2] Ross Cameron, ‘Truthmaker Necessitarianism and Maximalism’, Logique et Analyse 48(189-192), p43-56, 2005
[3] Josh Parsons, ‘There is no truthmaker argument against nominalism’, Australasian Journal of Philosophy 77(3), p325-334, 1999
Tuesday, August 08, 2006
Semantics for nihilists
Microphysical mereological nihilists believe that only simples exist---things like leptons and quarks, perhaps. You can be a mereological nihilist without being a microphysical mereological nihilist (e.g. you can believe that ordinary objects are simples, or that the whole world is one great lumpy simple. Elsewhere I use this observation to respond to some objections to microphysical mereological nihilism). But it's not so much fun.
If you're a microphysical mereological nihilist, you're likely to start getting worried that you're committed to an almost universal error-theory of ordinary discourse. (Even if you're not worried by that, your friends and readers are likely to be). So the MMN-ists tend to find ways of sweetening the pill. Van Inwagen paraphrases ordinary statements like "the cat is on the mat" into plural talk (the things arranged cat-wise are located above the things arranged mat-wise"). Dorr wants us to go fictionalist: "According to the fiction of composition, the cat is on the mat"). There'll be some dispute at this point about the status of these substitutes. I don't want to get into that here though.
I want to push for a different strategy. The way to do semantics is to do possible world semantics. And to do possible world semantics, you don't merely talk about things and sets of things drawn from the actual world: you assign possible-worlds intensions as semantic values. For example, the possible-worlds semantic value of "is a cordate" is going to be something like a function from possible worlds to the things which have hearts in those worlds. And (I assume, contra e.g. Williamson) that there could be something that doesn't exist in the actual world, but nevertheless has a heart. I'm assuming that this function is a set, and sets that have merely possible objects in their transitive closure are at least as dubious, ontologically speaking, as merely possible objects themselves.
Philosophers prepared to do pw-semantics, therefore, owe some account of this talk about stuff that doesn't actually exist, but might have done. And so they give some theories. The one that I like best is Ted Sider's "ersatz pluriverse" idea. You can think of this as a kind of fictionalism about possiblia-talk. You construct a big sentence that accurately describes all the possibilities. Statements about possibilia will be ok so long as they follow from the pluriverse sentence. (I know this is pretty sketchy: best to look at Sider's version for the details).
Let's call the possibilia talk vindicated by the construction Sider describes, the "initial" possibila talk. Sider mentions various things you might want to add into the pluriverse sentence. If you want to talk about sets containing possible objects drawn from different worlds (e.g. to do possible world semantics) then you'll want to put some set-existence principles into your pluriverse sentence. If you want to talk about transworld fusions, you need to put some mereological principles into the pluriverse sentence. If you add a principle of universal composition into the pluriverse sentence, your pluriverse sentence will allow you to go along with David Lewis's talk of arbitrary fusions of possibilia.
Now Sider himself believes that, in reality, universal composition holds. The microphysical mereological nihilist does not believe this. The pluriverse sentence we are considering says that in the actual world, there are lots of composite objects. Sider thinks this is a respect in which it describes reality aright; the MMN-ist will think that this is a respect in which it misdescribes reality.
I think the MMN-ist should use the pluriverse sentence we've just described to introduce possibilia talk. They will have to bear in mind that in some respects, it misdescribes reality: but after all, *everyone* has to agree with that. Sider thinks it misdescribes reality in saying that merely possible objects, and transworld fusions and sets thereof, exist---the MMN-ist simply thinks that it's inaccuracy extends to the actual world. Both sides, of course, can specify exactly which bits they think accurately describe reality, and which are artefactual.
The MMN-ist, along with everyone else, already has the burden of vindicating possibilia-talk (and sets of possibilia, etc) in order to get the ontology required for pw-semantics. But when the MMN-ist follows the pluriverse route (and includes composition priniciples within the pluriverse sentence), they get a welcome side-benefit. Not only do they gain the required "virtual" other-worldly objects; they also get "virtual" actual-worldy objects.
The upshot is that when it comes to doing possible-world semantics, the MMN-ist can happily assign to "cordate" an intension that (at the actual world) contains macroscopic objects, just as Sider and other assign to "cordate" an intension that (at other worlds) contain merely possible objects. And sentences such as "there exist cordates" will be true in exactly the same sense as it is for Sider: the intension maps the actual world to a non-empty set of entities.
So we've no need for special paraphrases, or special-purpose fictionalizing constructions, in pursuit of some novel sense in which "there are cordates" is true for the MMN-ist. The flipside is that we can't read off metaphysical commitments from such true existential sentences. Hey ho.
(cross posted on theories 'n things)
If you're a microphysical mereological nihilist, you're likely to start getting worried that you're committed to an almost universal error-theory of ordinary discourse. (Even if you're not worried by that, your friends and readers are likely to be). So the MMN-ists tend to find ways of sweetening the pill. Van Inwagen paraphrases ordinary statements like "the cat is on the mat" into plural talk (the things arranged cat-wise are located above the things arranged mat-wise"). Dorr wants us to go fictionalist: "According to the fiction of composition, the cat is on the mat"). There'll be some dispute at this point about the status of these substitutes. I don't want to get into that here though.
I want to push for a different strategy. The way to do semantics is to do possible world semantics. And to do possible world semantics, you don't merely talk about things and sets of things drawn from the actual world: you assign possible-worlds intensions as semantic values. For example, the possible-worlds semantic value of "is a cordate" is going to be something like a function from possible worlds to the things which have hearts in those worlds. And (I assume, contra e.g. Williamson) that there could be something that doesn't exist in the actual world, but nevertheless has a heart. I'm assuming that this function is a set, and sets that have merely possible objects in their transitive closure are at least as dubious, ontologically speaking, as merely possible objects themselves.
Philosophers prepared to do pw-semantics, therefore, owe some account of this talk about stuff that doesn't actually exist, but might have done. And so they give some theories. The one that I like best is Ted Sider's "ersatz pluriverse" idea. You can think of this as a kind of fictionalism about possiblia-talk. You construct a big sentence that accurately describes all the possibilities. Statements about possibilia will be ok so long as they follow from the pluriverse sentence. (I know this is pretty sketchy: best to look at Sider's version for the details).
Let's call the possibilia talk vindicated by the construction Sider describes, the "initial" possibila talk. Sider mentions various things you might want to add into the pluriverse sentence. If you want to talk about sets containing possible objects drawn from different worlds (e.g. to do possible world semantics) then you'll want to put some set-existence principles into your pluriverse sentence. If you want to talk about transworld fusions, you need to put some mereological principles into the pluriverse sentence. If you add a principle of universal composition into the pluriverse sentence, your pluriverse sentence will allow you to go along with David Lewis's talk of arbitrary fusions of possibilia.
Now Sider himself believes that, in reality, universal composition holds. The microphysical mereological nihilist does not believe this. The pluriverse sentence we are considering says that in the actual world, there are lots of composite objects. Sider thinks this is a respect in which it describes reality aright; the MMN-ist will think that this is a respect in which it misdescribes reality.
I think the MMN-ist should use the pluriverse sentence we've just described to introduce possibilia talk. They will have to bear in mind that in some respects, it misdescribes reality: but after all, *everyone* has to agree with that. Sider thinks it misdescribes reality in saying that merely possible objects, and transworld fusions and sets thereof, exist---the MMN-ist simply thinks that it's inaccuracy extends to the actual world. Both sides, of course, can specify exactly which bits they think accurately describe reality, and which are artefactual.
The MMN-ist, along with everyone else, already has the burden of vindicating possibilia-talk (and sets of possibilia, etc) in order to get the ontology required for pw-semantics. But when the MMN-ist follows the pluriverse route (and includes composition priniciples within the pluriverse sentence), they get a welcome side-benefit. Not only do they gain the required "virtual" other-worldly objects; they also get "virtual" actual-worldy objects.
The upshot is that when it comes to doing possible-world semantics, the MMN-ist can happily assign to "cordate" an intension that (at the actual world) contains macroscopic objects, just as Sider and other assign to "cordate" an intension that (at other worlds) contain merely possible objects. And sentences such as "there exist cordates" will be true in exactly the same sense as it is for Sider: the intension maps the actual world to a non-empty set of entities.
So we've no need for special paraphrases, or special-purpose fictionalizing constructions, in pursuit of some novel sense in which "there are cordates" is true for the MMN-ist. The flipside is that we can't read off metaphysical commitments from such true existential sentences. Hey ho.
(cross posted on theories 'n things)
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