A leeds-related blog post...

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...

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 Bob Hale has emphasised in his discussion of the necessity of identity). And surely (2) is no contingent truth – how could it fail? (Putting aside worries about the contingent existence of a.) (5) follows from (3) in any normal modal logic. Maybe one could resist the moves from (1) to (4) and (6) to (7) if one played silly-buggers with necessity as a predicate modifier – but that looks a bit desperate. The only other step is modus ponens. So the prospects don’t look bright. If you’re going to resist the standard argument, it shouldn’t be on Lowe’s grounds.

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 Austria? Is it enough to deny the truth of or must one assert the negation of it? I was thinking of a presentist who treats the past like Aristotle treats the future. So you think that only the present exists, and because you’re convinced by the truthmaker objection, you bite the bullet and hold that there’re no truths concerning the past or the future. So isn’t true. Nor is it false: it simply lacks a truth value. If I defend that view in Austria, will I get in trouble?

I heard Ned Markosian defend a presentist view whereby propositions concerning the past or the future are true to a certain degree, depending on how many of the possible (given the present laws of nature and the way things presently are) pasts/futures are the way the proposition says they are. So if every possible past is such that p then it is true that p was the case, but if only some possible pasts are such that p then it is true to some degree n (such that n is between zero and one) that p was the case. If Ned went to Austria and defended that view would he be in trouble to degree n?

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.

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 Jonathan Schaffer (UMass) at the Pacific APA in San Francisco next April. I’ve never been to SF, and am looking forward to it. Schaffer is defending the view that, necessarily, every true proposition is made true by the world, which is the only fundamental entity that there is. We’ve already had some correspondence over his paper, after meeting at Bellingham, and it’s been lots of fun – so this should be a good time. San Francisco was the home of the one and only Emperor of the United States, which is reason enough to visit.

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"!))

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.

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.