Substitutional Quantification and Supervaluations

(Cross-posted at Metaphysical Values.)

Let U be the (universal) substitutional quantifier: its truth-conditions are

"UxF(x)" is true iff, for every name n, "F(n)" is true.

(Normal quotes are doing double-duty as quasi-quotes here.)

Peter van Inwagen has an argument that we can't understand substitutional quantification. It goes like this:

(1) We can't understand a sentence unless we can specify what proposition it expresses.
(2) The only proposition we know of with the right truth-conditions to be expressed by "UxF(x)" is the proposition that, for every name n, "F(n)" is true. (Call this proposition "UU".)
(3) Friends of substitutional quantification say that UU is not what is expressed by "UxF(x)".
(4) There are no other candidates to be the proposition expressed by "UxF(x)".
(5) So if friends of substitutional quantification are right, we can't understand "UxF(x)".

I want to respond to this argument, but I don't know whether my response rejects premise (1) or (4). So I'll outline the basic idea, and then maybe someone can help me know which premise I'm rejecting.

Suppose some sort of supervaluationism is the right treatment of vagueness, and set aside higher order vagueness. Then a sentence like "Fido is red" doesn't express a proposition simpliciter; rather, it expresses a proposition relative to every precisification of "red".

(Since we can understand "Fido is red", this alone might be enough to lead us to deny (1). But it's not clear how this denial gives us any positive reason to think we should be able to understand substitutional quantification. I want to aim higher. So let's press on.)

The truth-conditions for this sentence with the determinacy operator are:

"Det(Fido is red)" is true iff "Fido is red" is true on every precisification of "red".

Now, we can think about precisifications in a number of ways. One of them is an explicitly semantic way: the precisifications of a term are the precise meanings it can have. But another is a bit more syntactic, relating more precise terms to less. If we have semantic precisifications, we can easily define syntactic ones as follows: T is a syntactic precisification of T* iff T's semantic value is a semantic precisification of T*. If we don't have semantic precisifications, we might take the syntactic ones as primitive, or we might be able to define them some other way (maybe by appealing to metalinguistic predicates like "admits of borderline cases" and some others).

If we have the syntactic understanding of precisification, then we have the truth-conditions

"Det(Fido is red)" is true iff "Fido is R" is true for every term R that is a precisification of "red",

which look remarkably similar to the ones we had for the substitutional quantifier.

So here's my basic idea: think of "x" as a maximally vague name --- a name such that every precise name is a (syntactic) precisification of it. Then think of "U" as a determinacy operator. This gives us essentially the truth-conditions we want.

How does van Inwagen's argument look now, with this understanding of the substitutional quantifiers? That depends, I think, on what we say about the proposition expressed by "Det(Fido is red)". I think there are very good reasons to think that this sentence does not express the proposition that "Fido is R" is true for every term R that is a precisification of red. (One very good reason is that it won't embed right at all --- it might be necessary, say, that Det(Fido is red), even though it certainly isn't necessary that "red" is even a word, much less that it has precisifications. And these thoughts extend to the truth-conditions that go via semantic precisifications, too.) But are we in any position at all to specify a proposition it expresses?

Here I don't know what to say, and this is why I don't know which premise I reject in van Inwagen's argument. On the one hand, maybe we have some recipe for specifying a proposition expressed by "Det(Fido is red)". If so, then we can use the same recipe to specify one expressed by "UxF(x)", and I deny premise (4). Maybe we think "Det(Fido is red)" expresses the conjunction of all the propositions expressed by "Fido is R", where R is a (syntactic) precisification of "red", for instance. If so, then we can say that "UxF(x)" expresses the conjunction of all propositions expressed by sentences of the form "F(a)" for some name "a".

On the other hand, maybe we can't specify any proposition expressed by "Det(Fido is red)". (Maybe we dislike the conjunction proposal for both the "Det" and "U" cases because we think it misses out on the "that's-all"-ish nature of the quantifications involved in the truth-conditions.) Nonetheless, I think it's entirely clear that we understand "Det(Fido is red)". And I also think (but I haven't argued for it) that one way we can come to understand a vague term by learning a recipe for figuring out what its precisifications are, so we can understand what the "x" in "UxF(x)" is doing. But in this case, "UxF(x)" is essentially just "Det F(x)"

There's a lot of details I've left out --- stuff about variable-binding, the viability of the syntactic characterization of precisifications, how to think of modally embedded substitutional quantifications, and so on. But setting these techy details aside, I'm wondering what the right thing to say about the argument is. Or, more to the point, I'm wondering what we should deny when we run a parody argument for our inability to understand the sentence "Det(Fido is red)".

Thoughts, anyone?

Conference: Relational vs. Constituent Ontologies (Notre Dame, Mar. 5-6)

Click here for more info.

Is My 3-and-1/2-Year-Old Daughter A Modal Realist?

This morning over breakfast my 3-and-1/2-yr-old daughter told me 'Golden shoes do not exist in this world'. 'Where do they exist then?' I asked. 'In another world' she replied with the tone of someone who is saying something obvious. I always thought modal realism was semantically revisionary but apparently this does not apply to the pre-school crowd! :-) (I still hope she just believes in island universes, though!)

A deflationary theory of diachronic identity

Thanks, Gabriele, for inviting me to this blog.

First, the easy version of the deflationary account. Here is a question about diachronic identity: What makes it be the case that:

1. Some F0 at t0 is diachronically identical with some F1 at t1.

Deflationary answer:

2. There exists an x such that x is an F0 at t0 and x is an F1 at t1.

Observe that (2) does not make use of "diachronic identity" in its statement. Moreover, all of the conceptual ingredients that (2) uses are ones that any substantive account of diachronic identity (the memory or bodily continuity theories in the case of persons are paradigms) will also have to use in analyzing (1): being an F0 at t0, being an F1 at t1, quantification and conjunction (I have a hard time imagining any substantive account of diachronic identity that somewhere doesn't presuppose conjunction!) So, (2) is simpler, and if it is conceptually circular, so is any substantive account.

Now, the somewhat harder version, the question of analyzing diachronic identity wffs. Question: What makes it be the case that:

3. x at t0 is diachronically identical with y at t1.

Deflationary answer:

4. x exists at t0 and x exists at t1 and y exists at t1 and x is synchronously identical at t1 with y.

Since we all need synchronous identity, and it does not seem to be posterior to diachronic identity, it seems fair to presuppose it in an account of diachronic identity. The result seems to be an account of diachronic identity much simpler than any substantive account.

If one is worried that "x exists at t" presupposes diachronic identity, consider this. What is it to exist at t? Here are some standard proposals:

• Presentism: At t: x exists.


• Perdurantism: a part of x is located within the spacelike hypersurface t.


• Eternalist endurantism: x is wholly located within the spacelike hypersurface t.

None of these proposals seem to presuppose diachronic identity. Now, the last two proposals require an analysis of being located or wholly located in a region R. But this could be just a matter of instantiating a primitive located-at relation to R, or a matter of having R if regions just are properties (I am fond of--though I do not endorse--the proposal that regions are properties, with containment being entailment, and that to be in a region is to have the region as a property), or a matter of being appropriately related to other entities by the nexus of spatiotemporal relations.

In any case, substantive accounts of diachronic identity do not clarify what it is to be located in a region of spacetime or what it is to exist at t. Substantive accounts of diachronic identity explain what it is for an object that is located in one region to exist in another region, but that still doesn't explain what it was for the object to be located in the first region. In fact, there is something really weird about substantive accounts of diachronic identity here. It would be very strange to claim to have a good account of what it is for a person who is queen of country x to also be queen of country y (for general non-identical x and y) without that account also being an account of what it is for a person to be queen of x (for a general x). Surely we all need an account of what it is for a person to be a queen of x, and once we have that, the account of what it is for the queen of country x to also be the queen of country y is just a matter of applying that account twice (and using synchronic identity to take care of the definite articles). But like the queen-identity theorist, the substantive diachronic identity theorist has an account of what it is for, say, a person who occupies R1 to also occupy R2, without having an account of what it is to occupy R1. And once we have an account of what it is to occupy R1, we get for free an account of what it is to occupy R1 and R2, at least if we have synchronic identity.

Maybe the simplest way to summarize the deflationary account is this. It is no more mysterious how it is that x at t0 is identical with y at t1 than it is how it is that x who is the Queen of England is identical with y who is the Queen of Canada.

However, the above arguments presupposed that we're dealing with entities facts about which do not wholly reduce to facts about some other entities. In the case of wholly reducible entities, my arguments fail. The reason for that is that in the case of a wholly reducible entity, what it is to exist at t will be reducible to facts about some other class of entities. For instance, for a reducible x to exist at t will not be a matter of x's instantiating some primitive located-at relations. In that case, the conceptual baggage of "exists at t" might be the same as the conceptual baggage of the substantive account of diachronic identity, and so the deflationary account may be incorrect. (I think of wholly reducible entities as akin to wholly stipulative meanings. In the case of words with wholly stipulative meanings, we might not expect deflationary accounts of truth and meaning to apply--we might want the stipulations to be expanded out, like abbreviations, before the deflationary account is applied.)

If I am right, then someone giving a substantive account of what diachronic identity for Ks consists in is committed to Ks being reducible.

Faculty Move: Schaffer from ANU to Rutgers (in 2011)

In case there is anyone out there who hasn't heard the news yet, Jonathan Schaffer has accepted an offer at the Professor from Rutgers and will be moving there from ANU in 2011. The temptation to leiter a bit about the significance of this move is really strong but, for the readers' sake, I'll resist it and just say: 'Congratulations, Jonathan (and Rutgers)!!!'

Constitution and Strong Coincidence

I was rereading Ryan Wasserman's 'The Standard Objection to the Standard Account' for a seminar on material constitution that I'm teaching this term. In it, Wasserman considers a number of "mereological" solutions to the "standard objection" (i.e. since Lump and David share all of their microphysical parts, there is nothing to explain their difference in kind and de re modal and temporal properties). Wasserman considers three responses to that objection: the no coincidence response (Lump and David share no parts), the weak coincidence response (Lump and David weakly coincide, which essentially boils down to the fact that all parts of Lump are parts of David but some parts of David (e.g. its arm) are not part of Lump), and the strong coincidence response (Lump and David strongly coincide share all their (material) parts at every time they both exist). While I think Wasserman's case against the first two views is strong, I'm not persuaded by his case for the third view. (In fact, I'm not even sure I understand what his proposal exactly is.)

The strong coincidence response (SCR) seems to be committed to the following claims:

1. For any time t, if Lump and David exist at t, they wholly exist at t.
2. For any time t, if Lump and David exist at t, they strongly materially coincide at t (i.e. every (material?) part of Lump at t is a part of David at t and every part of David at t is a (material?) part of Lump at t.)
3. For any time t, if Lump and David exist at t, they spatially coincide at t (i.e. every spatial part of Lump at t is a part of David at t and every spatial part of David at t is a part of Lump at t.)

So, one could wonder (at least I do) how can David and Lump differ in their parts given (1)-(3)? Since I'm not quite sure I understand Wasserman's answer, I'll let him do the talking now (I only divide the different claims and label them for the sake of the discussion):

[(a)][Both the defender of the standard account and the defender of the doctrine of temporal parts] will agree that David is a temporal part of Lump during the interval from t2 [when David came into existence] to t3 [when David and Lump ceased to exist]. For David exists only during that interval, David is a part of Lump during that interval and David overlaps during that interval everything that is a part of Lump during that interval.

[(b)] Moreover, both parties will agree that David is a proper temporal part of Lump during the interval in question since David is not identical to Lump.

[(c)]The two parties will not agree on everything, of course. Most importantly, the temporal parts theorist will assert, and the proponent of the standard account will deny, that Lump has temporal parts (during the interval from t1 [when Lump came into existence] to t2) that David lacks.

[(d)] Still, given that David is a proper temporal part of Lump, there must be some sense in which these two objects differ in parts.

[(e)] Indeed there is: Lump has spatial parts during the interval from t1 to t2 that David lacks.

I find it very hard to see how (a) and (even harder) (b) can be true. In fact, I can't see any good reason for the constitutionalist qua endurantist to hold that David is a temporal part of Lump between t2 and t3 let alone a proper temporal part of it. If one believes that Lump and David wholly exist at every time at which they exist, they would seem to have to believe that, at most, David and Lump can only have improper temporal parts at every time at which they exist (At t, if Lump exists, it is its only temporal part) but I can't see any plausible way to think that one can be a proper temporal part of the other (David can be a proper temporal part of Lump only if there are temporal parts of Lump that are not temporal parts of David, but since, given (1), it would seem that neither Lump nor David has (proper) temporal parts, I can't see how the latter can be a proper temporal part of the former).

I find it even harder to see how (b) can be true given (c). If the constitutionalist qua endurantist denies that Lump has temporal parts David lacks how can the latter be a proper temporal part of the former? According to Wasserman's (e), it would seem it can be so by virtue of Lump's having spatial parts between t1 and t2 that David does not have (after all, David doesn't exist during that period!).

Okay, so, suppose that you and Wasserman are standing in front of Lump and David and you ask 'But how can Lump and David have different kind, de re temporal and de re modal properties right now even if right now they are sharing all of their parts and their only parts are parts that exist right now?' I guess Wasserman's answer would be: 'Well, they do because they did not share all of their parts yesterday when David did not exist' But, at most this can explain why bakc then it was posssible for them to have different properties but not how it's possible now when the two share all of their parts (according to (2)).

I guess I'm missing something terribly obvious. Can anyone help me see what that something is?

(Let me mention a few other things Wasserman says that I find very puzzling:

Wasserman suggests that the standard objection applies not only to constitutionalism but also to fourdimensionalism and to the view that my hand is a spatial part of myself. But how can that be the case if the standard objection is predicated on the two objects sharing all of their parts? (of course the part of me that spatially coincides with my hand shares all of the parts with my hand (it is my hand after all!) but I don't)

And even if the standard objection applies to those views as well wouldn't that be a reason for those who hold those views to worry rather than a reason for the constitutionalist to feel relieved given that there are other views (most notably, nihilism) that are immune to that objection?

Finally, Wasserman seems to assume that a difference in temporal or spatial parts can explain a difference in kind, but I don't see any good reason to think so. There seems to be plenty of objects that differ in spatial and temporal parts without differing in kind and the reason why I am a human being and my hand is not is presumably not that I don't spatially coincide with my hands (althugh presumably it is a necessary condition for my being human).)

Schliesser on Metaphysics and "Scientifically Informed" Philosophy

Eric Schliesser has a post at It's Only A Theory in which he explains what he "find[s] problematic about mainstream contemporary metaphysics from the point of view of philosophy that wishes to be scientifically informed and open to learning from and be surprised by science".

I thought some readers of this blog might be interested in reading what he has to say and chime in!

Draft: From Possible Worlds to Possible Universes

I have uploaded a draft of a paper I've been working on on and off for quite a while. The paper develops a complete unorthodox possible-world analysis of modal sentences that can deal with modal possible-world sentences (i.e. sentences such as 'It is possible that there is a possible world at which there are talking donkeys'). I'd be interested to hear what people think about it. (For the record, as many of you already know, I believe that no possible world analysis of modal sentences is correct--the truthmakers for true modal propositions are irreducibly modal features of the actual world, not possible worlds)

In particular, I'd like to get some feedback on the argument I develop in Section 2. Most people don't seem to take modal possible-world sentences very seriously, but, if they take non-modal possible-world sentences seriously, I think they should. My main reason for thinking so is that, if basic modal sentences (e.g. ‘It is not possible that there are talking donkeys’)) are correctly analyzed as non-modal possible world sentences (i.e. ‘At no possible world, there are talking donkeys’)) (and incidentally I think they are not), then complex modal sentences (e.g. ‘It is possible that it is not possible that there are talking donkeys’)) should be analyzed as modal possible-world sentences (i.e. ‘It is possible that, at no possible world, there are talking donkeys’).

In my argument, I focus on that example and argue that, if 'It is not possible that there are talking donkeys’ is true if and only if there is no possible world at which there are talking donkeys, then ‘It is possible that it is not possible that there are talking donkeys’ is true if and only if it is possible that there is no possible world at which there are talking donkeys.

The argument for, if ‘It is possible that it is not possible that there are talking donkeys’ is true, then it is possible that there is no possible world at which there are talking donkeys goes like this.

1. ‘It is possible that it is not possible that there are talking donkeys’ is true. (A)
2. [It is necessary that] 'It is not possible that there are talking donkeys’ is true if and only if there is no possible world at which there are talking donkeys. (A)
   
3. For all p, ‘It is possible that p’ is true if and only if it is possible that ‘p’ is true. (A)
4. For all p and q, if [it is necessary that] p if and only if q, then it is possible that p if and only if it is possible that q. (A)
   
5. It is possible that ‘It is not possible that there are talking donkeys’ is true. (from 1 and 4)
6. It is possible that there is no possible world at which there are talking donkeys. (from 2, 3 and 5)

Here is the argument for the converse claim—if it is possible that, at no possible world, there are talking donkeys, then ‘It is possible that it is not possible that there are talking donkeys’ is true.

1. It is possible that, at no possible world, there are talking donkeys. (A)
   
2. [It is necessary that] 'It is not possible that there are talking donkeys’ is true if and only if at no possible world, there are talking donkeys. (A)
   
3. For all p and q, if [it is necessary that] p if and only if q, then it is possible that p if and only if it is possible that q. (A)
4. For all p, ‘It is possible that p’ is true if and only if it is possible that ‘p’ is true. (A)
5. It is possible that 'It is not possible that there are talking donkeys’ is true. (1 and 4).
6. 'It is possible that it is not possible that there are talking donkeys’ is true. (2, 3 and 5).

Barnes on Metametaphysics and Metametaphysics

Elizabeth Barnes has a really nice review of Metametaphysics here. Check it out!

New Metaphysics Drafts

I've got three new drafts of metaphysics papers up on my (new) website.

They are:
Balls and All
In this paper I lay out a rather unusual combination of views about spacetime, mereology and material objects. The view is coherent, I claim: and if it is coherent it seems to provide a counterexample to a number of assumptions that are made about what sorts of views have to go together. (In particular I use it to argue against a number of Ted Sider's arguments in his Four-Dimensionalism.)

Disposition Impossible, with C.S. Jenkins
In this paper Carrie and I investigate "unmanifestable dispositions": dispositions to PHI in C, where either PHI is impossible or C is. We argue that objects have such dispositions, and it is a non-trivial matter which ones they have. We also argue that these impossible dispositions play, or can play, significant theoretical roles. If we are right, a number of standard styles of theories of dispositions are in trouble.

The third is a piece of "applied metaphysics", I suppose, at least if work on counterfactuals counts as metaphysics. My impression is that it often is counted that way, even though it is at least as much philosophy of language and philosophy of science:

Why Historians (and Everyone Else) Should Care About Counterfactuals.

I discuss eight good reasons historians can usefully concern themselves with counterfatuals: some have been argued for before by others, but even in these cases I either have different characterisations of exactly why conditionals are important, or have different arguments for their importance in historical method.

Any feedback on any of the three papers would of course be welcome. (Obviously not any feedback. But you know what I mean.)

CFP: Special Issue of The Monist on Powers

The Monist

"Powers"

Deadline for Submissions: January 31, 2010
Advisory Editor: Neil Williams, University at Buffalo (new [at] buffalo.edu)

A sewing needle is swiped across a bar magnet, then pushed through a piece of cork and dropped into a glass of water. The needle will point immediately to the nearest pole. A female moth releases a small trace of sex pheromone; immediately males of the species up to two miles away will be attracted to her. The evidence for such causal powers is all around us. And as is shown in the response to the work of authors such as George Molnar and C. B. Martin, the thought that objects might be inherently powerful is on the rise. What is the nature of such causal powers? How are they to be characterised? What place do non-powers have within power-based ontologies? To what extent can powers be explanatory? Can powers exist entirely ungrounded? Contributions are invited addressing these and connected issues about the role and nature of powers.

Resemblance Nominalism and Tropes

Here’s the outline of a paper I´m starting to work on. If anybody has some spare time and wants to take a look, comments are very welcome (sorry for the length)!

Nominalists about the ontological constitution of material objects aim to dispense with both universals and bare particulars and yet provide an economic and compelling account of similarity and individuation.
Resemblance nominalism is the view that only concrete particulars exist, and properties are derivative on similarity classes of such particulars. This view has to deal with the traditional Goodmanian objections based on the possibility of coextension, imperfect community and companionship; it must also explain why the very same object couldn’t have any properties whatsoever (since an object’s belonging to a similarity class appears to be a contingent fact). Rodriguez-Pereyra recently defended resemblance nominalism by endorsing counterpart theory (every object possesses its properties - i.e., partakes in specific similarity classes - necessarily) and realism about possible worlds (the coextension problem is solved if similarity classes also comprise merely possible objects); and proposing a complex notion of resemblance, according to which resemblance holds in various degrees and in an iterative way - between pairs of objects, pairs of pairs of objects etc. (this latter move neutralises the problems of imperfect community and companionship). These are, clearly, non-negligible commitments. An alternative would be to give up the assumption that ordinary objects are the ‘unit of discourse’ and assume that the fundamental building blocks of reality are simple (=belonging to one similarity class) concrete particulars. This would immediately solve the Goodmanian difficulties. However, the problem with the contingency of property-possession remains. If one doesn’t like counterpart theory, it would seem, this problem can only be obviated by going trope-theoretic, that is, by identifying each simple concrete object belonging to only one similarity class with its ‘qualitative content’.

Trope theory, however, has the problem that at least some properties appear dependent on objects rather than constitutive of them (think of colour, or shape properties): with respect to their identity (this table’s hardness, not this hardness, which may or may not compose a table) and their number (since I can tear this white sheet in arbitrarily many pieces, it looks as though there is no fixed number of whiteness tropes in it - the so-called boundary problem). The obvious solution is to endorse a sparse and reductionist account according to which only physically basic, simple properties (e.g., the mass or charge of elementary particles) are genuine tropes. However, this seems to go in the direction of resemblance nominalism, as the trope-theorist attempts to defend the view by making tropes concrete, rather than abstract, particulars.

This may seem circular. However, think about the difference between an elementary particle and its qualitative aspects (mass, charge, spin, colour): do they belong to clearly distinct ontological categories? Or would it be plausible to regard mass etc. as material constituents of a more complex, but equally concrete, particular? A third way emerges, in which the nominalist (thanks to the abovementioned sparse-reductionist approach to properties) takes simple, concrete particulars essentially provided with a qualitative content as fundamental entities. Interestingly, this view was proposed by Sellars already in 1963 (‘Particulars’), where he argues in detail that the property/object distinction can and should be overcome, and proposes an ontology of ‘simple particulars’. Perhaps it would be interesting (for nominalists at least) to examine this Sellarsian option in more detail?

Call for Contributors

It looks like we may be able to add a few new contributors to this blog. New contributors will be expected to post and comment regularly on the blog and will normally be professional philosophers who work in metaphysics or closely related areas.

If you are interested in becoming a contributor, please send an e-mail with the subject line 'MoS Contributor Application' to gabriele_contessa 'at' carleton.ca and attach your CV or a link to your professional website. Please note that, due to limited resources, only successful candidates will be contacted.

Morganti Wins the 2008 dialectica Essay Prize

Matteo Morganti (Konstanz) is the winner of the 2008 dialectica essay prize for his paper 'Ontological Priority, Fundamentality and Monism', which appeared in the latest issue of dialectica.

Here is the paper's abstract:

In recent work, the interrelated questions of whether there is a fundamental level to reality, whether ontological dependence must have an ultimate ground, and whether the monist thesis should be endorsed that the whole universe is ontologically prior to its parts have been explored with renewed interest. Jonathan Schaffer has provided arguments in favour of 'priority monism' in a series of articles (2003, 2004, 2007a, 2007b, forthcoming). In this paper, these arguments are analysed, and it is claimed that they are not compelling: in particular, the possibility that there is no ultimate level of basic entities that compose everything else is on a par with the possibility of infinite 'upward' complexity. The idea that we must, at any rate, postulate an ontologically fundamental level for methodological reasons (Cameron 2008) is also discussed and found unconvincing: all things considered, there may be good reasons for endorsing 'metaphysical infinitism'. In any event, a higher degree of caution in formulating metaphysical claims than found in the extant literature appears advisable.

Congratulations, Matteo!!!

Conference: The New Ontology of the Mental Causation Debate

AHRC-Conference 14th-16th September 2009, Durham University, UK.
THE NEW ONTOLOGY OF THE MENTAL CAUSATION DEBATE
exploring the consequences of new advances in ontology for the issue of mental causation.

SPEAKERS
Prof. Tim Crane, Mental Substances and their Powers
Prof. John Heil, Causation and Mental Properties
Prof. Barry Loewer, Enough of Mental Causation? Already?
Prof. Paul Noordhof, Mental Causation: Ontology and Patterns of Variation
Prof. Tim O'Connor, Nonreductive Physicalism or Emergent Dualism? The Argument from 
Mental Causation
Prof. David Papineau, Variable Realization and Causal Laws
Prof. David Robb, Tropes, Types, and Mental Causation
Prof. Sydney Shoemaker, Physical Realization without Preemption
Prof. Peter Simons, Causation by Continuants: Loyal Opposition

CONVENORS
Dr. Sophie Gibb,
Prof. Jonathan Lowe
Dr. R.D. Ingthorsson

For further details see: http://www.dur.ac.uk/philosophy/ontologyofmentalcausation/conference

Sponsored by: AHRC, The Mind Association, The Analysis Trust, and Durham University

Abridging Lewis

I'm trying to abridge the first chapter of On the Plurality of Worlds for the new edition of the Blackwell metaphysics anthology. The cuts go pretty deep, because we’re trying to get it down from 95 pages to about 30. Many of you know the chapter (and the literature that has grown up around it) way better than I do -- and perhaps some of you will want to use the anthology in your classes -- so I’d greatly appreciate any feedback you might have on the proposed cuts.

Here’s a link to the pdf (large file): https://netfiles.uiuc.edu/dzkorman/www/LewisOTPW.pdf

Bennett on the Ideological Costs of "Low" Ontologies (Part II: Composition)

In a previous post, I discussed one of the two cases that Karen Bennett focuses on to argue that what one gains in terms of ontological simplicity is (usually?) lost in terms of ideological simplicity. I will now discuss the other case: the debate over composition. In this case, the "low-ontology" side of the dispute is occupied by the mereological nihilist who holds that simples never compose a whole.

Bennett's charge is that the nihilist's "low" ontology comes at the cost of "high" ideology. Here is how she puts her point:

[In order to recapture claims such as 'these paper clips are arranged in a chain', the nihilist] needs to introduce clever techniques that allow him to talk about the very complicated, highly structured ways in which simples can be arranged. On the face of it, however these very complicated predications of simples appear to commit nihilist to the claim that simples collectively instantiate very complicated structured properties. The simples instantiate (((being arranged quarkwise) arranged atomwise) arranged moleculewise) ... At least, the nihilist is committed to the complex structured plural predicates themselves. Here again, the high-ontologist is not committed to any such thing. The believer [who occupies the high-ontology side of this dispute because she believes that there are things whose proper parts are simples] need not countenance either these highly structured plural predicates, nor any properties that answer to them. She does not need to say that the simples themselves directly satisfy any such predicate or instantiate any such property. She can simply say that the simples directly satisfy 'arranged quarkwise'--or whatever the smallest items composed of simples are. Then the quarks satisfy 'arranged atomwise', and so forth up. It is molecules that get arranged into cells. (p.64)

It's not clear to me that Bennett is successful at showing that the ideological price of nihilism is higher than that of "believerism". Bennett concedes that the believer needs predicates such as 'being arranges X-wise' (and possibly the properties that come with them). Her claim, however, is that the nihilist needs the complex structured plural predicates. But her argument for it seems to be based on a premise that it is, say, molecules (not simples!) that get arranged into cells. But, of course, the nihilst would deny this--according to him, there are no molecules, there are only simples arranged moleculewise and simples arranged cellwise and some simples arranged moleculewise are arranged cellwise with other simples arranged moleculewise. So if he wants to say 'These molecules form a cell', he has to say 'These simples that are arranged molculewise (and these simples arranged molculewise and ... and these simples arranged molculewise) are arranged cellwise' but in doing so he does not seem to be using a complex predicate more than someone who is saying 'These children and these children are smart' is (yes 'being a child' is singular and distributive and 'being arranged moleculewise' is neither but Bennett seems to concede that the believer needs plural non-distributive predicates as much as the nihilist).
So, is believerism any cheaper ideologically? What should the believer say of 'These molecules form a cell'? Bennett seems to think that he could just say 'These molecules are arranged cellwise' but for the believer molecules are presumably sums of parts arranged moleculewise, parts which are themselves sums of parts arranged atomwise, etc. So, it's far from clear to me that she is better off ideologically, for the nihilist could just skip all the inbetween levels when she does not need them (after all, pace Bennett, it's ultimately the simples that are arranged atomwise, moleculewise, cellwise, etc.), while the believer would always have to mention that in order for this mereological sum to be a cell, it needs to have parts that are arranged moleculewise, and these parts need to have parts that are arranges atomwise, and these parst need to have parts that are arranged quarkwise, etc.

Bennett on The Ideological Price of "Low" Ontologies (Part I: Constitution)

I'm reading Karen Bennett's 'Composition, Colocation, and Metaontology' (which is published in this book). In it, Bennett draws a number of interesting metaontological morals by considering two ontological disputes--the one about composition and the one about constitution. In each dispute, she identifies a "low-ontology" side and a "high-ontology" side and at a certain point she argues that, in each dispute, what the low-ontologist gains in terms of ontological simplicity may be lost in terms of ideological simplicity. However, I'm not completely convinced by the specific cases she makes. In this post, I will focus on her case against for the ideological costs of the low-ontology side when it comes to constitution and focus on the composition case in another post.

As an example of the low-ontologist side in the constitution case, Bennett considers the Lewisian position that (let me over simplify here) even, if Statue and the Lump are identical, we can truly say that Statue would not survive being squashed into a ball while Lump would not by appealing to the different counterpart relations in which Lump/Statue stands with otherworldly things.

Bennett complains:

The heart of this strategy is to say that the relatively straightforward predicate 'being possibly squashed' in fact hides a multiplicity of more complex predicates that pack in some reference to the kind. (Lewis, of course, will invoke counterpart-theoretical properties like having a squashed counterpart under the lump-counterpart relation) Perhaps this require that the one-thinger [i.e. the one who takes the low-ontologist side in the constitution dispute] postulate a different complicated modal property for each object the multi-thinger [i.e. the one who takes the high-ontology side in the constitution dispute] countenances. Perhaps it just requires that she employ a different complicated modal predicate for each such object. That depends on the broader question about the viability of nominalism. What matters for my purposes is that the multi-thinger need not do either. (p.28)

In other words, what the low-ontologists saves on the cost of her ontology comes at the price of her ideology. Now, I have no sympathy for Lewis' modal realism or his counterpart theory, but Bennett's interpretation of the Lewisian position does not seem to be particularly charitable to me. Let me put aside the issue of nominalism and that of conceptual vs. ontological simplicity and focus on Bennett's interpretation of the Lewisian use of the counterpart relation in this case.

As far as I can see, the Lewisian's reply to Bennett should be that he does not need the complex predicates or the corresponding properties. When saying that 'Lump would survive being squashed' is true and 'Statue would survive being squashed' is not even if 'Lump' and 'Statue' refer to one and only one thing, the Lewisian would not directly appeal to the fact that the same thing has two different modal properties but to the fact that in different contexts the same thing can have different counterparts because the different contexts make different respects of similarirty with otherworldly things relevant. So, for example, when talking of Lump/Statue as 'Lump', we are making the material is made of, its mass, etc. salient, while when talking of it as 'Statue', we are making also its shape and history salient. So, there are things that are counteraprts of Lump/Statue qua lump of clay that are not counterparts of it qua statue (things that resemble it in being made of clay and having a certain mass, etc. but not in having a certain shape etc.) and some of this things are temporal parts of things whose other temporal parts were counterparts of Lump/Statue qua statue but are no longer counterparts of it because they no longer bear the right sort of resemblance to Lump/Statue qua statue because they have been squashed. So, the Lewisian really only needs the property having been squashed and claim that some counterparts of Lump/Staute qua lump of clay have it while some counterparts of it qua statue do not have it. It is only in virute of its counterparts having or not having the property having been squashed that Lump/Statue has or has not (derivatively) the modal property of being possibly squashed. Of course, Bennett could claim that the counterpart theory already comes at too high an ideological cost (I would just say that it is false, but I won't argue for that here), but Lewis and the Lewisians would claim it's a cost worth paying because of the benefit that it brings with it and, in any case, the Lewisian does not seem to need the strange predicates Bennett wants to saddle them with. Am I being too charitable to the Lewisian position or unfair to Bennett's objection?

Dispositions and Interferences (Part II)

In Part I of this post, I suggested that the simple counterfactual analysis of disposition (SCA) may be saved from the usual counterexamples by introducing clauses to the effect that nothing interferes with o's disposition to M (or not M) when S.

More specifically, the "intereference free" counterfactual analysis (IFCA) would maintain that:

(IFCA) o is disposed to M when S iff:

1. (If it were the case that S, o would M AND it is not the case that something interferes with o's not being disposed to M when S) OR
2. Something interferes with o's being disposed to M when S.

As I noted, this analysis would be circular unless one were able to provide an analysis of 'x interferes with o's disposition (not) to M when S' without employing the notion of disposition.
This is my a first stab at doing so. (be warned that it's more than a bit convoluted)

(Interference)
--> For all ks, I_k interferes with o's being disposed to M when S iff:

1. It is the case that I₁ and … and I_k and … and I_n,
2. For each j, if it were the case that not (I₁ or … or I_(j–1) or I_(j+1) or … or  I_n), then it would not be the case that, if it were that S, then o would M.
3. There is some property G such that o has G and if it were the case that not-(I₁ or … or I_n), then it would be the case that: (3.1.) if it were the case that S and o retained G, o would M, and (3.2.) it is not the case that, if it were the case that not-S, then it would be the case that M and (3.3.) it is not the case that, if it were the case that S and O did not retain G, then o would M.
4. There is no property H such that it is not the case that o has H, and, if it were the case that not-(I₁ or … or I_n), then o would have H and, if o didn’t have H, then it would not be the case that, if it were that S, o would M.

As far as I can see, this can deal with all the usual counterexamples to (SCA). For example, there being an (inverse) fink attached to this live wire comes out as interfering with the wire's disposition to conduct electricity when touched by a conductor (had the fink not been there, the wire would have conducted electricity when touched by a conductor) and there being a chalice-hating wizard interferes with the chalice's disposition not to break when touched (because had there been no wizard, the chalice would not have broken when touched).

(Question A) Am I wrong in thinking that IFCA avoids the standard counterexamples to SCA?
(Question B) Can anyone think of any new counterexamples lurking in the background? (My spidey senses tell me that there is a whole battery of them just waiting to be thought of... :-))

One last thing: I am assuming that properties are sparse. So, in (IFCA 4.), H cannot be something along the lines of being such that no chalice-hating wizard is around or the likes, for I take there is no such property to be had. However, H can be something along the lines of being made of glass (So that the fact that, for example, the live wire is not made of glass does not come out as interfering with its disposition to conduct electricity when touched by a conductor).

Postdoc: Philosophy of Physics/Metaphysics at Monash University

This may be of interest to some readers:

The School of Philosophy and Bioethics at Monash University invites applications for a one year postdoctoral fellowship (Level B, salary AUD79,269) to commence sometime between February and September 2010. The fellow will be employed to contribute to a research project relating to the metaphysics and physics of time, however there is considerable scope for latitude in the research to be pursued. Applicants are required to have a Ph.D. by the date of commencement, and to have expertise in philosophy of physics and/or metaphysics of time. Expertise in general relativity and recent work on quantum gravity may be an advantage. Enquiries graham.oppy@arts.monash.edu.au.

Applicants should send an application letter and CV to Sandra Bolton, School of Philosophy and Bioethics, Monash University, Victoria 3800 or electronically (preferred) to sandra.bolton@arts.monash.edu.au by Friday 23 October.

Conference: Fictionalism (Manchester, 15-17 September 2009)

This sounds like it's going to be a very interesting conference:

FICTIONALISM
15-17 September 2009
Chancellors Hotel and Conference Centre, University of Manchester

Stephen Yablo (MIT) Hyperbolic Geometry
Paul Horwich (NYU) The Fiction of Fictionalism
Mark Balaguer (California State, Los Angeles) (title TBA)
Jonas Olson (Stockholm) Getting Real about Moral Fictionalism
John Divers (Leeds) If You Don't Succeed, At Least Pretend To: The Explanatory Poverty of Modal Fictionalisms
Mary Leng (Liverpool) Mathematical Fictionalism and Constructive Empiricism
Daniel Nolan (Nottingham) There's No Justice: Ontological Moral Fictionalism
Anthony Everett (Bristol) Meinongian Fictionalism Reconsidered
Jussi Suikkanen (Reading) Saving the Moral Fiction: The Content Challenge
Antony Eagle (Oxford) Another Go at Modal Fictionalism
Robbie Williams (Leeds) Fictionalism about Reference: The Metaphysics of Radical Interpretation

Registration is now open. You can register via the conference website: http://www.socialsciences.manchester.ac.uk/disciplines/philosophy/events/fictionalism/
Registration will close on 28 August.
Organizers: Chris Daly and David Liggins (University of Manchester)
Email: fictionalism@manchester.ac.uk
The organizers gratefully acknowledge the financial support of the Aristotelian Society, the Mind Association, the Royal Institute of Philosophy, the Analysis Trust, and the School of Social Sciences, University of Manchester.

Dispositions and Interferences (Part I)

According to the naive counterfactual analysis of dispositions (NCA), o is disposed to M when S if and only if, if it were the case that S, o would M. Unfortunately, NCA is too nice and simple to be true and counterexamples to both sides of the biconditional abound. These include (on the "if" side) finks (the device that would turn a dead wire into a live one if it were to be touched by a conductor) and masks (the carefully wrapped but nonetheless fragile Ming vase) and (on the "only if" side) mimicks (the golden chalice hated by a wizard who would destroy it, if something where to touch it).

As a result of these counterexamples, some have abandoned NCA in favour of some different analysis, others have tried to fix it. Both projects, however, have proved to be quite tricky. Nevertheless, I still hope NCA can be fixed (it's too nice to give it up). The idea I'm exploring right now is that there is a common theme to all counterexamples to NCA. In all of them something is interfering with o's disposition to M when S. So, to avoid the counterexamples NCA should be fixed by adding 'unless something interferes with o's disposition to M when S'. Now, of course, this cannot be the whole story unless we are also able to give an analysis of 'something interferes with o's disposition to M when S' without mentioning 'o's disposition to M when S' otherwise our analysis would simply be circular (and this is far from being an easy task but I'll leave my suggestion for doing so for future post).

Now, the problem is that, as far as I can see, this general strategy seems to be quite obvious and yet, to my knowledge, no one has tried to pursue it so far. So, am I missing something? Have there been any attempts to pursue this general strategy I don't know of? And, if not, is this due to the fact that there is something clearly wrong with it (or is just due to the difficulty of analyzing the concept of interference in non-dispositional terms)? (One thing that could seem to be wrong is that in the case of mimicks there would seem to be no disposition to interfere with (and that is exactly the problem). However, I think this problem can be dealt with by claiming that there is, in fact, a disposition that is being interefered with--i.e. the chalyce's sturdiness. And that if nothing was interfering with that disposition the chalice would not appear to be fragile.)

Books: Metametaphysics and The Routledge Companion to Metaphysics

I've just received a copy of Metametaphysics (edited by fellow blogger David Manley together with Ryan Wasserman and David Chalmers), which I will be reviewing for The Philosophical Quarterly, and, from the little I have seen so far, it looks like it will make for a very interesting read! I'll keep you posted.

On a similar note, I can't wait to put my hands on a copy of The Routledge Companion to Metaphysics edited by fellow bloggers Ross Cameron and Peter Simons and by Robin Le Poidevin and Andrew McGonigal.

(Btw, contributors to this blog shouldn't hesitate to do a bit of shameless self-advertising when they have a new book out!)

Van Inwagen on the Rate of Time’s Passage

This post is co-authored by Hud Hudson, Ned Markosian, Ryan Wasserman, and Dennis Whitcomb. It is based on an unpublished paper by the four of us that is available online here.

In the 2^nd edition of his book, Metaphysics (Boulder, CO: Westview Press, 2002), Peter van Inwagen offers a new argument against the passage of time. In the 3^rd edition of the book (Westview Press, 2009) the same argument appears, and it also appears in a recent Analysis paper by Eric Olson (“The Rate of Time’s Passage,” Analysis 61: pp. 3-9). Here’s a quote from van Inwagen.

Does the apparent “movement” of time… raise a problem? Yes, indeed… the problem is raised by a simple question. If time is moving (or if the present is moving, or if we are moving in time) how fast is whatever it is that is moving moving? No answer to this question is possible. “Sixty seconds per minute” is not an answer to this question, for sixty seconds is one minute, and – if x is not 0 – x/x is always equal to 1 (and ‘per’ is simply a special way of writing a division sign). And ‘1’ is not, and cannot ever be, an answer to a question of the form, ‘How fast is such-and-such moving?’ – no matter what “such-and-such” may be… ‘One’, ‘one’ “all by itself,” ‘one’ period, ‘one’ full stop, can be an answer only to a question that asks for a number; typically these will be questions that start ‘How many…’… ‘one’ can never be an answer, not even a wrong one, to any other sort of question – including those questions that ask ‘how fast?’ or ‘at what rate?’. Therefore, if time is moving, it is not moving at any rate or speed. And isn’t it essential to the idea of motion that anything moving be moving at some speed…? (2002: 59)

Here’s the gist of van Inwagen’s argument. If time passes, then it has to pass at some rate. And even if that rate is expressible in a number of different ways (e.g., 60 minutes per hour, 24 hours per day, etc.), it must also be true (if time passes at all) that time passes at a rate of one minute per minute. But one minute per minute is equivalent to one minute divided by one minute. And when you divide one minute by one minute, you get one (since, van Inwagen says, “if x is not 0 – x/x is always equal to 1”). But ‘one’ (not ‘one’ of anything, but just plain old ‘one’) is the wrong kind of answer to any question of the form “How fast…?” So it must be that time does not pass after all. QED.

We can put the reductio part of van Inwagen’s argument a bit more carefully as follows.

(1) The rate of time’s passage = 1 minute per minute.

(2) 1 minute per minute = 1 minute ÷ 1 minute.

(3) 1 minute ÷ 1 minute = 1.

--------------------

(4) The rate of time’s passage = 1.

We have several problems with this argument, but will discuss only two of them here. (We discuss some other problems, and the two problems raised here in more detail, in the paper linked to above.)

First problem: It’s not true that for any x distinct from 0, x ÷ x = 1. Take for example the Eiffel Towel. If you divide the Eiffel Tower by itself, you don’t get 1. You don’t get anything, because division is not defined for national landmarks. Division is an operation on numbers, and a minute – like a meter or a tower or a car – is not a number. So 1 minute ÷ 1 minute is undefined, and thus (3) is false.

(One can, of course, say things like: 10kg divided by 5 kg is 2 kg. But we take this to be loose talk – it is the numbers, not the quantities, that are being divided. Similarly, one can show that a rate of one kilometer per minute is equal to sixty kilometers per hour by multiplying fractions and canceling out units: 1k/1m x 60m/1hour = 60k/1hour. Once again, we take this to be a loose way of speaking – it is the fractions, not the rates, that are being multiplied.)

Second problem: (2) is also false. Van Inwagen supports it by saying that “…‘per’ is simply a special way of writing the division sign.” (2002: 59) We disagree. The forward-slash (‘/’) can be used to abbreviate both ‘per’ (i.e., ‘for every’) and ‘divided by’, but it is a mistake to treat ‘per’ as synonymous with ‘divided by’. To see this, consider the claim that time passes at a rate of one minute per minute. This may be uninformative, but that doesn’t make it untrue. A minute does pass every time a minute passes, just as a car passes every time a car passes. So ‘1 minute per minute’ expresses a genuine rate. But now consider the claim that time passes at a rate of 1 minute ÷ 1 minute. This is worse than uninformative – it is nonsensical. That is because 1 minute ÷ 1 minute is a division problem (without a defined answer) and a division problem is not a rate of change. One might as well say that time passes at a rate of orange x banana. So ‘1 minute ÷ 1 minute’, unlike ‘1 minute per minute’, does not express a rate.

We conclude that van Inwagen’s anti-passage argument fails, for (2) and (3) are both false.

Intuitions about Cases in Metaphysics

I think it’s safe to say that intuitions about cases tend to be taken less seriously in material-object metaphysics than they are in (e.g.) epistemology, philosophy of language, philosophy of mind, and ethics. Does anyone know of any explicit discussion or defense of this differential treatment in the literature? In particular, is there any discussion (even in passing) of either of the following two claims:

(i) That we should be more skeptical of particular-case intuitions about material-object metaphysics (or metaphysics generally) than we are of particular-case intuitions about other matters (e.g., in epistemology, phil language, ethics).

(ii) That we should be more skeptical of particular-case intuitions about material-object metaphysics (or metaphysics generally) than we are of general-principle intuitions about material-object metaphysics (e.g., anti-colocation intuitions).

The can only think of two discussions. The first -- bearing on question (i) -- is in Rodriguez-Pereyra’s Resemblance Nominalism (p.217) where he contrasts intuitions about metaphysics with intuitions in philosophy of language, and he suggests that the latter are reliable only because the range of facts intuited (e.g., about meanings) are themselves determined by our conceptual activities. The other -- bearing on question (ii) -- is the last couple sentences of Ted Sider’s paper “Parthood,” where he suggests that general-principle intuitions are more trustworthy because judgments about cases tend to be “infused with irrelevant linguistic intuitions.” I’ve also encountered various responses in conversation, e.g., that metaphysics is about what exists, or that it’s misguided to rely on conceptual analysis in this domain. But I’ve never seen any proposal worked out in any detail, and I have my doubts that any of them can draw the line in the right place between (on the one hand) cases and principles and (on the other hand) metaphysics and other areas.

I’d be grateful for any references, as well as any thoughts on how (i) or (ii) should be defended.

Lewis and Vague Laws of Nature?

Sometimes people seem to assume that David Lewis took the notion of law of nature to be (somewhat) vague (which I take to mean that 'x is a law of nature at @' has borderline cases), but does Lewis say that explicitly anywhere? (On the face of it, it would seem to be in contrast with the best system thesis being expressed as a biconditional, but, on the other hand, Lewis seems to concede that strength and simplicity are somewhat vague criteria.) And would any other sophisticated regularity theorist be happy with that?

(Crossposted at It's Only A Theory)

The Age of Hyperintensionality

A place in a sentence is extensional if words with the same extension can always be substituted into it without changing the truth-value of the whole sentence. (That definition is a little too crude in about three ways, but bear with me.) A place in a sentence is intensional, in one sense of “intensional”, when words that necessarily share the same extension can always be substituted into it without changing the truth-value of the whole sentence.

It has become increasingly clear since the 1970s that we need to carve meanings more finely than by “intensions” in the sense associated with the specification above. Call the sorts of intensions employed, for example, by Richard Montague possible worlds intensions. Handling belief clauses by insisting that anyone who believes something believes everything necessarily equivalent to it has always caused problems. Once we accept that names are rigid designators, allowing their substitution in all sorts of representational and psychological contexts causes trouble: the Sheriff of Nottingham can be hunting for Robin Hood without hunting for Robin of Locksley, or so it seems.

There seem to be places outside our psychological talk that require hyperintensionality. Talk of entailment in the sense of logical consequence, for example: it does not logically follow from apples being red that all bachelors are unmarried, let alone that water is H2O, even though it does follow that either apples are red or apples are not red. Use of counter-possible conditionals is another example: two conditionals can have necessarily false antecedents but differ in truth-value. Talk about moral obligation and permission seems to be hyperintensional, as anyone struggling with substituting logical equivalents in the scope of deontic operators may have seen. I’m just back from a conference in Colorado where people were insisting that “in virtue of”, “because”, and other explanatory expressions were hyperintensional. (Benjamin Schnieder, Gideon Rosen and Kit Fine were three in particular.) Once you look around you see quite a bit of hyperintensionality.

There’s a piece of rhetoric I associate with Richard Sylvan about this. He was fond of suggesting that there would be a move from using possible-worlds intensions to using hyperintensional resources that would parallel the move made from extensionalism to possible-worlds intensionalism. In the nineteen-sixties, the big goal was to be able to do philosophy of language while treating language extensionally: think of Davidson’s project in particular, though Quine was also a big booster of the extensionalist program. I guess it was typical of that project to assign extensions to categories of expressions, and then have some syncatogramatic expressions that operated on extensions to yield other extensions. (E.g. “all” did not get an extension, but (All x)(Fx) operated on the extension of “F” to yield a sentence-extension, i.e. a truth-value)

There are still people trying to carry out that extensionalist project, but it came under increasingly severe attack since the early 1970s. (And maybe earlier: I think Carnap might be an important precursor here, along with Prior, and perhaps many others). The extensional programme was not very satisfying in its treatment of propositional attitude reports, entailment, normative discourse such as the use of “ought”, and a number of other areas. But the star witness against the extensional programme was modal vocabulary. Treating “necessarily” extensionally does not get you very far, and after Saul Kripke popularised possible-worlds semantics for “necessarily”, the floodgates started to open. Richard Montague and David Lewis were among the vanguard of those arguing for a systematic, intensional treatment of natural language, arguing that it handled all sorts of constructions that extensional treatments faced serious difficulty with.

The intensions that Montague and Lewis relied upon were set-theoretic constructions out of possible worlds and possible individuals. (Not just sets of possibilia or functions from possibilia to possiblia, but also sets of those sets, functions from those functions to other functions, etc. etc.) The Montague project of trying to handle all of language with these possible-worlds intensions is alive and well today: I take Robert Stalnaker to be one of its prominent contemporary philosophical defenders, though I haven’t scrutinised his recent work to see if any weakening has happened.

But I think that project is doomed. There is too much work that needs to be done that requires hyperintensional distinctions, and those trying to hold the line that everything can be done with possible-worlds intensions will look as outdated in thirty years as the extensionalists look to the intensionalists today.

Of course, even if we decided we wanted to do more justice to hyperintensional phenomena than standard possible-worlds semantics, we have several options about how to go on from here. The response that is perhaps closest to the standard possible-worlds tradition is to let the semantic value of a piece of language be a pair of a possible-worlds-intension plus some kind of constituent tree, that serves as a logical form or otherwise conveys information about the internal linguistic structure of the expression. Alternatively, we could let the semantic value of a complex expression be a tree whose nodes are possible-worlds intensions: Lewis discusses this way of going, for example, in OTPW p 49-50.

Another response that is close to the possible-worlds tradition is to use impossible worlds as well as possible ones. Since things that do not vary across possible worlds can vary across impossible worlds, impossible worlds give us finer-grained distinctions. If we allow logically impossible worlds, we can even get the effect of places in sentences where substitution of logical equivalents fail, since for example the worlds where (p or not-p) obtain need not be the ones where (q or not-q) obtain. I take it that semantics using situations instead of worlds is often a close cousin of this.

More radical responses to hyperintensionality include moving to an algebraic semantics, such as the sort advocated by George Bealer. Even these can be seen as successors to the possible-worlds tradition, since the structures of the algebras are often inspired by the structural relationships possible-worlds intensions stand in to each other. No doubt philosophers will come up with other approaches too - some revert to talking about Fregean senses and functions on them, though whether this is much more than a cosmetic difference from algebraic approaches I’m not sure.

Why does this matter for metaphysics? Well, one immediate reason it matters is that the metaphysics of language had better be able to cope with hyperintensionality and hyperintensions. One place that disputes in the philosophy of language often spill over is into the metaphysics of meaning, of truth (or at least truth-conditions), of propositions and so on.

A connected reason is that respect for hyperintensionality might go along with more warmth towards hyperintensional entities. We may be less likely to smile on the demand that properties that necessarily have the same instances are identical, for example. This in turn may motivate rejecting the picture of properties as sets of their actual and possible instances. Indeed, set theory might be of less use in metaphysics in general once we want to individuate things hyperintensionally.

There are other ways the hyperintensional turn could affect metaphysics. It might make us more sympathetic to impossible worlds, for example: I’ve argued elsewhere that counter-possible conditionals give us a good reason to postulate impossible worlds. It might make us think that some relational predicates are not associated with relations, or maybe are associated with finer-grained relata than they appear to be associated with: see Carrie Jenkins’s post about grounding. Modal analyses of hyperintensional pieces of language seem unappealing, since modal analyses are normally only intensional not hyperintensional. I could go on.

So, metaphysicians, join the hyperintensional revolution! You have nothing to lose but your coarse grains!

Presentism, causation and truthmakers for the past

I’m working on both causation and the truthmaker objection to presentism, and it seems to me that it might be possible to kill two birds with one stone. What follows is the basic idea, and I’d love to hear your thoughts.

Suppose that presentism is true. What is the nature of causation? It’s the relation between what and what? Or, more relevantly, between when and when? Since, according to presentism, the past does not exist, either causation is a relation between nothing and something in the present, or causation is simultaneous, or causation is not a relation at all. The first option seems dubius. A two place relation (I’m ignoring contrastivism, for the moment) has two relata, after all, not one.

What, then, about the second option? C. B. Martin defends this view in The Mind in Nature—or, at any rate, that’s my understanding of what Martin defends. But it’s not clear how to make sense of causal processes on this view. (Persistence intuitively has causal constraints; how are we to make sense of these constraints if all causation is simultaneous?)

The third option seems to me the route to go. Here’s an initial proposal: Causation is a fact about presently existing (Armstrongian) states of affairs, or tropes if you have them. It is a fact about e, say, that c brought it about. Suppose, however, that existentialism is true, so that if x does not exist, there are no singular propositions about x. If c is a state of affairs and the particular that is a non-merelogical constitutent of c no longer exists, then the fact that c caused e is the fact about e that something c-like brought it about. If c is a trope no longer instantiated and the instantiation condition is true, so that uninstantiated properties do not exist, then too causation is the fact that something c-like brought about e.

How are we to understand “something c-like”? Here’s one proposal: Properties are or of necessity confer causal powers, so we can understand “something c-like” as “something with the following causal powers profile...” (Of course the Neo-Humeans can’t really accept this view, but how many Neo-Humeans are presentists?)

What should we say about the fact in question, that e was brought about by something c-like? It might be a property of the world, as in Bigelow’s “Presentism and Properties.” It might be a property of e. Or it might not be a property, but a fact grounded in something else. Or a primitive fact about e.

Whatever answer one gives here seems also to be an answer to the objection to presentism from truthmakers about the past. Hence the presentist, so long as they can offer a theory about the nature of the fact that e was brought about by something c-like, can kill two birds with one stone, a theory of causation and a response to the truthmaker objection.

Here’s an initial proposal. Take property instances to be tropes. Then, with certain other assumptions about tropes, events can be understood as tropes. So trope c caused trope e. That turns out to be a fact about e: that it was brought about by c. Since I’m inclined to accept both existentialism and the instantiation condition, this will turn out to be the fact, about e, that it was brought about by something c-like. The fact is a basic truth, and e alone is its truthmaker. This is analagous to e’s also being, in virtue of either being or of necessity conferring causal powers, (part of) the truthmaker for counterfactuals describing what objects with e would do in various circumstances. It is a truthmaker for future truths and for the past truth about c.

One further claim, and we have a theory of truthmakers for the past. These basic causal facts about tropes are cumulative. So the fact that e was brought about by c is the fact that e was brought about by something c-like which was brought about by something...., which was brought about by something..., and so on. As long as there is a causal chain from some present state of affairs to every past state of affairs, there is a present truthmaker for every past state of affairs.

Tropes carry with them their entire causal history and their entire power profile, and so are truthmakers for past and future truths. Present property instances do a lot of work on this view, but that’s about what we should have expected given presentism.

Like Matteo, I've been thinking about haecceitism. I claim it is best pronounced the way Kaplan liked it: Hex'-ee-i-tis-m. I'm not sure why I care about this, but I do.

There is a lot of older stuff in the metaphysics literature (Black, Adams, etc.) and a lot of more recent work in the philosophy of physics literature (Saunders, Ladyman, French and Krause, etc.) and the two discussions don't have a lot of points of contact. (Disclaimer: I'm going to read Katherine Hawley's paper on the PII in the next week or so; perhaps this will join the two debates together a bit more for me.)

Here are a few things I find confusing. (1) The physics people often seem to run together (sometimes on purpose) epistemological issues about indiscernibility with metaphysical ones. The fact that two particles are indistinguishable for us seems to entail, to some, that they are indistinguishable simpliciter. I'm not clear on what, if any, metaphysical lessons can be learned when we take this sort of strong empiricist stance. (2) Haecceitism is often not well enough defined. Sometimes it means that objects have primitive thisnesses (following Adams) but sometimes it just means objects are (or could be) primitively different. This is an important distinction. The more minimal kind of haecceitism, which I'd argue doesn't even deserve the name, just says we can have objects that are perfect duplicates but nevertheless differ. They don't differ because they have special thisnesses, because they don't have thisnesses. They just differ even without differing in their (non-identity-based) properties. (3) Saunders and others want to sidestep the PII by denying that bosons are objects. They are some other sort of entity. But how does this supposed to help with anything metaphysically interesting? I always took the PII to apply to things of any sort.  

Finally, a note: physicists often make claims about particles being identical when they really mean they are of the same kind.  Argh!

From Borderline Tables to Count Indeterminacy

Imagine assembling a two-piece table: the top (T) is being affixed to the base (B). There are points in the assembly process at which T and B are just beginning to be fastened together and at which, intuitively, it is vague whether they compose anything. Ted Sider’s (riff on Lewis’s) argument from vagueness purports to show that (despite appearances) there can’t be borderline cases of composition. Here’s the argument: If it could be indeterminate whether some things compose something, then it could be indeterminate how many things there are (e.g., whether there are just two things – T and B – or three things – T, B, and a table). But there can’t be count indeterminacy. So there can’t be borderline composition. And (moreover) if there can’t be borderline composition, then composition must be unrestricted.

There are ways of blocking the argument, but they’re pretty nasty (e.g., nihilism, sharp cut-offs, ontic vagueness, relativism). So many prefer just to accept the conclusion, that composition is unrestricted (“universalism”). Some don’t even think they’re biting a bullet here because (for one reason or another) they think that universalism is innocuous.

I want to convince you that universalists aren’t out of the woods yet. Let’s grant that T and B definitely compose *something*: a mereological fusion (or MF for short). But surely T and B are, at the very least, a borderline case of composing a *table*. Even universalists should admit that. But here’s the rub. No table is identical to any MF. Tables can survive the annihilation of certain of their parts; MFs can’t. So if T and B don’t compose a table, there are three things: T, B, and the MF. If they do compose a table, there are four things: T, B, the MF, and the table. Since they’re a borderline case of composing a table, they’re a borderline case of composing something other than an MF. In which case it’s indeterminate whether there are three or four things. In which case there’s count indeterminacy. In which case the argument from vagueness fails.

Friends of the argument from vagueness need to find some way to block this argument from borderline tables to count indeterminacy. And they need to find a way of doing this that doesn’t undercut the argument from vagueness. As far as I can tell, friends of the argument from vagueness have two options. Both involve resisting the move from T and B’s being a borderline case of composing a table to their being a borderline case of composing something other than an MF. And both involve finding something that definitely exists and is definitely composed of T and B and that itself is a borderline case of being a table.

Option #1: They definitely don't compose anything other than an MF. Here the idea is that there is definitely only one thing composed of T and B – namely, the MF – and the MF itself is a borderline case of being a table. To get this response to work, you’re going to need some way of defusing the sort of Leibniz’s Law argument I gave above for the distinctness of MFs and tables. Here are some of the tasty options: you can deny that tables can survive the loss of parts, you can say (a la Burke) that the original MF ceases to exist when its parts come to be arranged tablewise, or (like Lewis and Sider) you can go for a counterpart-theoretic account.

Option#2: They definitely do compose something other than an MF. Here the idea is that there is a further thing composed of T and B which (unlike the MF) has a “tablish” modal profile, but it’s nevertheless indeterminate whether this further thing is a table, e.g., because it’s indeterminate whether its parts are sufficiently stuck together to count as a table. There are unprincipled ways of taking this line, e.g., by saying that exactly one modally table-like entity conveniently springs into existence as soon as the grey area begins, but let’s set those aside. The only principled way of taking this line (as far as I can tell) is to accept bazillionthingism (a.k.a., plenitude, explosivism, absolutism), on which there are a bazillion things, with different modal profiles, occupying the region that’s filled by T and B. In that case, there isn’t count indeterminacy. There are exactly a bazillion and two things: T, B, and the bazillion things composed of them.

So friends of the argument from vagueness are going to get saddled with some sort of non-innocuous commitment: either bazillionthingism or else one of the revisionary packages needed to block the Leibniz’s Law arguments. Some (e.g., Lewis and Sider) have already chosen their poison. But nobody escapes unscathed.

Haecceities and Haecceitism

Haecceities are primitive identities in a world. Haecceitism has to do with> primitive trans-world identities (allowing for de re differences between worlds without qualitative differences). My question regards the connection between the two. Prima facie, possession of haecceity implies haecceitistic differences between worlds. However, it has been pointed out that identity might be primitive with respect to a set of conditions but not others (Legenhausen (1989)), and showed that the two things can be kept distinct (Lewis (1986)), and in fact haecceitism can be true even if there are no haecceities. Adams (1979), one of the main recent proponents of primitive thisness, thinks haecceitism is also true, but feels compelled to provide an argument for it, additional to the existence of haecceities. Is counterpart theory the only way to believe in haecceities but not in haecceitism? Is it relevant whether haecceities are considered to be genuine properties (Duns Scotus), or just ‘aspects’ of things only separable via conceptual distinction (Ockham and other Scholastics, Adams himself)?
Generalising, it seems four possibilities are allowed; and if one introduces the distinction between moderate and extreme forms of haecceitism and/or anti-haecceitism (that is, as I understand it, primitive identity with or without essentialist constraints on the one hand, and non-primitive identity without or with the Identity of the Indiscernibles on the other) probably even more (8? I am not sure about extreme anti-haecceitism with primitive identities, maybe it only requires the Identity of the Indiscernibles to be a contingent truth). But which combinations are really possible/plausible? What conditions do they require exactly? What are people's intuitions/preferences?

Barker on Chance and Cause II

In my last post, I discussed Barker's CC1. I said I'd leave discussion of CC2 for later, and here it is. CC2, recall, is this principle

CC2: If at a time t, there is a non-zero chance of e and e obtains, then at least some of the conditions at t that determine the chance of e at t, caused e.

Of this principle, Barker says 'Unlike CC1, CC2 is bound to be controversial'; given our discussion of CC1, I guess this makes CC2 really controversial!

And indeed we found it objectionable. The easiest way to see it is to rehearse Humphreys' problem for propensity theories: if chances are probabilities, Bayes' theorem entails that in general if Ch(e|c) is non-trivial (i.e., not zero or one), then Ch(c|e) will be non-trivial. And this looks weird if this is conceived of as a conditional chance in line with CC2; if e occurs, then it looks like at the time of e, c will generally have some non-trivial chance, and e will be a condition which determines the chance of c but doesn't cause it. In general, as Barker notes, effects are evidence for causes, and so give their causes a probability, which cannot be a chance consistently with CC2 unless there is far more backwards causation than usually thought.

Barker doesn't opt for the idea that backwards causation is widespread. His primary response is that past-directed probabilities, like those that effects give to causes and that appear in inverse conditional probabilities, 'are not real chances'. And if they aren't real chances, then CC2 won't give us 'bogus backward causation'.

Now of course any counterexample can be defined away, which is in effect what Barker does here. But this isn't completely ad hoc, since he does offer an argument. Barker appeals to this principle:

RC: Where c and e occur, if the chance at t_c of e would have been lower, had c not obtained, then if there is no redundant causation in operation, c caused e.

RC basically expresses the counterfactual chance-raising account of causation, without the usual restriction to non-backtracking counterfactuals. As such, even when e is prior to c, RC still holds; so if there were widespread backwards chances, there would be widespread backwards causation. This is absurd; so Barker rejects the assumption that these backwards probabilities are chances.

Now, when some assumptions collectively lead to an absurdity, we are only required to reject some one of them, not any particular one. But it seemed to us that Barker had clearly chosen the wrong one: it is RC that has to go, not the assumption that chances are probabilities. I can't imagine even those who defend the counterfactual chance-raising view of causation as liking RC as a way of expressing what's right about it.

But let's say we do accept Barker's way out. If chances aren't probabilities, then what are they? About this I really am in the dark. They can't be the things that govern credences, since Lewis' arguments in 'A Subjectivist's Guide to Objective Chance' suggest that whatever function it is that regulates credence will be a probability function. They won't have much to do with frequencies, since past conditional frequencies will approximate the past probabilities which aren't the past chances, according to Barker. They won't obey the Basic Chance Principle of Bigelow, Collins, and Pargetter—or indeed many of the platitudes that circumscribe the conceptual role of chance that Jonathan Schaffer has recently outlined. (It won't meet these platitudes both through failing to be a probability, and because CC1 and the existence of backwards causation entail the existence of backwards chances, inconsistent with many of these platitudes, notably Schaffer's Realization Principle, Future Principle, and Lawful Magnitude Principle) Maybe Barker-chance meets other platitudes; but will it be genuinely chance if it doesn't meet these platitudes or something like them? It looks like only a probability can play the chance role.

One last thing: in his discussion of apparently spontaneous uncaused events, Barker makes the point that even in those cases the structure of the entities involved can be the cause. He discusses a case of radioactive decay; the decay is, he says, caused by the structure of the element that decays. Fine; but he then says that if the decay does not occur, it is not caused by the structure of the element. This I didn't see: it seems to me that the chance of decay is fixed by the structure, so why not say it causes the lack of decay just as much as the decay? Barker says 'one could not say that there was no decay because [the element] was present'—but why not?

Defining Measures Over Spaces Richer Than The Continuum

Cian Dorr asked an interesting question in the comments of my previous post:

I wonder how you would do physics in a spacetime finite volumes
of which contain more than continuum many points? The physical theories of spacetime I'm familiar with are all based in ordinary differential geometry, which is about finite-dimensional manifolds, which by definition are locally isomorphic to R^n. I don't know how you'd begin to define, e.g., the notion of the gradient of a scalar field, if you were trying to work in something bigger.

I'm probably not comfortable enough with the maths to come up with elegant treatments of mathematics with higher cardinalities than the continuum, but here's one way of doing it, though it is a bit kludgy. Let us start with a space that has 2^continuum many points. Instead of defining the fields, measures etc. over points, define them over equivalence classes of points, where the equivalence classes contain 2^continuum-many points each. For example, the distance measure needed to get the right predictions in the physics we do doesn't treat as different all the points "around" a given point. (I’ll talk in this entry about “space” though the remarks will carry over straightforwardly to spacetime.)

You might wonder what right these so-called points have to be called "points" if e.g. a distance metric does not distinguish them. Why aren’t the equivalence classes better candidates to be identified as the "points"? But there are a few answers available: maybe there's also a more discerning and more natural function F from points to somethings that does distinguish the points inside our equivalence classes, and our distance measure is a crude abstraction from F that is good enough for practical purposes. Or maybe the natural relation in the area is not a function on equivalence classes, but a relation between points that is uniform across these equivalence classes: that is, when we have two equivalence classes C and D, then if any member of C stands in R to any member of D, then every member of C stands in R to every member of D. Or it should be easy enough to come up with other marks of distinction that the members of the equivalence classes have that make them better candidates to count as points than the classes - maybe the members are the ultimate parts of spacetime, for example, or maybe we have general reasons for thinking classes can’t be points.

So the members of the equivalence classes might be the genuine points, and arbitrary fusions of them might have a good claim to be regions, thus giving us more than Beth2 regions. But the physical theories need not operate very differently - it just turns out that where we treated our mathematical physics as defining fields, measures, etc. over points, it should instead be treated as defining those quantities over equivalence classes of points. Of course, we are left with the question of what the fundamental physical relationships are that we are modelling with our functions, but I hope I’ve said enough to indicate that there are a number of options here.

If the model I have just given works, then it will be trivial to carry out a similar procedure to generate models of larger spaces: simply ensure that the equivalence classes contain N points, where N can be any cardinal you like. It does not work as smoothly once each equivalence class has more than set-many points, though that raises quite different sorts of problems.

These models mimic standard physics, and for some purposes we might want to see what sorts of models of higher-cardinality spaces we could come up with that exploit the extra structure of those spaces to produce more complicated “physical” structures. But the sort of model I described should be enough to raise an epistemic question I alluded to in my previous post. If physics as we do it would work just as well in these richer spaces, why be so sure that we are not in one of these spaces? I think some appeal to simplicity or parsimony is good enough to favour believing we are not in such a higher-cardinality space. But I seem to be more of a fan of parsimony than a lot of people. This case might be another one to support the view that many physicists implicitly employ parsimony considerations in theory choice, perhaps even considerations of quantitative parsimony!