Saturday, February 28, 2009

Barker on Chance and Cause

In our dispositions reading group, we've been reading some of the papers from Toby Handfield's recent OUP collection Dispositions and Causes. Yesterday Luke Glynn, Barbara Vetter, Alastair Wilson and myself discussed Stephen Barker's paper 'Leaving things to take their chances: Cause and disposition grounded in chance'. We had a number of concerns about the argument. I'm going to skip our worries about what seems to be significant circularity in the account, and the fact that in abandoning the claim that chances are probabilities, Barker leaves a central plank of his thesis fatally unclear.

What I want to discuss are Barker's central claims connecting chance and cause, which he calls CC1 and CC2.
CC1: If c causes e, c contributes to the chance of e at tc, the time at which c occurs.

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.
We found both of these principles objectionable. In this post I'll discuss some of our worries about CC1; I'll discuss CC2 in a later post I hope.

Discussing CC1, Barker says:
The general argument for CC1 might be summed up thus: causes explain their effects. If c causes e, then c explains e, and thus, at time t, c is a potential explanation of e. How then can c at t not contribute to fixing the chance of e at t?
The obvious problem we saw with this argument came from cases like Hesslow's birth control pill example, where it could be that taking the pill causes thrombosis despite the fact that it makes no difference to the chances of an individual getting a thrombosis (because it exactly balances the risk, by inhibiting pregnancy, a potent promotor of thrombosis), and hence doesn't make a contribution to fixing them at their actual values—or, at least, no more of a contribution than non-causes do. Perhaps Barker is using 'fixing the chance' in some non-standard way, but he gives no indication of doing so

There are other problems too. If backwards causation is possible, as seems plausible in light of the possibility of time travel (and perhaps of some interpretations of quantum mechanics, such as those Huw Price has defended), then CC1 entails that some past events have non-trivial chances. But how can this be? If H is the history up until t, then no matter how or whether history fixes chances, it should be that the present chance of an event in a world w should be the same as the chance conditional on the history:
  1. Chwt(A|H) = x and H is true iff Chwt(A) = x.
(1) doesn't commit us to a Humean picture of chance; its simply the thought that conditioning the present chances on the actual history shouldn't give different chances. (1) entails that if H implies A, then the present chance of A is 1; so the past isn't chancy after all. Barker's response to this line of objection will presumably be to reject the thought that all past events are in the history; if c causes e, and e is in the past, then e won't be in the history. But I am at a loss to understand how this is supposed to work.

Barker mentions Lewis in this connection, as someone who accepts (1), and says
The spirit of CC1 is that there may be non-trivial backwards-directed chances. Lewis then must be wrong to have taken this line. Indeed, it is not clear why he takes it. Lewis accepts a chance-raising view about causation, and embraces the conceptual possibility of backwards causation.
But Lewis does not accept a chance-raising view about backwards causation—in that case he explicitly thinks that (the ancestral of) regular non-backtracking counterfactual dependence is what enables prior effects to be caused (this is the case where a non-backtracking counterfactual just happens to have an antecedent made true after the time the consequent is made true, and doesn't have the evidential reading of backtracking counterfactuals). So I'm left no happier with CC1 despite these remarks about Lewis.

There are other worries about CC1 (e.g., Barker's invocation of infinitesimals despite the fact that it is no longer clear whether they can help with the problems of zero chance events, as Williamson recently argued). But I'll leave them, and invite comments on these problems here. Any defenders of CC1? I'm aware that the considerations I gave in favour of (1) aren't completely compelling, so anyone want to argue against it?

Thursday, February 26, 2009

How Many Regions of Spacetime Actually Exist?

I’ve been wondering how many regions of spacetime there are in the world. As often happens with philosophy, after thinking about the question I have no very firm opinion. But I think I can see what the plausible options are. So I thought I’d throw out a few of them, and commenters can tell me whether I’ve missed any important ones. I’d also be interested in what people think the right answer to the question is (I’ve indicated below what I’m guessing the majority answer will be.) For my purposes here I’m prepared to count both spatial regions and temporal regions as spatio-temporal regions, so if you believe in space and not time, for example, you may still believe in a lot of spatiotemporal regions in this generous sense.

Here’s what seems to me to be the main plausible options:

Zero: You’re likely to answer zero if you think that relationalism about spatiotemporality is true: that is, there are no pieces of space and time, just spatial and temporal relations between things. I suppose you might also answer zero if you think that ultimately science will reductively eliminate space and time in terms of some sub-spatiotemporal structure in the world.

One: I think this is probably the least plausible answer on this list. You might think the answer is one if you think spacetime is an _ens totum_ in a way that doesn’t even allow for sub-regions. Or you might think the answer is one if you’re a certain kind of monist.

A Large Finite Number: This covers a lot of options! When trying to work out which large finite number, the following considerations seem to be relevant:

1) Are there scattered sub-regions? I believe in unrestricted fusion for regions, but some people might not, if you think that the regions must all be connected, or have to partially be all at the same time, or something else. If you do believe in unrestricted fusion for regions, then that will put a constraint on the cardinality of regions: whenever the cardinality of jointly non-overlapping regions is N, the cardinality of regions altogether will be at least 2^N-1.

2) What is the size of the smallest regions? I think science is pointing us towards thinking the smallest regions of spacetime are a planck-length across and a planck-time long, which puts about 10^42 of them in each metre. But if you think the minimum size is bigger, or smaller, that’ll obviously make a difference to your final count.

3) How big space is and how long time is. If space or time was infinite in the large, then even if there were minimum-sized regions, the total number of them would be infinite. At least unless presentism or something were true - if space was finite, but “time was infinite” as the presentist understands that expression, we still wouldn’t have extra regions in the past or the future. Even if some sort of growing-block view were true, we could ignore an infinite future in our calculations, and just have to worry about past and present spatio-temporal regions.

A week ago I would have guessed the total number of space-time regions in the actual world was something less than 2^10^100. More even than the national debt of the USA, but significantly less than one googolplex.

Continuum-Many: If spacetime regions have a minimum, non-zero, non-infinitesimal size, then if spacetime is infinite in the large in the standard way (i.e. aleph0 metres or seconds), and we have unrestricted composition for regions, then the total number of spacetime regions will be 2^aleph0, which is the cardinality of the continuum. If forced to guess, this would be my current guess. You might also think this if you believe there are a continuum of distinct space-time regions in a small space-time region, but you do not think that unrestricted composition for regions is true.

Beth2: That is, 2^continuum many. I think this by far the most orthodox answer: if you think that space and time are made up of points in the usual way, or even gunk in the usual way, and you believe in unrestricted composition, then this seems to be the obvious way to go. If you have those common assumptions, it probably won’t matter to you for these purposes whether there are an infinite number of seconds in the universe, or an infinite number of metres. I predict this is the popular favourite.

Greater than Beth2, smaller than the first strongly inaccessible cardinal: This option doesn’t get a lot of love, but I don’t know why not. Why are the people who are so sure that there are points of space and time so sure that there is only a continuum of them in a metre or a second? There is a parsimony argument for picking the lowest infinity that will do the job, and I like those kinds of arguments, but does everyone else?

(Why stop at the first strongly inaccessible cardinal? No very good reason - though you’ll think it itself isn’t a great candidate, if you think the cardinality of regions is 2^(cardinality of points))

Proper class many: Maybe the spatial continuum has a greater cardinality than any set. Pierce thought something like that, though I don’t know anyone alive who does. Doing measure theory will be awkward if there are this many.

“More than proper class many”: if you think there are proper-class many points and you believe in unrestricted composition of regions, and that any fusion of points determines a region, you end up here. You might want to deny there’s a cardinality of regions at all if you think this, hence the scare quotes.

I’ve left out options for potential infinities, ontological indeterminacies and Meinongianism - this post is already too long!

Laws, Counterfactuals, and Essential Properties

I find it curious that nobody seems to be particularly bothered by the fact that the following three commonly-held and seemingly plausible theses seem to be somewhat at odds:
  1. Unlike accidental generalizations, nomic generalizations support counterfactual conditionals. (So, for example, if it is a law that copper is a good conductor, then, if this piece of wood was made of copper, it would be a good conductor.)
  2. Some properties are essential to their bearers (So, for example, it is metaphysically impossible for this piece of wood to be made of anything other than wood and a fortiori to be made of copper).
  3. Counterfactuals whose antecedent is necessarily false are vacuously true.
The conflict seems to arise from the fact that, since laws of nature often involve essential properties, if (2) and (3) are true, (1) would not seem to be generally true--many accidental generalization would seem to support (vacuously true) counterfactuals just like nomic generalizations do.

Now, I'd be curious to hear which one(s) of the above theses (if any) the readers of this blog think should be amended/rejected in order to resolve the conflict and why. (I do have a main suspect, but, in order to avoid skewing my little survey, I'm not going to reveal its identity for the moment).

Monday, February 23, 2009

Was Lewis wrong or a relativist about counterfactuals?

David Lewis persuasively argued that counterfactuals are sensitive to context. As a consequence, Lewis claimed, counterfactuals don’t obey rules that other types of propositions do, like antecedent strengthening, hypothetical syllogism and contraposition. (From the fact that, were I to strike the match, it would light, it does not follow that, were I to strike the match and were I underwater, it would light.)

Just how is context relevant? Let’s make two distinctions. First, distinguish between a counterfactual sentence, “P > Q”, and a counterfactual proposition, {P > Q}. (I can’t quite figure out how to use the less than sign for some reason, as is typical to denote a proposition, so I’ll use curly brackets.) Second, distinguish between relativism and contextualism. According to relativism, a given proposition {P} might be true in one context, but false in another. (Note: I’m speaking of the proposition; one and the same proposition can be true in one context but false in another.) According to contextualism, a given sentence, “P”, might express one proposition in one context and a different proposition in another context.

I should note two things about these definitions. First, I don’t know if they are the standard uses of the terms “relativist” and “contextualist”. But they sound appropriate to me, so I’ll use them here. Second, relativism and contextualism are independent. One could deny both, accept one but not the other, or accept both.

There are at least two ways context might be relevant to counterfactuals: 1) In determining the truth conditions for a given counterfactual proposition; 2) In determining which counterfactual proposition a given counterfactual sentence asserts.

Suppose that Lewis was a contextualist but not a relativist about counterfactuals. Context determines when a given counterfactual sentence expresses a given counterfactual proposition, but the truth conditions are fixed for counterfactual propositions. Were that Lewis’ view, then he would be wrong about the failure of, say, weakening with respect to counterfactuals. That’s what Berit Brogaard and Joe Solerno argue in “Counterfactuals and Context” (Analysis, 68(1), 2008). After all, when examining an argument for validity, we don’t allow context to shift from premise to premise or between premises and conclusion. Suppose I utter the words “I am hungry,” and you utter the words, “Therefore, I am hungry and tall.” If validity didn’t require us to hold context fixed, we’d have a counterexample to and introduction. Yet all of the supposed counterexamples to, say, antecedent strengthening, involve a shift in context. Moral: If Lewis is a contextualist, he was wrong to think that antecedent strengthening, hypothetical syllogism and contraposition are invalid.

Suppose we hold fixed, then, that Lewis believed these arguments invalid (and that he didn’t hold a false belief!). Then Lewis must have been a relativist about counterfactuals. Or is there some other option?

Friday, February 20, 2009

Proxy "Presentism"

Proxy “actualism,” as defined by Karen Bennett in her article by that name, is roughly the view that while everything that exists is actual, everything—even what could exist but doesn’t—has proxies that do exist. Every possible thing has a proxy that actually exists. (For Plantinga, my essence is my proxy; for Linsky and Zalta, I, when I am nonconcrete, am my proxy.)

Bennett argues that proxy “actualism” is not actualism. In drawing a sharp distinction between two sorts of things that actually exist, the proxies and the objects for which they are proxies, the proxy “actualist” introduced two domains of quantification, just as the possibilist does. The proxy “actualist” has simply moved the distinction between merely possible and actual individuals into the actual world.

Let proxy “presentism” be roughly the view that, while everything that exists is present, everything—even merely past and future objects—has a proxy that presently exists. While I’m not certain, I’m inclined to think Crisp’s view and the view offered to the presentist by Merricks in Truth and Ontology are each a version of proxy “presentism”.

Question: Isn’t proxy “presentism” just as presentist as proxy “actualism” is actualist? That is, if proxy “actualism” is not actualism, then isn’t proxy “presentism” not presentism?

Wednesday, February 18, 2009

Truthmaker Maximalism Without Remorses?

Let truthmaker maximalism be the view that every true truthbearer has a truthmaker and let me put aside questions about the nature of both truthmakers and truthbearers and assume, for the purposes of this post, that truthbearers are propositions and that truthmakers are ordinarily facts. Now, according to naive truthmaker maximalism (NTM), the proposition that p is true if and only if it is a fact that p. For all its naivete, NTM seems to be a nice, simple view of truthmaking. However, most truthmaker maximalists seem to be unwilling to embrace it, mostly because they seem to feel uneasy about admitting in their ontology certain kinds of facts as the truthmakers for certain uncontroversially true propositions. Two standard examples of facts truthmaker maximalists seem to be queasy about are negative and general facts and quite a bit of ink has been spilled in an effort to explain how (some) negative and general propositions can be true in the absence of negative and general facts.

The problem is that all these attempts sacrifice much of the simple charm of NTM to a worry I can't really understand because I still don't get what's so wrong with, say, negative and general facts. Yes, unlike Quine, I don't have a love for desert landscapes but not many metaphysicians seem to love them these days and, of course, I would have problems with someone thinking that negative or general facts are fundamental facts, but I don't see any problem with the view that such facts supervene on more fundamental, more respectable facts. In fact, as far as I can see, if you think that something makes true the propositon , that something better be the fact that Socrates is not a fool. So, if you and I are both remorseless truthmaker maximalists and we both agree on which propositions are true and which are false, we should also agree on what facts are there even though we might disagree as to which of those facts are fundamental and which are not. In general, if you accept that a propositions <p> is capable of being true or false, you should also accept that there is a fact of the matter as to whether it is true or false and that this is the existence or non-existence of the fact that <p> not whether or not its fundamentality.

Maybe I'm wrong in assuming that NMT has become a minority view among truthmaker maximalist (please let me know if you think my perception of state of the play is somehow distorted), but, if I'm not, can someone please explain me what's so wrong about superveneint negative and general facts that makes it preferrable to abandon a view of truthmaking as nice and simple as NMT rather than admitting them in one's ontology?

Tuesday, February 17, 2009


Well, this post is just to break the ice and get this blog rolling. Matters of Substance is meant to bring together people working in metaphysics and provide a forum for discussing ideas, exchanging information, and commenting about the status of the field.
Now, without further ado, let's start blogging!