Determinism and Counterfactuals

There are many ways of defining the doctrine of determinism, but here's one that seems fairly straightforward, taken from the beginning of John Earman's book A Primer on Determinism:

World W1 is deterministic just in case for any physically possible world W2, if W2 agrees with W1 at any time as far as relevant physical properties are concerned, then W2 agrees with W1 at all times. [p. 13]

If we understand the notion of a physically possible world to be any world that shares the same laws of nature, then it is a consequence of this definition that if the actual world is deterministic, there is no physically possible world (except the actual world itself, of course) that agrees at any time with the actual world as far as relevant physical properties are concerned.  Or, in other words, if determinism is true, then every physically possible world must have a completely different past, present, and future.

So far so good.  But what I'm wondering about is what effect determinism in this sense might have on the proper analysis of counterfactual conditionals.  According to the (perhaps) most promising approach to counterfactuals, in order to determine whether the conditional, "If A were the case, then B would be the case" is true, one needs to look at those possible worlds which are closest to the actual world where A obtains to see if B also obtains.  If so, then the counterfactual is true.  Of course, figuring out which worlds are closest to the actual world is a vexed question.  But it seems to me that if determinism is true, the question becomes a lot more vexed than usual.

If determinism is true, which worlds are closest to the actual world?  Surely none of the physically possible worlds are that close to the actual world, since as we saw above, all of those worlds have a completely different past, present, and future.  But that means that the worlds closest to the actual world must have different laws of nature than the actual world.  But that would be quite odd, too, because there is a strong intuition to think that worlds which are not physically possible are actually irrelevant to the truth or falsity of a counterfactual conditional.  For instance, if I want to know what would have been the case if I hadn't gone to graduate school, I don't think I would be satisfied with finding out what happens in some world that doesn't share the actual laws of nature.  I want to know what would have happened to me, in this world, if I hadn't gone to graduate school.  But that's not the answer I get.

So I guess the problem might be put in the form of a dilemma.  Assume that the correct analysis of counterfactuals is the one sketched above.  Now, either the worlds closest to the actual world are the physically possible worlds or they're not.  But all the physically possible worlds have a completely different past, present, and future, so those worlds can't be closest to the actual world.  So, the worlds closest to the actual world are not the physically possible worlds.  But the non-physically possible worlds don't seem relevant to the truth or falsity of certain counterfactual statements.  So -- should we reject this analysis of counterfactuals?   What other options sound better?

Comments

[Kip Werking]

First of all, this strikes me as a bad definition of determinism, and for an obvious reason: determinism doesn't imply that two worlds with the same time-slice physical properties must come to those properties in the same way.

It just says that, if any two worlds come to the same time-slice physical properties in the same way, then they are the same world *from now on*.

To give an example: suppose I come to typing this message at point X after coming home from work in world A. Suppose I come to typing this message at point X after staying home all day in world B. Suppose further that, at moment X, the physical properties are identitical in both worlds. What determinism says is that from now on, A and B will be the same. But it doesn't, or shouldn't, say that A or B can't be deterministic because of the existence of the other. In other words, any definition of determinism shouldn't render it impossible that different deterministic worlds converge upon the same time-slice state at some point in their histories.

To give a simpler example: consider these 1D cellular automata:

World A Rule: X->Y, Y->Y
World B Rule: X->X, Y->Y

At the beginning of both universes, suppose that World A is in state X and World B is in state Y. At this first moment, A and B are different. But at moment 2, World A changes to state Y, whereas World B remains state Y, so that both world are now in state Y. More importantly: they will remain in state Y forever. Furthermore, the worlds are deterministic (as their simple rules make explicit). Yet it is not the case that A and B have agreed at all times.

[Paul Torek]

I think the best way to help someone who's having trouble understanding counterfactuals is to cash them out in terms of causal relationships. So I don't worry too much about the idea of which possible worlds are "closest" to the actual world. Still, I don't see Earman's definition of determinism as making the "closeness" problem any worse than it already is.

It's still possible to say that most (maybe even all) of the closest worlds share the actual world's laws, even if deterministic. True, as you point out, that means they must differ throughout history (ignoring Kip's point for now). But they needn't differ in terribly dramatic ways. From our human point of view, the differences could be terribly minor and boring. A slight, boring shift in the distribution of matter and energy through most of the universe's history, perhaps.

Also, an analogy - or is it just a case in point - off the top of my head. There are two identical twins, Ann and Barb. Barb has a small birthmark that Ann lacks, however, and this difference persists throughout their lives. In all other physical respects, let's suppose, they are perfectly matched.

There is also a goddess, Carol. At her creation she is like Ann. But as soon as Carol can formulate a thought, she decides to magically make herself the perfect duplicate of Barb, right down to the birthmark. She stays that way for the rest of her life.

Now, all things considered, who is a closer physical match to Barb, Ann or Carol? My intuition strongly favors Ann. In other words, better to differ a little throughout history than to differ a lot in the fundamentals of how one may evolve over time.

[Richard]

I would think that we are after "closeness" at the appropriate moment in time. I'm not sure why we should care if the counterfactual world needs to have had a different history and future in order to accomodate the particular counterfactual state of affairs that we're interested in (e.g. that you didn't go to graduate school). So long as that key moment is similar in the relevant respects, we can look at "what happens next" as being genuinely informative, I would think.

[Jeffrey Giliam]

Dennett in his "Freedom Evolves" used the good ol' "Game of Life" in order to demonstrate that while W1 being the same as W2 means that the futures of both W1 and W2 will be the same, we cannot say the same about their pasts. Thus I wouldn't say they agree at all times.

[Mike]

_So, the worlds closest to the actual world are not the physically possible worlds. But the non-physically possible worlds don't seem relevant to the truth or falsity of certain counterfactual statements_

I don't think this can be right on Lewis's account of similarity. If we are in a deterministic world then the closest worlds where you don't go to graduate school have a past very similar to ours. What happens when you do not go to graduate school is that a law is broken. Or rather, an "almost-law" is broken. This is not to say (as Lewis notes) that you are able to break a law (or that anyone can). Rather, you are able to do something such that were you to do it, a law would have been broken. In Lewis's terms "a minor divergence miracle" would have occurred just prior to your deciding not to go to graduate school (or not going to graduate school, whichever event we're talking about). But this is old news. See D.K. Lewis, 'Are We Free to Break Laws?' Theoria 47(1981).

[Joe]

I am so glad for this post, Neal! It allows me to explain the importance of Lewis’s ‘local miracles’ model. Consider the following counterfactual:

(CF1) If Bush had been caught in a sex scandal in the summer of 2004, then Kerry would now be President of the US.

According to Neal’s story, in assessing the truth of (CF1) we’re interested in the set of worlds that is closest to the actual world save for the fact that Bush is caught in a sex scandal. Call this set of worlds, G-worlds. Given determinism, the G-worlds are going to be different in many respects from the actual world. More specifically, each G-world will have different facts about the past or different laws of nature or both.

Following Neal and Paul, we might say that only worlds with the laws of nature of the actual world should count as close worlds. That suggests that the G-worlds will have different facts about the past than the actual world. Paul contends that the G-worlds “needn’t differ in terribly dramatic ways. From our human point of view, the differences could be terribly minor and boring. A slight, boring shift in the distribution of matter and energy through most of the universe's history, perhaps.” But what kinds of facts are the ones that are “terribly minor and boring”? The answer to this question is going to differ depending on which counterfactuals we are evaluating. In evaluating (CF1), facts about birthmarks seem unimportant but what about when evaluating this counterfactual:

(CF2) If Bush had a large birthmark on the side of his face in 2004, then he would not have been elected President of the US.

Intuitively, the facts that are “minor and boring” are just those facts that we deem to be causally or explanatorily irrelevant. And those facts will differ depending on the counterfactuals under consideration. Moreover, there are dangers of circularity here since one way of determining whether a given causal claim is true is whether it supports certain counterfactuals. Other questions arise, too, like how many “birthmarks” would it take to get a physically possible world in which Bush gets caught in a sex scandal? I’m not saying that these points negate the possibility of telling the story the way that Paul wants to tell it but it is clear that the story is going to get pretty complicated.

A better approach would be to allow for ‘local miracles.’ Roughly, the G-worlds would now include worlds that were identical to the actual world up to the time at which a miracle occurs. The miracle would have the same effect as the alteration of “terribly minor and boring” facts on Paul’s model, e.g., it would provide us with situations that are as close to the actual world as possible save for the fact that Bush gets caught in a sex scandal. Moreover, it is arguable that these G-worlds would be closer to the actual world than the G-worlds generated by Paul’s model, for large chucks of the actual past would remain intact. (I’m speaking very loosely here, of course.)

None of the G-worlds on the ‘local miracle’ model will share the laws of nature of the actual world, of course. But that does not mean that the causal or explanatory relations in these worlds will be substantively different. Consider, for instance, Russell’s five-minute world argument for skepticism about memories. Russell imagines that the world was created five minutes ago yet everyone was given false memories that suggest that the world is in fact much older. Call the possible world noted in Russell’s example, ‘Russell’s world.’ Russell’s world, thus, is exactly like the actual world from, say, the summer of 2005 on but shares little or none of the past of the actual world. Given that determinism is true, it follows that the laws of nature of Russell’s world are different from the laws of nature of the actual world. But, of course, the worlds might be very similar from a causal and explanatory point of view.

All of this invites a closer look at some of the criticisms of Lewis’s ‘local miracle’ compatibilism. The motivation for ‘local miracles’ is independent of considerations about the problem of free will and determinism. It just so happens that the model provides one with a nice response to the incompatibilist!

[Mike]

*Given that determinism is true, it follows that the laws of nature of Russell’s world are different from the laws of nature of the actual world*

Joe,
I can't see why the laws of Russell's world need be any different from the laws of the actual world. Certainly the past in the Russell world is shorter than the past in our world. But, given assumptions about it's "late" start, that does not entail that the laws are different. And given the principle of plenitude (assuming Lewis is right about this) it does seem that there is a world that begins at t is exactly like the actual world (laws and all) from t onward. Of course many of our memories will be false there.

Neal,
I should also have mentioned that Lewis gives some general weights and priorities governing the similarity relation among worlds in 'Counterfactual Dependence and Times Arrow'. Maybe you're already familiar with this. For instance, "big, widespread, diverse violations of law" yields serious and major dissimilarity. On the otherhand, small diverence miracles do not. In any case, according to Lewis.

[Joe]

Mike -- I was using Neal's definition of 'determinism.' I should have been clearer about that. Neal notes Earman. Van Inwagen gives a similar definition:

"Determinism is the conjunction of the following two theses: [a] For every instant of time, there is a proposition that expresses the state of the world at that instant; [b] If p and q are any propositions that express the state of the world at some instants, then the conjunction of p with the laws of nature entails q (van Inwagen, 1983, 65)."

This is not to say that the Neal/Earman/van Inwagen definition of 'determinism' is the best one, but that gets back to Kip's point. Kip suggests the following definition:

Determinism is the conjunction of these theses: (a) For every instant of time, there is a proposition that expresses the state of the world at that instant; (b') If p is a proposition that expresses the state of the world at instant t and q is a proposition that expresses the state of the world at instant t* and t < t*, then the conjunction of p with the laws of nature entails q.

One day Rob Cummins convinced me that the Neal/Earman/van Inwagen definition was right and the other was wrong but I can't remember why. Any help here?

[Mike]

"Determinism is the conjunction of the following two theses: [a] For every instant of time, there is a proposition that expresses the state of the world at that instant; [b] If p and q are any propositions that express the state of the world at some instants, then the conjunction of p with the laws of nature entails q"

Joe,
The PVI definition of determinism is consistent with holding that the actual world and the Russell world have the same laws from t onward (where t is the onset of the Russell world). There is no problem there, that I can see. Unless (and this would be very weird) PVI is claiming that Laws + P entails Q, even if Q precedes P temporally. But I don't think he can mean that.
I'm *guessing* is that the Earman definition is (perhaps slightly) misquoted. Earman is just too good to make a minor error, esp. a technical error. My guess is that what he had in mind by ". . .then W2 agrees with W1 at all times" was it agrees at all future times. Maybe that is clear in context. I don't have the text with me.

[Joe]

I don't have the Earman volume in front of me either, but I do have a copy of his "Determinism: What We Have Learned and What We Still Don't Know" where he notes "the Laplacian variety of determinism according to which the instantaneous state of the world at any time uniquely determines the state AT ANY OTHER TIME" (Campbell, O'Rourke, and Shier, p. 21, MIT Press, 2004; my emphasis).

Again, it is my understanding that this is the generally accepted definition, though the reason why escapes me.

[Mike]

You might be right about that. Browsing through the Lewis Papers Vol. II there is a somewhat similar bidimensional definition of determinism. Lewis attributes it Montague, Deterministic Theories ('68): "A deterministic system of laws is one such that, whenever two possible worlds both obey the laws perfectly, then either they are exactly alike throughout all time or else they are not exactly alike through any stretch of time . . They do not diverge and they do not converge." (37ff, "CD&TA"). No question that there is no divergence. It's less obvious why there is no convergence (or rather no complete convergence). There can certainly be many events that are the same at some t in w and w1 though those worlds will never perfectly converge at any t. This seems consistent with our world and the Russell world having the same laws and being identical from t onward, since the Russell world, by hypothesis, starts at t and is intrinsically exactly like our world at t.

[Eddy Nahmias]

If I'm remembering a conversation I had with Al Mele and Tom Crisp correctly, we decided, after much debate on this topic, that there are simply two ways of defining determinism, one that from a description of world at one time (Pt) and the laws of nature (L) entails description of world at ALL times (in both directions) and another that from Pt and L entails description of world only at later times. Kip's description and example of latter type is certainly coherent, as is the PvI/Earman type (it just adds a further constraint). I think we also decided that for the free will debate, the "forward-looking" determinism was sufficient to generate any incompatibilist arguments (though I'm not sure I'm convinced since I think the only Consequence argument that is valid requires using Beta-box and hence requiring that the description of the laws be a part of the description of the past--i.e., the "broad past").

While we're on it, I continue to be confused about two issues with determinism and solicit any help anyone can provide:
1) How exactly can a Humean about laws be a determinist?
2) Are the LAWS supposed to be deterministic or is the UNIVERSE supposed to be deterministic (and that is a feature that goes beyond the nature of the laws)? If it's the laws, it seems that the same laws could result in deterministic causal interactions in one part (or one time) in the same universe where they result in probabilitist causal interactions in another part (or time) of that universe?

I'm also interested in how much work is done in incompatibilist arguments by limiting (explicitly or implicitly) the laws to physical laws and excluding psychological laws. But I'll leave that one for a later post.

[Neal Tognazzini]

Just to clear up the terminology a bit. Earman (at least at the beginning of his book) does intend his definition of determinism to cover both the future and the past. He then goes on to say that his definition "can be broken down into two subconcepts" [13]. On the one hand, a world can be futuristically deterministic, and on the other hand, a world can be historically deterministic. But he means his general definition to be both. So when I posed the question, I intended to be speaking of a determinism that is both. But even if we disagree with Earman and think that the only kind of determinism is futuristic determinism, I'm still unclear as to how that would affect the problem about counterfactuals.

And, in case you are interested, here is an excerpt from Carl Hoefer's Stanford Encyclopedia entry on "Causal Determinism":

"For a wide class of physical theories (i.e., proposed sets of laws of nature), if they can be viewed as deterministic at all, they can be viewed as bi-directionally deterministic. That is, a specification of the state of the world at a time t, along with the laws, determines not only how things go after t, but also how things go before t. Philosophers, while not exactly unaware of this symmetry, tend to ignore it when thinking of the bearing of determinism on the free will issue. The reason for this is that we tend to think of the past (and hence, states of the world in the past) as done, over, fixed and beyond our control. Forward-looking determinism then entails that these past states -- beyond our control, perhaps occurring long before humans even existed -- determine everything we do in our lives. It then seems a mere curious fact that it is equally true that the state of the world now determines everything that happened in the past. We have an ingrained habit of taking the direction of both causation and explanation as being past present, even when discussing physical theories free of any such asymmetry."

For anyone not already familiar with his defense of compatibilism, Hoefer uses this very fact that determinism is a bi-directional doctrine to argue that it is just as appropriate to view the past states of the world as determined by our actions as it is to view our action as determined by the past states of the world. He calls his view "Freedom from the Inside Out", and I think the article can be found in an anthology about time edited by Craig Callendar, but I could be wrong about that.

[Mike]

Eddy,
Why should it be any more difficult for a Humean to be a determinist? You ask (1),
1) How exactly can a Humean about laws be a determinist?
But for Humeans--just as for everyone else--laws (i.e., non-statistical laws) are exceptionless regularities. It is just that, for Humeans, that's all they are. The laws are not necessarily true, but you don't need that for determinism to hold. All you need is wide-scope necessity. For instance, something like D is I'm sure available to Humeans.
D. (e)[](Laws(L1-Ln) & History (p1-pn)) --> e.

[John Fischer]

I have a discussion of the relationship between David Lewis's "local-miracle" view of certain counterfactuals and causal determinism in *The Metaphysics of Free Will.* Also, John Perry's article in the INPC volume is helpful.

I was amused to read an article in the June 2005 Scientific American that contends that the laws of nature are changing. Actually. And the point is not supposed to be epistemological. (They are not changing as fast as the weather in Chicago, but they allegedly change insofar as the "constants" in them change--are not constant!)

Oy weh!

[Joe]

Interesting comments, John! See more on Perry's article below.

Mike,

On July 7 you wrote: “This seems consistent with our world and the Russell world having the same laws and being identical from t onward, since the Russell world, by hypothesis, starts at t and is intrinsically exactly like our world at t.”

If one adopts the bidirectional definition of 'determinism,' then our world and the Russell world cannot both be deterministic and share the same laws and be identical at any moment of time. Let L be a proposition expressing the conjunction of the laws of nature in either world. Let A(t) a proposition that expresses the state of the actual world at instant t, and let R(t) be a proposition that expresses the state of the Russell world at instant t. Suppose, for reductio, that both worlds are deterministic and share the same laws. Suppose also that A(now) is equivalent to R(now), that is, that a proposition that expresses the state of the actual world at this very instant is equivalent to a proposition that expresses the state of the Russell world at this very instant. Let P be proposition that I made a pot of coffee 30 minutes ago. P is true (in the actual world) but false in the Russell world. All of the following cannot be true.

Given the above, all of the following are true:

A(now) & L entails A(30 minutes ago)
R(now) & L entails R(30 minutes ago)
A(now) is equivalent to R(now)
A(30 minutes ago) entails P
R(30 minutes ago) entails not-P

This is impossible. QED.

Eddy,

Note that in Neal’s quotation, Hoefer writes: "For a wide class of physical theories (i.e., proposed sets of laws of nature), if they can be viewed as deterministic at all, they can be viewed as bi-directionally deterministic.” This suggests that there are not really two definitions of determinism but one. I’ll work on this some more and hopefully have a post on it today or later this week.

In response to your first question, want to go on record as noting that the phrase "Humean about laws" is ambiguous and picks out a variety of different folks. Below are two distinct Humean theories, for instance.

H1: Laws are exceptionless generalizations.

The problem with H1, as Mike's definition of 'determinism' above indicates, is that genuine laws seem to have a modal component. Laws are not mere generalizations they are generalizations that must hold, in some sense. Hume himself noted this, which is why he would have opted for a stronger theory (I'm speaking very loosely here since Hume talked mostly about the cause-effect relation, not laws of nature).

H2: Laws are exceptionless generalizations that we use to form our expectations.

According to H2, what makes the law of gravity a law and the generalization that all US presidents are men a mere generalization is that in the former case the true generalization is coupled with the expectation of, say, things falling down given that they been thrown in the air, whereas in the later case no such expectation is present.

One who adopts H2 accepts what John Perry calls “a weak conception of laws” (“Compatibilist Options,” in Freedom and Determinism, eds. Campbell et. al. pp. 237 ff.). Such a view is stronger than H1, since it rejects the claim that laws are mere generalizations, but weaker than a more metaphysically robust conception of laws. As Perry writes: “More is required: that we use [the generalization] to form our expectations. But that’s all. There is no big metaphysical condition, like a command from God, that is also required” (p. 239).

In any event, a Humean theory like H2 is able to distinguish genuine laws from mere generalizations and can, therefore, endorse something like Mike’s (D). It should be noted that one might still be a determinist even if he accepts H1. But in this case the problem of free will and determinism seems indistinguishable from the problem of fatalism.

In response to your final comment, you should see Jonathan Westphal’s “A New Way With the Consequence Argument, and the Fixity of Laws” which came out in Analysis in 2004 or so. Westphal claims that van Inwagen’s argument suffers from the fallacy of begging the question for reasons similar to those lurking behind your comment.

[Joe]

The Westphal paper is in Analysis 63.3 (July 2003): 208-212.

[Mike]

Joe,

That sort of argument occurred to me. I'm unpersuaded. Here's why. Let w0 be a possible world at t and t'. The big bang happens at t, w0 time, and time begins at our world @. The big bang happens at t', w0 time, and time begins at our world @'. Do I have any reason to believe that the laws at @ *must be* different from the laws at @'? Do I have any reason to believe that had the big bang not happened *precisely* when it did, our laws would be different? Well certainly bidirectional determinism gives me no reason to believe that. Bidirectional determinism concerns law-governed causal relations in time (and space). But there isn't any time before the big bang. So I can't see how determinism entails that @ and @' can't have the same laws.
-------------
On a different point you say,
"H2: Laws are exceptionless generalizations that we use to form our expectations.
According to H2, what makes the law of gravity a law and the generalization that all US presidents are men a mere generalization is that in the former case the true generalization is coupled with the expectation of, say, things falling down given that they been thrown in the air, whereas in the later case no such expectation is present."

By "mere" generalizations I take it you mean 'accidental generalizations'. But accidental generalizations support expectations, certainly. It is an accidental generalization that my dog greets me at the door everyday. And I can certainly form reliable expectations on that basis. It is an accidental generalization that every brick in my house weighs less than 40lbs. But I can form reliable expectations about the bricks in my house on that basis. That is, given that X is a brick in my house, I reliably expect it to weigh less than 40lbs. But maybe you weren't defending this view.
Typically the difference between laws and accidential generalizations is that the former (but not the latter) support the relevant subjunctive conditionals. But even then, much more refinement is necessary. Certainly the accidential generalization "were X a blade of grass on Mr. Grasscutter's lawn, X would not be two feet long" is true and supported by the accidental generalization that Grasscutter's lawn is always neatly mowed. Not easy to make that distinction between laws and accidental generalizations.

[Joe]

Mike,

Thanks! Let me think about the first point. I'll get back to you on that.

I agree entirely with the second point. I didn't mean to suggest that H2 was a good theory. My main point was that (1) H2 is close to Hume's own theory, (2) H2 is distinct from H1, and (3) H2 is a Humean theory of laws of nature that justifies some modal form of determinism like your (D). I also suggested that (4) H2 allows one (e.g. Hume) to distinguish between accidental generalizations and laws of nature but your points suggest that that is not quite right. Thanks again!

[Jonathan Farrell]

This is going back a few posts to the issue of whether determinism entails a closed past (i.e. one possible past given that the universe is as it is at present) or only a closed future. It seems to me that Joe is correct to suggest that there’s only one definition of determinism, but it doesn’t seem that acknowledging this allows us to resolve the issue of whether or not the past is closed under determinism.

I think that Kane gets it right when he says that determinism is “a kind of conditional necessity that can be described in a number of ways.” (p8 ‘The Significance of Free Will’). So Y is determined if the conditional ‘X then Y’ is true (and if X is the case). Depending on what X and Y stand for then, we can come up with all sorts of different kinds of determinism. For example, where Y is ‘event y occurs at time t1’, then if X is something like ‘God decrees that y occur at time t1,’ we have theological determinism. If X is something like ‘“y occurs at t1” is true, and the principle of bivalence is true,’ then we have logical determinism. And if X is something like ‘event x occurs at time t0 and the occurrence of x at t0 causes that of y at t1’ then we have causal determinism (and it seems to be this kind of determinism that is usually being referred to when people talk about (FW/MR and) determinism).

Whether or not two deterministic universes with the same laws and the same present state must have identical pasts depends on what kind of things X and Y are – i.e. depends on the kind of determinism we are talking about. As Neal points out above though, it’s not clear that what we can say about counterfactuals will depend on the kind of determinism we are considering.

[Neal Tognazzini]

John,

Actually, what got me thinking about some of these issues was your discussion in The Metaphysics of Free Will about 'can' claims and corresponding backtracking conditionals (in the same general area where you discuss Lewis' local-miracle compatibilism). Here's a pair of statements you use:

1) The Salty Seadog can go sailing at noon.
2) If the Salty Seadog were to go sailing at noon, then the weatherman would have told him at 9:00 that the weather would be fair at noon.

Your suggestion in the book is that we evaluate the truth of (1) while holding the past and the laws fixed, but that we evaluate the truth of (2) without holding the past and the laws fixed.

Part of my question came from the fact that it seems really weird to me NOT to hold the past and the laws fixed when evaluating the truth of a counterfactual conditional such as (2). In fact, it seems to me that any adequate account of counterfactuals better not count (2) as ever being true (at least when evaluated at any time prior to the Seadog's going sailing), precisely because my intuition is that the past and the laws should be held fixed while evaluating these future-oriented counterfactuals. But maybe that's just the incompatibilist in me coming out.

[Mark Smeltzer]

Given the degree of complexity involved in any of the contemporary (competing) theories of elementary physics, regardless whether these theories are viewed (prospectively) as being normative or descriptive in nature and regardless of whether a particular theory entails deterministic elementary interaction, it almost goes without saying that given any particular state of affairs S there will be a set of prior states of affairs which (can) yield S and this set will vary in size from one to infinity.

The ability to apply a function in reverse requires that the function has an inverse function for a given domain; functions which satisfy this condition for a given domain {x,y} are "regular" in that domain and functions that satisfy that condition across the domain {-∞,∞} are regular simplicter.

Given the complexity of any of the contemporary theories, it is implausible that the set of functions which jointly circumscribe events at the elementary level (whether normatively or descriptively) will be regular functions, or that the domains will happen to be limited such that they can be treated as regular functions. (Even a function as simple as F(x) = x^2 is irregular, except when limited to the domain {0, ∞}.)

[Mark Smeltzer]

I didn't mean to kill the conversation ;)

[Paul Torek]

Mark,

Large parts of physics (don't know about the whole) are time-reversible. For example, optics. I use the principle of time-reversibility of optical processes often. (I'm not a real optical engineer, but I play one at work.) So, it looks like optics does use regular functions to map one time to another. That doesn't mean it can't use irregular functions to map, say, field strengths to particle locations. That would not pose any inconsistency - I think.

Joe,

I probably ought to resist the temptation to discuss "minor miracles", but my will is weak. The reason I ought to resist is that I think our cognitive grasp on counterfactuals comes entirely from our understanding of causal (and logical) relationships. If I'm right, the project of giving a counterfactual analysis of causation is hopelessly circular at best, bass-ackwards at worst. Discarding that project, the metric of possible world closeness loses much of its interest. But perhaps not all. Let that be my excuse, then: perhaps not all.

Suppose the causal laws of the actual world form a very elegant, coherent package. In that case, even minor tinkering with the laws to describe a different possible world can seriously mar that beauty. (In your mind's eye, picture a perfect tetrahedron with equilateral sides. Now distort it ever so slightly. Wasn't that a horrible thing you just did?) In an intuitively compelling sense, small changes in the laws simply are not possible. A "small" change is a big change.

[Mark Smeltzer]

Paul,

The example you mentioned is, in essence, the idea that we can calculate the intersect between two data sets -- one resulting from a regular function, and one from an irregular function -- and use that result as a bounds to yield precise conclusions from what began as a hopeless mess. I'm not trying to argue otherwise. However, even if we could (conceptually) use this method to work a calculation backwards through time, it doesn't seem to imply two-way determinism so much as it does that we're pretty clever.

(That said, while I find the discussion very interesting, I've never thought the distinction between one-way and two-way determinism mattered much.)