Cian Dorr: Against Counterfactual Miracles

Cian Dorr writes, in the recent paper Against Counterfactual Miracles,

“It is natural to suppose that if…say, you had blinked one more time than you actually did while reading the previous sentence–the state of the world in the distant past would still have been…as it…was. … But if determinism is true….”

There is something slightly paradoxical going on here. In evaluating a counterfactual, we are, according to orthodoxy, put upon to alter the actual world as meagerly as possible while making the antecedent true, then judge the truth of the counterfactual according to whether the consequent is true, subsequent these alterations. But unless we change the laws underwriting determination, we need to alter the past in order to account for the extra blink.

The problem is general, of course. It infects at least those counterfactuals whose antecedents aren’t chance events. All counterfactuals, if determinism is true. Is it? Dorr writes:

“determinism…is a live possibility, one  that many physicists and philosophers of physics take quite seriously. So it is not a merely academic exercise to investigate which of our ordinary beliefs are consistent with it.”

I would urge an interpretation of counterfactuals on which the issue of determinism becomes a red herring. In particular, I would urge that when we imagine incorporating truth of the antecedent into actuality, we do so in a way that only fixes the epistemic position of the speaker.

On a certain view, this seems like a non-starter. On the table is

A♠ 9♠ 8♣ 9♥ 3♠

John, holding A♦  A♥, goes all in, whereupon Matt goes into cardiac arrest and dies. John then says, rather insensitively, “if Matt had called, I would have taken his money”.

On just about any extant view, this counterfactual appears to be true if and only John had a stronger hand than Matt, i.e. if Matt was not holding 9♣ 9♦.  In particular, its truth appears not to be a function of John’s epistemic situation….it depends on facts about the world that John doesn’t know. Apparently, then, I am surrendering the view that counterfactuals have truth conditions, and/or that their meaning is closely related to truth, or to when or how they are true.

So what did John mean by “if Matt had called, I would have taken his money”? We can imagine saying to him in reply “you don’t know that, John.” To which he might say “Well, no…I don’t know it.” (Is this merely contextualism?) Why then did you say it, we should then ask, to which we might get “I said it because, most of the time, when you’re someone like me playing against someone like Matt in situations like this with those cards up and you have aces full and go all in and the other guy calls, you take his money.” Most of the time, then. Not all. Indeed…not even this (ostending some counterfactual) time.

Is this a breed of unfashionable internalism? I don’t mind being unfashionable. (In fact, I tend to prefer it.) I just don’t want to get in trouble later on.

Maybe I will get in trouble later on, but for now, I’m doing quite well, for by “if I had blinked twice (rather than once, say), then the past would have been the same” just means something like “most of the time, when someone like me blinks twice in a scenario epistemically similar to mine, the past turns out to the be same”. Which is clearly just wrong. All of this squares with my own intuition.

I realize it will not square with everyone’s. Here, though, is some therapy. There is a strong conversational norm against asserting that which you don’t know to be true. (It’s not quite lying, but it’s close.) On the orthodox view, John would be in  violation of this norm in avowing “if Matt had called, I would have taken his money”. For he is clearly in violation of this norm in avowing “my hand was stronger than Matt’s” (he knows no such thing) and, on the orthodox view, these are truth-equivalent. But (I claim) our intuitions suggest that John is not in violation of this norm. What John’s words indicate is something a bit vaguer. Something along the lines of “I had a good hand” or “I wasn’t bluffing” or perhaps just “I think I had a better hand than Matt”.

Why “if Matt had called, I would have taken his money” is more assertible here than “I had a better hand than Matt” is something of a mystery, for if any counterfactual has truth conditions, this one does, and every semantics (that I know of) would agree on what they are. I believe the moral is that the two avowals aren’t truth-equivalent, and the only way I can imagine that being the case is if the counterfactual has no truth conditions at all.

Or: whatever I mean by “if it had been the case that F then it would have been the case that G”, it’s surely going to turn out to be something I think I know. (Otherwise, why exactly am I saying it.) So “given what I know” is implicit. It’s what I know that’s relevant to the fact that at least most of the pertinent F worlds are G worlds. In this case (thinks John) the fact that I have cards that win most of the time in scenarios like these.

But, I’m getting sidetracked. Let me try to get back on the paper. Dorr gives an example from Frank Jackson:

a. If I had jumped out of this tenth floor window, I would have been killed.

b. If I had jumped out of this tenth floor window, I would have done so only because someone had put a safety net in place.

On the similarity interpretation of counterfactuals, both a. and b. seem to have valid readings. (This is one of the big problems with the similarity interpretation…there are too many viable choices for a similarity metric.) The b. reading requires what Dorr, following Lewis, calls “backtracking”. In finding a similar world or worlds, one allows oneself to significantly alter the past. Presumably, worlds where there are some people who fear that I might be suicidal are more similar to ours than are worlds where I am suicidal. Now you have to decide whether backtracking is legitimate.

Which I think is fairly hopeless. “Similar” can mean too many different things. My own interpretation of counterfactuals is in no such trouble here. Since I am implicitly fixing my own epistemic position, b. has no viable reading. It would, in particular, be weaker to avow “If my epistemic position had been the same and I had jumped out this tenth floor window then my epistemic position would have been different”.

Hmm. There’s some subtlety here. I want to allow an epistemic reading of something like “If  had looked at that card, I would now know who the messenger is”, which seems to be stronger than “If my epistemic position were the same and I had looked at that card, my epistemic position would be different”. Though this is to say different now, not different at the moment where the counterfactual and the actual diverge. Hence “If my epistemic position were the same then and I had looked at that card, my epistemic position would be different now“. What it seems we want to fix is my epistemic situation at the moment of divergence.

Again, though…there are traps. How about “If I had known then what I know now, I would not have married Jane”. Clearly that is a valid counterfactual, but a satisfactory reading of it requires us not to fix my epistemic situation at the moment of divergence. Or does it? Maybe it doesn’t. My epistemic position is the same up to the moment of divergence…said divergence being the point at which I counterfactually learn then what I actually know now.

The apocryphal analysis is just as before. What I know now is that Jane is DKL-positive. (DKL is a dread virus that causes one to mishandle analysis of counterfactuals.) If I had know that then, it would have to have been (according to the apocryphal analysis) because I was also DKL-positive (you can only learn this sort of thing at a DKL-ics anonymous meeting, it seems), and so I would have married her anyway.

So…no backtracking! Not in any way that affects my epistemic situation prior to divergence, that is…though the divergence itself may involve a counterfactual epistemic position. What is distinctive about the epistemic perspective, then, is that I am free to backtrack the hidden variables, (if determinism is true) as freely as others evoke counterfactual chance outcomes (should it be false). At any rate it doesn’t really matter whether the relevant variables are merely hidden (determinism) or generated on the fly (chance). And plainly it should not matter!

This is the sense in which determinism is a red herring.

Okay…Dorr wants ultimately, he says, to hang blame on the following:

Past: Necessarily, whenever x is normal at t, there is a true history-proposition p such that p would still have been true if x had blinked at t.

He writes:

“We will be tempted to dismiss Past on the basis of our reactions to sentence like (2):

(2) If determinism is true and x does not blink at t, then if x had blinked at t, that would have been because of a prior history of determining factors differing all the way back.

(2) sounds incontrovertible and is plausibly true on its most natural interpretation.”

Whereupon he strikes an analogy between (2) and b. above and prescribes that all counterfactuals will be parsed in the spirit rather of a. The expedience of the epistemic perspective is now completely clear, as (2) no longer reads as “incontrovertible” (mostly it just reads as improperly formulated, i.e. confused) and no such prescription is necessary.

Now we come to footnote 5, which I reproduce in full.

“5. Note that the following also sounds obviously true:

(2′) If determinism is true and x does not blink at t, then if x had blinked at t, a miracle would have to have occurred.

Although I hold that Past fails in ordinary contexts, I am inclined to think that (2′), like (2), is true in the context it most naturally evokes. Lewis’s dichotomy between “backtracking” and “standard” contexts is not particularly helpful here. I believe the explanation turns on subtle ways in which epistemic necessity modals (like “have to”) can serve to signal that certain other propositions, serving as premises from which the asserted content can be inferred, are to be taken for granted.”

There are several issues here. First…what is a miracle? It can’t be a counterexample to a strict law–strict laws don’t admit of counterexamples. It can’t be an exception to a ceteris paribus law–exceptions to ceteris paribus laws aren’t miraculous. I think I see a way to make sense of “miracle”, but it requires my favored metaphysics. A miracle is an event of probability zero. The idea here is that the universe is infinite, admits of densities, and that the density of any metaphysically possible event is positive. Events that are of zero density are not metaphysically possible. If they do occur, however (with density zero), then I’m willing to let those occurrences be “miracles”. I’d bet against long odds that there are no miracles. But…who knows.

Of course there’s something funny in my terminology. If there are miracles, then they are actual but not metaphysically possible! Some better terminology is perhaps advisable, though if I am right and there are no miracles then the metaphysically possible and the actual coincide. Though…wouldn’t that be a relief? The notion of metaphysical possibility is rather vague in the hands of philosophers. (I don’t think anyone knows what in hell it means. Not to say this makes it any different from most extant philosophy!)

But getting back to (2′)…it’s bad enough that we had to worry about backtracking and standard contexts. Now we have some new ones, apparently? This is further evidence that the epistemic perspective is preferable.

The fourth section of the paper is fairly wild. Recall the counterfactual

“If Nixon had pressed the red button there would have been a nuclear war.”

This is often taken as a problem case for the Lewisian similarity analysis: worlds where there is a short in the wire preventing the signal getting through appear closer to ours than those where the mechanism functions properly and Armageddon follows. Lewis wants a similarity metric on which the counterfactual comes up true. So a “similar” world will be the same up to a time very close to the actual non-pressing of the red button, then a “small miracle” will occur and the red button will be pressed. Then we just follow that course according to physical law.

Lewis does explore the possibility of avoiding the small miracle with miniscule past differences. A naive solution would be to opt for some smallish differences in the past that eventually manifest in the pressing of the button. Lewis sees problems here. Dorr quotes him thus:

“…there is no guarantee whatever that [a world where the actual laws are true and were Nixon presses the button] can be chosen so that the differences diminish and eventually become negligible in the more and more remote past. Indeed, it is hard to imagine how two deterministic worlds anything like ours could possible remain just a little bit different for very long. There are altogether too many opportunities for little differences to give rise to bigger differences.”

Dorr disagrees:

“But…Our best deterministic physical theories have continuous dynamics, which means that so long as the past is not infinite, we can always find a nomologically possible world that stays arbitrarily close to the actual world throughout any finite initial segment of history, just by choosing an initial state that is close enough to that of the actual world. (paragraph) This is worth making precise. … (follows a tedious page I’ll skip) … Of course, the fact that there are nomically possible worlds that stay very similar to actuality until shortly before t but diverge after t does not by itself establish that there are nomically possible worlds to the kind that Lewis was worried about–for example, worlds that say very close to actuality until shortly before t and at which Nixon goes on to press the button at t.”

Dorr argues that there are such worlds on the basis of an “Independence Conjecture”, paraphrased as “the macropresent screens off the macrofuture from the macropast”. This is something that doesn’t appear to be true in systems with particularly trivial dynamics. Consider for example, a single object travelling through space, not interacting with any other objects. A macropresent view will tell us roughly where the object is, where it’s going, how fast. But there could be indeterminacy here (“macro”). Seeing where it was in the past will cut down on the indeterminacy of our future estimates. For systems with sufficiently complex (“mixing”) dynamics, however, the Independence Conjecture looks plausible. Here the idea is that if we take a set of “macroscopically described future” orbits, such as those comprising “Nixon presses the red button” and a set of “macroscopically described past” orbits, such as “close to the actual past” then these sets ought to be, at least approximately, probabilistically independent, so that the probability (everything conditional on the present macrostate), conditional on having a past state close to the actual past, of having a future state in which Nixon presses the red button, ought to be near the absolute probability that Nixon presses the red button, in particular non-zero.

Something along these lines ought to be true, but not everything…witness the fact that for orbits having past states “very very close” to the actual past state, the state at time t will be too close to actual for Nixon to press the red button (just what Dorr spent that page we skipped proving). On the other hand merely “close to the actual past” may not be close enough to stay close up to a time shortly prior to t. What Dorr seems to require is that at the in-between level of closeness (“very close”) one already has the sought-for independence kicking in. In other words…independence kicks in just as fast as the escape from closeness to a single state does. This strikes me as loose talk, but I’ll let it slide just the same. (I wonder though if he could do better to try to just manually get Nixon to press the button. So long as we are assuming continuous dynamics, we might as well assume smooth dynamics. Then we have derivatives, so that bulldozing the relevant particles and velocities around at will while leaving others relatively fixed by manipulating the distant past in the neighborhood of a point could come down to linear algebra.)

At any rate, suppose we indulge all of Dorr’s fancy here. Does it get him what he wants? He writes:

“We can regiment Lewis’s time-relative notion of similarity between possible worlds using a metric d on M.”

M is the the set of states of the world, by the way.

“The distance d(p, p’) represents the degree of dissimilarity between w at t and w’ at t’, when t instantiates p at w, t’ instantiates p’ at w’, and both w and w’ are nomically possible.”

I think Dorr means “w instantiates p at t”, etc. but I suppose a time could instantiate at state at a world, too, odd as it sounds to my ear.

The first thing that concerns me here is “We can regiment Lewis’s…notion of similarity…using a metric…”. Indeed, this sounds a lot like something Lewis explicitly rejects:

“We could…define exact distance measures…for…worlds. At worst, we might need a few numerical parameters. For instance, we might define on similarity measure for distribution of matter and another for distribution of fields, and w would then need to choose a weighting parameter to tell us how to combine these in arriving at the overall similarity of two worlds. All this would be easy work for those who like that sort of thing, and would yield an exact measure of something–something that we might be tempted to regard as the similarity distance’ between worlds. … We must resist temptation. The exact measure thus defined cannot be expected to correspond well to our own opinions about comparative similarity. Some of the similarities and differences most important to us involve idiosyncratic, subtle, Gestalt properties.”

Lewis goes on to talk about facial similarity and its irreducibility to similarity in a simple metric based on pixels. Notwithstanding the fact that today’s digital passport  readers seeming to do fairly well, the point is well taken. But maybe I misunderstand Dorr. It may be that he advocates using “Gestalt” properties, primarily, when evaluating closeness of worlds, but breaking ties using metric closeness…at least, metric closeness up to divergence. This could still save the intuition that if he had blinked twice the past would have still been (approximately) the same…assuming there is any such intuition…while avoiding certain problems. But I will set this aside for the moment and assume that Dorr does intend to use the metric as a measure of similarity.

A technical point…is the set of worlds where Nixon presses the button closed in the topology generated by said metric? I think probably it is, as the complement of this set surely has to be open by Dorr’s own reasoning. Probably then it follows that the set of distances between the actual world and a “Nixon presses the button” world has a minimum value. It doesn’t follow that there is a unique world w of this sort, but a moment’s reflection reveals that this is extremely likely. Suppose so.

Now if we follow the Lewisian semantics for counterfactuals, we can take any distant future truth P holding in w and the counterfactual “If Nixon had pressed the red button, then P” will come out true.” So for example “If Nixon had pressed the red button then in March of 3001 a winged mutant named April May would have become the first human descendant to survive one hundred unaided falls onto land from above one hundred meters” would come out true. And that’s highly counterintuitive. Among the worlds where Nixon presses the button, there are worlds all over the map having this property, true enough, but they are hardly concentrated in one place, and there are vastly more that do not. What should it matter to us that the one world closest to actual in the metric we have chosen is such a world? That fact appears to be an accident.

Far from rescuing Lewisian semantics from miracles, what Dorr’s argument points out is how deeply implausible Lewisian semantics are when based on such a metric. Let’s look again at the pretty pictures Lewis draws.

ls2

The only reason to utter a counterfactual “if phi had been, psi would have been” is to point out a correlation between (“nearby” if you like) phi worlds and psi worlds. If there’s no such correlation you shouldn’t say it…much less should it come out true. One might think that this situation is reflected in Lewis’s (D): among the most nearby phi worlds, some are psi worlds and some are not. But Lewis’s image pictures a discrete set of spheres, and if we buy into Dorr continuous variation assumption, such a picture is wrong. We get spheres of radius r for every real number r, so that, if phi is a closed set, we get (probably) a value of r for which the r-sphere meets phi in exactly one point, whereby we land in (B) or (C) irrespective of whether there is any correlation between phi worlds and psi worlds. But as Dorr teaches us here, there often won’t be any such correlation! Indeed, where phi and psi are macroscopically described events, the benign regions Lewis has drawn will need replaced by fractal regions that, quite often, will be approximately independent of fractal regions associated with different propositions. Looking at Lewis’s (B), it might seem reasonable to say “if the world had been phi then it would have been psi”. For if you asked (with apologies for the personification of worlds) the actual world to impersonate a phi world, it would plausibly (to some sort of intuition) gravitate mindlessly in the approximate direction of all of the phi worlds and, hitting a nearish one, find itself to be also a psi world something like every time. Suppose the regions are highly fractal, though; would the actual world gravitate to a tiny phi region .03032… units away or a much larger one .03033… units away? Even if we agree that it would gravitate to the nearest one…wouldn’t approximate independence imply that the psiness or non-psiness of the world it lighted on would be essentially random? An accident? There are worlds near that one that are psi worlds, and worlds near that one that are not psi worlds. And if you seek to save Dorr here by saying “well, most of the worlds are psi worlds” then you are just agreeing that it comes down to conditional probability, not the accidental properties of that one special phi world that is closest to actual. Nothing Lewisian about that.

On the picture Dorr paints for us we’d need to replace the clean Lewisian pictures by images more like:

lw2.jpg

(Sorry for the lame graphics. Anything beyond Microsoft Paint is beyond me as well.)

Somewhere at the center of those concentric spheres I’ve tried so feebly to draw is the actual world–a random dart toss at this rainbow colored fractal. If you want to think in terms of the earlier example, think maybe cool colors for Nixon doesn’t press the red button and reddish/purplish colors for Nixon presses the red button, with nuclear war occurring at all but magenta. Say the actual world lies in a greenish area (Nixon doesn’t press). The dart landed on green, but we can ask about the truth of “If the dart had landed on a reddish color, it wouldn’t have been magenta.” If there’s a miniscule patch of magenta somewhat nearby and no closer cool colored patch, Lewis might say that that counterfactual is false, regardless of how much magenta there is in the image (even somewhat nearby magenta…only the closest reddish patch counts). Indeed, one might just as correctly say “if the dart had landed on a reddish patch it would have landed here”, pointing at the nearest reddish patch, irrespective of the fact that the pointed-to patch is orders of magnitude smaller than other nearish patchs of red.

This is no longer compelling.

In favor of counterfactual miracles?

All right, so the treatment I have been recommending goes something like this. When I utter “If F had been, G would have been” and F is an outcome of a chance event in the past that did not occur, then what I am suggesting is that G has a highish probability conditional on F, what I know about the actual state of the world just prior to the chance event (the one that did not eventuate in F actually, but might have), and perhaps also the results of chance events after t that do not lie causally downstream of F. (So I can say “if Manfred had played, we would be champions” even though this counterfactual championship requires a subsequent very unlikely upset in a distant, causally isolated venue, provided it actually occurred.) I utter such a thing, to the extent that I am doing “communication”  with those words, as a way of imparting information to listeners…information about what I know about the actual state of the world just prior to the chance event, perhaps, or information gleaned from what I take to be a perceptive take on what (usually) follows from what.

Dorr has some cases that he presents in the next section that don’t fall so nicely in this category, however.

“Suppose that, on the phone to Mary at t, Fred speaks the truth by saying “If I were there right now, I would give you a hug.” On the operative interpretation of the counterfactual, how do we think Fred would have got to be with Mary at t? Would he have been whisked there quickly by a recent, antithermodynamic puff of wind, or would he have got there by a less showy method, requiring a somewhat earlier divergence from the approximate course of actual history? The latter option seems better. If we choose the puff of wind, we will need to combine it, rather artificially, with further unusual goings-on in Fred’s brain to ensure that he arrives still in a mood to give Mary a hug…”

Hilarious. I particularly enjoy the phrase “rather artificially”, given how jaw-droppingly artificial the whole “puffs of wind” notion is in the first place. (If you are already having Fred blown across a continent by an easterly gust of wind, does it qualify as a stretch to have him sleep through it?)

Here’s a problem with metric similarity: among all ways of getting Fred to Mary, the  “antithermodynamic puffs of wind” may do it with the most delayed deviation (and hence the greatest similarity of initial conditions) from the actual. Probably you could get Fred across a continent in just a few minutes using them, and on Dorr’s continuous dynamics view there ought to be states near the actual state say a half hour ago that do this.

Dorr now wants to distance himself from metric similarity, Lewis, or both, and I don’t blame him. Fred’s Ripley’s moment may be close in the metric, but that doesn’t make it closest to actuality. It doesn’t “get the Gestalt”.

I asked my wife (she learned Lewis’s semantics for counterfactuals from George Schumm, who was apparently rather animated about it) what she thought about this. At the risk of misinterpreting her (which is likely) she thinks it’s important not to fix too much…you only fix what’s relevant. In particular you have to have a rather plastic notion of similarity, presumably different for each counterfactual utterance. For the case of Fred and Mary, the important thing is that Fred’s and Mary’s general moods be fixed in the inner spheres…probably also their identities and the semi-normalcy of their current experiences, blah blah blah…and not much else. So “in nomically accessible worlds where our needs and desires are as they actually are and we are together, I give you a hug” or something. (“So romantic”, Mary no doubt replied.)

Let’s see if my own view is in any trouble here. To avoid the possibility of running several issues together, I am going to change to third person and put the situation in the past. So let’s say I utter “If Ted had been there, he would have hugged Mary.” I think it would be within your rights to say something like “Ted was 3000 miles away at the time…so what are you saying? Are you saying that if Ted had gotten on a plane that morning and they were together then, he would have hugged her?” Dorr rightly notes in a footnote that in most worlds of this sort where they are together at t, the circumstances that led me to utter “If Ted had been there, he would have hugged Mary” aren’t operating at all. (He may have said it because she missed him so much, which she wouldn’t, were he there.)  I think I might reply: “well, I suppose if he had gotten on a plane, unbeknownst to her, and were just then knocking on her hotel room door during the same sort of phone conversation, then, sure, when she answered, he would have hugged her.” Then you might ask “so are you saying that if he had been there then he would have come in secret and been in the hallway talking to her on a cell phone?” And I would have to confess that, no, that isn’t what I meant.

What to do? Do I follow my wife and say that I can just change the circumstances for different counterfactual utterances? That seems ugly. I would much rather have a uniform treatment. But I despair of one. Consider this: it’s New Year’s Eve. Ted’s flight was cancelled, so he can’t be with Mary. On the way home from the airport, he got in a fender bender and slammed his mouth on the steering wheel. It’s shortly before midnight and Mary laments that he can’t kiss her at he stroke of midnight. Well, notes Ted, I couldn’t kiss you anyway…my lips have been smashed. But I would give you a hug…. What do we make of that? Surely the closest worlds where Ted is there with Mary are worlds in which Ted’s flight wasn’t cancelled. But if his flight wasn’t cancelled and he’s there, he doesn’t hug Mary…he kisses her! Notwithstanding that, what Ted says seems incontrovertibly “true”. (For those who favor a truth value semantics for counterfactuals, anyway.)

I think we have some notion of what Dorr would say, as in a different context he writes: “…we are free to hold fixed both approximate history up to, say, one day before t, and also the facts about whatever Mary said just before t that inspired Fred’s impulse to give her a hug.” In the current case, then, Dorr would perhaps say that we are free to hold fixed both approximate history up to the point where Fred’s flight was cancelled and the fact that he later smashed his lip…of course now he has to do it in the cab to her hotel room (for example) rather than on his drive back home.

This however I cannot abide. We can make the situation even worse: perhaps Mary has said she would not kiss Ted now because, after his flight was cancelled, he got a haircut, breaking his promise to Mary not to make unnecessary expenditures in the state of New York (where, in Mary’s mind, corrupt politicians skim income tax dollars). How are you going to fix that fact if the fight isn’t cancelled? We could probably make it worse still…probably we could make holding fixed both the approximate past and some future event require a genuine miracle. Even if not a miracle, though, surely it requires implausible coincidence. It can’t be part of “if I were there, I would give you a hug” that Ted has worked out in his mind what would have happened if his flight weren’t cancelled and he’d wound up with Mary with a differently acquired lip smash because such a thing would never occur to anyone unless they were writing a philosophy paper. On the contrary, Ted is probably thinking “man, if I were with Mary, my lip wouldn’t have been smashed”. Granted, he’s also thinking “man, if I were with Mary, I would give her a hug”though if he puts this all together he won’t think “if I were with Mary, my lip wouldn’t have been smashed and I would give her a hug”…rather he would think “if I were with Mary, my lip wouldn’t have been smashed and I would kiss her.”

I think the upshot of this is that counterfactuals where the antecedent isn’t a chance event at t, occurrence of which implies (macroscopic or epistemic) divergence from the actual at t, but rather a consequence of an earlier (vaguely formulated or perhaps unformulated) divergence, are a different beast. Strictly speaking, they should probably be discouraged in favor of utterances such as “this may sound quite strange, Mary…given that you are not, unfortunately, actually here with me, but I am, at this very instant, experiencing a most discernible impulse…to give you a hug.” Hugh Grant, I think, would do it that way, and we should too..to whatever extent we want to come off as charming, anyway.

Quick Summary

Let’s look at it this way. On one view, the evolution of the world requires what one might think of as some real time random number generation. (I.e. there are chance events.) You can think of these random numbers as coming from Godly coin tosses, or whatnot. On the deterministic view, this isn’t the case…every outcome is determined by initial data. It changes nothing, however, if the universe evolves in identical fashion, with the random numbers not coming from Godly coin tosses but from a random number table. (The table is part of the initial data.) What’s the difference, when it comes to how we should analyze counterfactuals? Nothing whatsoever, clearly. Where F is a non-actual “outcome” at t, “if F had been then G would have been” means

a. “if such-and-such Godly coin toss had landed differently…” or

b. “if such and such entry in the random number table had been different…” or,

c. “…if the initial data had been different…”.

Nobody has trouble seeing a. and b. as essentially equivalent from the standpoint of counterfactual analysis. Here’s why: it’s easy enough to know which counterfactual world we’re in, in these cases. We are in the world where everything is the same except for the result of that one Godly coin toss, or that one entry in the random number table. In case c. we don’t know for sure what counterfactual world we are in, and the reason for this is that, as Lewis points out, there are too many opportunities for small differences to give rise to large ones. If the initial data had been different, everything about the past would have been different. If determinism is true, there aren’t nomically accessible worlds where everything (including what it is I think I know that led me to assert the counterfactual) about the past is fixed but F happens. So in saying “if F had been”, says Lewis, we are saying “if there had been a miracle, and F had been”.

Dorr, in this paper, wants to get out of this by making c. look like b. That is, he wants the data to be so fine-grained that the “Nth-and-beyond” digits of it, as N gets ridiculously large, act much like numbers read off of a random number table, at least insofar as they don’t have visible effects prior to some t and have huge effect after that. (Just like pseudo-chance events whose outcomes are determined by lookup.) I doubt that’s the way it works…I don’t think the world deals with that much data (infinite data, it seems, from Dorr’s explanations) at every update. Still, it does seem to reduce situation c. to situation b.

However, we found a problem. The whole reason for wanting to evaluate the truth of a counterfactual “if F had been, G would have been” at a “nearby” F world is that (recall) my whole reason for asserting the conditional in the first place was to pass information I have about the actual state of the world at t. (And insight I may think I have about what follows from what.) If I evaluate at a far away world, some of what I know will no doubt be no longer the case. Indeed, some of what I know (not F, for example) will surely be no longer the case, but the idea is to make there be as little of that as possible. But…and here is the problem…sensitivity to initial conditions may make it the case that, even for nearby worlds, F-ness and G-ness may be essentially independent. At the very least, there are G worlds and not-G worlds near to the “nearest” F world, and in cases where there’s reason to think the closest ones are one or the other, it might not be the one you’d want. Consider:

“If the Blazers hadn’t drafted Sam Bowie, they would have won multiple NBA titles in the nineties.”

The idea here is that Michael Jordan was second on the Blazer’s draft board, that they thought long and hard about picking him, and if they had, things would probably have gone very well for them in the nineties. But on the metric  similarity view, the nearest world in which the Blazer’s don’t draft Sam Bowie probably isn’t a world where they draft Michael Jordan…it’s more likely a world where they draft Sam Perkins. Because, well…such a world can closely match the actual world all the way through the recording of the pick’s first name on the card that is about to be handed to the commissioner! Whether then the Blazers go on to win multiple NBA titles in such a world is anybody’s guess. Suffice it to say it’s less likely with Perkins than with Jordan, and it’s its relative likelihood with Jordan that justifies the avowal. As is the case almost everywhere in philosophy, but most especially on the view we’re discussing, where the local neighborhood is teeming with possible futures encompassing just about everything under the sun, everything comes down to probability.

So why don’t I want to fix more than the speaker’s epistemic situation? In normal assertions we do. If John says “Matt wasn’t holding 9♣ 9♦”,  his assertion is true or false according to whether or not Matt was holding 9♣ 9♦, and those truth conditions are surely the better part of the meaning of John’s assertion. John doesn’t mean by “Matt wasn’t holding 9♣ 9♦” that in most cases epistemically similar to his, the person referred to as “Matt” isn’t holding 9♣ 9♦; he means that in this case, Matt isn’t holding 9♣ 9♦!

That’s just the problem, though. When John utters a counterfactual, there is no obvious candidate for “this” case, i.e. the actual case. We aren’t interested in the actual case. When John says “if Matt had called, he would have lost”, he isn’t claiming that he lost in “that” case, ostending by “that” a particular counterfactual world. On the other hand John will probably admit that he was “wrong”…he may even say that what he avowed was “false”…if we turn over Matt’s cards, revealing 9♣ 9♦. Why is that? Perhaps it is part of the meaning of “if Matt had called he’d have lost” that Matt doesn’t have 9♣ 9♦.

Hmm. I was hoping not to get into trouble, but I fear I am. What I’d like to do is keep this in the realm of philosophy of probability, but I feel it creeping into philosophy of language, where I will be unceremoniously flayed. Obviously all I can ever hope to impart via any utterance is some aspect of my epistemic position, yet we do hold most of them accountable to how the world is apart from what I know. There doesn’t seem to be any principled reason why counterfactuals would be unique in this regard. On the other hand, I don’t want my utterance of a counterfactual to be held accountable to how another world is…whether it be a near one or a far. Surely my avowal of “if F had been, then G would have been” when F is a chance event at t that isn’t actual will go by probability of G conditional on F and whatever else I know about the state of the world at t, but I may disavow if I subsequently learn more about the state of the world at t. Part of the meaning of the utterance then, may be that I would not disavow were I to know more. Namely, I am expressing a confidence that I know enough of the relevant stuff that I need not disavow should I know more. That’s the way it works for ordinary assertions, after all. When I say “P is the case” I don’t just intend that P is likely given my epistemic situation. If so I should not then admit I was wrong when it turns out that P is not the case. Rather I intend to suggest that P really is the case…so that in particular, I should continue to avow P should I know more. Or…well, not exactly. There is always the chance that I will be misled, even though I am right. It’s perhaps not part of what I am claiming that this won’t happen. Though if I say “I know that P is the case”, maybe then it is.

Clearly I’m just rambling by now so I will just quit.

 

 

 

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