I recently pointed out a curious implication of the no-duplicate-worlds view: whether you break a perfect symmetry on one side or the other, this amounts to the same possibility. Suppose our two-sphere world comes with an arrow in the middle which points directly to one sphere, which we dub Bob1. Could it have pointed to the other (Bob2) instead? Scrap the 'instead'. It could have pointed to Bob2, but this is not a possibility grounded in any other possible world. Bob1 is a perfect counterpart of Bob2, after all. So the possibility claim can be made true by this very same world.
Jack has an interesting post on his new blog which aims to make this a tougher bullet to bite. His trick is to ask us to imagine a variation where it's random which way the arrow ends up pointing. Now, the "two" possible results may be accommodated exactly as above. So there is the one result, and then there is the "other" possibility which simply consists in a counterpart-theoretic reinterpretation of this very same possible world. So far so good. But now I'm struck by a new concern: how are we to distinguish this randomized case from the deterministic arrow world I described previously? What is it that makes this newly described world an indeterministic one, if not a plurality of possible futures?
Here's my solution: randomness consists in symmetry. There is nothing in the initial makeup of the world which tilts in one direction rather than the other. (Imagine the arrow points straight up until an indeterministic physical process causes it to fall to one side and break the perfect symmetry.) In a deterministic world, by contrast, the initial state of the world is physically 'tilted' towards one sphere, so it stands in different qualitative relations from the other sphere; they are no longer perfect (incl. extrinsic) duplicates. Thus we can distinguish the worlds where the asymmetry is introduced randomly vs. deterministically.
Tuesday, March 04, 2008
Random Duplicates
Friday, February 01, 2008
The Ultimate Question: Kripke or Lewis?
Perhaps the most interesting question in metaphysics, to my mind, is whether identity facts are among the base facts; whether worlds or their constituent objects are prior; whether de dicto or de re modality is fundamental. (I take these to be different angles on the same core question.) We can illustrate the issue by way of my old example of duplicates Bob1 and Bob2 in the perfectly symmetrical universe. Although this possible world contains two of everything, presumably things could have been different. In particular, there might have been no duplication. But now we ask: how many ways are there for a world to be exactly like the mirror world, minus the duplication?
(A) The Kripkean Answer: Many. At the very least, you might have just Bob1's half of the universe, or just Bob2's half of the universe. So that's two possibilities. We might even mix and match, conceiving of a possibility containing precisely Bob2's world except that Bob1 exists in Bob2's place. To generalize: if there are n independent objects in each half of the symmetrical universe, then there will be 2^n ways to populate a possible world containing just one of each object. (Essentialists may deny that all the objects are independent in this way, though: perhaps Bob1 could not have been born to Bob2's mother. Such details needn't concern us here, though.)
(B) The Lewisian Answer: There is really just one possibility here. There is no difference between the various possibilities mentioned in the Kripkean answer. They are all describing one and the same way for a world to be. What we have imagined is a world which contains but a single Bob counterpart (and similarly for each other object in the mirror world). Whether he is really Bob1 or Bob2 is an empty question. In the strictest sense of identity, he is plainly neither. But as a counterpart, he can play a truthmaking role for counterfactual claims made about either. (E.g. "Bob1 might have existed without Bob2," and vice versa.)
I lean heavily in the Lewisian direction, since the idea that there could be any number of qualitatively identical worlds which nonetheless differ in the identities of their constituents strikes me as completely nutty. (There's nothing there to ground such a difference -- nothing in Bob's metaphysical makeup that could fix whether he is Bob1 or Bob2. Well, unless you care to introduce a 'haecceity' for just this purpose, but haecceities seem mysterious and insufficiently motivated posits.)
"That's nuts" does not, however, seem to convince the Kripkeans of my acquaintance. Can anyone suggest a better way to make progress on this issue? (Or some good papers to read? I'm not at all familiar with the literature.) I think Jack is with me on the specific case of time-points, at least, so maybe I just need a few more compelling examples to form a base from which to generalize...? More seriously, though, it seems like such a central issue that it cannot be settled on its own. Rather, we must do the hard work of exploring the implications for whole systems of Kripkean and Lewisian metaphysics, to see which approach ultimately bears fruit. What do you think?
Friday, October 05, 2007
Flimsy Sketch of an Ironclad Universe
I would call this 'An Argument for the Necessity of the Universe', riffing off the WMU post where I've been commenting, but I don't really have any arguments to offer. Just a nice picture. Here's how it looks:
The world (universe) is essentially spatiotemporal. Each so-called 'possible world' constitutes a different form the physical manifold might take -- a way the world could be. Collectively, they exhaust the possibilities. That is, the world must instantiate one of them. The manifold is given; all that varies is its form -- but it must take some form or other. Big or small, the one necessity is that it is something, rather than nothing at all.
Pretty, no? (Admittedly, there's still the question why it takes this form rather than some other.)
Tuesday, May 15, 2007
Coherence and Comprehension
Responding to my post on verificationism and base facts, Jim Ryan writes:
I wonder whether Richard's view entails that one can understand an incoherent term (such as "square with only three sides"). After all, "I know what it means, I understand it, but I just don't see how it could be rendered coherent" sounds Richardesque. I suppose he might say that the incoherence precludes comprehension. But that seems arbitrary. Why won't he also allow that evidential vacuity precludes comprehension, as well? Again I say that the mind is large and its imagination powerful. It can imagine a logically impossible thing (especially if it's in a sort of dreamy state: try it, you can do it. Or if the contradiction is buried deep enough, you can accomplish the task in a clear-headed state.) It can mistake this for comprehension. It can imagine the correct application of an evidentially vacuous term (e.g., "zombie") and mistake this for comprehension, too. How can Richard distinguish these two, such that in the latter case there is in fact no mistake?
Granted, our claims to understanding are fallible -- one can't be certain that further reflection won't reveal some hidden incoherence in a notion. There's a gap between prima facie conceivability and ideal conceivability. A nice example of this is the Grim Reaper paradox:
There are countably many grim reapers, one for every positive integer. Grim reaper 1 is disposed to kill you with a scythe at 1pm, if and only if you are still alive then (otherwise his scythe remains immobile throughout), taking 30 minutes about it. Grim reaper 2 is disposed to kill you with a scythe at 12:30 pm, if and only if you are still alive then, taking 15 minutes about it. Grim reaper 3 is disposed to kill you with a scythe at 12:15 pm, and so on. You are still alive just before 12pm, you can only die through the motion of a grim reaper's scythe, and once dead you stay dead. On the face of it, this situation seems conceivable — each reaper seems conceivable individually and intrinsically, and it seems reasonable to combine distinct individuals with distinct intrinsic properties into one situation. But a little reflection reveals that the situation as described is contradictory. I cannot survive to any moment past 12pm (a grim reaper would get me first), but I cannot be killed (for grim reaper n to kill me, I must have survived grim reaper n+1, which is impossible). So the description D of the situation is prima facie positively conceivable but not ideally positively conceivable.
How should we interpret this? I guess I am a bit tempted by the line Jim attributes to me: "I can understand the set-up, I know what it means, and I see that it's incoherent!" But this trades on an equivocation. I can understand each of the descriptive components in isolation, but that's all. It remains a total mystery how they fit together -- what is supposed to happen after the strike of 12? It can't be understood. It's incoherent. But I repeat myself.
It's not arbitrary to say that "incoherence precludes comprehension." On the contrary, it's analytic! Coherence just is comprehensibility. To call something "incoherent" is precisely to say that it cannot be comprehended by any rational mind whatsoever. (Of course, something coherent but complicated might be "incomprehensible to me" in the limited sense that, due to my contingent cognitive limitations, I simply happen to not understand it. But that's not the relevant sense of the term here.)
On the other hand, I just don't see any reason to think that evidential vacuity precludes comprehension. And I do see reasons -- in the form of apparently coherent counterexamples (zombies, multiverses, etc.) -- to reject such a stringent requirement.
Jim concludes:
Richard needs to say what is the difference between "comprehensible" and "suspiciously incomprehensible" other than a feeling of "I've got it!" I don't trust that feeling. I need epistemic, evidential terms.
That seems fair enough, given how fallible such intuitions are. The difference between true and false intuitions is a matter of fact that won't always be transparent to us, namely: would further reflection lead me to change my mind?
Monday, April 23, 2007
Does Philosophy Need Science?
I reckon not. (Well, perhaps in practice, e.g. as an imaginative aid, but not in principle.) Whenever you're tempted to appeal to empirical data, simply conditionalize it out and you can safely carry on philosophizing in the a priori realm of possibilities.
Of course, we may be most interested in actual-world problems, e.g. interpreting modern physics, addressing salient ethical and political issues, etc. But there doesn't seem any reason why they couldn't in principle be addressed just as well from an empirically neutral position which entertained our actual situation as a merely hypothetical scenario. Indeed, given sufficient imaginative and rational powers, the armchair philosopher (or even the disembodied, floating-in-the-void philosopher) should be capable of achieving a kind of "limited omniscience", knowing everything there is to know about the various possibilities (except for which one happens to be actual -- but never mind that one little fact).
It might be objected that science brings to light new possibilities that would otherwise seem inconceivable -- e.g. space-time relativity. But this is merely to note that experience is a useful imaginative aid; it plays no necessary role in the actual justification of our philosophical beliefs. Einstein's theory is enough; it need not be borne out by the empirical data. His conceptual scheme alone is enough to show how space and time could turn out not to be absolute. (Unless there's really a hidden contradiction in there, in which case ideal rational reflection should suffice to expose the impossibility.)
Am I wrong? (And do you have to conduct an experiment before you can tell?)P.S. Thanks to Jack for getting me thinking about this topic.
Saturday, April 21, 2007
Philosophy, de dicto and de re
There are two things I really want to know. Unfortunately, I'm not too sure what they are. (So maybe that makes three!) The de dicto/de re distinction seems relevant to both. Let's see if writing this post can help me get a grasp on them at all...
1) What's the story with philosophical analyses? What's the relationship between a concept and its analysis, which provides necessary and sufficient conditions for something to fall under the concept? For example, suppose I could mentally grasp the entire set of all possible knowledge-instances, or goodness-instances. Do our concepts of 'knowledge' and 'goodness' invoke anything beyond these infinite sets (or their compression into systematic formulae)? Aren't the concepts normative in a way that their object-involving intensions cannot be? Is this what allows there to be substantive disagreements involving the concept? What's the central issue here?
*pulls hair*
2) What's the deal with numerical identity? Is there even any such thing, fundamentally, I mean? Or is all modality fundamentally de dicto, concerned with the distribution of descriptive qualities across the Humean tapestry of spacetime, with other possible "me"s bearing a relation to me that's merely a counterpart-theoretic construction? In what sense is this really the same chair as it was a moment ago? There's a certain physical continuity between the two temporal parts, of course. But does the fact of numerical identity -- being one and the same object -- consist in anything over and above this? My clearest thinking on this topic is here, but I suspect even that is hopelessly confused.
Combining the two problems: what does our concept of identity add to the raw, bleeding reality -- the set of temporal parts and counterparts that we'd classify as belonging to a single object? Where's the interpretation? What meaning do we project onto this raw stuff through our classification of it as numerically identical? (And is this merely a projection on our part, or something independently real?)
Argh! I really need to do more metaphysics and philosophy of language. (Though if anyone out there is able and willing to clarify these issues in a comment, that'd be just grand...)
Thursday, April 12, 2007
@
East of Dulwich cleverly came up with the symbol '@' to indicate claims or descriptions that don't correspond to the actual world.
It'd make for a nice red stamp, I imagine...
Saturday, March 03, 2007
Strong Possibilities
Wo makes an interesting point: if someones believes in strong necessities despite appropriately conceivable counterexamples, on what grounds do they reject the idea of "strong possibilities", i.e. contradictions or inconceivabilities that are nonetheless held to be metaphysically possible?
In fact, I used to be pretty sympathetic to such a view. If modality isn't tied to the rational sphere, then it's hard to see how we could say anything much about it at all! (Though I recently took a shot at reconciling a deeply "realist" conception of modality with the epistemic strength of the modal rationalist, here.)
Friday, October 13, 2006
Thesis Conclusion [draft]
[The concluding summary of my honours thesis. Links to the earlier chapters are interspersed with the text...]
It’s natural to expect that what can be known without needing to look at the world is closely tied to how the world metaphysically could or must have been. If we can only learn a fact a posteriori, through empirical investigation, we may expect that this is because there are other possible worlds in which the fact in question fails to hold. Assuming that possible worlds are wholly self-contained, we would not expect that examining the actual world could tell us anything informative about other, non-actual possibilities. Modal rationalism draws on these intuitive ideas by positing an intimate link between apriority and necessity, according to which an ideally rational agent could in principle grasp modal space – or apprehend what is possible and what is not – through the exercise of reason alone.
Kripke’s discovery of the necessary a posteriori casts doubt on this picture. There are some necessary truths – e.g. ‘water is H2O’ – which can only be known after empirical investigation. But the modal rationalist suggests that the problem here is merely semantic. We can know a priori how all the various possible worlds are in themselves; what we don’t always know is how to apply our words to them. Some terms, like ‘water’, are not semantically neutral – their application to counterfactual worlds is contingent on how the actual world turns out. That’s why empirical inquiry may be required before we can accurately assess various modal claims. The extra work is required to grant us semantic, not metaphysical, knowledge. We may avoid this need by restating a claim in neutral terms, for which the semantic values are unaffected by whether we consider a world “as actual” or “as counterfactual”. Chapter One thus established that the Kripkean challenge to modal rationalism is toothless after all; the link between apriority and necessity may be restored by restriction to semantically neutral vocabulary.
What’s needed to refute modal rationalism are “strong necessities”, i.e. claims that are true in all worlds considered as actual, despite being conceivably false. This requires that there be coherent scenarios that would not be verified by any possible world. Chapter Two explored this idea further, and assessed Yablo’s arguments for the claim that modal rationalists must recognize such strong necessities. Arguments from meta-modal conceivability provide the greatest challenge here, but I proposed that modal rationalists should respond by treating scenarios as epistemically fundamental, so that meta-modal conceivability is then uniquely determined by the sum of individually conceivable scenarios. Other arguments assume that there are unknowable necessities – an assumption we have no reason to grant, but that at least suggests the intuitive need for a non-epistemic foundation to modality.
Chapter Three set about exploring this idea further. I presented a metaphysically ‘realist’ understanding of metaphysical modality, and defended it against the conceptualist’s skepticism by highlighting its connection to our intuitive ideas about physical indeterminism, objective chance, and the open future. The realist’s primitive conception of modality forces us to take seriously the idea of strong necessities, but they need not give up on modal rationalism altogether. I suggest two principles of modal expansion – the presumption of possibility, and the consistency principle – which together serve to ground modal rationalism on a realist foundation. The end result is, I think, an attractive and defensible view, which preserves many of the intuitive claims we would wish to make about modality. And although it is arguably the conceptualist’s epistemic space that matters for key theoretical purposes, many would dispute this claim – which cannot be fully defended here – so it is worth establishing the viability of realist modal rationalism for those who would place greater weight on this metaphysical modal space.
Monday, September 18, 2006
A Worldly Metaphysics
I propose that we treat individual possible worlds or scenarios as (metaphysically and epistemically) fundamental. Doing so has interesting implications in either case. First, it grounds an attractive and plausible theory of ontological deflationism. On this view, disputes about what exists are only substantive if they involve carving up the space of possible worlds in different ways. If metaphysicians agree about which world is actual, but disagree about its constituents (e.g. whether it contains tables or merely "particles arranged tablewise"), their apparent disagreement is empty. It is whole worlds that are fundamental; we might break them down in any number of ways, and it is pointless to argue that any one of these is the One True Ontology. (See the linked post for further explanation.) Second, I think the epistemic fundamentality of possible worlds has important implications for meta-modal conceivability. But this will take a bit more explanation...
Let us begin with Yablo. In ‘Is Conceivability a Guide to Possibility?’, he isolates the particular kind of conceivability that best serves as evidence of metaphysical possibility. Note that any number of necessary falsehoods might seem conceivable in some sense. Consider the statement (P): "There is a greatest prime number." Mathematicians can easily prove the impossibility of P, yet you might have thought it conceivable in some sense. For example, you might not be certain that it isn't actually true. (As humble fallibilists, we might even be inclined to grant that absolutely anything is "conceivable" in this weak sense!)
However, Yablo suggests that it is whole scenarios (epistemically possible worlds) that are fundamental for modally-relevant conceivability claims. Used in this sense, the "conceivability" of a statement X consists in there being a scenario which we take to verify X. (That is, we endorse the indicative conditional "if scenario V is actual, then X is true", or we judge that the conditional probability of X given V is near 1.) This allows us to deny that the aforementioned P is conceivable in the relevant sense, since there is no scenario which we take to verify the claim. There is no way the world might turn out, such that if things did turn out that way, there would be a greatest prime number.
At best, we might imagine a scenario in which mathematicians report discovering such a "fact" -- but there is nothing in the given description to rule out this being a scenario in which the mathematicians are simply deluded. So even the mathematically ignorant should not take this scenario to verify P. Instead, they should suspend judgment; they are not sure whether P is true in the scenario or not. That is, they are not sure whether P is conceivable. Hence, their imaginings provide no evidence about the possibility of P -- which is just as it should be. Yablo's account seems spot on. (See also Chalmers' discussion of positive conceivability in section 2 of Does Conceivability Entail Possibility?)
Yablo works down from scenarios to the first-order claims that they verify. He thus treats worlds as fundamental, at least in this respect. But he could go further. I think we should also work upwards, from scenarios to the meta-modal claims that are true of all of them. Let me explain. First, some background context:
Yablo objects to modal rationalism -- or the claim that ideal conceivability entails (primary) possibility -- on grounds of meta-modal conceivability. Even if the modal rationalist is right about the scope of possibility, there are (Yablo claims) coherently conceivable alternatives. For example, it's conceivable that a necessary being exists, and the negation of this is likewise conceivable. But they cannot both be possible, for by S5, the possibility of a modal claim entails its actual truth! Conflicting meta-modal possibilities would thus entail actual contradictions. So there cannot be conflicting meta-modal possibilities. The conceivability of conflicting meta-modal claims thus provides a counterexample to the thesis that conceivability entails possibility.
However, I want to suggest that meta-modal claims are, in a sense, similar to mathematical claims like P above. Considered in isolation, you might mistakenly consider them to be conceivable, but this error is remedied by recalling the fundamentality of worlds (or scenarios). First-order claims require us to work down from the total scenario of which they are part. Similarly, I suggest, meta-modal claims require us to work up from the individual scenarios that comprise epistemic modal space. By treating scenarios as fundamental, we close the gap between epistemically possible necessity and epistemic necessity tout court. (S5 applied to the intersection of epistemic and metaphysical modal space?)
On this proposal, for a necessary being to be coherently conceivable, it must be the case that the being exists in every scenario one can coherently conceive of. The failure of the latter condition suffices to render the necessary being inconceivable. (Assume I can conceive of a Godless world. That possible world doesn't disappear when I turn to the question of whether God might necessarily exist. It can rightly influence my modal reasoning. In particular, it rightly precludes the possibility of God existing in every possible world, for I can see all along that he doesn't exist in that one.) More generally: there are not multiple conceivable modal spaces, for that would require, impossibly, that there be more than one maximal space of individually coherent scenarios.
This view effectively rules out from the start the challenge from meta-modal conceivability posed to modal rationalism. One might thereby complain that it is question-begging. But I think the picture I've presented is independently attractive, and so might be better described as disarming the challenge. At the very least, it may be employed defensively by the modal rationalist to explain why they are not troubled by the meta-modal arguments, even if the challenger remains unconvinced. What do you think?
Tuesday, August 08, 2006
Actuality and Counterfactuality
Suppose that, homicidal maniac that you are, you confess to me: "I would kill all my enemies if I thought I could get away with it." (I'll condense this to "SAFE []--> KILL ENEMIES".) What does this mean, exactly? Brit Brogaard suggests that the consequent is triply ambiguous. It could refer to your actual enemies, or to the enemies you would have if the antecedent (SAFE) were satisfied, or else to those of your actual enemies that would still exist were SAFE satisfied. (I may have picked a bad example, if the antecedent is itself similarly ambiguous, but we could replace it with, e.g., "if I could turn invisible...", to ensure that the same possible world w is invoked in all three analyses.)
None of these analyses seems entirely satisfactory, though. Suppose that the nearest possible world where you can turn invisible (or whatever) is also one where you became a pacifist. So, in that world w, you wouldn't kill anyone: not your local enemies, and certainly not your actual enemies (who may just as well be strangers or friends to you in w). Understood in possible-worlds terms, the counterfactual is then strictly false, no matter which way you interpret it. Still, it seems to me, the original confession need not be mistaken, if the only thing holding back your homicidal tendencies in the actual world is the fear of getting caught.
What happens in other possible worlds seems less relevant here. So what if it happens that the satisfaction of the SAFE condition would coincide with your becoming a pacifist? It doesn't change the fact that, as things stand, you're a dangerous maniac. (No offense, heh.) Your confession serves to relate your actual dispositions, rather than claiming anything about (potentially deviant) counterfactuals.
[I should note that Brandon and Chris offer some interesting discussion on related issues.]
But perhaps that's extra pragmatic information that we take away from the conversation, beyond its literal truth conditions. My intuitions are a bit vague here, but I guess there's some pull to concede that your assertion would be literally false in the scenario I've described. Perhaps the point is simply that it isn't meant to be understood literally.
Quick poll: what do you think are the truth conditions of the confession? What about its meaning?
Monday, July 24, 2006
Essence and Identity
Essentialists take seriously the idea of de re modality, and claim that "the modal properties of an individual (properties such as being essentially F or possibly G) are had independently of the way in which the individual is referred to." (Della Rocca, p.226.)
I once outlined a couple of Quinean anti-essentialist arguments in this old post:Quine points out that a single object X can be equally well specified by either of the following two descriptions:
(1) The number of planets in our solar system
(2) 7 + 2
Now, he asks, is it a necessary truth about X that it is a number greater than 7? Well, it depends which specification you use. Of course [7 + 2] is necessarily greater than 7; but [the number of planets in our solar system] surely is not. So, it seems, we can't really say anything about X objectively, i.e. independently of how we specify it.
Such concerns may be countered by noting that description (2), but not (1), is a rigid designator, referring to the same object X -- the number 9 -- in all possible worlds. There are possible worlds in which description (1) would be satisfied by some object other than X, but this does nothing to show that the object X itself could fail to be greater than 7.
But note that rigid designation presupposes trans-world identity. You can't pick out the same object in all possible worlds unless there's some criterion to determine which other-worldly objects are the same as each other. It requires that possible worlds come with objects' identities "built in", so to speak. (Kripke proposes that we simply stipulate that we're talking about the possibility in which this very man wins the election, or whatever.) Well, perhaps that's too strict. Really all we require is that there be an objective answer to the question of "which object is X?" in any given possible world. The answer needn't be explicitly "built in", so long as we can extract it, say with an appropriate counterpart theory. If the counterpart relation is objective and determinate, then the essentialist could obtain something close enough to "rigid designation" simply by adopting that intension which picks out the counterpart of X in each world where one exists.
What the anti-essentialist requires, then, is a relativistic counterpart theory. That would mean that there's no uniquely correct answer to "which object is [the counterpart of] X?" in a possible world W. Rather, it will depend on which actual properties of X are most salient in the present context. The counterpart of X in W will be whatever W-object is most relevantly similar to the actual X, but what's "relevant" can vary from context to context. So one cannot hope to rigidly designate X any longer, since there's no objective fact as to which W-object is X. (Sometimes you'll want Y as the counterpart, and other times, Z.)
On this view (recently mentioned in passing here), there are no haecceities, or deep metaphysical facts about identity. Of course it's trivially true that each object (in world w at time t) is self-identical. But there are no objective facts about trans-world identities (nor presumably cross-temporal ones either -- compare Parfitian reductionism about personal identity). There are merely distributions of property-clusters across space and time, and there is no "further fact" about whether two such clusters are really the "same" object. Once we settle the qualitative facts, there is no further work to do. If it's agreed that the Twin Earth scenario is possible, no deep question remains as to whether the watery stuff in the lakes and rivers is really water. The difference is merely semantic.
We can still talk about modal properties, but they really belong to the words, not the objects. To say that water is necessary H2O is merely to say that our terms 'water' and 'H2O' have the same (secondary) intension. It's a metalinguistic claim, not a metaphysical one. To say that I'm "essentially human" is merely to say that anything non-human is excluded from the intension of 'RC'. It's not really saying anything deep about me, or my nature across other possible worlds. For the anti-essentialist, there's nothing deep to be said. (That's not to deny that there can be practical reasons for adopting some intensions rather than others.)
Suppose the world could have been such as to contain nothing but a pair of qualitatively indiscernible dice. We can give a full description of them: red with white pips, a certain size, etc. Are they the same dice as the ones on my desk? Or a pair that happen to actually be in Las Vegas? Or are they not to be identified with any actual dice at all? The anti-essentialist suggests that these are empty questions. The qualitative description gave you the possibility. There aren't any further "identity facts" to settle. There aren't different possibilities corresponding to each possible identity of the dice. No, there's just the one scenario being described, and we've already said what it contains.
I find that part of the story pretty plausible. Here's a more radical step: the dice roll, and one lands on '3', the other on '4'. Might it instead have happened that the former landed on '4', and the other on '3'? Is that a different possibility? It could be if this time the '4' lands first, or in a different position, or otherwise involves a different distribution of qualitative properties through space and time. But suppose all that remains the same. What we're considering is a switch in identities alone, with all else held fixed. If you think identity is a "further fact", then such an haecceital "switch" should be possible. But I think I want to deny this, and again claim that there's just the one scenario here, so that once the full qualitative description is given, there's nothing more left open.
After all, if you allow the two dice to switch identities without any outward symptom of the change, where do you draw the line? Couldn't just one of them switch identities with another non-existent die? Or perhaps the other could become the Las Vegas die? There would be an infinity of qualitatively indiscernible possible worlds, and that seems a tad excessive.
Are there any serious disadvantages to the anti-essentialist, anti-haecceitist view? One might worry that it returns the wrong probability verdicts: we should think it twice as likely to roll a 3 and 4 than two 4s, presumably because there are two ways the former can occur. But you don't need haecceities to recognize that. When you look at the full range of qualitative possibilities, including some where the 3 lands x seconds before the 4, and vice versa, there may be indefinitely many qualitatively discernible possibilities. If we look at the ratios of resulting frequencies, we'd presumably find that twice as many of these scenarios involve a 3 and a 4, as opposed to two 4s. No haecceities needed.
P.S. I think this view might be equivalent to a super-essentialist view which sees all -- even extrinsic or relational -- properties as "essential" to an object. We could effectively deny that anything in other possible worlds is identical to the actual me, just like, strictly speaking, my future temporal parts are non-identical to my past temporal parts. We have no essence that endures through time, nor across modal space either. You can construct four-dimensional spacetime "worms", and if we add other possible worlds into the mix then that could give a fifth dimension. But there's something a little bit arbitrary about the resulting entities. Some are more gerrymandered than others, and we'll generally find it more useful to talk about the less blatantly gerrymandered ones. But we might deny that these are wholly natural divisions of reality in the first place. We might have at least some discretion to divide up the worlds into 5-D "objects" as we please. And of course when you draw the lines yourself, it doesn't mean a lot when you later note that they never cross certain boundaries. You're merely commenting on your own classificatory habits, not the deep structure of reality-in-itself.Reference: Michael Della Rocca (2002) 'Essentialism versus Essentialism', in Gendler and Hawthorne (eds.) Conceivability and Possibility.
Sunday, July 23, 2006
Modal Quasi-Realism
In his paper 'Morals and Modals', Simon Blackburn extends his quasi-realism into the realm of modality, apparently inviting us to simply identify possibility with ideal conceivability:The context here is that Craig had demonstrated decisively the imaginative block that faces us when we try to conceive, in proper detail, of a counterarithmetical reality. The projectivist is then poised to see this imaginative block as something expressed when we insist upon the necessity of arithmetic. But Wright commented, 'If as Craig makes plausible, we are unable to conceive of how any alternative determination might be viable, then that is how things are with us; it is a further, tendentious step to inflate our imaginative limitations into a metaphysical discovery'. And Craig, acknowledging that he and Wright agree that we should not ask the imagination to do too much, concedes immediately: 'It certainly is a further step'. Is it so clear that there is a further step? Only if claims of necessity are 'metaphysical discoveries', and this the projectivist will query. (Essays in Quasi-Realism, p.60)
He clarifies this by analogy to his meta-ethical position (p.70):We do not find it trivial to cross from a sentiment to a moral judgment. Only certain sentiments -- those of a certain strength, or with certain objects, or those accompanied by sentiments about others who do not share them -- form a jumping-off point. We are also conscious that there are doubtless flaws and failures in our sentiments, which are perhaps capable of explanation in the same way that we explain the defects of those who are worse than ourselves. But when the sentiments are strong and nothing on the cards explains them by the presence of defects, we go ahead and moralize. We may be aware that our opinion is fallible, but that is because we can do something with the thought of an improved perspective, even when we are fairly certain that one will not be found, and here as elsewhere commitment can coexist with knowledge that we may be wrong. The 'step' from a fully integrated sentiment of sufficient strength to the moral expression now becomes no step at all: the moral is just the vocabulary in which to express that state. Avoiding it would not be an exercise in modesty, but an impoverishing idiosyncracy of expression.
Why should it not be like this with logical necessity? We have arrived at the residual class of propositions of whose truth we can make nothing. We cannot see our failure to make anything of them as the result of a contingent limitation in our own experience, nor of a misapprehension making us think that their truth should be open to display in a way in which it need not be. We express ourselves by saying that they cannot be true -- that their negations are necessary. There is the bare possibility of being shown wrong -- perhaps our search into the causes of our imaginative block was inadequate, or perhaps we were under a misapprehension of what it might be for the proposition to be true. We may be uncomfortably aware of even great philosophers who mistakenly projected what turned out to be rectifiable limitations of imagination -- the a priori has a bad history. But as Wright notices, we should have no wish to make ourselves infallible when deeming things a priori. We make the commitment in light of the best we can do. There is no step, and no illusion.
Yet I think I can make something of the idea that ideal conceivability and metaphysical possibility might come apart. Talk of how the world could have been, and talk of what can be coherently imagined (with idealized cognitive powers), are not obviously synonymous. There's plausibly a link of sorts: we typically take conceivability as at least a guide to possibility. There may even be a perfect coincidence between them, so that all and only logical possibilities are ideally conceivable. But does that really mean that apriority and necessity are one and the same thing? Or can we somehow separate them, even without any metaphysical divergence that we can latch on to? (Might there be a sense in which one holds "in virtue of" the other, for instance? Or are they the same thing just under different "modes of presentation"? How else might we make sense of this?)
Monday, July 17, 2006
Possible Alternatives You Can't Possibly Take
Here's another way to illuminate the distinction between content-based and brute modality. The former is merely a matter of identifying alternatives ways for worlds to be. The latter is concerned with whether those ways really had a chance to be actualized.
Imagine yourself wanting to buy a Ford back in the days when you could have "any colour you want, so long as it's black." All the cars are black. But blue cars were still possible, in the sense that a car's being blue is an alternative to its being black. (On this understanding, "possible alternative" is redundant. Possibilities just are alternatives to the way things are.) But it's not an alternative you, as a car-buyer, have access to. It's not an option you can take. So a blue car is not a possibility in this more involved sense.
Of course, that latter sense is a lot narrower than metaphysical possibility, even of the brute sort that I have in mind. The analogy is imperfect. But I hope it is at least suggestive. We can imagine other world-states that are alternatives to this one. That gives us the standard space of possible worlds. But it's a separate question whether they're possibilities that "could have been taken" (by God, or the cosmos, or whatever). We can still ask whether they are really possible, in this more demanding sense.
The question can be reworded using the lump/property picture described in my previous post (but ignore the essentialism stuff). Each alternative is a property. But, we may think, that by itself is a merely ontological fact: these abstract states exist. One of them is actually instantiated by the world-lump. But what is the modal status of the other world-properties? They're alternative properties to the one that's actually instantiated, but are they ones that "could have been taken", that really could have been instantiated by the lump? (It probably isn't fair to make the word "really" do so much work here. Unfortunately, I can't think of any better alternatives...)
Some questions:
1) Am I making any sense here? Are there any clearer ways to get at this "brute modal" notion?
2) Is the notion itself fully coherent?
3) Does it correspond to reality? (Is this brute modal status held by some events but not others, say?)
4) Can we establish either way whether all possible worlds are "really possible" in this sense?
5) Are there any other questions I should be asking here?
World Essentialism
Recall the distinction between the singular world vs. the various possible ways a world could be. (The latter are misleadingly called "possible worlds", but are better understood as world-states, or maximal properties.) We may think of the universe as a "lump", and the actualized possible world as the maximal "property" instantiated by the lump. But note that in general, it isn't the case that every object could instantiate any property. The entity that I am, for instance, is essentially human, and so couldn't instantiate the property of being a poached egg. (If an evil wizard transformed me into a poached egg, then the resulting object wouldn't be me any more.) This then raises the question of whether the world-lump has any essential properties, or whether it could actualize any possible world-state whatsoever whilst retaining its identity. Put in more intuitive terms, we can ask: could our world have turned out in any possible way? Or are some possibilities so extreme that they could only be realized by a different underlying universe?
I'm inclined towards anti-essentialism here. It seems tidiest to say that each possible world-state is a way our world could have been. But to explore the alternative, I think the most likely candidates for essential world-properties would be the laws of nature. We would then say that our world could have turned out in any nomologically possible way. It remains true that there could have been different laws of nature, but not in our universe. A change so radical would disrupt its very identity, and turn it into a different universe. (Just like turning me into a poached egg. The radically different properties can be realized, but only by a different entity.)
One might also want to build in the "initial conditions" of the universe as being part of its essential nature. Then, if the laws are deterministic, we would reach the conclusion that our world couldn't have turned out differently at all. (Again, things could have turned out differently. But that would be because a totally different universe existed in place of ours.) If indeterminism is true, at least a few more possibilities are opened up for us. But they will still be extremely limited compared to what philosophers usually take to be possible ways our world could have been.
This narrow account of local possibility might line up with pessimistic accounts of primitive modality. It doesn't settle those broader questions though. We are still left wondering whether, say, another universe with different laws really could have existed in place of ours. (This lack of progress is unsurprising, though, since I'm inclined towards a deflationary understanding of de re modality and debates about essentialism as merely terminological. There are no deep facts about my not possibly being a poached egg. All this really means is that of any entity that was a poached egg, we would refuse to hold it in the extension (or intension) of 'Richard Chappell'. Haeccaeities or identity facts are not fundamental aspects of modal reality. But that's a post for another day.)
But for those who take essentialism more seriously, do you think anything is essential to our world-lump?
Sunday, June 25, 2006
Bootstrapping Possibility as Conceivability
I previously introduced epistemic modality as effectively involving the familiar space of possible worlds under a different mode of presentation. (I hope that's not too misleading a summary; do read the linked post if you're not familiar with it.) This view assumes a plenitude of metaphysical possibilities, which is very plausible but might be denied by some. For example, a theist who holds that God's existence is metaphysically necessary but not a priori thereby admits more epistemic scenarios than he does possible worlds, and so must insist that the two modal spaces are distinct. To accommodate such views, Dave Chalmers (see, e.g., section 5 of his epistemic space paper) describes how we could construct epistemic modal space from purely epistemic notions. Say, P is (deeply) epistemically possible iff P is ideally conceivable (i.e. ~P is not knowable a priori). But what kind of modality is involved in those "ables" (knowable, conceivable)?
Metaphysical modality won't do, since that would defeat the stated purpose. For example, one might hold that ideally rational agents are brutely impossible. But we require such an idealization for this epistemic modality nonetheless. ~P might be a priori even if there is no brute metaphysically possible world containing an agent who a priori knows ~P. So this is not the appropriate sense of "a priori knowable".
Given our independent grasp of apriority (as demonstrated in the previous paragraph), we might simply take as a modal primitive the kind of possibility involved in something's being "a priori knowable". That seems the safest option.
Intriguingly, Chalmers hopes that we might instead be able to take it to be epistemic possibility. This seems circular: P is epistemically possible iff it is not epistemically possible that an agent knows ~P a priori? Where has the idealization gone? Here Chalmers appeals to a kind of "bootstrapping" effect. The core idea is that although we're far from ideal reasoners ourselves, we can conceive of slightly more ideal reasoners, who in turn could conceive of even better reasoners, and so forth, until we reach ideal conceivability.
It's a neat idea, but still seems to rest pretty heavily on an independent primitive modality. We need it to fill out the claim that our imagined reasoners could do better than us, and to let their improved results be sufficiently "real" to contribute to modal reality. If our actual reasoning powers were bedrock, then it's hard to see how we could get beyond them. Second-order possibility (what we imagine our better reasoners could imagine) would seem to revert back to first-order modality, with all our limitations. The bootstrapping effect just can't get off the ground. It needs some independent modal element, so that the imagined agents could do more than we can conceive of them as being capable of.
We could then say that our non-ideal imaginings tap into this irreducible modal reality. It might even be traceable through the kind of bootstrapping procedure described above. Plausibly, we can imagine better reasoners, and they in turn also could imagine better yet, and tracing these conceptions through modal space would eventually map out the full idealization. But the "can" and "could" here presuppose the full idealization, and so cannot be used to reductively construct it. We can find our way to the end point only if we have its help right from the start.
(Disclaimer: I'm not entirely confident that I've understood Dave's position here. When I asked him about it after the conference, he suggested that we might be able to imagine a kind of general "blueprint" for a better reasoner, and that this would suffice to determine -- perhaps through some kind of mathematical necessity -- the stage-2 modal facts, even if the details go beyond what we can grasp in our ground position. So that doesn't sound entirely reductionist in any case. The modal properties of the blueprint must be grounded in something other than our actual epistemic capabilities. *shrug*)
P.S. This is all inspired by the recent Epistemic Modality conference -- Kenny offers a general overview.
Wednesday, May 24, 2006
Considering as Actual
Jessica Owensby-Sandifer (not to be confused with the other Sandefur!) offers an interesting argument against Chalmers' two-dimensionalism. It's a thoughtful piece which nicely (though unintentionally) illustrates the confusion which can arise from the standard picture of modal space.
The core problem, which Jessica recognizes, is that the standard picture leaves no room for the possibility of any other world being actual, "because for each universe there can be only one actual world." (I assume 'universe' here denotes modal space, or what I sometimes call the 'modalverse'.) She accepts this result and in response proposes a meta-modal space, i.e. a space of modalverses, so that each possible world can be actualized in a different modalverse. I guess this would mean that even though no other world can (in fact) possibly be actual, perhaps it's possible that this could have been possible. It's not true in any possible world of our modalverse. But it is true of another possible world in another possible modalverse. (I find such meta-modal claims deeply fascinating, but of dubious coherence.)
I think that's the wrong response, though. We should instead take the above 'narrow fatalism' to be a reductio of the standard picture. Jessica writes, "Central to the intuitive notions underlying a theory of actuality is the idea that something distinguishes the actual world from being a merely possible world." Indeed. I say that this concrete lump of ours isn't any kind of possible world at all ("merely" or otherwise!). If we think of possible worlds as being maximal properties, then our lump instantiates just one of those properties, which we might call the "actualized world-state". But the lump should not be identified with the property. It could have instantiated a different property, after all (whereas the first property has its identity essentially, and so could not have been the second property). In that case, a different possible world-state would have been actualized. And, intuitively, that's exactly what it means to say that another possible world could have been actual. It means that our concrete lump (*thumps table*) could have turned out a different way. It happens to instantiate world-property w1, but it could have had w2 instead. (Note that these are primitive extra-modal facts which cannot be spelled out using the standard "possible worlds" semantics.)
Now, Jessica wants to suggest a special problem for the two-dimensionalist's notion of "considering a world as actual". She writes:It my contention that, no matter which theory of actuality one assumes, to consider another world as actual is to make a metamodal claim about the possibility that some other world is actual in another universe or cosmos.
But that can't be right. To consider a world as actual is to invoke the epistemic rather than subjunctive mode of possibility. To consider w2 as actual is to entertain the hypothesis that our lump (not some other one) actually instantiates w2. After all, this might really be the case for all we know a priori.
The lump/property distinction is crucial for making sense of this. For suppose all we could refer to as the 'actual world' is our world-property w1. Then to consider the distinct world w2 "as actual" would be to consider w2 as w1. But that's incoherent. Of course, that's not what anyone takes themselves to be doing when they consider worlds as actual. We're not considering one "world" or property to be another world/property. Rather, we're considering that world to be actual (*bangs table*), i.e. for the property to be actualized by the extra-modal lump.
A simple example might help clarify matters. Let w2 be the Twin Earth world, where XYZ fills the lakes and rivers. We can consider this world as actual, and come to the conclusion that 'water is XYZ' is 1-possible. This is because we're told that XYZ plays the water role in w2, and it's a priori that water actually plays the water role, and hence the indicative conditional "if w2 is actual then XYZ is water" is a priori. No problems.
Even if water is actually H2O, that doesn't mean we were entertaining the hypothesis that H2O is XYZ. That's not how epistemic possibility works: 'H2O' and 'water' are distinct concepts, even if they are actually the same substance. It certainly isn't a priori that "if w2 is actual then XYZ is H2O" -- indeed, that's a priori false! So we need to take care to distinguish the general notion of 'actuality' from the specific world-property which happens to be actualized.
(Another way to respond here would be to invoke the de dicto/de re distinction as it applies to the indexical analysis of 'actual'. For more on this, see my post: P iff actually P.)
Sunday, May 14, 2006
In Good Company
Re-reading Naming and Necessity, I find that Kripke anticipates my claim that The Actual World is not a Possible World:The 'actual world' -- better, the actual state, or history of the world -- should not be confused with the enormous scattered object that surrounds us. The latter might also have been called 'the (actual) world', but it is not the relevant object here. Thus the possible but not actual worlds are not phantom duplicates of the 'world' in this other sense. Perhaps such confusions would have been less likely but for the terminological accident that 'possible worlds' rather than 'possible states', or 'histories', of the world, or 'counterfactual situations' had been used. (pp.19-20)
Note that what he calls the 'actual world' is what I would call the possible world/scenario corresponding to our concrete world. But despite the terminological difference, the key point is the same: this correspondence is not identity.
Thursday, May 11, 2006
Global Supervenience and Physicalism
One class of facts supervene on another if the former couldn't differ without a change in the latter. I've previously talked about this a lot in connection with morality, for instance: you couldn't have a world that was identical to our own in all respects except that Hitler was a good person. Because the moral facts supervene on the non-moral, the only way to change the former would be also to change the latter. (If Hitler had stayed out of politics and instead become a harmless hermit, then perhaps he would not have been so evil.)
Now, it seems to me that mostly all facts supervene on the physical. (The main exceptions being facts about phenomenal consciousness, and anything else which in turn supervenes upon those.) Indeed, this seems kind of obvious. But sometimes people object to such claims by adopting an overly restrictive view of the physical. For example, they might consider two objects which share all their intrinsic physical properties and yet differ in the supposedly supervening property X. But that merely demonstrates a failure of "local supervenience". X doesn't supervene on this restricted cluster of "local" physical facts. But that does nothing to refute the claim that X supervenes on the totality of physical facts. You can't just ignore all the relational physical properties and pretend you have a counterexample. Not that some people don't try.
A recent example is provided by the Maverick Philosopher, who writes:But the reference is indeterminate if we go by the physical properties of the representations alone. Suppose I hand you two drawings of your mother, one an exact copy of the other, but you do not know which is the orig[i]nal and which is the copy. You cannot, by inspection of these drawings, tell which is which. Thus you cannot determine the reference from the physical properties.
But you cannot, by inspection alone, tell all of the physical properties of the drawings. You cannot tell, for instance, at what time each was drawn. But that's clearly a physical fact about the drawings. And clearly if someone knew all the physical facts, in this appropriately broad sense, they would no longer have any difficulty determining which drawing was the copy.
So BV has done nothing at all to show "that materialism doesn't work" (where "materialism" is synonymous with "physicalism", i.e. the claim that all facts supervene on the physical facts). He's shown that intentionality doesn't locally supervene on some restricted class of physical facts. But that shouldn't be surprising. Of course if we overlook some physical facts, then we won't be able to derive some other truths (say, about what a drawing refers to). That's because you're ignoring some crucial facts! The appropriate response is to open your eyes, not reject physicalism. (Actually, I think we should reject physicalism for other reasons. But this sorry argument surely isn't one of them.)
This confusion can also arise in discussions of scientific reductionism, and whether the biological supervenes on the physical. You couldn't have a world physically identical to our own in all respects, but somehow biologically different. There couldn't be any differences in species, for example, or in which organisms are living or dead, without some physical difference in the world. One might suggest that biological kinds aren't determined by the laws of physics alone; they also depend on physical history. But of course physical history is included in the class of physical facts, so we never should have excluded that in the first place. The thing to consider here is the entire 4-dimensional space-time "loaf" (encompassing past, present, and future), not just little bits of it.
Incidentally, this is a nice chance to talk about misusing the "vitalism" analogy. Recall our past discussion of how Kripkean examples of conceivable impossibities (e.g. Hesperus' being non-identical to Phosphorus) do nothing to support the impossibility of zombies. Another bad analogy often invoked in defence of materialism is that of vitalism: "People used to think that being alive was something beyond the physical, but science later proved them wrong. Why think consciousness is any different?"
But 'life' can clearly be analysed in functional and structural terms. There is no sense to be given to the notion of something that is functionally and structurally indiscernible from a duck, having all the same kinds of relations to other objects as another duck does, and yet somehow fails to really be a living duck. To be a living duck just is to have the right kinds of functional relations and so forth. There's nothing more to it than that. Not even vitalists disagreed, as Chalmers explains:Vitalists typically accepted, implicitly or explicitly, that the biological functions in question were what needed explaining. Their vitalism arose because they thought that the functions (adaptation, growth, reproduction, and so on) would not be physically explained. So this is quite different from the case of consciousness. The disanalogy is very clear in the case of Broad. Broad was a vitalist about life, holding that the functions would require a non-mechanical explanation. But at the same time, he held that in the case of life, unlike the case of consciousness, the only evidence we have for the phenomenon is behavioral, and that "being alive" means exhibiting certain sorts of behavior. Other vitalists were less explicit, but very few of them held that something more than the functions needed explaining (except consciousness itself, in some cases). If a vitalist had held this, the obvious reply would have been that there is no reason to believe in such an explanandum. So there is no analogy here.
Now, we do indeed have every reason to believe that physical science can provide adequate functional explanations. But consciousness is different in that it cannot be analysed in functional terms. That's what zombies show us, for example: we can imagine creatures functionally indiscernable from ourselves, that nevertheless lacks conscious experience. Whatever consciousness is, it isn't just the having of certain functional relations. That's not what we mean by the term - our phenomenal concepts are something quite different.
One might more plausibly hold that our brain states "give rise to" our conscious states. But this is already to recognize that they are two different things, even if a (natural) lawful connection holds between them. The natural laws might have been different, after all. And in that case there might have been the same physical stuff but without giving rise to any phenomenal stuff. So that's why the phenomenal isn't reducible to the physical. (At most it supervenes nomologically, not metaphysically.)