Posts on: Modality
Friends of primitive powers and dispositions often contrast their
view with an alternative view, usually attributed to Lewis, on which
modal facts about powers, dispositions, laws, counterfactuals etc. are
grounded in facts about other possible worlds. But Lewis never held
that alternative view – nor did anyone else, as far as I
know. The allegedly mainstream alternative is entirely made of
straw. The real alternative that should be addressed is the
reductionist view that powers and dispositions are reducible to
ultimately non-modal elements of the actual world.
The two-dimensionalist account of a posteriori (metaphysical)
necessity can be motivated by two observations.
First, all good examples of a posteriori necessities follow a priori
from non-modal truths. For example, as Kripke pointed out, that his
table could not have been made of ice follows a priori from the
contingent, non-modal truth that the table is made of wood. Simply
taking metaphysical modality as a primitive kind of modality would
make a mystery of this fact.
In On the Plurality or Worlds, Lewis argues that any account
of what possible worlds are should explain why possible worlds
represent what they represent. I am never quite sure what to make of
this point. On the one hand, I have sympathy for the response that
possible worlds are ways things might be; they are not things
that somehow need to encode or represent how things might be. On the
other hand, I can (dimly) see Lewis's point: if we have in our
ontology an entity called 'the possibility that there are talking
donkeys', surely the entity must have certain features that make it
deserve that name. In other words, there should be an answer to the
question why this particular entity X, rather than that other entity
Y, is the possibility that there are talking donkeys.
For every way things might have been there is a possible world where
they are that way. What does that tell us about the number of worlds?
If we identify ways things might have been ("propositions") with
sentences of a particular language, or with semantic values of such
sentences, the answer will depend on the language and will generally
be small (countable). But that's not what I have in mind. It might
have been that a dart is thrown at a spatially continuous dartboard,
and each point on the board is a location where the dart's centre
might have landed. These are continuum many possibilities, although
they cannot be expressed, one by one, in English.
It is natural to think of a possible world as something like an extremely specific story or theory. Unlike an ordinary story or theory, a possible world leaves no question open. If we identify a theory with a set of propositions, a possible world could be defined as a theory T which is
- maximally specific: T contains either P or ~P, for every proposition P;
- consistent: T does not contain P and ~P, for any proposition P;
- closed under conjunction and logical consequence: if T contains both P and Q, then it contains their conjunction P & Q, and if T contains P, and P entails Q, then T contains Q.
It is often useful to go in the other direction and identify propositions with sets of possible worlds. We can then analyse entailment as the subset relation, negation as complement and conjunction as intersection. Of course, we may not want to say that a world is a (non-empty) set of (consistent) propositions and also that a consistent proposition is a non-empty set of worlds, since these sets should eventually bottom out. But that doesn't seem very problematic, and it is easily fixed as long as there is a simple 1-1 correspondence between worlds and logically closed, consistent and maximally specific theories. In particular, one might suspect that on the present definitions, every logically closed, consistent and maximally specific theory uniquely corresponds to a possible world, namely the sole member of the intersection of the theory's members.
As a principle of plentitude, Recombination for Individuals is far too weak. If there happens to be nothing that is both red and dodecagonal, the recombination principle for individuals gives us no world where anything is. Likewise, if it happens that no red thing is on top of a blue thing, the principle gives us no world where this is different. But combinatorial reasoning seems to give us such worlds.
Many versions of the recombination principle are floating
around in the literature. Most of them are principles for individuals,
saying, roughly, that you get a possible world by patching together
(copies of) arbitrary parts of other possible worlds. (I will have
more on principles for properties later.)
It is surprisingly difficult to make this precise. All attempts I
know of fail in one way or another. To illustrate some of the
pitfalls, let's begin with this classic version from Daniel Nolan's
"Recombination Unbound".
Here's something puzzling. Suppose sometime in 1869, Frege uttered
1) more people today die of tuberculosis than of cancer.
As far as I know, this was true in 1871, but it is no longer true now. Today, more people die of cancer than of tuberculosis. On the other hand, suppose Frege also uttered
2) I am not particularly well-known among philosophers.
This, too, is no longer true. Today, Frege is exceptionally well-known among philosophers.
Here is a short paper version of my GAP.6 talk "Modal metaphysics and conceptual metaphysics", to appear in the GAP.6 proceedings. It has a lot less formulas than the talk.
I distinguish two metaphysical projects: modal metaphysics and conceptual metaphysics. I show that the two projects really are distinct, and that Frank Jackson's argument for the opposite conclusion doesn't work. Then I have a closer look at how the projects come apart, and suggest that when they do, the modal project always becomes metaphysically uninteresting. Thus the term "metaphysical modality" is a misnomer: metaphysical entailment only matters for metaphysics insofar as it coincides with conceptual entailment.
I suppose I should say a little more on what I call "modal back-reference", and on the sense in which what a sentence expresses can be conceptually independent of how things are in the actual world: doesn't what a sentence express always depend on what the sentence means? Unfortunately, I don't have a simple and uncontroversial answer to that, so I just ignored this point. Hopefully no-one will notice.
Just when I thought all viruses are specific, I caught an 'unspecific virus' last weekend -- at least that's what the doctors at the hospital identified it as. So I've been knocked out for about a week, but now I'm back with an exciting new theory of modality.
The theory is simple. It says that everything is possible. Pace Kripke, there are possible worlds where Queen Elizabeth is a poached egg and where Hesperus isn't Phosphorus. And pace almost everybody else, there are possible worlds where squares are round, bachelors married and where Hesperus isn't even self-identical.
Is it metaphysically necessary that like charges repel? One might think so: one might think that "charge" is partly defined by its theoretical role, so that this claim comes out analytic. Or one might think that science reveals to us the essence of properties, and that it is part of this essence of charge that like charges repel.
If that law about charges is metaphysically necessary, one might suspect that quite generally, nomological necessity coincides with metaphysical necessity (though see below for an argument against this suspicion):
So I was given a replacement computer now until the other one arrives. If you're waiting for a sign of life from me, I'll probably contact you soon.
But first some philosophy. I want to argue that necessitarianism is compatible with Humean recombinatorialism because powers aren't intrinsic in the sense relevant to this. I also want to suggest that in an ontology of powers, what's fundamental aren't really the powers, but the causal or nomic relations.
Necessitarianism is the view that properties like mass and spin have their causal or nomic role essentially: if a property doesn't behave like mass, it isn't mass. It follows that the laws about mass are metaphysically necessary. (There are many different views in the vicinity here, maybe more about this later.)
Here's an odd passage from Armstrong's A Combinatorial Theory of Possibility, p.116:
[Hume's Distinct Existences Principle], as we shall uphold it, may be stated thus:
If A and B are wholly distinct existences, then it is possible for A to exist while no part of B does (and vice versa).
The principle applies straightforwardly to individuals, properties and relations. [...]
It is interesting to notice that the converse of Hume's principle also seems to be true:
Roughly, the principle of recombination says that anything can coexist and
fail to coexist with anything else. But that's too strong: things do
have essential extrinsic properties; if Kripke's origin is essential
to Kripke, Kripke cannot fail to coexist with his ancestors. However, a
perfect intrinsic duplicate of Kripke could fail to coexist with Kripke's ancestors.
So less roughly, the principle of recombination goes somehow like this:
For any things in any possible world there is a world
which contains any number of perfect intrinsic duplicates of all those
things and nothing else (i.e. nothing distinct from all these
duplicates).
What is a perfect intrinsic duplicate? Something that has exactly
the same intrinsic properties as the original. What
is an intrinsic property? A property that belongs to objects
independently of what exists and goes on around them. The
instantiation of an intrinsic property in some region of a world is
independent of the instantiation of intrinsic properties in other
regions.
I would like to believe that all necessary truths fall into the following two kinds.
1. Analytic truths. By processing the semantic content of such a sentence we can find out that its truth conditions are universally satisfied, no matter how the world turns out and no matter what
other world we talk about.
2. Truths whose evaluation at other worlds depends on contingent features of the actual situation. What we can know by linguistic processing is that if these features are so as to make such a sentence true, then it remains true even when we talk about other worlds, that is, when the sentence is embedded in "at world such-and-such" or "necessarily". For example, if we know that there are sheep, we can figure out that "actually, there are sheep" is necessary, because
it is a rule of our language that (roughly) "actually p" is true at a
world w iff p is true at the actual world. Knowledge about ordinary,
contingent features of the current situation together with linguistic
competence always suffices to learn that these a posteriori necessary
sentences are true.
Imagine a world with nothing but infinitely many duplicate dragons, aligned in one long row. Consider the second dragon in the row. Call it "Fred".
Fred could have failed to exist. There are many worlds where he does not exist. (The actual world is probably one of them). Some of these worlds where Fred does not exist contain no dragons at all, others contain some of the other dragons in Fred's row. In particular, there are worlds where all the other dragons exist, but not Fred. The dragons are after all distinct existences, and there are no necessary connections between those.
Note to self: I sometimes say that metaphysical modality is of S5 type, when I should rather say only that it satisfies the characteristic axiom of S5, Mp -> LMp.
It isn't clear to me that metaphysical modality obeys all the S5 principles because it isn't even clear that it obeys T. One of the problems is what to say about Lp if p contains names of objects which may exist only contingently. The two most obvious proposals are: a) Lp is true iff p holds at all worlds where the named objects exist (in this sense, Hesperus is necessarily Hesperus, even though Hesperus exists contingently); b) Lp is true if p holds at all worlds (in this sense, Hesperus is not necessarily Hesperus, but it is necessary that if Hesperus exists then Hesperus is Hesperus). Either way violates T. On (a), let "F" express the property of coexisting with Hubert Humphrey; then "L(F(Hesperus) & F(Humphrey) -> F(Hesperus)) -> L(F(Hesperus) & F(Humphrey)) -> LF(Hesperus)" is false, even though it's an axiom of T. On (b), "L(Hesperus = Hesperus -> Hesperus = Hesperus)" is false, even though it's a theorem of T.
Well, I know what Counterpart Theory is not: it is not a theory according to which ordinary things do not really exist at other possible worlds.
There are two readings of "ordinary things do not exist at other worlds". The first is a neutral reading on which things exist at another world in the way they sleep at another world or win elections at another world: whatever possible worlds are, they somehow represent things as existing and sleeping and winning. In this sense, something exists at a world iff the world represents it as existing. Anyone who accepts possible worlds talk at all accepts that ordinary things exist at other worlds in this sense.
The difference between linguistic ersatzism, where possible worlds are replaced by sets of sentences, and modal fictionalism, where the pluriverse of all worlds is replaced by a large set of sentences describing all worlds at once, appears to be small. Nevertheless, I (still) think the analytic power of fictionalism is greatly diminished compared to that of linguistic ersatzism.
One of the great advantages of possibilia is that they provide a unified framework to reduce lots of kinds of things: properties can be identified with sets of possibilia, propositions with sets of worlds, meanings with functions from worlds to extensions, events with functions from worlds to regions, and so on. But suppose possibilia don't really exist, but exist only according to some fiction. Then properties can't be sets of possibilia. By the usual rule of interpreting statements about fictional entities, it will at most be true that according to the fiction, properties are sets of possibilia. But that doesn't help us if we're looking for a unified ontology. We'd like to know what properties really are, not what they are according to some fiction. If as fictionalists we think that properties really are sets of possibilia, then we have to conclude that properties don't really exist, just as the (other-worldly) possibilia don't really exist.
According to the Principle of Recombination,
for any things at any worlds there is a world containing a duplicate
of each of these things and nothing else (that is, nothing that is not
a part of the fusion of the duplicates).
Applied to the mereological fusion of David Hume and David Lewis, this says that there is a world containing nothing but a duplicate of the fusion of Hume and Lewis. This duplicate presumably has a part that is a duplicate of Hume and another that is a duplicate of Lewis. How are these parts spatiotemporally related?
The whole four-dimensional universe, including past, present and future times, does not change; it will not be different tomorrow; it remains the same at all times.
If the whole four-dimensional universe remains the same at all times, then presumably no part of it will ever fail to exist or has ever failed to exist.
So for example, the apple I'm just about to eat will never fail to exist. It will exist forevermore. As will I, and you, and this weblog.
There is but one totality of worlds; it is not a world; it could not have been different. (Lewis, Plurality, p.80)
If the totality of worlds could not have been different, then presumably no possible world could have failed to exist.
Then in particular, the actual world, @, could not have failed to exist.
So there is an actually existing thing, namely @, that could not have failed to exist.
Even worse, arguably @ has some of its parts essentially. So there are some actually existing things besides @ that could not have failed to exist.
One might even say that all worlds have all their parts essentially, simply because worlds do not exist at other worlds. Then it follows that no actually existing thing could have failed to exist.
1. There is nowadays considerable evidence for the existence of pulsars. Still, it isn't incoherent to worry that the evidence might be misleading and pulsars don't exist after all. But it is incoherent to worry that pulsars might be the apple trees in my parents' garden. These apple trees aren't neutron stars, and they don't emit regular pulses of electromagnetic radiation, and things that don't do that don't deserve the name "pulsar".
2. Suppose we are convinced by van Inwagen's arguments that fictional characters are abstract entities created by authors and denoted by our fictional names. This suggests the following picture: Over and above our material universe there is a special realm of abstract fictional characters. Everytime an author writes a novel, new entities pop up in this fictional realm. There is no causal connection from the fictional realm to our world. But then how do we know about the fictional characters? How can we be sure for example that the creation of fictional characters is reliable? Couldn't it happen from time to time that a fictional character fails to be created? If so, perhaps Madame Bovary exists, but Sherlock Holmes doesn't. In which case it would be false (on the Kripke-van Inwagen account) that Sherlock Holmes was invented by Conan Doyle or that he is a widely known fictional character. Isn't our confidence in such assertions rather mysterious and irresponsible given that really we have no access at all to the fictional realm? At the very least, the exceptionless correspondence between what our authors do here on Earth and what happens in the fictional realm cries for explanation!
In "The Varieties of Necessity", Kit Fine defends Modal Pluralism. Does he thereby threaten Modal Realism? He says he does (in footnote 5). But does he really?
Well, what is Fine's thesis of Modal Pluralism? Here is his summary:
I conclude that there are three distinct sources of necessity -- the identity of things, the natural order, and the normative order -- and that each gives rise to its own peculiar form of necessity. Neither form of necessity can be subsumed, defined, or otherwise understood by reference to any other form of necessity. (p.279 of Conceivability and Possibility)
It seems that he is mixing several different theses here. In particular,
If haecceitism is true, materialism is false. For if haecceitism is true, there is a world w just like ours except that you and I have traded places. By that I don't mean that in w someone with my origin or my DNA or my soul leads a life quite like yours. No, haecceitism holds that it is possible for us to trade places completely, so that in w not only my life is just like your actual life, but also my origin, DNA and soul are just like your actual origin, DNA and soul. w and our world do not differ in any qualitative respect at all. They differ only in facts that essentially involve you or me, such as the fact that in w it's you who is writing this posting. Whatever 'physical' means, it is clear that the physical facts are not of this kind. That's why materialism is false if haecceitism is true: Materialism demands that there is no difference at all between our world and any minimal physical duplicate of it.
Geoff at Too Much Text points out that the implausible hyper-essentialism implied by Kripke's account of rigidity can be avoided by adopting radical anti-essentialism, the view that there are no non-trivial (qualitative) essential properties at all. On this view, even though there is a precise boundary between a thing's essential and non-essential properties, the boundary is not very mysterious because it classifies virtually all properties as non-essential.
Brute necessity is hard to accept, much harder than brute possibility. If someone claims that necessarily there are no purple cows, I expect an explanation. Perhaps he knows what kind of DNA is essential for cowhood and also that this kind of DNA can never produce purple beings, and he also believes that the laws of nature are necessary. This would make his claim understandable. But suppose he had no such explanation. Suppose in fact that we all know that only a minor mutation would be required to produce purple cows, a mutation perfectly compossible with the laws of nature. And still he claims that there could not be any purple cows. This would seem bizarre.
According to the epistemic account of vagueness, there aren't really any vague statements: When we're uncertain whether to call somebody bald that's not because he is a borderline case of baldness. There are no borderline cases. The border between being bald and not being bald is perfectly precise. It's only that we don't quite know were it runs.
Not many people believe in this account. That's surprising, because many people do believe that there are rigid designators -- terms denoting the same thing in every possible world --, and this seems to imply something that looks to me just like (an application of) the epistemic account of vagueness.
Humeans distinguish between how things are in themselves and how they are related to other things. The latter, they say, is always a contingent matter: Even though this cup of tea is about 20m away from a book and stands on a table, it could very well not be 20m away from the book and not stand on the table. In slogan form, there are no necessary connections between distinct entities.
Understood literally, this leads to a position one might call strong humeanism:
Yesterday, I said that it doesn't really matter whether we regard identity simpliciter as identity-at-our world -- individuationg referents extensionally -- or as identity-at-every-world -- individuating referents intensionally. Suppose we want to do the latter, so that the referent of "the amazon" determines a function from worlds to world-bound individuals, that is, an intension. So on the present account, we identify the amazon with something that completely determines the intension of "the amazon". The intension? What if, as two-dimensionalists argue, "the amazon" has two intensions? Which one is the one we want extensions to determine?
The Brock/Rosen objection against modal fictionalism goes as follows. The modal fictionalist holds that
1) Necessarily p iff according to the modal fiction, at all worlds, P*,
where P* is the modal realist's paraphrase of P, and the modal fiction is the modal realists' theory. But the modal realist holds that it is true at every world that there are many worlds. That is,
2) According to the modal fiction, at all worlds, there are many worlds.
It follows from (1) and (2) that
Lewis does not want to take the worldmate relation (that holds between two things iff they belong to the same world) as primitive. He proposes two alternatives. The first is that things belong to the same world iff they stand in ("analogously") spatiotemporal relations to each other. According to the second, more general, proposal things belong to the same world iff they stand in fundamental external relations to each other, whether or not these relatios are (analogously) spatiotemporal. I'm not sure if I fully understand the difference between these three alternatives. Here is why.
Yesterday I said that Lewis might just shrug off arguments about other-wordly people who, despite being in the same evidential situation as we are and despite using the same kind of reasoning, get the laws of nature and the reference of their terms completely wrong: He could agree that such people are just as possible as similarly deluded people in counter-inductive worlds or even more deluded brains in vats.
But Lewis himself uses an argument of the same form against the non-indexical account of actuality (Pluarlity, p.93):
Fictionalism about a certain discourse is the view that statements belonging to this discourse are to be interpreted like statements in fictional discourse.
Now as Brian has observed, on the common account of fictional discourse, "Fictional(Fa)" implies "(Ex)Fictional(Fx)" (even though it normally doesn't imply "(Ex)Fx"). So one might think that on the common account, fictionalism can't do with fewer entities than realism, even though it can do with different entities. However, the common account is not committed to "Fictional(a != b)" implying "(Ex)(Ey)(x != y)". After all, it usually allows for "(Ex)(Fictional(Fx) and Fictional (not-Fx))", so why not allow for "(Ex)(Fictional(x != b) and Fictional(x = b))"? So maybe one could endorse fictionalism about mathematics and the common account of fictional discourse without being committed to an infinity of entities by claiming that all the "numbers" talked about in mathematics are in fact identical.
In chapter 10 of The Varieties of Reference, Gareth Evans endorses a
counterfactual analysis of truth in games of make-believe: When children
play the mud pie game, an utterance of "Harry placed the pie in the oven"
is true (in the game) iff (roughly) it would be true given that these globs
of mud were pies and this metal object were an oven.
He then notices that this is a problem for the possible worlds analysis of
counterfactuals because the relevant counterfactuals seem to have
impossible antecedents: "there simply are no possible worlds in which these
mud pats are pies" (p.355).
Here comes a positive theory of fictional characters. Disclaimer: Only
read when you are very bored. I've started thinking and reading about
this topic just a weak ago, so probably the following 1) doesn't make much
sense, 2) fails for all kinds of well-known reasons, and 3) is not original
at all. The main thesis certainly isn't original: it is simply that
fictional characters are possibilia. Anyway, I begin with an account of
truth in fiction, which largely derives from what Lewis says in "Truth in
Fiction".
I've been thinking about yesterday's problem from Brian Weatherson's
interactive philosophy blog. Instead of a solution I've found a name:
"Forrest's Paradox" (see §2.5 in Lewis, On the Plurality of
Worlds).
Knowing the name, it is now easy to create even stranger problems of the
same kind. First a reformulation of the original problem.
I am not an expert on modal fictionalism, so probably something is obviously wrong with the following objection. But anyway, here it is.
Modal fictionalism claims that any statement S about possible worlds (and other possibilia) is to be analysed as "According to the possible-world-story, S". Now possible worlds are used in reductive analyses of all kinds of concepts: modality, counterfactuals, causation, laws, properties, propositions, meanings, probabilities, supervenience, fictions, etc. For instance, an analysis of indexicals usually talks about extensions in possible contexts of utterance. If fictionalism is right, then this analysis must in turn be analysed in terms of extension in possible contexts according to the possible-worlds-story. And this seems rather odd. Suppose I propose some theory T of indexicals (or laws or whatever). If fictionalism is right then T is correct iff it is implied by some story about possible worlds. Firstly, intuitively this is not at all what I would have thought my theory was about. Secondly, which possible-world-story is relevant here? If we take the five or six claims about recombination and other worlds being of the same kind as ours usually presented by fictionalists (e.g. Rosen 1990), all the analytic projects mentioned above appear to be doomed: That simple story will not imply anything at all about indexicals, or laws, or causation. Unless of course we extend it by some analysis of these notions. Which analysis? The obvious candidate is the analysis we believe to be true, that is, T. But then all the analytic projects mentioned above come out as trivially true: Even the craziest theory will be good enough to imply itself.
The principle of recombination states what other possible worlds there must
be, given the existence of some possible worlds. In sec. 1.8 of On the
Plurality of Worlds, David Lewis suggests something like this:
L) For any parts of any worlds there is some world containing
any number of duplicates of all those parts, and nothing else , provided that they all fit
into a possible space-time.
Daniel Nolan argues in "Recombination Unbound" that the clause 'and
nothing else' should be dropped, because if some thing B consists of two
duplicates of A, there couldn't be a world containing one B, one A, and
nothing else. Unfortunately, without the clause the principle doesn't
exclude the necessary coexistence of distinct possibilia. In fact, it is
even compatible with all possibilia having duplicates in all worlds. I
think it would be better to leave the clause and instead restrict the
principle to distinct parts of worlds.
It seems to be: I've never heard of anyone being converted to modal realism, or giving it up. In particular, Lewis himself endorses it in his earliest papers, e.g. in the conclusion of 'Convention'. According to this article from the Daily Princetonian, he "worked on" the topic already at the age of 16. Strange.
I'm currently writing a chapter on modal realism.
I don't like this topic because it always confuses me. Here is one such
confusion.
In some world w, pretty much resembling our world, there are two
individuals A and B. Let 'A-in-w' be an extremely rich descriptions of A
that implies every qualitative truth about w, similarly for 'B-in-w'
and B. Now the following two sentences might both be true:
1) If I were A-in-w, I would do X.
2) If I were B-in-w, I wouldn't do X.
Are all truths a priori entailed by the fundamental truths upon which
everything else supervenes? If 'entailed' means 'strictly implied', this
is trivially true. The more interesting question is: Are all truths
deducible from the fundamental truths (deducible, say, in
first-order logic) with the help of a priori principles?
If yes, then it seems that Lewis' 'primitive modality' argument against
linguistic ersatzism (On the Plurality of Worlds, pp.150-157) fails.
Recall: Lewis argues that if you take a very impoverished worldmaking
language then even though it will be feasible to specify (syntactically) what
it is for a set of sentences to be maximally consistent, it will be
infeasible to specify exactly when such a set represents that, e.g., there
are talking donkeys. Now if all truths are a priori deducible from
fundamental truths, and -- as seems plausible -- fundamental truths are
specifiable in a very impoverished language, then we can simply say that a
maximal set of such sentences represents that p iff p is a priori deducible
from it.
Unfortunately, I find the 'primitive modality' argument quite
compelling. So, by modus tollens, I have to conclude that not all truths
can be a priori deducible from fundamental truths. Does anyone know
whether Lewis himself believes the deducibility claim he attributes to
Jackson in 'Tharp's Third Theorem' (Analysis 62/2, 2002)?