Posts on: Two Dimensionalism
An interesting new paper by David Mackay, Mackay (2022), raises a challenge to popular ideas about the semantics of modals. Mackay presents some data that look incompatible with classical two-dimensional semantics. But the data nicely fit classical two-dimensionalism, if we combine that with a flexible form of counterpart semantics.
Before I discuss the data, here's a reminder of some differences between epistemic modals and non-epistemic ("metaphysical") modals.
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.
Let's call the class of counterfactual circumstances at which a sentence S is true the C-proposition expressed by S. This is more or less what Kaplan calls the "content" of S. Here are three reasons why the circumstances constituting a C-proposition should be understood as centered possible worlds rather than old-fashioned uncentered worlds.
First reason: centering is needed for modal embeddings. The standard use of C-propositions is the analysis of modal constructions: "it is possible that hummingbirds can fly backwards" is true iff there is at least one relevant circumstance w at which "hummingbirds can fly backwards" is true. Now take a sentence such as "it is early afternoon", or "it is starting to rain". It doesn't make much sense to say of an entire world that it is early afternoon there, or starting to rain. So on the standard view, on which the circumstances in C-propositions are uncentered worlds, we first have to fix a time and place, presumably by drawing on the utterance context: "necessarily, it is early afternoon" is true iff it is early afternoon at every possible world at the time and place of the utterance. So "necessarily, it is early afternoon" is true whenever it is uttered on an early afternoon. That seems wrong.
Everyone who has taught Kripke and Putnam to undergraduates knows that philosophers nowadays use "truth at a world" in a special, technical sense that requires a lot of explaining. The most straightforward way to assign a sentence a truth value at another world w is to consider an utterance of the same words in w and ask whether or not that utterance is true. But this is not what we mean. Nor do we ask what truth value the sentence has conditional on the assumption that our world is w. (Lewis uses "truth at a world" in roughly this sense in "How to define theoretical terms"; the current convention appears to be really quite new.) What, then, do we mean? I find most introductions of the concept utterly obscure: I'm told to identify the 'proposition expressed' by a sentence in the actual world, and then to 'evaluate' this entity at another possible world. What on earth does that mean?
Does the conceivability of zombies threaten type-A materialism, the claim that all mental truths are a priori entailed by the physical truths?
We can imagine beings exactly like us in all physical respects, but lacking consciousness. But this doesn't threaten type-A materialism (as I mentioned here). After all, it isn't a priori that materialism is true. It could have turned out that ectoplasmic states, rather than brain states, occupy the causal roles that, by analytic necessity, belong to mental states. Suppose it turned out that way. Then duplicating only our physical constitution would result in a being that is physically just like us, but lacking consciousness. So by type-A materialist lights, it is conceivable that things are such that there are beings physically just like us without consciousness.
Sorry, the server has been down quite a lot recently. Hope it's back to normal now.
Here's the talk I gave at Kioloa. It's partly identical to the talk I gave at GAP.6 in Berlin, but with more speculative ideas towards the end and less missionary appeals in between.
Are all truths entailed by logical truths? Depends on what we mean by "all truths" and "entailed" and "logical".
Let's understand a truth to be a true sentence of English, possibly enriched by logical vocabulary. As for entailment, let's distinguish metaphysical entailment (necessarily, if P then Q) from analytical (or conceptual or a priori) entailment. The precise definition of these notions, and the differences between them, won't matter.
*) Oskar Minkowski discovered that dogs whose pancreas is removed develop the symptoms of diabetes.
Suppose this is the first time you've heard the name "Oskar Minkowski". Cases like this are good candidates for causal descriptivism. According to causal descriptivism, my utterance of (*) is true iff there is a person standing at the origin of a certain chain of communication leading to my present use of "Oskar Minkowski", and this person discovered that dogs whose pancreas is removed develop the symptoms of diabetes. This comes close to many people's intuitions about possible cases.
Once upon a time, two quite different roles were assigned to truth-conditions: 1) they are what you know when you understand a sentence and what people communicate with utterances of the sentence; 2) they determine the truth value of the sentence when prefixed with modal operators. Unfortunately, there are sentences where these two roles come apart, namely context-dependent sentences, like "it's raining" and "I am late", and sentences containing rigid designators, like "London is overcrowded" and "Hesperus = Phosphorus". Since virtually all sentences ever uttered belong to one of these two classes (or both), the idea that we can assign to sentences truth-conditions that serve both (1) and (2) must be given up. The common strategy to deal with this at least among philosophers is to regard truth-conditions in the sense of (2) as the proper topic of compositional semantics and to assume that some other ("pragmatic") story will deliver truth-conditions in the sense of (1) out of the truth-conditions in the sense of (2) and various contextual features. I find that cumbersome and unmotivated. In my view, truth-conditions in the sense of (1) should be the primary topic of semantics, and I don't see any reason for the roundabout two-step procedure via truth-conditions in the sense of (2). I wouldn't complain if that procedure turned out to work sufficiently well, but for all I can tell, it doesn't work well at all. So I think it would be better to do compositional semantics directly for truth-conditions in the sense of (1). Since Frank Jackson calls such truth conditions "A-propositions" or "A-intensions", I use "A-intensional semantics" for that project.
I would like to say that
If X necessarily entails all truths, and if X's
A-intension coincides with its C-intension, then X a priori entails
all truths.
For suppose X -> P is not a priori for some truth
P. Then X -> P is an a posteriori necessity. So we need
information about the actual world to know what C-intension X -> P expresses, and whether it is true. But by assumption, this
information is already contained in X, and since X's C-intension
coincides with its A-intension, it cannot be hidden away in X so that
we'd need further information to find out that X contains that
information. Hence X a priori entails X -> P; and so
X -> P is itself a priori.
What would you say if it turns out that the watery stuff in our rivers and lakes doesn't actually consist of H2O, but of XYZ: would you say that water consists of H2O or XYZ?
What would you say if it turns out that you are Leverrier's wife living in 1845 and the heavenly body your husband calls "Neptune" is not a planet, but a spaceship: would you say that Neptune is a spaceship or a planet?
There's something odd about the second question.
I am disposed to assent to certain sentences under certain conditions, to "it's raining" if it's raining, etc. For each sentence, this determines a function from conditions -- sets of centered worlds -- to truth values. (If I am disposed to assent to S under condition C, that doesn't mean I assent to S in all C-worlds. I need only do so in the closest C-worlds. I am not disposed to assent to "it's raining" under the condition that it's raining and I am halluzinating that it doesn't rain.)
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.
I'm trying to catch up with Dave Chalmers's reading of Scott Soames's Reference and Description. I'm still at chapter 4, and my reaction to it is not quite the same as Dave's. (I began this entry as a comment over there, but it somehow grew way too long.)
Let's stipulate that "Lee" (rigidly) denotes the youngest spy (if there is one). Soames argues that if
Call an expression E scrutable with respect to a class of expressions C iff it is a priori that all true sentences involving both C and E are a priori deducible from all true sentences involving only C. Equivalently, E is scrutable with respect to C iff there are no worlds w1 and w2 of which exactly one is in the 1-intension of some C+E-sentence, whereas all 1-intensions of C-sentences contain either both worlds or neither.
Is every expression scrutable with respect to some class of expressions to which it does not belong? If the relevant language has synonyms for all expressions, that's trivial. We should better ask about families of expressions: what classes of expressions are scrutable only with respect to expressions containing other members of their class? Call such classes indispensible. Large classes of expressions like the class of all expressions are obviously indespensible, as is probably the class of indexicals and the class of quantifiers. Dave Chalmers would also add the class of phenomenal expressions. As a type-A materialist, I would rather not.
David Chalmers has an interesting post on the differences between his and Frank Jackson's versions of two-dimensionalism. It turns out that my reading of a certain passage in "Why we need A-intensions" was right: Jackson believes that truth at a world considered as actual is somehow reducible via de-rigidification to truth at a world considered as counterfactual.
I've written a little paper in German about the connections between metaphysical (modal) and analytical implication for the Olaf Müller-Kolloquium here at Humboldt University: "Fundamentale Wahrheiten" (PDF). It brings together some things I've already written about here. The main ideas are entirely due to Lewis, Jackson and Chalmers.
Since I haven't slept last night and feel unable to do anything productive, here is an abbreviated translation.
In "Tharp's Third Theorem", Lewis agrees with Jackson that "all of us are committed to the a priori deducibility of the manifest way things are from the fundamental way things are (whatever that may be)" (TTT, p.96). His somewhat cryptic argument isn't quite the same as Jackson's though, and it seems that he avoids the mistake I mentioned yesterday.
Note that Lewis doesn't say we're committed to the a priori deducibility of all truths from the fundamental truths. Instead, he speaks of the "fundamental way things are", or from "contingent truths, supervenient on the fundamental way things are" (TTT 96). (In case that's not clear: Like Lewis, I use "truth" for "true sentence", not e.g. for "true proposition".)
Let logicalism ("logicism" was already taken) be the claim that all truths supervene upon purely logical truths, where a purely logical truth is a truth that contains only logical terms, including terms from second order modal logic.
Logicalism immediately follows from this purely logical truth ('[]' is the box, 'ACT' the actually operator):
p <-> []((x)(F)(Fx <-> ACT(Fx)) -> p)
While all truths therefore supervene upon the purely logical truths, not all truths are a priori deducible from the purely logical truths. For instance, that water covers most of the earth isn't. So we have a counterexample to the claim that whenever all truths supervene on the F-truths, then all truths are a priori deducible from the F-truths.
A zombie world is a world physically just like our world but in which
there is no consciousness. Must a type-A materialist deny the
conceivability of zombie worlds? No, not quite.
Compare the rather uncontroversial hypothesis that "the HI virus" denotes the (type of) virus responsible for most AIDS infections. Is it
conceivable that a world could be biologically just like ours but not
contain the HI virus? Yes, for it might turn out that scientists
have been wrong all the time and no virus is involved in most AIDS
infections. If it turned out this way, our own world would be a world
biologically just like ours but not containing the HI virus.
A sentence is true in a fiction iff it is true at certain worlds, say, at the closest worlds where the pretense which the narrator and the audience engage in is not only pretense. But to evaluate whether the sentence is true at a world, do we treat the world as actual or as counterfactual?
It seems that there could easily be stories in which water isn't H20, and Hesperus isn't Phosphorus. This suggests that the worlds must be treated as actual. However, it isn't clear that these terms ("water" etc.) are sufficiently rigid, and if not, there are also worlds as counterfactual where the identities fail. Could there be a story in which the stuff that actually is water isn't the stuff that actually is H2O? I'm not sure.
I'm back. Here's a question that occurred to me while I was listening to Dave Chalmers's talk on scrutability.
First some background. One might think that for every world w there is a complete description D true at w such that all and only the sentences true at w follow a priori from D: simply let D contain all sentences true at w. Then all sentences true at w will be a priori entailed by D. However, if "true at" is read counterfactually, sometimes sentences false at w will also be so entailed. Consider Twin World where XYZ occupies the water role. "Water doesn't occupy the water role" is true at Twin World. But "water occupies the water role" is a priori, and hence a priori entailed by everything1. Thus every complete description of Twin World a priori entails a contradiction (and every sentence whatever).
Something interesting seems to happen on pp.261f. of Frank Jackson's "Why We Need A-Intensions" (Phil. Studies, March 2004):
How is truth at a world under the supposition that that world is the actual world related to truth at a world simpliciter? It would be good to have an assurance that there are no problems special to the former, as Ned Block convinced me [...]. For some sentences, their A-intension is one and the same as their C-intension. [...] For them, truth at a world and truth at a world under the supposition [that] it is the actual world are one and the same. There is a difference between a sentence's A- and C-intensions if and only if the evaluation of the sentence at a world requires reference back to the way the actual world is as a result of some explicit or implicit appearance of "actually", or an equivalent rigidification device, in the sentence. But when this happens, the role of worlds in settling truth values is the standard one, the one that applies when it is C-intensions that are in question. The only difference is that the value at every world but one depends in part or in whole on how things are at another world. There is no difference in the role of how things are at worlds in settling truth values; the difference is in which worlds are in play. To put the point in terms of a simple example: (a) "The actual F is G" is true at w under the supposition that w is the actual world iff "The F is G" is true at w; and (b) what follows "iff" in (a) contains "is true at w" and not "is true at w under the supposition that w is the actual world".
Many people have complained that they don't understand what it means to evaluate a sentence in a world considered as actual, or that however that is to be done, it won't deliver the results Jackson promises.
On page 305 of "Assertion Revisited" (in the latest issue of Phil.Studies), Robert Stalnaker suggests that the information conveyed by an utterance is the diagonal proposition associated with the utterance iff it is unclear in the relevant context which horizontal proposition the utterance expresses:
[T]he relevant maxim is that speakers presume that their addressees understand what they are saying. In terms of the two-dimensional apparatus, this presumption will be satisfied if and only if the propositional concept for the utterance [a function that assigns to every relevant possible context the horizontal proposition expressed by the utterance in that context] is constant, relative to the possible worlds that are compatible with the context. Our problematic example [of saying "Hesperus is Phosphorus" to O'Leary who doesn't yet know that Hesperus is Phosphorus], and all cases of necessary truths that would be informative (in the sense that the addressee does not already know that they are true) will be prima facie counterexamples to this maxim, and so will require reinterpretation [so that what is said is the diagonal, not the horizontal proposition].
Three comments:
There is a curious problem about rejecting both premise 2 and 3 in this familiar argument:
- It is conceivable that pain is not CFF.
- If it is conceivable that pain is not CFF then it is possible that pain is not CFF.
- If it is possible that pain is not CFF then pain is not CFF.
- Therefore: pain is not CFF.
I believe that premise 3 is almost certainly false: why can't 'pain' denote CFF at our world and D-fiber firing at other worlds? Or, even better, CFF in humans at our world and other states in other beings here and elsewhere? Some claim that 'pain' must rigidly denote a kind of diagonal state that all beings who are in pain share. But I've never seen a convincing argument why this should be so. Crispin Wright argues (in "The Conceivability of Naturalism") that a) the reference-fixing description for 'pain' is something like 'state of feeling painful', which is itself rigid, and b) necessarily, pain satisfies this description. But it is not at all obvious to me that the reference-fixing description for 'pain' is 'state of feeling painful', rather than, for example, the non-rigid 'state that feels painful' or something physicalistically more acceptable.
I take back what said at the end of my last post about the need to distinguish two kinds of A-intension, one transparent and one intransparent. There's not really any need to do so, and it only leads to a lot of trouble. (For instance, is it a priori that elms satisfy the transparent intension, or the intransparent intension, or both, or neither?) I thought I needed a transparent conception to explicate some sort of speaker meaning and to account for rationality. Certainly, what we need for this is a conception of meanings that it in some sense 'transparent' or 'narrow', but that does not preclude it from making reference to unknown facts about other people or causal chains. For example, the belief that the actual F is not the actual G should not count as irrational (for suitable F and G) even if the actual F is (necessesary) the actual G. But 'F's and 'G's whose A-intension is full of causal and deferential components can nevertheless provide for that, as long as it isn't a priori that the F is the G.
I want to write something about rigidity in the philosophy of mind. But first I have to say more about rigidity. (Apologies in advance: this is all going to be rather basic. But I'll need it, and I found that many people disagree with it.)
Recently I argued that the assumption that ordinary proper names are rigid designators leads to an implausibly excessive form of essentialism. But I don't want to deny the useful distinction between rigid and non-rigid designators. That is, in a sense I do believe in rigid designators. But they are not quite what rigid designators are usually supposed to be.
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?
Here's a little question about David Chalmers' paper "Does Conceivability entail Possibility?". I'm interested in the relation between what Chalmers calls strong scrutability and what he just calls scrutability. In particular, I wonder if strong scrutability is really stronger than mere scrutability. This depends on a claim Chalmers makes in sections 10 and 11: that if there are inscrutable truths, it follows that some statements are epistemically possible (not ruled out a priori) but yet not really (primarily) possible. My question is: why does that follow?
This is a rewrite of last week's posting, which I now find rather
obscure. Basically, I'm trying to introduce A-intensions in a way
different from the possibilities discussed in David Chalmers' "Foundations". The "contextual" approaches he discusses look
like non-starters to me, and I don't like his own "epistemic" account,
partly because of worries about his use of ideal language and partly
because I would very much like to explain a priori knowledge with knowledge
of A-intensions rather than the converse. Most importantly, I think there
is something wrong with the very question he asks. Or at least there's
something wrong with where the question is asked.
"Content" and its cognates are rather theoretical notions. We need them
to do semantics and psychology, but we don't have immediate acquaintance
with them. That's why I find it slightly puzzling when people say that the
content of a sentence or a mental state can be represented by, say,
a set of possible worlds or some kind of labeled tree, whereas in fact it
is no such thing. What do these people think the content is in fact?
Anyway, let's assume that (at least for a certain fragment of English)
sets of centered possible worlds can do duty for (or represent) the content
of sentences. On this account, the content of "it is raining" is
identified with a certain set of centered worlds, namely the set of worlds
where it is raining at the center. By the semantics of negation, the
content of "it is not raining" is the complement of this set. Analogously,
the content of "language exists" is a certain set of centered worlds,
namely the set of worlds where language exists, and the content of
"language does not exist" is the complement of that set.
Brian Weatherson now says that 'the world exists' is exactly as natural as
'there is a G', where G applies to worlds that are exactly like this one.
I agree. But this only makes things worse, because the class G denotes
seems very natural: It contains our world and all its exact intrinsic
duplicates. Is this a gruesome gerrymander? We still need a
further restriction on best theories apart from naturalness.
It is often said, correctly I think, that there are contingent but a priori
sentences, e.g. "water is the dominant liquid on earth". Are these
sentences analytic or synthetic? That is, what puts you in a position to
know these sentences? Does understanding suffice, or do you have to invoke
some other a priori means, like Gödelian insight? To me this seems
wildly and unnecessarily mysterious. Of course understanding suffices, at
least in ordinary cases. So there are contingent but analytic sentences. I
wonder why this is hardly ever said. Does anyone really believe that those
statements are synthetic a priori?
Dave Chalmers kindly explained his views on deducibility to me. He thinks that anything one could reasonably call non-deferential understanding of the fundamental truths would suffice for being able in principle to deduce macrophysical facts, provided that these fundamental truths, unlike my P, contain phenomenal facts and laws of nature. He also notes that I shouldn't have called these restrictions (to non-deferential understanding and the rich content of fundamental truths) assumptions, since they are really just restrictions. I'm still not sure if any kind of non-deferential understanding would suffice, but with the restrictions in place it's not as easy to come up with counterexamples as I thought.
Back to the question of deducibility.
According to the deducibility thesis, the fundamental truths (plus
indexicals, plus a 'that's all' statement) a priori entail every truth.
More precisely, when P is a complete description of the fundamental
truths and M any other truth, then, according to the deducibility thesis,
the material conditional 'P
M' is a priori.
When I tried to spell out the 'modus tollens' I mentioned on monday, I
came across something that may be interesting.
Frank Jackson argues that facts about water are a priori deducible from facts about H2O:
1. H2O covers most of the earth.
2. H2O is the watery stuff.
3. The watery stuff (if it exists) is water.
C. Therefore, water covers most of the earth.
1 and 2 are a posteriori physical truths, 3 is an a priori conceptual
truth.
Here are, very quickly, some more thoughts on the matters I talked about here
and there, inspired by another discussion with Christian.
You don't have to know much about plutonium to be a competent member of our
linguistic community. One thing you have to know is that plutonium is the
stuff called 'plutonium' in our community. Maybe that alone suffices.
Of course, if noone knew more about plutonium than this, the meaning of
'plutonium' would be quite undetermined. To fix the meaning, it would
suffice if a few persons, the 'plutonium experts', knew in addition
that this element (where each of the experts points at some
heap of plutonium) is plutonium.
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)?
This is a continuation of my last post and also partly a reply to concerns raised by my tutor Brian Weatherson.
Imagine a small community consisting of three elm experts A, B, and C.
First case: Each of A, B, and C knows enough to determine the reference of 'elm',
but their reference-fixing knowledge differs. However, they belief that
their different notions of 'elm' necessarily corefer. This is the case Lewis
discusses in 'Naming the Colours'.
Some days ago, Christian and I had an interesting discussion about two-dimensionalism.
While I don't agree with many of his criticisms (forthcoming in Synthese),
I do agree that two-dimensionalism works best if both dimensions belong to
an expression's public meaning. I think that Christian thinks that this
holds only for context-dependent expressions. I think it holds almost
universally. But this may be a matter of terminology: For me it is
part of the meaning of 'the liquid that actually flows in rivers' that this
would not denote H2O if it would turn out that XYZ flows in rivers, whereas
for Christian this is a metasemantic fact. Anyway, problems for
two-dimensionalism come when the first dimension doesn't belong to public
meaning.