Put this baldly, one might wonder if anyone actually thinks it is possible. In fact—waiving certain qualifications for dramatic effect—David Chalmers, Frank Jackson and David Lewis all think it is.^[5] Concentrating on some recent arguments of Chalmers and Jackson, I shall be arguing that there is no reason to suppose that cosmic hermeneutics is possible.

Cosmic hermeneutics is possible iff, for every true ψ, there is some true physical sentence φ such that 'φ —> ψ' is knowable a priori. (Left to right: suppose that the demon can deductively infer ψ from a true physical premise φ and an a priori premise σ (we can always conjoin multiple physical or a priori premises into one big physical or a priori premise). Then '(φ & s) —> ψ' is a priori. So 'σ —> (φ —> ψ)' is a priori. But as σ is a priori, so is 'φ —> ψ'. Right to left: suppose 'φ —> ψ' is a priori. Then the demon knows 'φ —> ψ', and since he knows φ, he can deductively infer ψ.^[6])

Setting aside the contingent a priori as a rare special case^[7], it follows that cosmic hermeneutics is possible only if, for every true ψ, there is a true physical sentence φ such that 'φ —> ψ' is (metaphysically) necessary. (Henceforth the variable ‘φ’ will signal that we are quantifying over (consistent) sentences in some suitable physical vocabulary.)

This necessary condition for the possibility of cosmic hermeneutics, that every truth is metaphysically determined by some physical truth, is, near enough, the contemporary thesis of physicalism. But now we must face an irritating complication.

In fact, (P) is equivalent to the necessary condition for cosmic hermeneutics just discussed—that every truth is metaphysically determined by some physical truth. (Left to right: we may assume that there is a physical sentence φ_w*that is true at a world w iff w is a physical duplicate of world w*. Suppose (P) is true at w*. Then for every true ψ, 'φ_w* —> ψ' is necessary. Right to left: suppose that, for every ψ true at world w* there is a φ true at w* such that 'φ —> ψ' is necessary. Now a world is a physical duplicate of w* iff the same physical sentences are true at both; and a world is a duplicate simpliciter of w* iff the same sentences are true at both.^[8] Let w be a physical duplicate of w* and ψ be a sentence true at w*. Then there is a φ true at w* such that 'φ —> ψ' is necessary, and so ψ is true at w. Now let ψ´ be a sentence true at w; if ψ´ is false at w*, it’s false at w, so it’s true at w*. Thus the same sentences are true at w and w*, as required.)

(P), unfortunately, is too strong, for many physicalists will accept that some physical duplicate of this world has items that do not interact with anything physical—immaterial spirits, as it might be—and that our world lacks.

For illustration suppose that, at time t, one and no more than one politician is in pain, and one and no more than one White House “coffee” is occurring. Then if (P) is true, there are physical sentences φ₁, φ₂, φ₃, φ₄ such that:

Now the problem just raised does not affect the physicalist’s commitment to necessary truths of the form (i) and (ii). No amount of epiphenomenal ectoplasm added to matters physical will prevent a politician from being in pain, or a White House coffee occuring—at least according to physicalism. But it might create some immaterial politician in pain, or a ghostly coffee. For this reason, (many) physicalists will deny that any sentence of the form (iii) or (iv) is necessary.

A number of ways of patching this difficulty with (P) have been proposed^[9]; let us adopt Frank Jackson’s, and formulate physicalism thus:

Now, if nothing stronger than (P^-) is true, cosmic hermeneutics, at any rate as originally explained, is not possible: the demon will not be able to infer, for example, that exactly one politician is in pain at t, for there is no appropriate necessarily true conditional. Can this barrier be removed, with only a minor adjustment to the demon’s initial stock of knowledge?

Yes. For we can simply allow the demon to know (P^-) (assuming, of course, that (P^-) is true). Letting ‘π’ abbreviate the sentence (displayed above) that expresses (P^-), and φ_@ be a sentence true at a world w iff w is a physical duplicate of the actual world, any physicalist will regard '(φ_@ & π) —> exactly one politician is in pain at t' as necessarily true. For consider a world w at which φ_@ is true and the consequent is false: a world just like ours physically but in which some immaterial politician is in pain at t. Given that (P^-) is contingent, ‘π’ is false at w, and so the conditional is true at w.

Let us conveniently stipulate that ‘π’ is a physical sentence^[10], and amend the task of cosmic hermeneutics by adding (P^-) to the demon’s initial stock of knowledge (so if (P^-) is false, then cosmic hermeneutics is not possible). From this stipulation, amendment, and what we have established earlier, it follows that cosmic hermeneutics is possible iff physicalism is true and, for every true ψ, there is a true φ such that 'φ —> ψ' is necessary a priori.

The conclusion of the paper can now be put more specifically: there is no reason to suppose that cosmic hermeneutics is possible, even if physicalism is true.

According to Jackson, at any rate at the time of “Epiphenomenal Qualia” (1982), the answer is no.^[11] When Mary is released from her black-and-white cell, and sees a ripe tomato for the first time, she will come to learn that some visual experiences are red-feeling. That is something she could not have known beforehand.^[12]

Jackson drew the conclusion that physicalism was false. To this it was objected that the knowledge argument only shows (at best) that no conditional of the form 'φ —> some visual experiences are red-feeling' is a priori, and that is consistent with some such conditional being necessary, as physicalism requires.^[13] Although that reply is fine as an opening move, charity demands we take Jackson to be tacitly assuming that, if physicalism is true, cosmic hermeneutics is possible (which, indeed, he was: see Jackson 1994b).

Example 2: Morality
(For the purposes of this example, assume that moral sentences have truth values.) On one interpretation of ‘you can’t derive an ought from an is’, no conditional of the form 'δ —> μ' is a priori, where δ and μ are, respectively, descriptive and moral (contingent a posteriori) sentences.^[14] Almost universally held is that the moral supervenes on the descriptive, from which it follows that some such conditionals are necessarily true (of course the necessity here is metaphysical, not merely nomological.) The conjunction of ‘no ought from an is’ and supervenience would seem to be eminently defensible.^[15] But if cosmic hermeneutics is possible, it is mistaken.

Example 3: Kripke’s Wittgenstein
Kripke’s Wittgenstein purports to show that “[t]here can be no fact as to what I mean by ‘plus’, or any word at any time” (Kripke 1982, 21). Some have argued that the sceptical argument only shows, at best, something epistemological, namely that semantic/intentional facts—that Jones means addition by ‘+’ , that Jones intends to add, etc.—are not a priori consequences of non-semantic/non-intentional facts.^[16] So, this line of thought continues, the sceptical argument is no threat to the modest claim that intentional/semantic facts supervene on the physical, and thus Kripke’s Wittgenstein’s apparent irrealism about meaning (and intentionality) may be resisted. But if cosmic hermeneutics is possible if physicalism is true, the sceptical argument is reinstated.

Example 4: A posteriori necessity
Suppose that physicalism is true, and that cosmic hermeneutics is not possible with respect to many facts, for example psychological ones. Then we have a class of a posteriori necessities (of the form 'φ —> Alfred believes that snow is white' , etc.) that appear to be quite different from those that Kripke famously drew to our attention.

The second example helps bring out the point that physicalism is best thought of as being a prominent test case in the discussion to follow. Let fundamentalism be the view that everything supervenes (with metaphysical necessity) on some (interestingly proper) portion of everything. Physicalism is, of course, a variety of fundamentalism. So is descriptivism: everything supervenes on the descriptive. So is Humean supervenience: everything supervenes on “local matters of particular fact” (Lewis 1986b, ix). And so is phenomeno-physicalism: everything supervenes on the physical and the phenomenal (Chalmers 1996, 72). Fundamentalism is a highly popular position: probably the only dissenters would be those sceptical of metaphysical necessity.^[17] For each variety of fundamentalism, we can ask whether a demon equipped with knowledge of the appropriate supervenience base could deductively infer everything. Although the considerations pro and con will not be quite the same in each case, there will be considerable overlap. The conclusion of this paper could, I think, be readily extended to cover fundamentalism in general. But I shall not take the space to do that.

First, the Laplacian demon’s initial stock of a posteriori knowledge is specified in a “physical language”—but what is that, exactly? Fortunately for present purposes the details won’t much matter. It will suffice to think of it as the language of contemporary physics, or perhaps of a future physics “somewhat improved” (Lewis 1983, 361; see also Chalmers 1996, 33, and Jackson 1998a, 6-8). All physicalists would agree that the physical supervenience base can be specified in something like a language of this sort. (Having said that, for the sake of some later examples, one of which will be touched on in the next paragraph, I shall augment the physical language with expressions from chemistry and geology.)

Second, something should be said at the start about the examples Kripke gave of the necessary a posteriori, for they are the obvious first candidates for counterexamples to the claim that cosmic hermeneutics is possible. Take, for instance, the fact that water covers most of the Earth. The following argument is tempting. If the demon can know that water covers most of the Earth, he must be able deductively to infer this from the fact that H₂O covers most of the Earth (if he can’t do that, how else could he come to know that water covers most of the Earth?). But if he can perform such a deduction, the necessary conditional ‘H₂O covers most of the Earth —> water covers most of the Earth’ must be a priori, whereas in fact it is a posteriori. So the demon cannot know that water covers most of the Earth, and hence cosmic hermeneutics is not possible.

This problem will take center stage when we examine Jackson’s arguments (2.4 below). I mention it now to stress that only needless complexity will come of raising Kripkean examples of the necessary a posteriori before then; so until we arrive at 2.4, forget them.^[18]

However, although we cannot be sure of very much as far as the future of philosophy goes, we can be quite sure that successful conceptual analyses, let alone physicalistically acceptable ones, will remain almost as rare as an uncontroversial philosophical argument.^[20] Jackson, discussing an example of Stephen Stich’s, concedes that “Stich is right that we cannot write down necessary and sufficient conditions for an animal displaying grooming behaviour in austerely physical terms” (1998a, 62). And in general the proponents of cosmic hermeneutics do not pretend to supply conceptual analyses, at least not physically acceptable ones.

Yet all is not lost. For suppose we had a theory of analysis itself, that told us that in so-and-so circumstances, A-vocabulary can be analysed in terms of B-vocabulary. Then maybe we could apply the theory to particular cases of non-physical vocabulary to show that they can be analysed in a physicalistically acceptable way, whether we know how to do this or not. If so, we would have argued “non-constructively” for certain physicalistically acceptable analyses.

There is only one (partial) theory of analysis that might deliver this happy result, and that is David Lewis’s elegant account of the meanings of “theoretical terms” (1970).

Somewhat simplified, Lewis’s central idea is as follows. Sometimes new words are introduced into the language without being explicitly defined beforehand. Suppose, for illustration, that some engineer introduced the words ‘nut’ and ‘bolt’, not by explicitly telling us what they meant, but by uttering the following sentences:

Here, more generally and accurately, is Lewis’s proposal. Let T be a theory written using two sorts of vocabulary—the T-vocabulary (the Theoretical vocabulary) and the O-vocabulary (the Old or Other vocabulary). If T implicitly defines the T-vocabulary in terms of the O-vocabulary, then the implicit definitions can be made explicit as follows. Convert the T-vocabulary to names by writing, for instance, 'has the property Fness' for 'is F'. Write out the theory in question as a long conjunctive sentence 'T[τ₁,..., τ_n]'—the postulate of T—where τ_i is a name in the amended T-vocabulary. Replace τ_i by the variable x_i to get the open sentence 'T[x₁,..., x_n]'—the realization formula of T. Define the T-term τ_i by:
'The y_i: (some)y₁...y_i-1y_i+1...y_n(all)x₁...x_n(T[x₁,..., x_n] iff y₁=x₁&...&y_n=x_n)'.
Thus, if τ_i refers at all, it refers to the ith member of the n-tuple that uniquely realizes the realization formula of T. (We can ignore subtleties concerning multiple or partial realization of the realization formula.^[21])

Let us go through this procedure for our example. Converting the T-vocabulary to names, and writing out T (the nuts-and-bolts theory) as a long conjunctive sentence gives:

Let us understand a claim of the form: so-and-so vocabulary is implicitly defined by such-and-such vocabulary, to mean that there is some theory T (the defining theory) with so-and-so the T-vocabulary and such-and-such the O-vocabulary, such that applying Lewis’s method correctly defines the former vocabulary by means of the latter.

Then we can put one thesis that is at least strongly suggested by Lewis’s original (1970) paper thus: the “theoretical” vocabulary of science (‘electron’, ‘gene’, ‘mollusc’, ‘white dwarf’, etc.) is implicitly defined by the rest of the scientific vocabulary (i.e. relatively commonsense and topic neutral words plus, presumably, mathematical vocabulary).

This is important, and if it is right then the theoretical vocabulary of science can be analysed in more-or-less everyday vocabulary (plus math). But discussion of this can be dropped, because for present purposes we want an analysis in the other direction.

The most well-known purported example of the desired sort is the core of commonsense (or analytic) functionalism: mental vocabulary is implicitly defined by non-mental/non-semantic vocabulary, with the defining theory being folk psychology.^[24] And recently Frank Jackson and Philip Pettit have defended moral functionalism: moral vocabulary is implicitly defined by non-moral vocabulary, with the defining theory being folk morality (Jackson and Pettit 1995; Jackson 1992, 1998a). (This isn’t quite enough for our needs, of course: the non-mental/non-semantic and non-moral vocabulary might not be physicalistically acceptable without further analysis; but we can set this complication aside.) Let us concentrate on the former example.^[25]

In Lewis’s 1970 paper, some opening assumptions are that “the best scientific explanation we can devise for a body of data includes a new theory T, formulated by means of a postulate in which there occur some new terms τ₁...τ_n, terms we have never used before...Our only clue to their meaning is the postulate of T that introduced them” (79-80). What is relevant for present purposes is not the bit about “the best scientific explanation”, but the assumption that the “only clue” to the meaning of the “new terms” is the postulate of T. The form of this crucial assumption can be set out thus:

(A) is important because, if it’s right, Lewis’s suggestion that the new terms are implicitly defined by the remainder of the vocabulary in the postulate is obviously worth taking seriously—for if they are not, how could we have learned what they mean? That question is not unanswerable, but let us grant for the sake of the argument that if (A) holds in a particular case, then Lewis’s suggestion is plausible.^[26]

Perhaps, idealizing only slightly, (A) holds for some scientific terms like ‘electron’ and ‘gene’.^[27] But however that may be, it certainly does not hold for mental vocabulary. Further, no one has actually produced a reasonable candidate for the (alleged) defining theory for psychological vocabulary, for good reason. First, any such candidate must be a very rich theory—it is clear that psychological terms do not have simple reductive definitions.^[28] Second, generalizing a point noted at the end of the “nuts-and-bolts” example, if T implicitly defines τ₁,..., τ_n, then 'if τ₁,..., τ_n exist, T is true' is analytic. Putting these two together, we need a rich folk psychology meeting the analytic constraint. But a little experimentation will soon show that analytic psychology is a difficult business—the kinds of analytic-smelling psychological truths seem relatively few in number.

To sum up, in the case of mental vocabulary, (A) fails, and no one is likely to display a theory that stands a chance of being defining. So why suppose that we have here the basis of an argument for the existence of analyses of mental vocabulary?

Consider the following passage from Lewis:

Why believe this “working hypothesis”? It is not absolutely clear in this passage just how strong Lewis takes his “item of evidence” to be, but in any case, how strong is it? First, it surely cannot be that the working hypothesis is the best explanation of psychological analyticities and the plausibility of behaviourism. As far as the analyticities go, let us suppose, following Lewis (1969), that they can be explained in terms of truth in all possible worlds together with our conventions of language. True, those conventions may be such that every item of mental vocabulary is analytically equivalent to some non-mental expression. However, the analyticities might well be accounted for by conventions that do not have this strong consequence. Why think otherwise? And surely the plausibility of behaviourism can be explained in other ways.^[30]

It seems to me, then, that Lewis has not convincingly argued that mental vocabulary is implicitly defined, by physical vocabulary or anything else.^[31] And no other attempt that I am aware of—in either the mental or the moral case—comes any closer.^[32]

In any event, the entire strategy is piecemeal, with each claim that so-and-so vocabulary is implicitly defined needing to be treated individually. We now turn to a series of arguments with more global pretensions.

On an alternative and more plausible reading of what we are supposed to imagine, it is something like:

where ‘Φ’ is replaced by a certain very complex physical sentence specifying, for example, the distribution of every particle in the wombat enclosure at Taronga Park Zoo. Running the argument as before, we get:

(6) It is a priori that if Φ then there is a wombat with two offspring,

from which (1) follows. The difficulty here is that we don’t actually know what the right replacement for ‘Φ’ is, and it seems entirely a matter for speculation whether the result would be inconceivable (remember that a physical sentence is from the language of physics: it can mention “mass, charge, spatiotemporal position; properties characterizing the distribution of various spatiotemporal fields, the exertion of various forces, and the form of various waves; and so on...[but] [s]uch “high-level properties as juiciness, lumpiness, giraffehood, and the like are excluded, even though there is a sense in which these properties are physical” (Chalmers 1996, 33)).

Another way of arguing for (1) is suggested by the very last portion of the quoted passage. First establish that a Laplacian demon who imagines the physical facts would “have automatically imagined” that a wombat has two offspring, then argue that (1) follows. Although this suggestion is not developed under the heading of ‘conceivability’, Chalmers later gives an argument that appears somewhat related, to which we now turn.

The mental simulation argument, then, simply boils down to Chalmers’ assertions that one could infer from the physical description that there is an object that “can fold and unfold”, that “was hanging on a stand that morning”, that “was made in a factory with others of a similar kind, and so on”, eventually arriving at the conclusion that there’s a man carrying an umbrella.

However, this attempt to show how one might infer by a series of steps that there’s a man carrying an umbrella is somewhat cosmetic, because the conclusion is supposed to apply to “almost any sort of high-level phenomena” (77), and the umbrella example is the only one discussed in any detail. Even if cosmic hermeneutics is possible here, for all Chalmers has said it might fail elsewhere, for a very different kind of sentence. And in any case the brief treatment of the example is unconvincing, for two reasons. First, even if we allow that one could infer that there is an object that can “fold and unfold”, that “was hanging on a stand that morning”, etc., this only helps if these conclusions amount to jointly a priori sufficient conditions for the existence of an umbrella. As stated, they do not: tablecloths, Panama hats and briefcases all fold and unfold, can hang on stands, are made in factories, and can be used as shelter from rain. Chalmers’ use of ‘and so on’ indicates that he recognizes this fact, but it is not obvious what else to add. Second, and more importantly, if it is initially quite unclear whether one can infer that there’s a man carrying an umbrella from the physical facts (as it surely is, especially when the physically austere nature of the premises is emphasized—see 2.2 above), it ought to be equally unclear whether one can infer, for example, that an object has been “made in a factory with others of a similar kind”. That is, factory-facts and umbrella-facts are at the same “high-level”. Thus we are no further forward.

According to Jackson, his central argument needs the premise that a certain semantic framework—two-dimensionalism—is correct. So, the first order of business is to explain two-dimensionalism and Jackson’s motivation for it (2.41). Next, the central argument (2.42), which in fact does not need the distinctively “two-dimensional” part of two-dimensionalism as a premise, but instead another component of it, that every necessary proposition is knowable a priori. Moreover, this component is inadequately defended. Some of Jackson’s remarks suggest another argument, which does indeed require something “two-dimensional”. However, this could at best only fend off an objection to Jackson’s conclusion (2.43).

We can see Jackson’s puzzle as generated by the following pair of schematic claims:

Importantly, Jackson’s solution is not to deny (8). Rather, he denies (7) (for sentences like ‘Water is H₂O’). Thus two dimensionalism is motivated because, as we’ll see in a moment, it provides an elegant alternative account of what it takes to understand sentences like ‘Water is H₂O’. So before turning to two dimensionalism, we should pause to consider why Jackson thinks it would be wrong to deny (8) instead. (8) says, taking ‘Water is H₂O’ as an instance, that anyone who knows which proposition it expresses knows:

Jackson’s official motivation for two-dimensionalism, then, is uncompelling. But let us set this difficulty aside, and turn to two-dimensionalism itself.

Are there any uncontroversial cases where a speaker may be said to understand a sentence without knowing which proposition it expresses? Of course: if I tack a note saying ‘Back in 10 minutes’ or, less elliptically, ‘I’ll be back here in 10 minutes’, to my office door, plainly someone could be said to understand the (token) sentence without knowing which proposition it expresses. For he may have no idea when the note was placed on the door, whose office it is, or even where the office is.

In the example of the note, the speaker understands the (token) sentence because he knows how the proposition expressed by tokens of the type ‘Back in 10 minutes’ varies with arbitrary context of utterance (cf. Kaplan 1989, 520-1). (We may give exactly the same account of understanding the sentence type ‘Back in 10 minutes’.)

And similarly, Jackson thinks, with ‘Water is H₂O’ and other sentences containing ‘water’, for instance ‘Water covers most of the Earth’. According to him, “understanding ‘Water covers most of the Earth’, does not require knowing the conditions under which it is true, that is, the proposition it expresses. Rather it requires knowing how the proposition expressed depends on context of utterance” (1998a, 73). (See also Jackson 1994a, 38-9, 1994c, 489-90.)

To fill in the details of this idea, Jackson uses some formal machinery borrowed from two-dimensional modal logic, which we now need briefly to explain. (A slightly expanded version of what follows can be found in Jackson 1998a, 47-52; Chalmers 1996, 56-65; and Block and Stalnaker forthcoming; a highly compressed version is in Lewis 1994, 415.^[39]) Take the sentence ‘Water covers most of the Earth’ (understood as we English speakers understand it). According to Jackson, thought experiments of the Twin Earth variety (Putnam 1975) tell us how the proposition this sentence expresses varies with the immediate environment of the speaker. For example, the proposition expressed by an utterance of that sentence in a context in which H₂O falls as rain, flows in streams, etc., is true at a world w iff, in w, H₂O covers most of the Earth. And the proposition expressed in a context in which XYZ falls as rain, flows in streams, etc., is true at a world w iff, in w, XYZ covers most of the Earth. These facts, about how the proposition expressed depends on context, are (because they are knowable via appropriate thought experiments) knowable a priori.

Now (we are supposing, with Jackson) two tokens of ‘Water covers most of the Earth’ uttered in different possible worlds, or within the same world, may express different propositions. An example of the latter is a world containing both Earth and Twin Earth (with tokens uttered in both places). It will greatly ease exposition at no significant cost if we just ignore this second alleged aspect of context relativity.^[40] (Perhaps the easiest way of doing this is to pretend that every world has exactly one privileged context of utterance, and that the privileged context for the actual world is the one enjoyed by speakers of English here on Earth.)

So, imagine some possible world w. Ask: what proposition would ‘Water covers most of the Earth’ express (in the privileged context) if w had turned out to be actual? Here we are, in the terminology of Davies and Humberstone 1980, considering w as actual. (An analogous question is: what proposition would (my token of) ‘I am depraved’ express if Clinton had turned out to be me?, understood so that the correct answer is: the proposition that Clinton is depraved; here, we might say, we are considering Clinton as the speaker.) For example, let w* be a world where XYZ falls as rain, flows in streams, etc. Considering w* as actual and according to Jackson, ‘Water covers most of the Earth’ expresses a proposition true at a world w iff, in w, XYZ covers most of the Earth.

We can also conduct a similar exercise with the word ‘water’. We can ask, for any worlds w, w´: what is the reference of ‘water’ in w, if w´ had turned out to be actual? If w´=w*, Jackson’s answer is, of course, XYZ. Let ‘the watery stuff’ be a non-rigid description with the same descriptive content as ‘water’, whatever that is (cf. Chalmers 1996, 57). Then ‘the watery stuff’ refers to a substance S in w iff, considering w as actual, ‘water’ refers to S in w. And, considering a world w´ as actual, ‘Water covers most of the Earth’ expresses a proposition true at a world w iff, in w, the substance that is the watery stuff in w´ covers most of the Earth.

Of course, because H₂O falls as rain, etc., ‘Water covers most of the Earth’ in fact expresses a proposition that is true at a world w iff, in w, H₂O covers most of the Earth. (We are here considering each world w as counterfactual.)

Thus ‘Water covers most of the Earth’ determines a function F from worlds to propositions, F(w) being the proposition that ‘Water covers most of the Earth’ expresses, considering w as actual. Let us follow Jackson’s exposition of two-dimensionalism and assume that propositions are sets of possible worlds (or functions from worlds to truth values).^[41] Then we can display F in the following matrix:

Here @ is the actual world, w* is a Twin Earth world, and w† is a world much like ours except that the oceans have largely dried up (all the other possible worlds have been omitted for reasons of space). A horizontal row specifies the proposition expressed by ‘Water covers most of the Earth’, considering the row-world as actual. So, considering @ as actual, the proposition expressed by ‘Water covers most of the Earth’ is a set of worlds that has @, but not w* or w†, as members. And that proposition (i.e. the proposition that water covers most of the Earth), given that we are now identifying propositions with sets of worlds, is the proposition that H₂O covers most of the Earth.

As we’ve seen, Jackson maintains that understanding ‘Water covers most of the Earth’ does not require knowing which proposition it expresses, but rather “knowing how the proposition expressed depends on context of utterance”. We can use the two-dimensional apparatus to give a more precise formulation of the second of these claims. The proposition expressed depends on the context of utterance in this way: if the context is w’, (i.e. if w’ is considered as actual), then ‘Water covers most of the Earth’ expresses a proposition that is true at any world iff, in that world, the substance that is the watery stuff in w’ covers most of the Earth. So, according to Jackson, understanding ‘Water covers most of the Earth’ requires knowing:

Turn now to the necessary a posteriori truth ‘Water is H₂O’. According to two-dimensionalism, it has the following matrix:

On this way of analysing the necessary a posteriori, as Lewis says, “there is no such thing as a necessary a posteriori proposition” (1994, 415; see also Jackson 1998a, 84-6, 1994c, 489). Instead, it is the sentence ‘Water is H₂O’ that is properly described as necessary a posteriori, understood to mean that the proposition it expresses is necessary (and a priori) and that the diagonal proposition associated with it is a posteriori (and contingent).^[45]

Turn now to ‘The watery stuff is water’. Within the two-dimensional framework, it is a contingent a priori sentence. It expresses, of course, the same (contingent) proposition as ‘The watery stuff is H₂O’. However, someone who understands ‘The watery stuff is water’ knows that it, unlike ‘The watery stuff is H₂O’, expresses a truth in every context. In other words, the diagonal proposition associated with ‘The watery stuff is water’ is necessary.

On this way of analysing the contingent a priori, there is no such thing as a contingent a priori proposition. Instead, it is the sentence ‘The watery stuff is water’ that is properly described as contingent a priori, understood to mean that the proposition it expresses is contingent (and a posteriori) and that the diagonal proposition associated with it is necessary (and a priori) (cf. Stalnaker 1978).

It is important to realize that two-dimensionalism has two independent components. First, that the semantics of a sentence (e.g. ‘Water covers most of the Earth’) determines a matrix of the sort discussed. Second, that there are no necessary a posteriori propositions (nor contingent a priori ones). (The identification of propositions with sets of worlds is one way, but not the only way, of securing the second component.) Neither component implies the other. In particular, as we will see in the section after next, a popular view of the semantics of words like ‘water’ retains the first and rejects the second.^[46]

After some discussion of Jackson’s argument from two-dimensionalism, in the following section, it will turn out that the only component of two-dimensionalism he needs is the second.

Jackson first notes that A is modally valid: “every world where the...proposition expressed by (13)...is true is a world where...the proposition expressed by (14)...is true” (1998a, 81, n35). But, he continues, “the conditional with the premiss as antecedent and the conclusion as consequent is necessary a posteriori, not a priori” (81-2); and a little further on: “the passage from (13) to (14) is a posteriori” (82).

It is clear from these remarks that, on Jackson’s usage, '(ν)' placed to the left of sentence α names α. (Earlier in this paper, obvious exceptions aside, '(ν)' placed to the left of sentence α named the proposition expressed by α.) For the remainder of this section, let us adopt Jackson’s convention.

The following three consequences of applying two-dimensionalism to A are important.

First, the proposition expressed by ‘Water covers most of the Earth’ is distinct from the diagonal proposition associated with it. The former is the proposition that water covers most of the Earth, the latter the proposition that the watery stuff covers most of the Earth. (We may assume, apparently with Jackson, that the proposition expressed by ‘H₂O covers most of the Earth’ is the diagonal proposition associated with it.)

Second, because we are taking propositions to be sets of possible worlds, the proposition expressed by (13) is the proposition expressed by (14). Thus, if we ask, of the propositions expressed by the sentences in A, whether the first entails the second a priori, the answer is, quite trivially, yes.

Third, although, as just pointed out, the passage from the proposition expressed by (13) to the proposition expressed by (14) is a priori, evidently even a keen logician, who understands both (13) and (14), and believes (13) to be true, will not thereby conclude that (14) is true. The reason for this is that the conditional:

Say that sentence a a priori implies b iff the diagonal proposition associated with 'a —> b' is the necessary proposition. Now we can sum up Jackson’s comments about A as follows: the proposition expressed by (13) entails the proposition expressed by (14), but (13) does not a priori imply (14).

Let us return to Jackson’s argument. He continues:

After discussing the example of water and H₂O, Jackson finally argues for the promised conclusion, the possibility of cosmic hermeneutics (if physicalism is true), as follows:

This is perhaps a little compressed. Step back and quickly review what two-dimensionalism has told us about A.

Suppose our demon knows that H₂O covers most of the Earth. Can he thereby conclude that water covers most of the Earth? Yes—he knows it already! This is implied solely by the claim that propositions are sets of worlds.^[50]

As a competent user of English, can he thereby conclude that the sentence ‘Water covers most of the Earth’ expresses a true proposition? No, he can’t. But if he knows, in addition, that H₂O is the watery stuff, then he can conclude that ‘Water covers most of the Earth’ expresses a true proposition. But does the demon know that H₂O is the watery stuff? That is the question, I take it, that the above quotation from Jackson is designed to answer in the affirmative.^[51]

So, is Jackson right? Although the expression ‘H₂O’ is (we have been granting) part of the physical lexicon, we should not grant that ‘H₂O is the watery stuff’ is a physical sentence—’the watery stuff’ is admittedly a bit of technical terminology, but it is supposed to be simply ‘water’ unrigidified, and so it belongs among our everyday vocabulary. Morever, there is a conclusive reason for extruding it from the physical lexicon: any physicalist will agree that the supervenience base for everything can be stated in a language without any expression remotely cognate with ‘the watery stuff’. Hence it does not trivially follow from the fact that the demon knows everything expressed by true physical sentences that he knows that H₂O is the watery stuff. Here is the relevant part of the quoted passage, where Jackson gives the argument that the demon does know this:

And what is presumably the same point is made in an earlier paper as follows:

But if this is Jackson’s point, again the only part of two-dimensionalism that is doing any work is the claim that every necessary proposition is a priori. There was no need to introduce argument B: Jackson could have argued directly that, if physicalism is true, then there is some φsuch that 'φ —> ‘Water covers most of the Earth’ expresses a true proposition' is necessary, and hence (given that every necessary proposition is a priori and the relevant instance of (C)) the demon can know that ‘Water covers most of the Earth’ expresses a true proposition. (So, substituting any true sentence for '‘Water covers most of the Earth’ expresses a true proposition', and running the argument again, we get the conclusion that, if physicalism is true, cosmic hermeneutics is possible.)

An argument for the crucial premise that every necessary proposition is a priori can be extracted from Jackson’s “puzzle”, discussed above in section 2.41, about understanding a necessarily true sentence without knowing that it’s true. Entertaining a proposition, the extracted argument goes, involves knowing its truth-conditions, and thus entertaining a necessary proposition involves knowing that it is true in every condition, and so true; therefore every (entertainable) necessary proposition is a priori. But the reply is essentially the same as the one to Jackson’s original puzzle. Someone who entertains that water is H₂O thereby knows (more exactly: can know, if he’s conceptually sophisticated) that the proposition that water is H₂O is true at a world w iff, in w, water is H₂O. That is the only uncontroversial sense in which entertaining a proposition involves knowing its truth conditions, and it does not imply that someone who entertains that water is H₂O can thereby know that the proposition is true at every world.^[52]

Alternatively, one might first try to argue for the identification of propositions with sets of possible worlds, from which the crucial premise follows. We cannot investigate the merits of this identification here.^[53] But we should note that the identification provides some motivation for denying the seemingly trivial (instances of) (C). This is because the two together make it hard to avoid the unpalatable conclusion that knowledge and belief are closed under necessary consequence.^[54] So I think it fair to say that the strategy of establishing the crucial premise via the possible worlds conception of a proposition may reasonably be resisted.^[55]

However, for all we have said so far, perhaps the first component of two-dimensionalism, that the semantics of a sentence determines a matrix of the sort explained earlier, might be turned to the advantage of cosmic hermeneutics (this is at least suggested by Jackson 1992, 1994a, b). That is what we shall finally examine.

It must be stressed that the question we are now focussing on is quite different from the one that occupied most of the previous section. That question was: what more information does someone who understands ‘H₂O covers most of the Earth’ and ‘Water covers most of the Earth’, and who knows that H₂O covers most of the Earth, require in order to infer deductively that ‘Water covers most of the Earth’ expresses a true proposition? The present question is: what more information does someone who knows that H₂O covers most of the Earth require in order to infer deductively that water covers most of the Earth? Recall that with the assumptions of the previous section our present question had an easy answer, namely that no additional information is required. But with our present assumptions that is no longer true.

However, suppose we want to retain one key idea of the two-dimensionalist analysis of the necessary a posteriori, that the reference of ‘water’ is fixed by the world of utterance. An obvious way to do that is to identify the semantic content of ‘water’ with a rigidified description: something like ‘the actual potable liquid that falls as rain and flows in streams’ (cf. Davies and Humberstone 1980, 18-20; Chalmers 1996, 59; Jackson 1992, 483-4, 1994a, 39, 1994b, 187), abbreviated as ‘the actual watery stuff’. Thus, uttered in the actual world, the sentence ‘Water covers most of the Earth’ expresses a proposition that is true at a world w iff, in w, the stuff that is watery in the actual world covers most of the Earth. (Note: we are still working with the simplifying assumption that utterances of ‘water’ within a world do not differ in reference.)

So, according to this proposal:

With the assumptions now in force, the addition of (13d) turns the modally valid but a priori invalid A into the a priori valid B:

Argument B

Compare the previous argument—the mislabelled “argument from two-dimensionalism”—with the one under discussion. The previous argument certainly has the desired conclusion, that cosmic hermeneutics is possible if physicalism is true. But one of its premises (that every necessary proposition is a priori) is contentious and without visible support. The present argument does not have this premise, but neither does it have the desired conclusion. Taking a premise of the argument to be that every natural kind term can be analysed as a rigidified description (not itself containing any natural kind terms), the conclusion is this: Kripkean examples of the necessary a posteriori involving natural kind terms, like ‘Water is H₂O’, are not counterexamples to the claim that cosmic hermeneutics is possible (if physicalism is true). If this argument is sound, an objection is successfully rebutted. But that is all, for we are still left wondering whether, for example, there are a priori truths of the form 'φ —> H₂O is a liquidish stuff'.^[57] (And anyway, this is an extremely large ‘if’.^[58])

Kripke pointed out that the notions of necessity and a prioricity are distinct: the former is from metaphysics, the latter from epistemology. (He then went on to give examples where the two notions came apart, but all we need is the initial observation.)

The first insight leads us to wonder whether, if physicalism is true, cosmic hermeneutics is possible. The second insight suggests that it may well not be. We have found no reason to revise this conclusion.