The Nature of Narrow Content[*]

David J. Chalmers

Department of Philosophy
University of Arizona
Tucson, AZ 85721.

chalmers@arizona.edu

*[[The material here overlaps a little with the earlier sections of "The Components of Content" (Chalmers 2002b), the later sections of which provide further details on the analysis and application of the notion of narrow content developed here, and relate it to other accounts of narrow content that have been proposed. Also relevant are "The Nature of Epistemic Space" (Chalmers forthcoming b), which develops the foundational ideas about epistemic possibility and the space of scenarios, and "The Foundations of Two-Dimensional Semantics" (Chalmers forthcoming a), which situates this approach as a variety of two-dimensional semantics and fills in many further details that are passed over here.]]

1 Introduction

A content of a subject's mental state is narrow when it is determined by the subject's intrinsic properties: that is, when any possible intrinsic duplicate of the subject has a corresponding mental state with the same content. A content of a subject's mental state is wide when it depends in part on the subject's extrinsic properties: that is, when there is a possible intrinsic duplicate of the subject whose corresponding mental state lacks this content.

It is commonly accepted that many mental states have wide content. For example, where Oscar on Earth believes that water is wet, his intrinsic duplicate Twin Oscar on Twin Earth (just like Earth, except that H2O is replaced by the superficially identical XYZ) does not: he believes that twin water is wet.[*] Further, it appears that Oscar and Twin Oscar have corresponding beliefs with different truth-conditions: Oscar's belief is true of worlds where H2O is wet, while Twin Oscar's belief is true of worlds where XYZ is wet. So insofar as these belief ascriptions and truth-conditions reflect the beliefs' contents, those contents are wide.

*[[Putnam 1975, as adapted by McGinn 1977 and Burge 1982.]]

The existence of wide content is compatible in principle with the hypothesis that every mental state has narrow content: that is, that there is a (different) sort of content such that corresponding mental states of intrinsic duplicates have the same content of this sort. This hypothesis has intuitive appeal, but it has proven difficult to explicate an acceptable notion of narrow content. On my view, to understand narrow content, one must ground the notion in epistemic terms. In this paper I develop an account of this sort.

2 Epistemic space

I will be centrally concerned with propositional attitudes with a mind-to-world direction of fit: believing that P, expecting that P, hypothesizing that P, and so on. Let us call the most general propositional attitude in this class thought: so when one believes or expects or hypothesizes that P, one thinks that P. Let us say that a thought is an occurrent propositional attitude token of this type: roughly, an entertaining of a given content. Then a thought aims to represent the world, and can be assessed for truth or falsity. Note that understood this way, thoughts are tokens rather than types.

The account I will give will be grounded in a basic notion of the epistemic necessity of thoughts. This notion can be understood in various ways, but on the account I prefer, epistemic necessity is understood in terms of apriority. We can say that a thought is epistemically necessary when it can be justified independently of experience, yielding a priori knowledge. We can then say that a thought is epistemically possible when the negation of the thought is not epistemically necessary.[*] Epistemic possibility corresponds to rational coherence, on idealized a priori reflection.

*[[To handle cases of a priori indeterminacy, it is arguably better to say that a thought T is epistemically possible when ~det(T) is not epistemically necessary, where det(T) is a thought that is true when T is determinately true and false when T is false or indeterminate; and ~det(T) is its negation. I will abstract away from concerns about indeterminacy in what follows.]]

It is a common intuitive idea that when a thought is epistemically possible, there are specific epistemically possible scenarios that the thought endorses. In effect, any thought divides the space of scenarios into a class of scenarios that the thought endorses, and the class of scenarios that the thought excludes. When both a thought and its negation are epistemically possible, there will be scenarios in both classes. The basic idea I will pursue is that the narrow content of a thought is given by the way that the thought divides epistemic space: the space of epistemically possible scenarios.

We can start by thinking about Earth and Twin Earth. Imagine that Oscar does not know the chemical structure of the liquids in their world, but is speculating about it. He expresses a thought by saying 'water is XYZ'. Then Oscar's thought is false, but it is nevertheless epistemically possible: no amount of a priori reasoning can reveal the thought's falsity. Intuitively, the epistemic possibility of this thought reflects the epistemic possibility of various scenarios, in which (for example) the environment contains XYZ in the oceans and lakes. We can say, intuitively, that Oscar's thought endorses this sort of scenario, and that a scenario of this sort verifies Oscar's thought. We can equally say that Oscar's thought excludes other scenarios, in which the oceans and lakes contain H2O, and that a scenario of this sort falsifies Oscar's thought. So Oscar's thought seems to impose a division in epistemic space.

One can bring out this idea as follows. Consider a thought that the XYZ-scenario is actual: that is, that the environment contains XYZ with a specific appearance and distribution in the oceans and lakes. Then this thought is epistemically compatible with Oscar's thought that water is XYZ: there is no rational inconsistency in his accepting both. On the other hand, a thought that the H2O-scenario is actual is epistemically incompatible with Oscar's thought that water is XYZ: if Oscar accepts that an H2O-scenario is actual, he should rationally reject the thought that water is XYZ.

Note that nothing here contradicts the claims of Kripke (1980) and Putnam (1975) that water is necessarily H2O. Kripke allows that even if it is metaphysically impossible that water is not H2O, it is epistemically possible that water is not H2O: for all we know a priori, we could discover that water is XYZ. If we discover that the XYZ-scenario is actual - that the liquids in the oceans and lakes is XYZ, and so on - we will then be in a position to conclude that water is XYZ. This is quite compatible with Putnam's claim that in a counterfactual situation in which the oceans contain XYZ, XYZ is merely watery stuff and not water. In thinking about epistemic space, it is always epistemic possibility that is relevant.

What applies to Oscar applies also to Twin Oscar. Imagine that Twin Oscar is in a similar position, and also expresses a thought by saying 'water is XYZ'. Then his thought, unlike Oscar's, is true. But more importantly here, his thought is also epistemically possible: it endorses various epistemically possible scenarios in which the environment contains XYZ in the oceans and lakes, and excludes others in which the environment contains H2O. Twin Oscar's thought is epistemically compatible with the thought that an XYZ-scenario is actual, and it is epistemically incompatible with the thought that an H2O-scenario is actual: if he accepts that the H2O-scenario is actual, he should rationally reject his thought that water is XYZ. This is the same pattern that was present for Oscar. So it seems that Oscar's and Twin Oscar's beliefs divide epistemic space in very similar ways.

This holds out the promise that if we can make sense of the intuitive idea of a thought's dividing epistemic space, it may yield a notion of narrow content. To make this intuitive idea more precise, we need to say more about the space of scenarios, and about what it is for a scenario to be endorsed by a thought.

3 Scenarios

What is a scenario? Intuitively, a scenario corresponds to a maximally specific epistemically possible hypothesis, such that every epistemically possible belief is verified by at least one scenario. One could simply postulate a space of scenarios satisfying this and other principles; but to make the case that the notion is coherent, and to see how scenarios behave in specific cases, it is useful to try to construct scenarios directly from materials that are at hand. There are two sorts of construction strategies one can appeal to here. I have examined these at length elsewhere (Chalmers forthcoming b), but I will say a little about them here.

The first strategy constructs scenarios using possible worlds. Intuitively, any possible world corresponds to a highly specific hypothesis. For any given world W, we can entertain the hypothesis that W is actual: that is, that our own world is qualitatively just like W. For example, given a specific H2O-world (where the oceans contain H2O), we can entertain the hypothesis that the H2O-world is actual: that is, that our world is qualitatively just like the H2O-world. The same goes for an XYZ-world. So possible worlds seem to behave at least something like scenarios.

Possible worlds are not quite as fine-grained as scenarios, however: an objectively specified possible world does not correspond to a maximally specific hypothesis. The reason is that no amount of objective information can tell me my location within a world. Say that a world W contains XYZ in the oceans and lakes on one planet, and H2O in the oceans and lakes on another. Then if I know merely that W is actual, I do not know whether my environment contains H2O or XYZ, and I do not know whether today is Tuesday. To know these things, my location in the world must be specified. For this reason, scenarios are better modeled by centered worlds: worlds marked with an individual and a time as the world's center.[*] When I consider the hypothesis that a centered world W is actual, I consider that the world is qualitatively just like W, that I am the individual marked at the center of W, and that now is the time at the center. The added information given by the center will be enough to settle the indexical claims mentioned above.

*[[See Quine 1968 and Lewis 1979. The account I give here is very much compatible with Lewis's suggestion that belief content should be modeled using centered worlds, although Lewis does not ground his account in the epistemic domain.]]

One might worry about the Kripke/Putnam point mentioned earlier. If water is H2O in all possible worlds, how can we use possible worlds to verify a thought that water is XYZ? But again, this worry goes away if we think of things in terms of epistemic possibility. Consider an XYZ-world, in which the liquid in the oceans and lakes around the center is XYZ. Considered as a counterfactual metaphysical possibility, one might describe this as a world in which XYZ is not water but merely watery stuff. But considered as an epistemic possibility, the world functions differently. Here, we consider the hypothesis that the XYZ-world is our world: that is, the hypothesis that our world is qualitatively just like the XYZ-world, with XYZ in the oceans and lakes around us. When we consider this hypothesis, as before, it verifies the thought that water is XYZ: if I accept that the XYZ-world is my world, I should rationally accept that water is XYZ. So the world behaves just as we wish.

This raises an issue: in considering the hypothesis that a world W is actual, it matters how the world is described. In effect, one considers the hypothesis that D is the case, where D is a canonical description of W. What is contained in the description matters: if our description D of the XYZ-world contains "XYZ is not water", then the hypothesis that D is the case is epistemically incompatible with the thought that water is XYZ. To avoid this sort of thing, we can require that canonical descriptions be restricted to a semantically neutral vocabulary. To a first approximation, a semantically neutral expression is one that is not susceptible to Twin Earth thought-experiments: if corresponding semantically neutral expressions are used by intrinsic duplicates in different environments, they will have the same meaning.[*] Names, natural kind terms, and demonstratives are not semantically neutral, so no such expressions should be used in a canonical description of a world for our purposes. What remains is a neutral vocabulary for characterizing a world's qualitative structure. To this we can adjoin pure indexicals such as "I" and "now", in order to specify the location of a world's center. In this restricted vocabulary, problems of the above sort will not arise.

*[[This first approximation to semantic neutrality is a version of what Bealer (1996) calls "semantic stability". For reasons discussed in Chalmers (forthcoming a), semantic stability is not a perfect explication of the required notion of semantic neutrality, but it is good enough for present purposes. It should also be stipulated that to consider W as actual is to nondeferentially consider the hypothesis that D is the case (with a full grasp of the concepts involved in D); deferential consideration (with an incomplete grasp) does not qualify here.]]

The second way to deal with scenarios is to characterize them in wholly epistemic terms, so that non-epistemic notions of possibility are inessential to their definition. One natural way to do this is to construct the class using sentences in an idealized language with no expressive limitations.[*] Here we can presuppose an epistemic necessity operator over sentences: on the current account, S will be epistemically necessary when it is a priori. Let us say that S and T are epistemically equivalent when the biconditional S<->T is epistemically necessary. Let us say that a sentence S leaves a sentence T open when the conjunctions S&T and S&~T are both epistemically possible. And let us say that a sentence is epistemically complete when it leaves no sentence open. Then intuitively, an epistemically complete sentence in an idealized language corresponds to a maximal epistemic possibility. Two epistemically equivalent such sentences may correspond to the same maximal epistemic possibility. So we can naturally identify scenarios with equivalence classes of epistemically complete sentences (under the epistemic equivalence relation), in the idealized language.

What is the nature of the idealized language? In order that the idealized language have a sentence for every intuitive maximal epistemic possibility, we can assume that it has the capacity for infinitary conjunctions, as well as an arbitrarily large lexicon (subject to the following constraint). Because the construction ascribes epistemic possibility and necessity to sentence types rather than tokens, the vocabulary of the language must be restricted to epistemically invariant expressions: roughly, a vocabulary such that for any expression type in that vocabulary, all tokens of that type have the same epistemic properties when used by fully competent speakers. In particular, if a token of a sentence using such a vocabulary is epistemically necessary for a fully competent user (i.e., it expresses an epistemically necessary thought), then any token of that sentence type is epistemically necessary. (See Chalmers forthcoming a for more details here.)

On the epistemic construction, scenarios are tailor-made to serve as maximal epistemic possibilities. To consider the hypothesis that a scenario W is actual, one considers the hypothesis that D is the case, where D is a canonical description of W. Here, a canonical description of W is simply any of the epistemically complete sentences in W's equivalence class. An epistemically complete claim of this form will leave no questions open, so it will be maximally specific, and it will be perfectly suited to model a specific location in epistemic space.

Which of these two constructions of scenarios is to be preferred? On my view, the two are near-equivalent: for every scenario on the first construction, there is a corresponding scenario on the second construction, and vice versa. However, this claim is nontrivial, and some philosophical views will deny it. For example, consider a theist view on which it is necessary that a god exists, but it is not a priori that a god exists. On such a view, 'No god exists' will be epistemically possible, and there should be maximal epistemic possibilities involving no gods. On the epistemic construction of scenarios, this will hold straightforwardly. But on the metaphysical construction, there will be no such scenario: every centered world will contain a god, so that no centered world corresponds to the maximal epistemic possibility in question. Something similar applies to certain philosophical views on which the laws of nature hold necessarily: there will be epistemically possible hypotheses involving different laws, but no centered worlds in the vicinity. And something similar applies to certain views on which zombies and other creatures are epistemically possible but metaphysically impossible: there will be epistemically possible hypotheses involving zombies, but no centered world to verify these hypotheses.

Elsewhere, I have argued that all these views involve "strong necessities" of a sort much stronger than the ordinary a posteriori necessities made familiar by Kripke, and I have argued that we have no reason to believe in them. Nevertheless, this is a substantive philosophical claim about metaphysical possibility and necessity with which some will disagree. For this reason, the metaphysical construction involves more philosophical commitments than the epistemic construction, and the latter construction is arguably more neutral. The epistemic construction has the advantage of defining the space of scenarios in wholly epistemic terms from the start, so that it is guaranteed to give the right sort of epistemic results. It avoids entanglement with issues about metaphysical possibility and necessity, and also avoids the tricky issues about the descriptions of worlds discussed above.

For these and other reasons, I think that the epistemic construction of scenarios is more fundamental. All the same, the notion of a possible world is much more familiar to most philosophers, so I will often use centered worlds to represent maximal epistemic possibilities in what follows. When relevant issues arise, I will indicate where how the two approaches handle them differently.

On either approach to scenarios, there will be one scenario that is distinguished for a given subject at a given time as the subject's actualized scenario. On the metaphysical approach, this will be the centered world that consists of the subject's own world, centered on the subject at the time in question. On the epistemic approach, this will correspond to a sentence that expresses the complete truth about the world, from the point of view of the subject. The subject's actualized scenario is in effect the point in a subject's epistemic space that corresponds to reality.

On either approach to scenarios, one can also distinguish a special class of thoughts: the thought that a given scenario is actual. For a given scenario W, a thought that W is actual is a thought that D is the case (or a thought that could be expressed by uttering D), where D is a canonical description of W. Such a thought will usually be extraordinarily specific, and beyond the capacity of any human thinker to think. Nevertheless, these thoughts play a useful role as a sort of idealization in understanding the present framework.

How much information is required to specify a scenario? That is, what is the minimal information required for a canonical description of a scenario? This is one of the deepest questions in philosophy, and we do not need to take a position on it here. But it is useful to flesh out the picture a little by considering what sort of information might be required to specify an actualized scenario in our world, corresponding to the complete truth about the actual world from an individual's perspective.

First, a full description of the actual world must include or imply the complete microphysical truth about the world, specifying the microphysical laws and the distribution and properties of particles, fields, and waves in space and time. It must also include or imply the complete mental truth about the world, specifying the conscious experiences of all individuals at all times. On some views (e.g. some analytic functionalist views), the mental information will itself be derivable from the physical information, and on other views (e.g. some idealist or phenomenalist views) the physical information will itself be derivable from the mental information. If these views are correct, physical or mental information alone will suffice; but if these views are incorrect (as I think is plausible), then both sorts of information is required to specify a maximal epistemic possibility.

The information given so far leaves open further claims about additional material in the world: it is compatible with the hypothesis that there is additional nonphysical, nonmental ectoplasm in the world, for example. So assuming that no such further material exists, the information needs to be supplemented with information about the limits of the world: a "that's-all" clause that says that the world contains no more than what follows from what is already specified. Finally, all this objective information leaves open indexical claims about the subject's own location in the world, so it needs to be supplemented by indexical information (of the form 'I am X' and 'now is Y') specifying which individual within the world is the subject, and what is the current time.

Elsewhere (Chalmers and Jackson 2001; Chalmers 2002a) I have called this conjunction of physical, mental, "that's-all", and indexical information PQTI, and have argued that it is not implausible that PQTI epistemically necessitates all truths about the world. If this is correct, then PQTI itself specifies a maximal epistemic possibility, and so is all one needs to specify one's actualized scenario. If this is incorrect, then PQTI needs to be supplemented by further information in order to specify a maximal epistemic possibility. We do not need to settle this matter here, but this at least gives an illustration.

Strictly speaking, a canonical description of a scenario is restricted to epistemically invariant terms (on the epistemic construction) and semantically neutral terms plus indexicals (on the metaphysical construction). It is plausible that the terms in Q, T, and I are of the right form here. But one can argue that the microphysical terms in P are neither epistemically invariant, nor semantically neutral, as they are natural kind terms that involve rigid designation and that allow epistemic differences between individuals. So while PQTI specifies a scenario, it may not do so in canonical form. To handle this matter, one can replace P by a complete Ramsey-sentence formulation of its content, ultimately cashed out in terms of causal and other lawful relations between a class of basic elements, and causal relations to experiences. It is plausible, although nontrivial, that one can give such a formulation in epistemically invariant and semantically neutral terms.

More generally, the current framework requires that one can specify any maximal epistemic possibility using epistemically invariant terms (on the epistemic construction) or semantically neutral terms plus indexicals (on the metaphysical construction). This claim is again plausible but nontrivial: one can argue for this by arguing that epistemic variance and semantic non-neutrality in themselves give no extra power in the specification of epistemic possibilities: at most, they give variation between users (in the first case) and additional power in specifying counterfactual metaphysical possibilities (in the second case).

4 Epistemic intensions

If I had no empirical beliefs, then the whole of epistemic space would be open to me. With each of my empirical beliefs, the portion of epistemic space open to me is narrowed down. Each belief endorses some scenarios, and excludes others. When I come to believe that the earth is round, having had no previous beliefs about the matter, I exclude a number of scenarios that were previously open to me: scenarios involving a flat earth or a cubical earth, for example. As more beliefs accumulate, more scenarios are excluded. I never narrow down the class of scenarios open to me to just one, but I may narrow down the class to a small fraction of the original space.

This way of thinking yields a natural conception of the content of a thought. For any thought, there is a class of scenarios that it endorses, or equivalently a class of scenarios that verify the thought. At the same time, there is a class of scenarios that the thought excludes, or equivalently a class of scenarios that falsify the thought. There may also be a class of scenarios that the thought neither endorses nor excludes, perhaps because they constitute borderline cases. We can think of this division of scenarios as constituting the epistemic content of the thought.

Let us say that two thoughts of a subject are epistemically compatible if their conjunction is epistemically possible, and epistemically incompatible otherwise. One thought epistemically necessitates (or implies) another when the first is epistemically incompatible with the negation of the second.

What is it for a scenario to verify a thought? Using the notions above, one can say that a scenario W verifies a thought T when a thought that W is actual implies T: that is, when a thought that W is actual is epistemically incompatible with the negation of T. When this is the case, the hypothetical assumption that W is actual will rationally lead to the acceptance of T. One can similarly say that W falsifies T when a thought that W is actual implies the negation of T, or when a thought that W is actual is epistemically incompatible with T. In all these cases, the thought that W is actual is in effect a thought that D is the case, where D is a canonical description of W.

We can then associate every thought with an epistemic intension. An intension is a function from a space of possibilities of some sort to truth-values, or to some other sort of extension. A belief's epistemic intension is a function from scenarios to truth-values. For a given thought T and scenario W, the epistemic intension of T is true at W if W verifies T; the epistemic intension of T is false at W is W falsifies T; and the epistemic intension of T is indeterminate at W if W neither verifies nor falsifies T. I will say more about this shortly, but first, it is useful to look at some examples. For the purposes of these examples, I will use the understanding of scenarios as centered worlds.

Let B1 be my belief that I am a philosopher. Let W1 be the actual world, centered on David Chalmers, practicing philosophy, at a certain moment in September 2001. Let W2 be a world centered on David Chalmers at a certain time, in which he is a mathematician, not a philosopher. Let W3 be a world centered on Bertrand Russell in 1900, practicing philosophy. Let W4 be a world centered on Isaac Newton in 1600, practicing mathematics but no philosophy. All four of these correspond to epistemic possibilities, in the broad sense: the hypothesis that W1 is actual (that is, the hypothesis that the world is objectively like W1, and that I am the being marked at the center, and that now is the time marked at the center) is not ruled out a priori, and the same goes for hypotheses concerning W2, W3, and W4.

My belief that I am a philosopher is verified by W1 and W3. The thought that W1 is actual is epistemically incompatible with the belief that I am not a philosopher: the conjunction of the two can be ruled out a priori. The same goes for W3. I can know a priori that if W1 is actual, then I am a philosopher; and I can know a priori that if W3 is actual, then I am a philosopher. On the other side, W2 and W4 falsify my belief that I am a philosopher. My belief is epistemically incompatible with the thought that W2 is actual, and with the thought that W4 is actual. I can know a priori that if W2 is actual, then I am not a philosopher, and I can know a priori that if W4 is actual, then I am not a philosopher. So the epistemic intension of my belief is true at W1 and W3, and false at W2 and W4.

To generalize: the epistemic intension of my belief that I am a philosopher will be true at all centered worlds where the being at the center is a philosopher, and it will be false at all centered worlds where the being at the center is not a philosopher. This seems to capture something about how my belief that I am a philosopher puts epistemic constraints on how the world might be.

Let B2 be my belief that there is water in my pool. Let W1 be the actual world, centered on me now, with H2O in the oceans and H2O in my pool. Let W2 be a "Twin Earth" world, centered on my Twin Earth counterpart, where XYZ is the watery liquid in the oceans and lakes surrounding my counterpart, and where there is XYZ in my counterpart's pool. Let W3 be a modified Twin Earth world, with XYZ as the watery liquid in the oceans and lakes, but where my counterpart's pool contains no XYZ, just a small residue of H2O.

The hypothesis that W1 is actual clearly verifies B2. So does the hypothesis that W2 is actual. The thought that W2 is actual is epistemically incompatible with a belief that there is no water in my pool. I can know a priori that if W2 is actual, then there is water in my pool. On the other side, the hypothesis that W3 is actual falsifies B2. If I accept that W3 is actual, I must rationally accept that water is XYZ, and that there is no water in my pool. So the epistemic intension of B2 is true at W1 and W2, but false at W3.

To generalize: the epistemic intension of my belief that there is water in the pool is true in a centered world, very roughly, when the dominant watery stuff in the environment of the being at the center is present in that being's pool; and it is false, very roughly, when the dominant watery stuff in the environment of the being at the center is not present in that being's pool. Again, the epistemic intensions seem to capture something about how my beliefs put epistemic constraints on how the world might be.

Let B3 be my belief that water is H2O, and let W1, W2, and W3 be as above. Then the thought that W1 is actual verifies B3, but the thought that W2 is actual falsifies B3, as does the thought that W3 is actual. I cannot rationally accept both that W2 is actual and that water is H2O. Indeed, if I accept that W2 is actual, I should accept that water is XYZ. The same goes for W3. So the epistemic intension of B3 is true at W1, but false at W2 and W3. To generalize, the epistemic intension of my belief that water is H2O is true in a centered world, very roughly, when the dominant watery stuff in the environment has a certain sort of chemical structure.

Let B4 be my belief that two plus two is four. This belief is plausibly a priori. If so, then any scenario W verifies B4, as B4's negation is epistemically impossible. So B4's epistemic intension is true at all scenarios. If B5 is a belief that two plus two is five, on the other hand, then B5 can be ruled out a priori, so B' is falsified by all scenarios. So the epistemic intension of B5 is false at all scenarios. More generally: any a priori belief has an epistemic intension that is true at all scenarios, and any contradictory belief has an epistemic intension that is false at all scenarios.

Apart from the official definition, various heuristics can be useful in evaluating the epistemic intension of a belief B at a scenario W. One such is the indicative conditional heuristic suggested above by cases such as "if W2 is actual, then there is water in my pool". This sort of heuristic can be used be a subject to evaluate the epistemic intensions of his or her beliefs. The heuristic is most easily applied when a belief B is expressible by a sentence S. To evaluate the epistemic intension of B in W, the subject can ask: if W is actual, is S the case? This is an indicative conditional, and so should be interpreted epistemically. (To stress the epistemic character, one can also ask: if W turns out to be actual, will it turn out that S?) Like other indicatives, a subject evaluates it by the Ramsey test: one adopts the hypothesis that W is actual, and considers whether this hypothesis rationally leads to the conclusion that S is the case.

For example, when I adopt the hypothesis that the Twin Earth scenario is my actual scenario - that is, that the watery stuff in my environment is and has always been XYZ, and so on - this rationally leads to the conclusion that water is XYZ. I can reasonably say that if the Twin Earth scenario is actual, then water is XYZ. Similarly, when I adopt the hypothesis that the scenario centered on Isaac Newton is my actual scenario, this rationally leads to the conclusion that I am a mathematician. I can reasonably say that if the Newton scenario is my actual scenario, than I am a mathematician.

It should be noted that a beliefs epistemic intension involves a rational idealization. What matters is not whether a subject would actually judge that a belief is true, given the information that a scenario W is actual; rather, what matters is whether a priori reasoning would allow the subject to do in principle. Here, we idealize away from contingent limitations on a subject's actual cognitive capacity (mistakes, memory limitations, processing limitations, and so on), and assume the same sort of ideal rational reflection that is invoked by the notion of whether a claim is knowable a priori.

This idealization entails that certain intuitive distinctions in content are lost. For example, any a priori truth will have a necessary epistemic intension: so assuming all mathematical truths are a priori, then they all have the same epistemic intension. Likewise, two empirical truths that are equivalent to each other by highly nontrivial a priori reasoning will have the same epistemic intension. We can think of a belief's epistemic intension as representing its ideal epistemic content: this captures the way it constrains epistemic possibilities when ideal reasoning is assumed. It is possible to relax this idealization, yielding a more fine-grained notion of epistemic content, by starting with a more demanding notion of epistemic necessity (some details are given in Chalmers forthcoming b).

I note also that skeptics about the a priori can define epistemic intensions without appealing to that notion, for example by appealing to the Ramsey-test heuristic instead, or by appealing to another notion of epistemic necessity. On my view, the notion defined in terms of apriority is the most fundamental here; but the general framework is not entirely dependent on the notion of apriority, in that one can reconstruct many of its properties without that notion.

An important note: to evaluate the epistemic intension of a thought at a scenario W, it is not required that the thought itself be present within W. To evaluate whether a thought is epistemically compatible with the hypothesis that W is actual, only the original thought is relevant; the presence or absence of thoughts in W is usually irrelevant. For example, my belief that I am a philosopher endorses a world centered on Nietzsche philosophizing, whether or not he thinks that he is a philosopher. As an extreme case, it is arguably knowable only a posteriori (through introspection and observation) that thoughts exist, in which case a thought that there are no thoughts is epistemically possible. Such a thought will be verified by a scenario in which no thoughts are present. So to evaluate a thought's epistemic intension in a scenario W, one should not in general use the heuristic: is the thought true, as thought in W? Instead, the evaluation is grounded in the epistemic domain.[*]

*[[For much more on this, see Chalmers (forthcoming a) on the distinction between "contextual" and "epistemic" understandings of two-dimensional semantics. The current approach is of the broadly epistemic type, which differs fundamentally from the broadly contextual approach put forward by Stalnaker (1978) and others. As a result, the approach here is not subject to the problems noted by Stalnaker (1990) in using his two-dimensional approach to yield an account of narrow content.]]

It should be noted that epistemic content is a truth-conditional variety of content. A thought's epistemic intension can be true in some scenarios and false in others, and in effect, it tells us what is required for the thought to be true, depending on which scenario turns out to be actual. We might think of this as providing the epistemic truth-conditions of the thought.

5 Epistemic intensions for concepts

Thoughts are often (perhaps always) composed from concepts. My thought that water is H2O, for example, is plausibly composed by my concept water, my concept H2O, and perhaps my concept of identity. As with thoughts, we can think of a concept here as a mental token, tied to a specific thinker. Where thoughts can be expressed by sentences, concepts can be expressed by words and other subsentential expressions. Just as one defines epistemic intensions for thoughts, one can also define epistemic intensions for concepts.

Where beliefs have a truth-value, concepts have an extension. Different sorts of concepts have different sorts of extensions: singular concepts (such as my concept Bill Clinton) have individuals as extensions; general concepts (such as my concept doctor) plausibly have classes as extensions; predicative concepts (such as hot) might have either properties or classes as extensions, depending on how one does things, and so on. A concept's epistemic intension will then be a function from scenarios to extensions of the relevant type.

Formally defining a concept's epistemic intension requires some fine details, which I will summarize briefly here (see Chalmers forthcoming a for more). First, one has to ensure that scenarios contain entities that can serve as extensions. On the metaphysical construction this is automatic; on the epistemic construction, this requires some work. We can say that two singular terms C1 and C2 are coextensive under a scenario if a canonical description of the scenario implies 'C1=C2', and that two singular concepts are coextensive under a scenario when a canonical description of the scenario implies an analogous thought. Then one can identify an individual in a scenario with an equivalence class of epistemically invariant singular terms under that scenario. One can analogously construct classes, properties, and the like in a scenario, by invoking analogous notions of the coextensiveness of general concepts, predicates, and proceeding from there. Second, one has to identify a concept's C's extension at a scenario W. Here we rely on concepts with which C is coextensive under W. On the epistemic construction, C will be coextensive under W with a concept expressible as an epistemically invariant expression B. On the metaphysical construction, C will be coextensive under W with a concept expressible as an expression B using only semantically neutral terms and indexicals. Either way, B will straightforwardly pick out an extension in W. We can then say that the epistemic intension of C in W returns that extension.

This definition above is somewhat technical, but the underlying notion of a concept's epistemic intension is quite intuitive. One can get the general idea by evaluating the epistemic intensions of one's own concepts using an indicative-conditional heuristic. If a concept C is expressible by a term C', we can ask: if W is actual, what is C'? (Here C' is used rather than mentioned.)

For example, to evaluate the epistemic intension of my concept water at the Twin Earth scenario W, I ask: if W is actual, then what is water? The answer seems clear: if W is actual, then water is XYZ, as before. (Or: if W turns out to be actual, it will turn out that water is XYZ.) So at the Twin Earth scenario, the epistemic intension of my concept water refers to XYZ. Similarly, to evaluate the epistemic intension of my concept I at the world W1 centered on Isaac Newton, I ask: if W1 is actual, who am I? The answer seems clear: if W1 is actual (i.e. is my actual world), then I am Isaac Newton. So in the Newton world, the epistemic intension of my concept I picks out Isaac Newton.

The epistemic intension of a concept I across centered worlds is particularly straightforward: it picks out the individual at the center of a world. The epistemic intension of a concept now picks out the time indicated at the center, and the epistemic intension of a concept here picks out the location of the individual at the time in question. As for a concept such as my concept water: we can see that it picks out H2O in the actual centered world, XYZ in the Twin Earth centered world, and so on. Roughly speaking, one might say that it picks out the clear, drinkable liquid in common use near the center of a world.

This suggests that the epistemic intension of a concept such as my concept water can be often be roughly encapsulated in a description. But this sort of description is not a substitute for the intension itself. The intension of my concept water can be evaluated at any scenario W, by hypothetically accepting that W is actual, and reaching rational conclusions about the nature of water under that hypothesis. In examining cases, one can note that a given substance seems to qualify as the extension of 'water' in a scenario in virtue of that substance's appearance, behavior, and connection to the center of the world; and one might try to summarize this pattern by giving a description such as the above. But it is likely that any such description will be at best an approximation, and in any case, a description will only be useful insofar as it mirrors the character of the intension. So it is the epistemic intension, not any associated description, that has priority.

It should be noted that in some cases, the epistemic intension of a concept expressed by a term may vary between competent users of a term. For example, it may happen that given complete information about a scenario, different subjects may make different rational judgments involving the term 'water' under that scenario. In such a case, it is plausible that the associated concepts have different epistemic intensions. It is for this reason that epistemic intensions are associated in the first instances with tokens rather than types. For some expressions, epistemic intensions might not vary between competent users in this way: examples might include pure indexicals such as 'I', and perhaps certain descriptive terms such as 'circular'. These expressions are precisely the epistemically invariant expressions discussed earlier.

Any concept of the sort that has an extension also has an epistemic intension. This applies equally to concepts that can be expressed as names (e.g. Gödel), as descriptions (e.g. the largest planet in the solar system), as predicates (e.g. hot), and so on. For any such concept, a subject who is given a full description of a scenario is in a position to determine its extension under that scenario. This pattern of determination corresponds to the concept's epistemic intension.

When a concept's epistemic is evaluated at a subject's actual scenario, it will return the concept's actual extension. This provides a clear sense in a concept's epistemic intension can be said to determine its extension, in conjunction with facts about the subject's world. The epistemic intension of a thought can be said to determine its truth-value in the same way, in conjunction with facts about the subject's world.

When a thought is composed of concepts, the truth-value of the belief is usually some function of the extensions of the concepts. For example, given a belief of the form B is C, the belief will be true if the extensions of B and C coincide. In such a case, the epistemic intension of the belief will be a function of the epistemic intensions of the concepts. At a given world, the truth-value of the belief will depend on the extensions of the concepts by the same function according to which the actual truth-value depends on the actual extensions. So the epistemic intension of B is C will be true at a world if the epistemic intensions of B and C coincide there, and so on.

As a consequence, it is easy to see that when B is C is epistemically necessary, B and C have the same epistemic intension. So if we think of Hesperus as a concept whose reference is fixed to the evening star, Hesperus is the evening star is a priori, so Hesperus and the evening star have the same epistemic intension. Similarly, equiangular triangle and equilateral triangle plausibly have the same epistemic intension (abstracting away from issues about nonEuclidean space). In effect, a concept's epistemic intension individuates that concept up to a priori equivalence.

6 Epistemic content is narrow

As promised, epistemic content is a sort of narrow content. This is best illustrated by familiar examples. Consider Oscar on Earth, and Twin Oscar on Twin Earth. Setting aside the inessential fact that Oscar's body contains H2O and Twin Oscar's body contains XYZ, Oscar and Twin Oscar are physical and phenomenal duplicates. Oscar and Twin Oscar both have beliefs that they express by saying 'clouds contain water'.

Consider the epistemic intensions of Oscar's belief B1 and Twin Oscar's beliefs B2. Let W1 be Oscar's actual scenario, centered on Oscar with H2O around him, filling the oceans and lakes and present in the clouds. Let W2 be Twin Oscar's actual scenario, centered on Twin Oscar with XYZ around him, in oceans, lakes, and clouds. Clearly, as B1 and B2 are both true, the epistemic intension of B1 is true at W1, and the epistemic intension of B2 is true at W2. Further, the epistemic intension of B1 is true at W2: if Oscar accepts that W2 is actual, he should rationally accept B1. Symmetrically, the epistemic intension of B2 is true at W1: if Twin Oscar accepts that W1 is actual, he should rationally accept B2. So the epistemic intension of B1 is true at both W1 and W2, and so is the epistemic intension of B2.

Something similar applies to other scenarios. Let W3 be a scenario in which XYZ fills the oceans and lakes around the center, but is not present in clouds (perhaps clouds merely trigger rainfall from other invisible bodies of XYZ). If Oscar accepts that W3 is actual, he should rationally reject his belief B1: the hypothesis that W3 is actual is epistemically incompatible with his belief that clouds contain water. So W3 falsifies B1. The same goes for Twin Oscar: the hypothesis that W3 is actual falsifies his belief B2. So B1 and B2 are both false at W3.

More generally: if any scenario W verifies Oscar's belief B1, it verifies Twin Oscar's belief B2. If W falsifies B1, it falsifies B2. So B1 and B2 have the same epistemic intension. At a first approximation, we can say that both of these endorse those centered worlds in which the clear, drinkable liquid around the center of the worlds is present in some form in the cloudlike objects around the center of the world. This is a first approximation to the way that this belief divides epistemic space, and it is shared between both beliefs.

Something similar applies to any twin of Oscar. For any such twin with corresponding belief B3, if a thought that W is actual implies B1 for Oscar, it will imply B3 for the twin. So B3 will have the same epistemic intension as B1 and B2. So it seems that the epistemic content of these beliefs is a sort of narrow content.

One can generalize this pattern to concepts. Take Oscar's and Twin Oscar's water concepts. At W1, the epistemic intension of both concepts picks out H2O. At W2, it picks out XYZ. At W3, it picks out XYZ. At W4, a scenario in which both H2O and XYZ are equally distributed near the center, it might pick out both. So both concepts have the same epistemic intension. Roughly speaking, it seems to be an epistemic intension that picks out in any given scenario a substance in the environment of the center of the scenario, on the basis of the substance's role and its superficial properties.

Something similar applies to any natural kind concept: there is nothing special about water here. The same applies also to indexical concepts. For example, both Oscar's and Twin Oscar's I concepts pick out the individual at the center of any given scenario, so both have the same epistemic intension. For all these concepts, their epistemic intension is a sort of narrow content.

One can give a related analysis of the cases that Burge (1979) uses to argue for the external nature of content. Bert, who lives in our community, has a belief that he expresses by saying 'arthritis sometimes occurs in the thighs'. In fact, arthritis is a disease of the joints and cannot occur in the thigh, so it seems that Bert has a false belief about arthritis. Twin Bert, a physical and phenomenal duplicate of Bert, also has a belief that he expresses by saying 'arthritis sometimes occurs in the thighs'. But Twin Bert lives in a community in which the word 'arthritis' is used for a different disease, one that affects the muscles as well as the joints: we might call it 'twarthritis'. It seems that Twin Bert has a true belief about twarthritis. Where Bert believes (falsely) that he has arthritis in his thigh, Twin Bert does not: Twin Bert believes (truly) that he has twarthritis in his thigh. Burge concludes that in this sort of case, belief content is not in the head.

Here, the crucial factor is that Bert uses the term 'arthritis' with semantic deference, intending (at least tacitly) to use the word for the same phenomenon for which others in the community use it. If Bert decided on his own to use the term 'arthritis' for a sort of headache, without caring how others use the term, then his term 'arthritis' would refer to a sort of headache, not to arthritis. With nondeferential uses like this, one cannot construct a twin scenario of the above sort. But with a deferential use, the content of a concept seems to depends on practices within a subject's linguistic community, which are themselves external to the subject.

Let B1 and B2 be the beliefs that Bert and Twin Bert express by saying 'arthritis sometimes occurs in the thighs'. Let V1 be Bert's actual scenario, with a surrounding community that uses the term `arthritis' to refer to a disease that occurs only in joints. Let V2 be Twin Bert's actual scenario, with a surrounding community that uses the term `arthritis' to refer to a disease that sometimes occurs in the muscles. The epistemic intension of B1 is clearly false at V1. What about V2? Bert can entertain the hypothesis that V2 is actual: that is, he can entertain the hypothesis that in his community, the term `arthritis' is used to refer to a disease of the muscles and joints. If Bert adopts this hypothesis, then given that he uses the term `arthritis' with semantic deference, he will rationally be led to the conclusion that arthritis can occur in the muscles: that is, he will be led to accept B1. In fact, for Bert, the hypothesis that V2 is actual is epistemically incompatible with B1. So the epistemic intension of B1 is true at V2. In a similar way, the epistemic intension of B2 is false at V1.

So the epistemic intensions of both B1 and B2 are false at V1 and true at V2. Something similar applies to any other scenario: when Bert and Twin Bert rationally evaluate their beliefs under the hypothesis that a given scenario is actual, they will obtain the same truth-value. And something similar applies to any other duplicate of Bert or Twin Bert. For any scenario V, any such duplicate can entertain the thought that V is actual. If such a thought implies Bert's belief B1, such a thought will also imply the duplicate's belief B3. So B1 and B3 have the same epistemic intension, and once again, the belief's epistemic intension is a sort of narrow content.

The same goes for Bert's and Twin Bert's concepts. The epistemic intension of Bert's concept arthritis picks out a disease of the joints in V1, and a disease of the muscles and joints in V2. The epistemic intension of Twin Bert's concept does the same. If one wanted to characterize the common epistemic intension in descriptive terms, one might say very roughly that in a given scenario, it picks out the disease referred to as `arthritis' by speakers in the linguistic community of the individual at the center of the scenario. This seems to roughly capture the dependence of referent on community that semantic deference involves, and it seems to mirror the way that Bert's and Twin Bert's beliefs will be rationally evaluated at various epistemic possibilities.

(Of course this sort of epistemic intension will attach only to deferential concepts: that is, concepts expressible by terms used with semantic deference. If an expert uses 'arthritis' nondeferentially to refer to a certain disease of the joints, then even if he were to accept that others use the term 'arthritis' differently, this would not rationally lead him to reject the belief B1 that he expresses as 'arthritis is a disease of the joints'. The epistemic intension of his concept arthritis would pick out (roughly) a disease of the joints in any scenario, regardless of the way the word `arthritis' is used there.)

We can treat Putnam's case of 'elm' and 'beech' similarly. I may know almost nothing to distinguish elms and beeches, but my terms nevertheless refer to different entities, through "the division of linguistic labor". In a scenario in which the community around me refers to X-trees by 'elm', the epistemic intension of my concept elm picks out X-trees; in a scenario where the community refers to Y-trees by 'elm', the epistemic intension picks out Y-trees. To characterize the epistemic intension of my concept, we might say roughly that it picks out the object referred to as 'elm' by the community of the individual at the center of a given scenario. So my concepts elm and beech will have different epistemic intensions, both narrowly determined. As always, a concept's extension depends epistemically on the character of the actual world; it is just that in these cases, some of the relevant facts about the actual world are linguistic.

So far we have seen that epistemic content is narrow by looking at the cases used to argue for wide content, and by noting that in these cases the corresponding thoughts of intrinsic duplicates have the same epistemic content, so that the factors responsible for the width of some content do not affect epistemic content. To complete the case, it would be useful to give a positive argument that epistemic content is narrow. Such an argument requires an extended treatment, but here I will briefly sketch how such an argument might go.

Such an argument can proceed from two plausible theses. The first is the thesis that epistemic necessity is narrow: that is, if a belief of a subject is epistemically necessary, the corresponding belief of a duplicate subject will also be epistemically necessary. Where epistemic necessity is understood as apriority, this claim is grounded in turn in the claim that when a subject's belief is a priori justifiable, a duplicate's corresponding belief is also a priori justifiable. This plausible claim is entirely unaffected by the arguments of Putnam, Burge, and the like. If a subject's thought can be justified by an a priori reasoning process, a corresponding thought in a duplicate can be justified by a corresponding a priori reasoning process.[*]

*[[One might be tempted to suggest a Burge-like cases where a subject with incomplete competence with the term 'bachelor' deferentially believes that bachelors are unmarried, and a duplicate deferentially believes that all lawyers are unmarried, and hold that the first belief is epistemically necessary but the second is not. But as defined here, neither belief is epistemically necessary: even the first subject's belief cannot be justified independently of experience. At most, other (nondeferential) beliefs in the same proposition might be epistemically necessary. Here it is important to recall that epistemic necessity is attributed to tokens rather than types.]]

The second is the thesis that considering a scenario is narrow: that is, if a subject thinks a thought that a scenario V is actual, any intrinsic duplicate of the subject will think a corresponding thought that V is actual. Where scenarios are understood using worlds, this follows from the fact that the thought that V is actual is equivalent to the (nondeferential) thought that D is the case, where D is a semantically neutral claim that is not vulnerable to Twin-Earth-style shifts in meaning. Where scenarios are understood using the epistemic construction, this follows from the fact that scenarios are themselves grounded in the narrow notions of epistemic possibility and necessity.

Given these two theses, it is not hard to see that if one subject's thought that V is actual epistemically necessitates a thought T, any intrinsic duplicate has a corresponding thought that V is actual that epistemically necessitates a corresponding thought T'. From here, it can be seen that for any scenario V and any corresponding thoughts T1 and T2 of intrinsic duplicates, V verifies T1 iff V verifies T2. And from this, it follows that any two corresponding thoughts of intrinsic duplicates have the same epistemic intension. So epistemic content is narrow.

Ultimately, the narrowness of epistemic content is grounded in the narrowness of certain epistemic properties of thoughts. A priori justifiability is one such property. There are others: for example, it is plausible that if two thoughts stand in the "Ramsey test" relation (if the first is accepted, it is rational to accept the second), then the corresponding thoughts of any intrinsic duplicate stand in that relation. This suggests that even without appealing to the notion of apriority, one could use a framework of this general sort to explicate a notion of narrow content.

7 Conclusion

How does this notion of narrow content relate to more familiar notions of wide content? Very briefly (details are in Chalmers 2002b): where one can define epistemic intensions in terms of epistemic possibility and necessity, one can also define subjunctive intensions in terms of subjunctive (or "metaphysical") possibility and necessity. (Roughly: P is subjunctively possible when it might have been the case that P.) Where epistemic necessity is narrow, subjunctive necessity is often wide; as a result, subjunctive intensions yield a sort of wide content. This corresponds to the more familiar variety of truth-conditional content in contemporary philosophy of language and mind.

Any given thought has both epistemic and subjunctive content, and these two sorts of content can be seen to co-exist naturally in a two-dimensional approach to the content of thought and language. One can argue that because it is constitutively tied to the epistemic and rational domains, epistemic content has an especially crucial role to play in the explanation of cognition and of behavior. But that is a story to be told elsewhere.

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