The Components of Content (1995 version)

## The Components of Content (1995 version)

### David J. Chalmers

Department of Philosophy
University of Arizona
Tucson, AZ 85721.

chalmers@arizona.edu

*[[This is the 1995 version of "The Components of Content", published in heavily revised form in 2002..]]

### 1 Introduction

Here are six puzzles about the contents of thought.[*]

*[[For background material on the six puzzles, see: (1) Putnam 1975, Burge 1979; (2) Frege 1892; (3) Kripke 1979; (4) Perry 1979; (5) Schiffer 1990; (6) Kripke 1980.]]

(1) Is content in the head? I believe that water is wet. My twin on Twin Earth, which is just like Earth except that H2O is replaced by the superficially identical XYZ, does not. His thoughts concern not water but twin water: I believe that water is wet, but he believes that twin water is wet. It follows that that what a subject believes is not wholly determined by the internal state of the believer. Nevertheless, the cognitive similarities between me and my twin are striking. Is there some wholly internal aspect of content that we might share?

(2) Frege's puzzle. The thought that Hesperus is Hesperus seems to express the same proposition as the thought that Hesperus is Phosphorus, but the former is trivial and the latter is not. How can this difference in cognitive significance be reflected in a theory of semantic content?

(3) Kripke's puzzle. In France, Pierre is told that "Londres est jolie", and he believes it. Later, he arrives in London and thinks it is ugly, never suspecting that "London" and "Londres" name the same city. It seems that Pierre simultaneously believes that London is pretty and that London is not pretty. But Pierre is highly rational, and would never believe a contradiction. What is going on?

(4) The problem of the essential indexical. When I believe that I am in danger, I will take evasive action. This belief state seems to be essentially indexical, or self-directed; if I merely believe that x is in danger, where x happens to be me, I might do something else entirely. How can we square this indexical aspect with a propositional account of the contents of thought?

(5) The mode-of-presentation problem. If Jimmy says "Lois believes that Superman can fly", he speaks truly. If he says "Lois believes that Clark Kent can fly", he speaks falsely. But on many accounts, the proposition that Clark Kent can fly is the same as the proposition that Superman can fly. If so, it seems that to believe that Clark Kent can fly, it is not enough to believe in the corresponding proposition; one must believe it under an appropriate mode of presentation. But what is a mode of presentation, and how can these be integrated into an account of belief ascription?

(6) The contingent a priori. Say it is stipulated that one meter is the length of a certain stick in Paris. Then one knows a priori that the stick is one meter long, if it exists. But the corresponding proposition is contingent, as the stick might have been longer or shorter. How can one have a priori knowledge of the truth of a contingent proposition?

These puzzles are not unrelated. All of them suggest an incompleteness in a propositional view of thought content, on which the content of a belief that P is identified with the conditions under which P is true, or with some other version of the content of the proposition that P. In particular, most of them raise questions about how well a propositional account of thought content reflects rational or cognitive aspects of thought. Because a thought's propositional content is strongly tied to the external objects of the thought, a propositional account seems to have trouble capturing the rational relationships between thoughts (as witnessed by puzzles 2, 3, and 6), and their role in guiding cognition and action (as witnessed by puzzles 1 and 4).

To resolve these and other puzzles, many have postulated a separate internal dimension of content - so-called "narrow content" - that is more closely tied to cognition and action.[*] But the road from intuition to theory has been a difficult one, and no account of narrow content has yet gained widespread acceptance. Perhaps the greatest difficulty is that because narrow content is internal, it seems to lack the sort of relation to the external world that is required to qualify as content. Many have thought that narrow content is not the sort of thing that can be true or false, for example, as the Twin Earth cases show us that truth-conditions are not determined internally.[*]

*[[Arguments for narrow content can be found in Fodor 1987, Lewis 1994, Loar 1988, and White 1982.]]

*[[Even supporters of narrow content have often conceded this point: e.g. Fodor 1987, Block 1988.]]

I think that these problems are illusory, and that there is a robust and natural notion of narrow content such that narrow content has truth-conditions of its own. This can be seen by developing the insight, implicit in much contemporary work in the philosophy of mind and language, that content is two-dimensional. It turns out that the content of a thought can be decomposed into two components: its notional and relational content. Relational content is the familiar external variety of propositional content. Notional content is the additional component, with the following properties: (1) it is determined by the internal state of a cognitive system; (2) it is itself a sort of propositional content, with its own truth-conditions; (3) it governs the rational relations between thoughts. The first property ensures that notional content is a variety of narrow content. The second ensures that it is a truly semantic variety of content. The third ensures that it is central to the dynamics of cognition and action. These three properties together, placed within the two-dimensional framework, allow many problems in the philosophy of mind and language, including the six puzzles above, to be straightforwardly resolved.[*]

*[[The framework I outline was suggested by a reading of Kripke 1980 and Putnam 1975, but it has much in common with other existing ideas in the philosophy of mind and language that I will point to along the way. Most obviously there is a clear relationship to the two-dimensional accounts of the semantics and pragmatics of language given by Kaplan (1989) and Stalnaker (1978), but there are deep links to many other ideas besides. I hope that it is a virtue of the present proposal that it suggests direct links between ideas that might at first glance seem only distantly related.]]

### 2 Primary and Secondary Intensions

In what follows, an intension is a function over the space of possible worlds, taking a world as argument and returning an entity in that world. A centered world is a possible world with a marked individual and time (the "center" of that world).[*] W and W^* are the spaces of possible worlds and centered worlds respectively, and R is the space of entities in those worlds. A concept, pre-theoretically, is an element of a specific thought, of the sort that is an appropriate candidate for reference - that is, it either refers or has empty reference. (Note that a concept is a token rather than a type, tied to a specific thinker on a specific occasion.) A concept, in thought, is the analog of a term in language. For ease of exposition I will restrict attention to concepts that are associated with terms in the thinker's language ("I", "water", "arthritis"), but the account can be easily extended to concepts without linguistic counterparts.

*[[This notion is introduced by Quine (1968), who defines a centered world as a world with a marked space-time point. The definition above is due to Lewis (1979).]]

It is a familiar idea that every concept has an associated intension, mapping a possible world to the referent of the concept within that world. It is less commonly acknowledged that there are in fact two intensions associated with a concept, although this point is implicit in much recent work on meaning and reference. It is central to the work of Kripke and Putnam, for example, that there are two ways in which the reference of a concept in a world can depend on that world. First there is a dependency whereby reference is fixed in the actual world, depending on how the world turns out. My concept "water" refers to H2O given that the world has turned out one way, but if it had turned out differently my concept might have referred to XYZ. Second, there is a dependency whereby reference in counterfactual worlds is determined, given that the actual world is held constant. For example, given that the actual world turns out as it has, my concept "water" picks out H2O in all counterfactual worlds. Corresponding to these two dependencies are two intensions, a concept's primary and secondary intensions.

The primary intension of a concept is a function f_1: W^* -> R from centered worlds to referents. At a centered world w, the primary intension returns the referent of the concept in w when w is considered as actual[*] - that is, when it is considered as a candidate for the actual world of the thinker. This captures the way the reference of the concept is fixed, depending on how the actual world turns out - that is, depending on which centered world turns out to be the thinker's actual world. We can think of the primary intension as encapsulating what it takes for an entity in the actual world to qualify as the concept's referent.

*[[This phrase is due to Davies and Humberstone (1980). It is a familiar idea from two-dimensional modal logic that statements about possible worlds can be evaluated differently depending on whether the worlds are considered as actual or considered as counterfactual. The basic idea is presented in Evans 1979.]]

To evaluate a concept's primary intension at a centered world w, we can ask as a heuristic: to what would the concept refer, if w turned out to be actual? For example, if the actual world turned out to contain XYZ as the dominant clear liquid in the oceans and lakes on my planet, then my concept "water" would refer to XYZ. So the primary intension maps the XYZ-world to XYZ. On the other hand, given that the actual world turns out as it has, with H2O in the oceans and lakes, my concept "water" refers to H2O. So the primary intension maps the H2O-world (the real actual world[*]) to H2O.

*[[This is another construction familiar from two-dimensional modal logic (Davies and Humberstone, p. 10), to make explicit the fact that of the various worlds that might turn out to be actual, one of them is actual.]]

An alternative heuristic for determining the primary intensions of one's own concepts (such as "water") is to ask questions analogous to: if w turned out to be actual, what would it turn out that water is? There is a clear sense of the "turns out" locution on which it is reasonable to say that if the XYZ-world turned out to be actual, it would turn out that water is XYZ; this is the sense that is relevant in the heuristic. (On this reading, "it would turn out that" creates an intensional context even for a rigid designator.) I avoid this locution for the most part, as it can be interpreted in different ways,[*] but once the ambiguity is resolved this heuristic seems quite clear.[*] (In one way it may be better than the heuristic above, as it makes it clearer that the concept itself need not be present in w, as discussed below.)

*[[Sometimes philosophers resist this intensional reading of the "turns out" locution under the influence of Kripke (1980), but the commonsense reading remains viable even once Kripke's main point is granted. Kripke himself (p. 143) allows a sense in which gold could turn out not to have atomic number 79, although he insists that gold could not have turned out not to have atomic number 79. (To my ear, "could have turned out that" sounds ambiguous in a similar way). The notion that it would turn out that water is XYZ if the XYZ-world turned out to be actual is entirely compatible with the claim that water is necessarily H2O. Again, this is simply a commonsense reading of the "turns out" locution, a reading on which it behaves differently from a standard modal locution.]]

*[[One must be careful to ask the question from the personal point of view, rather than from a community's point of view, to handle the cases of semantic deference discussed below. That is, we must adopt the (reasonable) reading of the locution on which I can say truly (in a case where I defer to my community) that if it turned out that the community uses "elm" to refer to X-trees, it would turn out that elms are X-trees.]]

There is often an element of indexicality in the fixation of reference, so the location of a center must be specified for reference in an actual-world candidate to be determined. For example, if it is specified that an actual-world candidate contains both H2O and XYZ on otherwise similar planets, the referent of my concept "water" is undetermined until we specify where in that world my "viewpoint" - the center - is located. This indexicality is most obvious for a concept such as "I", whose primary intension picks out the individual at the center of a centered world. In general, an actual-world candidate is a world-as-I-find-it, marked with a viewpoint at its center.[*]

*[[Actual-world candidates resemble the "contexts of utterance" of Kaplan 1989, although the resemblance is imperfect. Counterfactual-world candidates, discussed below, correspond to Kaplan's "circumstances of evaluation".]]

The primary intension of a concept is determined independently of the concept's actual referent; it must be, as the intension itself specifies the way in which the referent depends on how the world turns out. This is reflected in the a priori thought-experimental methodology in the investigation of primary intensions. Given my concept "Gödel", I can ask (with Kripke): to what would it refer if it turned out that a man named "Schmidt" had proved the incompleteness of arithmetic, before the proof was stolen and published by a man named "Gödel"? Empirical knowledge about the actual world is irrelevant here, as specification of the basic facts about the centered world in question gives me all the facts that could possibly be relevant.

It is a central fact about concepts that for a wide range of actual-world candidates, the referent of a concept in such a world is both determinate and accessible to the thinker. To see this, note that once we know all about the qualitative structure of the actual world and our location within it, we have all the information we need to ascertain the nature and existence of our concepts' referents (think of "Hesperus", "water", "Jack the Ripper"). And if the actual world had turned out differently, we could have done the same. Information about the world's structure and our location within it would have sufficed, in principle, for knowledge of reference. Given this ability, we can do the same in cases of counterfactual speculation about actual-world candidates, provided that we are supplied with the relevant information about those worlds. Indeed, such thought-experiments are the basic currency of the theory of reference. The primary intension of a concept is therefore accessible in principle to the thinker, and accessible prior to investigation of the thinker's external world.

We need not require that an actual-world candidate itself contains a copy of the concept in question. A primary intension specifies what it takes for an entity in the actual world to qualify as the referent of the concept; these conditions of application will often build in no requirements about the presence of the concept itself. In evaluating the referent at an actual-world candidate, we retain the concept from the real actual world. For example, in an actual-world candidate in which the individual at the center is in a coma, the primary intension of my concept "I" (from the real actual world) picks out the comatose individual. Intuitively, we would say that if this world turned out to be actual, it would turn out that I am comatose, in the same sense in which if the XYZ-world turned out to be actual, it would turn out that water is XYZ. Not all concepts are so straightforward. We will see later that the primary intensions of some concepts are not determinate across all centered worlds, picking out a referent only if certain background conditions are satisfied. All that matters for now, however, is that the primary intension of a concept is a non-trivial partial function, determinate across a large class of worlds.

The secondary intension of a concept is more familiar, but works quite differently. This is a function f_2: W -> R from uncentered worlds to referents, returning the referent of the concept in a world when it is considered as counterfactual, given that the actual world has already been fixed. To evaluate the secondary intension of one's concept "water" at a world w, one asks: what is water in w? The same goes for other concepts, mutatis mutandis.[*] In the case of "water", if we accept the intuitions of Kripke and Putnam, then given that water is H2O in the actual world, water is H2O in all worlds, so the secondary intension of the concept picks out H2O in all worlds. Similarly, if Putnam and Kripke are correct, I am DJC in all counterfactual worlds, so the secondary intension of my concept "I" picks out DJC in all worlds. Note that these counterfactual worlds require no center; in evaluating the secondary intension at a world, the viewpoint of a thinker within that world is irrelevant.

*[[So the rules-of-thumb for determining primary and secondary intensions each have two formulations, depending on whether the concept is mentioned or used. On the "mention" formulation: the primary intension picks out the referent of a concept in w when it is considered as actual, whereas the secondary intension picks out the referent of a concept in w when w is considered as counterfactual. On the "use" formulation, the primary intension picks out what (for example) it would turn out that water is if w turned out to be actual (where the "turns out" locution is interpreted appropriately), whereas the secondary intension picks out what water is in w.]]

Unlike the primary intension, the secondary intension is often determined by a posteriori factors, as it depends on how the world of the thinker turns out. Given that the liquid in the oceans and the lakes in this world is H2O, the secondary intension of my concept "water" picks out H2O in all worlds, but if the liquid had turned out to be XYZ, then the secondary intension would have picked out XYZ in all worlds instead.

The full story about a concept can be summed up in a two-dimensional intension F: W^* \times W -> R, where F(v,w) is the referent of the concept in w, if v turns out to be actual (for v \in W^* and w \in W). The primary intension is f_1: v \mapsto F(v,v'), where v \in W^* and where v' is the uncentered world obtained by "unmarking" the center of v. The secondary intension is f_2: w \mapsto F(a,w), where a is the actual world of the thinker. Because f_2 depends on a, it is in general accessible only a posteriori. Note that the primary intension and the secondary intension always pick out the same referent in the actual world: f_1(a)=f_2(a')=F(a,a').

The secondary intension of a concept is usually determined by the primary intension and the actual world, but the way in which it is determined depends on the concept involved. There are a few basic patterns of determination, corresponding to different types of concepts.[*] The simplest case is that of ordinary "descriptive" concepts - perhaps "doctor" and "circle", although semantic intuitions differ - for which the conditions of application in a counterfactual world are the same as they are in the actual world. For these concepts, the secondary intension is simply a copy of the primary intension, over the space of uncentered worlds: f_2(w) = f_1(v), where v'=w. This requires f_1(u) = f_1(v) for all u, v \in W^* such that u' = v' - that is, the value of the primary intension at a centered world cannot depend on the position of the center - so the primary intensions of such concepts cannot be in any way indexical. In these cases, the secondary intension is independent of a posteriori factors.

*[[I count at least four basic patterns: those for descriptive concepts, rigid designators, natural kind concepts, and semantically deferential concepts. There may be others. The pattern itself is independent of a posteriori factors; for example, the fact that we use "water" to pick out in counterfactual worlds whatever has the common underlying structure of the stuff in the actual world (if such a common structure exists) is conceptually prior to investigation of the empirical details. We can think of these patterns as written into the a priori two-dimensional structure of a concept.]]

More interesting are cases in which the secondary intension differs significantly from the primary intension, and is determined only a posteriori. The most straightforward version of this phenomenon occurs with concepts corresponding to rigid designators, such as indexicals and names. For such concepts, the secondary intension is determined by rigidifying the primary intension - that is, by evaluating it at the actual world, and picking out the same referent in all possible worlds. For example, it turns out that the primary intension of my concept "I" picks out DJC at the actual world, so the secondary intension picks out DJC at all worlds in which he exists. A similar dependence, with minor complications, holds for natural kind terms.[*]

*[[Strictly speaking, natural-kind concepts are not rigid designators: "cat" does not pick out the same referent at every world, as there are different cats in each. One way around this is to stipulate that "cat" picks out the property of cathood at every world. Less artificially, we can give a two-stage story according to which "cathood" picks out the same property in each world, and "cat" picks out the objects satisfying the property in that world. Or we might simply say that "cat" picks out the objects with the same underlying explanatory structure as the cats in the actual world. I will ignore these complications in what follows.]]

For rigid-designator concepts, the structure of the secondary intension is easy to characterize, but the structure of a primary intension is generally more complex. Often the best one can do is give a rough summary. For example, it is not too far off the mark to say that the primary intension of my concept "water" picks out the dominant clear, drinkable liquid in the environment that stands in an appropriate causal relation to the center of a world, but this is far from perfect. One can characterize the primary intension more carefully by considering difficult cases (what would the referent be if there was both XYZ and H2O in the lakes? what would it be if the liquid that falls from the sky turns out to differ from the liquid we drink, due to a complex reaction? what if most "liquids" turned out to be made of fine particles of sand?), but we cannot expect to arrive at a perfect characterization of any manageable length. Indeed, a perfect finite characterization may be impossible. It is sometimes useful to appeal to rough-and-ready characterizations for the purposes of illustration, but it must be stressed that the real object of interest is always the full intension, to which any such descriptive characterization is a mere approximation.

It should be noted that this picture is entirely neutral between "causal" and "descriptive" theories of reference. On any account of how reference is fixed, there will be some way in which the referent of a concept depends on how the actual world turns out: if the actual world turns out this way, then "elm" refers to these things; if it turns out another way, then "elm" refers to those things. That is, on any theory of reference a concept will have a primary intension. The subject matter of the theory of reference is the precise structure of primary intensions; this is something about which the present account is neutral.[*] When I occasionally characterize a primary intension in descriptive terms, this is only an approximation for the purposes of illustration, and nothing will depend on the details.

*[[Some may think that an account involving primary intensions "feels" like a description theory, and perhaps it does. But note that even Kripke's (1980) argument against description theories presupposes something like a primary intension. It proceeds by considering the referent of a concept such as "Gödel" at various actual-world candidates, thus evaluating the primary intension, and arguing that any given description gives the wrong result. It follows that either an account involving primary intensions need not be a description theory, or there is a class of description theories that Kripke's arguments do not refute. The choice between these conclusions presumably depends on just what one takes a description theory to be.]]

The framework applies equally to concepts that are used with semantic deference. As Putnam and Burge have pointed out, my concepts of "elm" and "arthritis" can refer appropriately despite my knowing very little about the relevant subject matter. In these cases, I refer via the division of linguistic labor. At a first approximation, if those around me (and especially the "experts" in my community) refer to X-trees by "elm", then my concept "elm" refers to X-trees; if they refer to Y-trees by "elm", then I refer to Y-trees, and so on. The concept therefore determines a perfectly good primary intension. To characterize this primary intension even approximately, we have to involve the name of the concept: thus, at a first approximation, my concept "elm" picks out whatever trees those around me (particularly experts) refer to as "elms". As always, reference of a concept depends on how the actual world turns out; it is just that in these cases, some of the relevant facts about the actual world are linguistic.

Putnam suggests that concepts like "water" and "elm" show that the intension of a concept cannot determine the extension, if an intension is internally determined. The two-dimensional analysis shows that this is only half-true. The primary intension of a concept determines its extension, and the primary intension is internally determined. Of course, the primary intension is a centered intension, taking a centered world as argument, so Putnam's claim still holds for uncentered intensions. But any intension requires facts about the actual world to determine extension, and it is most natural to regard the actual world of a thinker as centered, so it is no surprise that centered intensions should be central in the fixation of reference.

In some ways, the primary intension of a concept resembles a Fregean sense. It is the primary intension that fixes reference in the actual world, and the primary intension is generally cognitively accessible. We will see that instances of Frege's puzzle arise precisely when the concepts involved have different primary intensions, so insofar as senses are introduced to solve these problems, primary intensions can play the role. On the other hand, Frege required that senses determine reference non-indexically, stipulating that the sense of a concept such as "here" is tied to a particular place. Here, the secondary intension seems to be a closer fit. Many have noted that nothing can satisfy all Frege's requirements on sense,[*] and it may be fruitful to view the present account as dividing the notion of sense into two distinct components. Alternatively, one might make the case that Frege's requirement of non-indexicality is misguided, and that primary intensions can do much of the important work that senses are introduced to do, despite this and other differences of detail with Frege's account.

*[[E.g., Perry 1977.]]

There should be no question of whether the primary or secondary intension is the intension associated with a given concept. The full story can only be given two-dimensionally. One or the other may be more useful for various specific purposes. In matters of linguistic content, the secondary intension may play the major role, as different users of a term may have quite different associated primary intensions, whereas the secondary intension will generally be constant. This is particularly clear in the case of names, for which primary intensions can vary wildly across a community. For questions about thought and its role in governing action, however, we will see that the primary intension is central.

### 3 Notional and Relational Content

So far we have been concerned with the semantics of concepts. Now we move to the central topic, the semantics of thoughts, which stand to concepts roughly as sentences stand to terms. As before, I will be concerned with thoughts (usually beliefs) that are associated with sentences in the thinker's language, but the account generalizes. Just as concepts are associated with intensions, thoughts are associated with propositions, which here will be regarded as functions from possible worlds into truth-values, or more simply as sets of possible worlds. (The framework can be adapted to other accounts of propositions, e.g. on which they are seen as structured groups of intensions.) Propositions be regarded as the contents of thoughts and of sentences, just as intensions can be regarded as the contents of concepts and of terms.

Just as there are two intensions associated with every concept, there are two propositions associated with every thought. The primary proposition is a centered proposition - a set of centered worlds, or a function from centered worlds to truth-value. At a centered world w, it returns the truth-value of the thought in w when w is considered as actual.[*] As a heuristic, we can ask: would the thought be true, if w turned out to be actual?[*]

*[[Stalnaker (1978) introduces a proposition like this as the "diagonal proposition" associated with an utterance. Just as the primary intension can be seen as the "diagonal" of a two-dimensional intension - f_1(v) = F(v, v') - the primary proposition can be seen as the diagonal of a "two-dimensional proposition", or a function from W^* \times W into truth-values. For reasons that will become clear, however, I find this terminology misleading in its suggestion that primary intensions and propositions are in some way derivative on secondary intensions and propositions.]]

*[[As before, we might also ask questions analogous to "if w turned out to be actual, would it turn out that water is wet?", where the "turns out" locution is read as before. As before, with either heuristic we retain the thought from the real actual world.]]

For example, the primary proposition associated with my thought "I am a philosopher" is the set of centered worlds in which the individual at the center is a philosopher. Or consider my thought "There is water on this table". If the actual world turned out to contain XYZ as the dominant liquid in the oceans and lakes, and if there were a table in front of me supporting a glass of XYZ, then my thought would be true. As things really are, the world contains H2O in the oceans and lakes, and there is only an empty glass on the table in front of me, so my thought is false. At a rough approximation, the primary proposition associated with my thought is the set of centered worlds in which there is a sample of the dominant clear liquid in the environment on a table in front of the individual at the center, although as usual the approximation is no substitute for the proposition itself, which can be obtained only from careful consideration of cases.

The secondary proposition is an uncentered proposition, returning at w the truth-value of the thought at w when w is considered as counterfactual. As a heuristic, we can ask questions of the form: "in w, is it the case that water is wet?", and similarly mutatis mutandis for other thoughts. Like secondary intensions, secondary propositions are often determined only a posteriori, as they depends on how the actual world turns out. For example, the secondary proposition of my thought "I am a philosopher" is the set of worlds in which DJC is a philosopher. Or take my thought "there is water on this table". Given that the actual world turns out as it has, with H2O in the oceans, my study table T in front of me, and with my thought occurring at time t, the secondary proposition is that set of worlds in which there is a sample of H2O on table T at time t.

The primary proposition associated with a thought can usually be determined by composing the primary intensions of the concepts involved.[*] For example, the primary proposition of a thought "Hesperus is Phosphorus" will be true at a centered world if the individual picked out by the primary intension of "Hesperus" in that world is also picked out by the primary intension of "Phosphorus" in that world - that is, roughly at those worlds in which the morning star is the evening star. A similar relation holds between secondary intensions and secondary propositions. The secondary intensions of "Hesperus" and "Phosphorus" pick out the same object in all worlds in which the referent of either exists, so the secondary proposition of "Hesperus is Phosphorus" is true of all such worlds.

*[[This does not require a "language of thought": it requires only that thoughts are semantically composed of concepts, not that they are syntactically composed of concepts. Even the assumption of semantic compositionality is inessential, although it eases discussion. The definition of primary and secondary propositions requires only that thoughts are the kind of thing that can be true or false of the world.]]

I will call the primary proposition associated with a thought the thought's notional content, because it most directly reflects how things seem from the point of view of the thinker. I will call the secondary proposition the thought's relational content, as it often (although not always) depends on the relations that the thinker bears to objects in the external world. For example, when you think "I am hungry" and I think "You are hungry", our thoughts have different notional content, but similar relational content. When we both think "I am hungry", the situation is reversed.

Importantly, the notional content of a thought is determined entirely by the internal state of the thinker.[*] Like the primary intension, the primary proposition cannot depend constitutively on the external world, as the proposition itself specifies how the truth of a thought depends on how the actual world turns out. I can investigate the primary proposition associated with my thought without investigating the environment: all I need to do is ask, if the environment turns out like so, will my thought be true? This is an entirely internal enterprise; facts about the actual environment have no role to play. Of course, the notional content of a thought will almost always depend causally on the external world, but whenever the external world affects the notional contents of our thoughts, it will do so my affecting the internal state of the thinker.

*[[Thus even a brain in a vat might have thoughts with notional content. This can be used to defuse Putnam's (1981) anti-skeptical argument that if he were a brain in a vat, he could not think "I am a brain in a vat". A brain in a vat could think a thought with the appropriate notional content, if not the appropriate relational content, and the notional content of the thought would seem sufficient to express a significant skeptical possibility, true only in worlds in which the individual at the center lacks the usual sort of epistemic contact with the surrounding world.]]

Every thought has both notional and relational content. As notional content is internally determined, we may stipulate that a thought's narrow content is its notional content. Similarly, we can stipulate that a thought's wide content is its relational content. It should be noted, however, that relational content is not always dependent on the environment. In particular, if a thought involves only non-rigid concepts used without semantic deference, the associated secondary proposition will be a simple twist on the primary proposition, so that relational content will be internally determined.[*]

*[[For similar reasons, this differs from Quine's usage on which "notional" and "relational" belief properties correspond to those attributed by de dicto and de re ascriptions respectively. De re belief properties and relational content come apart where nonrigid concepts are concerned: the relational content of my belief that the shortest spy is a spy might be shared by many twins in different environments, but the corresponding de re belief property requires a specific referent. Further, de dicto belief ascriptions often ascribe a combination of notional and relational content, as I discuss later.]]

As promised, this sort of narrow content is truth-conditional. The notional content of a thought delivers the conditions a centered world must satisfy, in order for the thought to be true in that world. The notional content of my thought "There is water on the moon" is true in a centered world with XYZ in the oceans and lakes and XYZ on the moon, even though the relational content of my thought is false there. At a rough approximation, the notional content will be true in those centered worlds in which the dominant clear liquid found in the oceans and lakes surrounding the center can also be found on the heavenly body bearing the appropriate relation to the center. We can think of the notional truth-conditions of a thought as expressing the way the actual world has to be, in order for the thought to be true.

The notional truth-conditions of a thought are often very different from the relational truth-conditions. One might worry that a thought could then turn out to be both true and false, but this is impossible. Just as the primary and secondary intensions pick out the same referent in the actual world, the primary and secondary propositions share the same truth-value there, so there is no danger of a thought's being both true and false in actuality. It is only at other worlds that the truth-conditions will give different results, and this is a consequence of the way those worlds are treated. In evaluating the primary proposition they are considered as actual, whereas in evaluating the secondary proposition they are considered as counterfactual. We might say that notional truth-conditions tell us what it is for a thought to be true in a world, whereas relational truth-conditions tell us what it is for a thought to be true of a world.

The distinction between notional and relational truth-conditions parallels Kripke's distinction between the a priori and the necessary. A thought is knowable a priori if its notional content is true in all centered worlds; and it is necessarily true, in Kripke's sense, if its relational content is true of all worlds. Cases of the contingent a priori, such as the thought that the stick in Paris is a meter long if it exists, are cases in which a thought has a necessary primary proposition but a contingent secondary proposition. Cases of the necessary a posteriori are the reverse.[*]

*[[A related two-dimensional account can be given of the corresponding phenomenon in language, yielding in a certain sense a semantic explanation of a posteriori necessity. I develop such an account in Chalmers 1996, where it is used to analyze some applications of a posteriori necessity in the mind-body problem. Upon analysis, the two-dimensional account suggests that some of the more ambitious applications of a posteriori necessity (in defence of certain sorts of materialism and of certain sorts of moral realism, for example) are unlikely to succeed.]]

### 4 The Advantages of Notional Content.

In recent times, the "content" of a thought has generally been identified with its relational content; but the notional content seems to be an equally good candidate. As before, there is no need to decide which is the content; but that being said, there many ways in which the notional content of a thought is responsible for most of the explanatory work that we would expect a notion of content to do.

First, notional content determines the rational relations between thoughts. If one thought implies another thought a priori, it is because the primary proposition associated with the first implies the primary proposition associated with the second. If I know that it is hot where I am now, I know that it is hot here, and vice versa; this is reflected in the fact that the notional contents of the two thoughts are the same. The relational contents of the thoughts are very different, however: there is no obvious relation between the proposition that it is hot where DJC is at time t and the proposition that it is hot at place P then.

It is straightforward to see why this is so. If one thought implies another a priori, then in any centered world in which the first turns out to be true, the second will turn out to be true, so the notional content of the first will imply the notional content of the second. Conversely, if the notional content of one thought implies the notional content of another, then a thinker should in principle be able to infer one from the other a priori (setting aside problems with complex mathematical statements and the like[*]), as the relationship between the thoughts is independent of facts about the external world. This is not so for relational content: the relational content of a thought may depend on facts about the external world that are unknown to the thinker, so that relations between thoughts in virtue of their relational content may lie outside the realm of cognitive access.

*[[The hard cases involve thoughts that are true in all contexts, but whose truth is extremely difficult for us to determine; perhaps Goldbach's conjecture is such a case. How these cases should be treated depends on whether we regard our limitations here as arising from imperfect rationality. If so, the link between notional content and rational relations remains precise; if not, it needs a small qualification. In any case, this issue arises only in rare cases.]]

This can be applied straightforwardly to explain the informativeness of a statement such as "Hesperus is Phosphorus". Although its associated secondary proposition is equivalent to that of the trivial "Hesperus is Hesperus", its associated primary proposition is quite distinct, so it is not cognitively trivial. If a thought is notionally equivalent to a thought that is knowable a priori, it will itself be knowable a priori,[*] but an equivalence in relational content carries no such guarantee.

*[[Subject to the qualification in the previous note.]]

We can also invoke notional content in the case of Kripke's Pierre, who paradoxically seems to believe that London is pretty and that London is not pretty, without any breakdown in rationality. The two-dimensional framework shows why there is no paradox. Pierre's concepts "Londres" and "London" have quite different primary intensions - in a given centered world, the first picks out (approximately) the famous city called "Londres" that the individual at the center has heard about, whereas the second picks out the grimy city in which that individual has been living. The secondary intensions are identical, of course, picking out London in every world. Pierre's two beliefs, then, have contradictory associated secondary propositions, but their primary propositions are compatible. Contradictory secondary propositions support no charge of irrationality, as rational relations are determined by the first dimension of content.

Intuitively, Pierre's two beliefs are rationally compatible because there is some way the world could turn out such that both are true. There is a centered world in which "Londres" names a faraway, beautiful city (maybe it is in India), and in which the individual at the center inhabits an entirely distinct ugly city called "London"; and for all Pierre knows and believes, such a world could be actual. As long as there is such a world, satisfying the notional content of all Pierre's thoughts - that is, as long as the notional contents of his thoughts are compatible - his rationality is not in danger.

This brings out the relation between this account and Dennett's (1981) suggestion that the narrow content of a thought is reflected in the notional world of the thinker. The notional world we can take to be a world (really a class of worlds) in which all of a thinker's beliefs (or as many as possible, in cases of irrationality) would be true.[*] A notional world is to be thought of as a world as the thinker finds it, so of course it is a centered world; and beliefs are to be evaluated in that world according to their primary propositions. Pierre's notional world is a world in which there is a beautiful faraway city called "Londres", and a grimy city close at hand called "London". If Pierre really lived in his notional world, he would be right about everything and rarely surprised.

*[[Dennett suggests that the relevant worlds are "the environment (or class of environments) to which the organism as currently constituted is best fitted." I think that this gives imperfect results in some cases, most obviously for beliefs about the past; see also the criticisms in White 1991, and the more refined account put forward there. Dennett's and White's suggestions here are in effect first attempts at giving a naturalistic reduction of notional content. Such a reduction is likely to be a major project in its own right.]]

On similar grounds, one can make the case that notional content governs the cognitive relations between thoughts. Here there is an important qualification, however, as notional content as I have defined it does not distinguish the various cognitive relations that might hold between thoughts that are deductively equivalent. From the point of view of notional content, a complex mathematical proof is as trivial as modus ponens; so the fine-grained cognitive dynamics of deduction lies beyond the reach of notional content. Perhaps a refined variety of notional content might handle these cases, but in any case I will set these issues aside here, as relational content does not handle them any better, and they are largely independent of the issues at play in this paper.

A qualified thesis would be the following: insofar as notional content or relational content governs the cognitive relations between thoughts, it is notional content that does the work. This can straightforwardly by seen by examining cases in which thoughts are cognitively related, and by observing that (1) in related cases in which relational content of these thoughts is varied but notional content is held constant, the cognitive relations are preserved (except insofar as cognitive relations can be affected by varying factors independent of both notional and relational content, as in the deductive case), and that (2) in cases in which the relational content is preserved but the notional content is not, the cognitive relations are often destroyed. The details here parallel those of the discussion of the explanation of behavior, below, so I will not duplicate them here.

A third advantage of notional content is its suitability for a role in the explanation of behavior. It is often noted that relational content seems slightly out of synchrony with what one would expect of an explanatory psychological state. To use an example of Kaplan's,[*] if you are watching me and my pants catch fire, our respective beliefs that my pants are on fire now will have the same relational content (they are true in all worlds in which DJC's pants are on fire at time t), but will lead to very different actions (I might jump into a river, while you just sit there). The difference between our actions does not seem to be something that a characterization in terms of relational content alone can explain. In a similar way, belief states can produce very similar behavior for apparently systematic reasons, even when the beliefs have very different relational content - witness the behavior that my twin and I produce when we think about twin water and water respectively, or the similarity between the actions of two people who think "I am hungry". A whole dimension of the explanation of behavior seems out of the reach of relational content.

These explanations can be easily handled in terms of notional content. If you and I think "I am hungry", the notional contents of our thoughts are very similar - our thoughts are associated with similar primary propositions, although different secondary propositions - and that similarity is reflected in the similarity of our actions. When you and I both believe that my pants are on fire, on the other hand, our notional contents are very different, and our actions differ correspondingly. Note that this provides a straightforward solution to Perry's problem of the essential indexical: it is notional content, not relational content, that governs action, and notional content, unlike relational content, is a centered proposition.[*]

*[[Perry (1979) considers the possibility that centered ("relativized") propositions might provide a solution, but dismisses it on the grounds that believing that such a proposition P is "true for me" does not distinguish me from third parties who also believe that P is true for me, but act differently. The trouble is that Perry's locution "true for me" introduces an unnecessary element of relational content. What distinguishes me from the third parties is rather that I believe P simpliciter, or better, that my belief has P as its notional content.]]

Notional content also accounts for the similarity of action between twin cases; this similarity reflects the fact that my beliefs about water and my twin's beliefs about twin water have the same associated primary propositions. But we need not move to the realm of science fiction to see the point. Two thoughts can share notional content even when two thinkers are quite different, as our thoughts "I am hungry" show, and even in these cases, similarities in narrow content will lead to similarities in action, other things being equal. Say I think that Superman is across the road, and I want to have Superman's autograph; then other things being equal, I will cross the road.[*] If you have thoughts with similar notional content to mine, then you will do the same. But if your thoughts only share relational content with mine, but have different notional content - say you think that Clark Kent is across the road, but want Superman's autograph -- then your behavior may be correspondingly quite different.

*[[To simplify the discussion, I make the happy assumption that Superman is actual and is identical to Clark Kent.]]

In general, whenever the content of a thought is causally relevant to behavior, its contribution is screened off by that of notional content in the following sense: if the thought had had the same notional content but different relational content, the behavior would have indiscernible (except insofar it might be affected by changing factors independent of both sorts of content), whereas if it had had the same relational content but different notional content, the behavior might have been quite different.

To see the latter point, we need only examine cases like those above. The thoughts "I am hungry" and "The guy over there is hungry" (unknowingly looking in a mirror) will lead to very different behavior, even though their relational content is the same. When Lois Lane is trying to cut Clark Kent's hair, her observation "Clark's hair breaks the scissors" will prompt a reaction very different from that provoked by a corresponding thought concerning Superman. If I hear that Cary Grant is starring in a movie, I might be more likely to watch than if I hear that the movie stars Archie Leach. In all these cases, different reactions are provoked by a difference in the notional content of a thought. In general, whenever the notional content of a thought is varied, different consequences can be expected, even if relational content is preserved throughout.[*] Given that notional content governs cognition and that cognition governs action, this is just what we would expect.

*[[Of course, thoughts like "Cary Grant is in the movie" and "Archie Leach is in the movie" might lead to the same actions despite their different notional content, if I know that Cary Grant is Archie Leach. But even here, there exist circumstances under which the thoughts might play a different role - if someone tells me that Cary Grant is not Archie Leach after all, for instance. In general, whenever two thoughts have different notional content, there are at least hypothetical circumstances under which the action-governing roles of the thoughts will differ.]]

By contrast, if the relational content of a thought is varied but notional content is kept constant, behavior stays indistinguishable throughout. Perhaps, unbeknownst to me, Cary Grant is an elaborate hoax, a co-operative construction by avant-garde animators and the mass media. In such a case, my thought about Cary Grant will have no relational content at all, but as long as it has the same notional content my behavior will be indistinguishable from that in the case in which he is real. Or perhaps Cary Grant is really Ludwig Wittgenstein in disguise: if so, very different relational content, but the same behavior. Similarly, when my twin and I think "I need some more water for this pot", the relational contents of our thoughts differ, but we both rush for the sink.

We can make a similar point within a single system. To use an example of Evans', let Julius be a name that functions to rigidly designate whoever invented the zip. Then the primary intensions of my concepts "Julius" and "the inventor of the zip" will be the same, but the secondary intensions will be very different. Despite the difference in secondary intensions, however, it is clear that any thoughts that "Julius is P" will play the same role in directing cognition and action as thoughts that "The inventor of the zip is P". The rigidification and consequent difference in secondary intension is simply irrelevant.[*]

*[[With one slight exception: the two concepts will behave differently in modal thought, as when one judges that it is necessary that Julius is Julius but not necessary that Julius is the inventor of the zip. But even here the difference is accounted for by a difference in the internally determined two-dimensional intension, rather than by a difference in relational content per se.]]

Some might object that there are cases in which we individuate behavior extrinsically - for example, my twin and I might behave differently in that I drink water where he drinks twin water - so that there is a dimension of behavior that escapes notional content. But even in this sort of case, relational content does not usually help. Even my twin, with the different relational content, would drink water if he was in my present context. What is relevant to behavior here is not relational content but current context, as we can see by an extension of the varying-factors strategy; and I certainly do not wish to deny that current context is relevant in the explanation of behavior.

The only cases in which there is a direct tie between relational content and behavior are cases in which behavior is individuated by an intentional object, such as that in which we say that search for a glass of water whereas my twin searches for a glass of twin water. This connection holds across all contexts, as behavior only counts as water-searching if it is caused by water-thoughts. But for the same reason, this is a very weak sort of relevance for relational content: as Fodor (1990) notes, the relational contents of thoughts are not causally relevant to action here, but instead are conceptually relevant, in effect determining the category the action falls under.[*] And relational content gives us very little purchase in the explanation of action here, as we will only know that some behavior is water-searching if we already know that water-thoughts lie behind it. In a causal (as opposed to a conceptual) explanation of the action, notional content will still play the central role.

*[[See Fodor 1990 for a detailed argument along these lines. I note also that one can individuate this sort behavior intentionally but still narrowly if one individuates intentional objects notionally.]]

Why is notional content primary? To answer this question, it is useful to think of my belief contents as constituting a model of my world, a kind of map by which I steer. My model is a model of the world as I find it, a centered world with me at the center, and my beliefs are constraints on that world. One belief might rule out these centered worlds as a candidate for the world where I am, another might rule out these, until only a limited class of worlds is left. I operate under the assumption that my world is one of those worlds, and if I am lucky I will not be too surprised.

My world-model is ultimately a notional world: a set of centered worlds, such that none of these would overly surprise me if they turned out to be actual. The constraints on this model are those of notional content. Relational content puts some additional constraints on the world, but these are not constraints that are useful to me. The relational content of my belief that the liquid in thermometers is mercury endorses only those worlds in which thermometers contain the element with atomic number X, but this constraint is so deeply inaccessible to me that if it turned out that the liquid has atomic number Y, I would not be in the least surprised. In an important sense, this constraint is not reflected in my world-model at all. Insofar as my world-model is useful to me, the constraints on it are entirely those of notional content; and insofar as content is useful to me, it is notional content that carries the burden.

It is worth noting that in making a case for the primacy of notional content, I have not appealed to any a priori methodological principles such as the dictum that what governs behavior is in the head. The case for notional content has been made directly, independently of questions about physical realization. Indeed, it should be stressed that nothing I have said implies that facts about a thinker's environment are irrelevant to the explanation of behavior. Facts about the proximal environment will clearly play an important role insofar as they affect the thinker;[*] facts about the current environment are crucial to explaining the success or failure of various actions; and facts about environmental history will at least be central to a causal explanation of a thinker's current cognitive state. All that follows from the present framework is that the environment is not relevant to the explanation of behavior in virtue of its role in constituting relational content. The kind of content that governs behavior is purely notional.

*[[It may even be that in certain cases, notional content can be constituted by an organism's proximal environment. For example, one could argue that the contents of a notebook with a list of addresses can constrain my notional world in the same way that my memory might. In these cases, one is effectively individuating the cognitive system as a coupled system whose boundaries lies beyond the skin, with notional content internal to the coupled system. Of course one could always keep the notional contents within the skin by insisting that the relevant contents are of the form "the address in this notebook" rather than "53rd Street", but in some cases one may gain explanatory purchase by taking the broader view of the system and the more constrained view of its notional worlds. This kind of consideration leads to an "externalism" very different from that deriving from considerations about relational content, and arguably more relevant to the explanation of behavior; it is discussed in much more detail by Clark and Chalmers (1995). Of course notional content remains internal in the deepest sense; it is just that the skin is not a God-given boundary of a cognitive system. Still, this is another way in which the issue between notional and relational content runs deeper than the issue between internalism and externalism.]]

### 5 Belief Ascription and Psychological Explanation

This raises something of a puzzle about the role of belief ascriptions in psychological explanation. If what has gone before is correct, the kind of content that governs cognition and action is notional, and therefore narrow. But at the same time, there is strong evidence that the kind of content attributed by belief ascriptions is at least sometimes wide. Does this mean that the common-sense framework of explanation in terms of belief ascription should be discarded? Alternatively, is the apparent success of the common-sense framework evidence that something in these arguments has gone badly wrong?

Neither conclusion is justified. The present framework shows how it can at once be true that (1) belief ascriptions ascribe wide content, (2) narrow content governs action, and (3) belief ascriptions explain action. In short: Belief ascriptions ascribe a combination of notional and relational content. It is in virtue of the relational component that the ascribed content is wide, and it is in virtue of the notional component that the ascribed content is explanatory.

A full justification of this answer requires two things: first, an analysis of what is attributed in belief ascriptions, so that we can see precisely what sorts of notional and relational content are attributed; second, an analysis of the role of belief ascriptions in psychological explanation, so that we can see that even in ordinary practice, it is the notional content attributed that carries the explanatory burden. I cannot provide anything like a complete treatment of these matters - the analysis of belief ascriptions deserves entire volumes of its own - but I can provide a preliminary sketch.

It is easy to see that ordinary belief ascriptions ascribe both notional and relational content. If I say "Ralph believes that Clark Kent is muscular", in order for my utterance to be true Ralph must have a belief that satisfies two sorts of constraints. First, the belief must have the relational content of the proposition that Clark Kent is muscular (perhaps we can allow a certain amount of variation in the relational content, if for example his concept of muscularity is slightly different from the norm). But that alone is not enough: a belief that Superman is muscular would have the same relational content, but would not make my ascription true. For the ascription to be true, his belief must involve a concept that refers to Clark Kent under an appropriate primary intension: perhaps an intension that picks out whoever is called "Clark Kent", or one that picks out whoever is that reporter with glasses at the Daily Planet, or more likely some complex intension in the vicinity. A variety of primary intensions will do, in order for the ascription to be true, but still a narrow class compared to all the primary intensions that in fact refer to Clark Kent.[*] A rigidified concept whose primary intension picks out the guy in the cape, or the strongest man in the world, might refer to Clark Kent, but the thought that the person in question is muscular would not make my ascription true.

More straightforwardly, if I am right in saying "Tom believes that he is hungry", then Tom must have a belief with more or less the appropriate relational content, true of all those worlds in which Tom is hungry at time t, but there is a strong constraint on notional content too. In particular, Tom must refer to himself via the primary intension that picks out the individual at the center in every centered world. If he sees someone in the distance clutching their belly, without realizing that he is in fact looking into mirrors, then a thought that that person is hungry has the right relational content, but on the most natural reading it does not make my ascription true. The ascription will only be true if Tom's belief refers to himself as himself; that is, only if its notional content is appropriate.

We have seen that content decomposes naturally into notional and relational content; we now see that belief ascription puts strong constraints on both. The precise nature of these constraints is the subject matter of a theory of belief ascription. Ideally, such a theory will yield, for any given ascription, the conditions that a beliefs' notional and relational contents must satisfy in order to make the ascription true. We can think of a belief ascription as marking out a subspace in the space of (notional content, relational content) ordered pairs.

The constraints on relational content are generally fairly straightforward, as the examples above show. Usually, these constraints can be derived from the reference or meaning of the terms involved in the ascription. The constraints on notional content are vaguer and more subtle. Certainly not every primary intension referring to Clark Kent qualifies a concept to play a role in making a "Clark Kent" belief ascription true, but the precise restrictions on what counts as a "Clark Kent" primary intension are not at all obvious. Similarly, to believe that water contains hydrogen atoms, it presumably does not suffice to have a relevant belief about H2O (imagine a very theoretical chemist who only knows about H2O's chemical properties); a "water"-appropriate primary intension is required, but just what are the conditions here? This is a matter for careful linguistic investigation. The constraints on notional content will be somewhat indeterminate in intermediate cases, and they will probably be context-sensitive, but they will be there, and they will generally be quite strong.

This provides a solution to the fifth puzzle mentioned at the start. The "modes of presentation" central to a theory of beliefs ascription can be seen as primary intensions and primary propositions.[*] To satisfy a belief ascription, a believer must not only have a belief with the appropriate (secondary) proposition, but must also believe it under an appropriate mode of presentation in this sense.[*] As a bonus, the fact that modes of presentation are themselves intensional or propositional allows for a certain elegance and symmetry in the theory of belief ascriptions, as well as potentially allowing a specificity of analysis that might not otherwise be present.

*[[This possibility seems to have been widely overlooked. For example, it is not mentioned in Schiffer's (1990) otherwise thorough survey of potential modes of presentation, even though primary intensions seem tailor-made to satisfy what Schiffer calls "Frege's constraint" on modes of presentation.]]

*[[Thus we are left with a framework for the semantics of belief ascription of the same general form (ascription of a propositional content plus constraint of a cognitive element) as the proposals described in Crimmins 1991, Richard 1990, and Schiffer 1992, although I have left the question of the logical form of these ascriptions open. Many of the insights of these and other philosophers on the semantics of belief ascription should be straightforwardly adaptable to the present framework.]]

(The fact that the constraints on primary intensions are only partial helps us to explain how Kripke's Pierre can believe that London is pretty and that London is not pretty without contradiction. What is going on is that Pierre's two concepts of London have different primary intensions (as we saw earlier), so that the beliefs' notional contents are compatible, but the primary intensions are both the sort that can make a "London" belief ascription true. Thus, what Kripke calls the "Principle of Non-Contradiction" is false: someone can rationally believe that P and believe that not-P as long as the beliefs involve two different primary intensions both of which satisfy the appropriate constraint.)

Given that notional content governs action, it follows that if belief ascriptions are to causally explain action, it must be in virtue of the notional content ascribed; the relational content ascribed is redundant to the explanation. To make this case more directly requires an examination of many specific examples wherein belief ascriptions are used to explain action, but the general point can be straightforwardly illustrated. One way to see the primacy of notional content is to consider beliefs involving empty names, such as "Santa Claus". These beliefs have no non-trivial relational content, and no non-trivial relational content is ascribed by the corresponding ascriptions, but ascription of beliefs about Santa Claus seem to function in precisely the same way in the explanation of action as do ascriptions of beliefs about real people. We might explain young Karen's agitation on Christmas Eve in terms of her belief that Santa Claus is coming, that he will not fit down the chimney, and so on. Santa's non-existence and the corresponding absence of relational content make little difference to the success of such an explanation. What governs Karen's actions are her notions of Santa Claus; and what governs the success of the explanation is the notional content that these ascriptions ascribe to her. And this is a typical case of the role of belief ascriptions in explanation: even when non-trivial relational content is ascribed (as when the referent of the name exists), it makes little difference to the patterns of explanation.

In a very wide variety of cases in which content explains action, we can see that the explanation succeeds even if the relational content attributed is ignored. For instance, if we explain my opening the refrigerator in terms of my belief that there is water in the refrigerator and my desire for a glass of water, we never need to invoke the H2O-involving relational content. The explanation gains sufficient purchase from the notional content ascribed alone - roughly, the content that there is some of the liquid with the appropriate properties in the refrigerator, and that I want some of that liquid, and so on.

It might be objected that there are cases in which the constraints on the notional content ascribed by a belief ascription are weak, so that relational content must be doing any explanatory work. I think that ascriptions putting weak constraints on notional content are rare, but assume they occur - perhaps an attribution of a belief about Smith constrains the relevant primary intension very little. Even so, if we look at how such an ascription can be used in explanatory practice, we see that notional content is still doing the real work. For example, perhaps we explain why Bev goes to the pub by saying that she wants to see Smith and believes that Smith is at the pub. Leaving aside constraints in the concepts of seeing, the pub, and so on, there is even a constraint on notional content implicit in the "Smith" attributions. For notice: it is implicit here that the two "Smith" concepts in Bev's thoughts have the same primary intensions. If her belief and her desire had very different notional content where "Smith" is concerned - perhaps she wants to see Batman and believes that Smith is at the pub, not knowing that Smith is Batman - the inference from those states to her action would fail. So there is a strong joint constraint on notional content: despite a lack of constraint on the individual beliefs, Bev is implicitly ascribed the belief that a person she wants to see is at the pub. It is this ascribed belief that is doing the real explanatory work, and this ascription clearly puts a heavy constraint on notional content. To make the case that all such examples can be similarly analyzed requires a detailed treatment, but this illustrates the general pattern.

It follows that the centrality of narrow content in the causation of action need not overthrow the role of belief ascriptions in explaining behavior, as some have suggested it should. At most we have shown that belief ascriptions are a somewhat rough-edged tool, due to the way they wrap both components of content into a single parcel, bringing the idle relational content into play alongside the notional content that does all the work.[*] But this should not surprise us; we cannot expect a folk theory to be maximally efficient.

*[[One might wonder why relational content is ascribed at all, given its explanatory idleness. I think there are two answers, both tied to language. First, given that we ascribe beliefs in the same language we use to describe the world, it is natural to do so in a world-involving way. When we use world-involving language to ascribe notional content, constraints on relational content come along for free. Second, relational content is important to understanding the success of communication and of collective action. When I tell you that I have a cold, you acquire a thought whose notional content is different from mine, but whose relational content is the same. Communication very frequently involves transmission of relational content, and our collective cohesion (if not our individual actions) can often be understood in terms of shared relational content. But both of these points deserve a much more extensive development.]]

In moving from common-sense psychology toward a developed cognitive psychology, we might expect that the kind of content that is invoked will become more purely notional, and that relational content will be relegated to a secondary role or dropped entirely.[*] We might also expect that better tools will be developed to specify the notional contents of thoughts than the current rough-and-ready language of belief ascription. This might qualify as a revision of our folk notion of belief, emphasizing and refining the notional elements that are already present within it. But precisely because those elements are already present and playing a central role in our practices, such a development would fall well short of elimination.

*[[It is not implausible to argue that cognitive psychology is already most concerned with notional content rather than relational content, insofar as it is concerned with content at all. For example, the psychological literature on concepts seems to be largely concerned with how concepts are applied to the actual world, concentrating on something like the primary intensions of the concepts involved. See Smith and Medin 1981 and Patterson 1991.]]

### 6 Related Suggestions and Some Objections

There are various existing proposals to which the framework I have suggested is closely related. Perhaps the most obvious relationship is to Kaplan's (1989) two-dimensional framework for the semantics of demonstratives. Kaplan defines the "content" of a statement or term as a function from circumstances of evaluation into extension, and defines its "character" as a function from context of utterance into content. Kaplan's circumstances and contexts play the much same role as the uncentered and centered worlds used here. His content is just relational content as I have defined it, and something like a primary intension can be recovered from character by evaluating character in a centered world and evaluating the resulting content in the same world.

Because it is tied to language rather than thought, however, Kaplan's account has some marked differences with the account I have presented. On Kaplan's account, a name or a natural-kind term has the same content in any context, so that its character is relatively trivial. The English term "water" picks out H2O in all contexts, for example. (Twin Earth "water" picks out XYZ, but it is a different word in a different language.) For similar reasons, co-referential names such as "Hesperus" and "Phosphorus" have identical character. As Kaplan notes, this means that his account does not have the resources to handle cognitive puzzles such as Frege's in general, although it works well in the case of indexicals and demonstratives. And because character often depends on reference, this does not yield an account of narrow content.

A generalization to thought has been made by Fodor (1987) (and in a related suggestion by White (1982)), who defines the content of a thought the usual way (as relational content), and defines the narrow content of a thought as a function from contexts to content. Unlike its linguistic counterpart, a "water" thought can have different contents in different contexts, so the results are more fine-grained than on Kaplan's account. The resulting formalism is similar to the present one, with the crucial difference that by making relational content primary, narrow content becomes entirely derivative and its independent semantic function is lost. Fodor says as much:

Indeed, if you mean by content what can be semantically evaluated, then what my water-thoughts share with Twin "water"-thoughts isn't content. Narrow content is radically inexpressible, because it's only content potentially; it's what gets to be content when - and only when - it gets to be anchored. We can't - to put it in a nutshell - say what Twin thoughts have in common. This is because what can be said is ipso facto semantically evaluable; and what Twin-thoughts have in common is ipso facto not. (Fodor 1987, p. 50.)

Fodor and White nowhere suggest that narrow content has truth-conditions of its own. Despite the formal similarities, these accounts miss the crucial point that by making narrow content a function from context into truth-value (or from context into referent, for concepts), narrow content becomes semantically evaluable in its own right, along an independent semantic dimension. This small difference is entirely responsible for the explanatory power of the current framework. By allowing semantic relations such as implication between narrow contents, for example, it allows us to draw the direct link between narrow content and rationality. It is also this that allows us to analyze narrow content in terms of the worlds that the content endorses.

Another related suggestion that is canvassed occasionally (e.g. in Fodor (unpublished)) is the proposal that the narrow content of a concept such as "water" corresponds to a surface-level description of its referent, or a list of its apparent properties, such as "the clear, potable, thirst-quenching liquid found in the oceans and lakes". But as many have pointed out,[*] this strategy suffers from the problem that the resulting content is not narrow but wide. The content of a term like "liquid", for instance, may be bound to the empirical internal structure of liquids. We can construct a twin case, where liquids are replaced by superficially identical masses of fine grains of sand. Intuitively, my twin does not share even the content specified above with me, as his beliefs are not about liquids at all.

*[[E.g., LePore and Loewer 1986; Taylor 1989; White 1982.]]

It might be thought that this criticism applies to the present approach. After all, I have said that the primary intension of "water" picks out approximately the clear liquid with the properties mentioned. But importantly, this is only to get a rough handle on the intension for the purposes of illustration. The real narrow content is an abstract function from centered worlds into extensions, and is only imperfectly captured by a given description. We can only characterize the intension fully by detailed consideration of its value at specific worlds. As soon as we move to a summarizing description in language, imperfections are introduced, and the narrowness of the content is impurified. But the intension itself remains narrow; we should not mistake the linguistic description for the real thing.[*]

*[[This might suggest that notional content is "ineffable", but the real problem is that linguistic descriptions of intensions are usually read relationally, and it is hard to capture one concept's notional content in terms of others' relational content. To express notional contents, we might use a device such as square brackets to indicate that descriptions of intensions are to be read notionally (when the relevant linguistic expressions have an associated notional content, as many do). For example, we might say that the notional content of my "water" concept is approximately the function that picks out [the dominant clear liquid in my environment] in a given centered world; that is, the referent of the former in an actual-world candidate is approximately the referent of the latter. This way all relational elements are removed. Of course this is characterizing a notional content in terms of another notional content, but it is hard to see why this is any more objectionable than characterizing a relational content in terms of another relational content. (Thanks to Frank Jackson for discussion on this point.)]]

One would obtain a more closely related sort of "description" theory of notional content if one abstracted away from linguistic characterizations and regarded the relevant "descriptions" simply as properties that a referent must satisfy, or better, as relations to the thinker. If we speak merely of properties and relations, the linguistic contamination is avoided. Schiffer (1978) gives a description theory of this sort, on which there is irreducibly de re reference by a thinker to himself or herself, with reference to everything else is mediated by a property or relation. If we map the irreducible self-reference here to the appeal to centered worlds, and map the properties and relations to primary intensions, the resemblance between the accounts is clear, although Schiffer does not appeal to a two-dimensional framework, and addresses his proposal largely to the question of accounting for de re thought.

An even closer relationship to notional content as I have described it is present in Lewis's (1979) proposal that belief is a self-ascription of a property. The set of individuals satisfying a property corresponds directly to a class of centered worlds, as Lewis notes, and the relevant worlds are of the notional-world variety, so that for example "water" beliefs endorse individuals in H2O-worlds and XYZ-worlds equally. Lewis (1994) argues that this sort of content is narrow and is primary in explanation. Lewis's account is one-dimensional, but he indicates various ways in which wide content can be seen to be derivative.

Something very like the present two-dimensional proposal has been canvassed by Stalnaker (1990), in a paper that is generally critical of narrow content. Stalnaker takes wide (relational) content to be primary, and defines the "diagonal" proposition associated with a thought as the function that evaluates a thought's wide content in its own context. He suggests that the diagonal proposition might be what advocates of narrow content have in mind. The diagonal proposition is of course very similar to the primary proposition, which I have suggested is the notional content of a thought.

In his brief but rich discussion, Stalnaker makes three objections to this construal of narrow content, all of which are worth addressing. The first is as follows.

First, this explanation makes clear that the determination of narrow content presupposes that we can identify a thought independently of its content. [...] It is not at all clear in the case of beliefs, intentions, and other states and attitudes that one can identify something that is the belief and intention in abstraction from its content, something about which we can ask, what would the content of that belief have been if it had been a belief I had on twin earth. (Stalnaker 1990, p. 135.)

This is surely misguided. If we could not fix reference to a thought by something other than its content, it would be impossible for us to have non-trivial knowledge of any thought's content; any knowledge that a thought has a given content would be trivial, like our knowledge that Julius is the inventor of the zip. In practice, we identify mental states in all sorts of ways - as something like this belief, or the belief expressed by such-and-such an utterance - and then we notice how they behave under evaluation. We can evaluate a thought in worlds one way, and thus determine its relational content; and we can evaluate the thought in centered worlds another way, thus determining its notional content. The situation with respect to the two kinds of content are quite symmetrical. It is even possible for us to fix reference to a particular belief by wide content, and then investigate its notional content. For example, we can talk about "Pierre's belief that London is pretty", and ask how its truth-value and relational content might vary in different centered worlds.

Someone might argue that relational content is so central to a thought that we cannot even talk about how the thought's reference and relational content might vary if different centered worlds are considered as actual. For example, it might be held that any concept that could potentially refer to XYZ in a different centered world could not be our concept "water"; perhaps we are inadvertently importing our twins' different concept instead. But this is to trivialize the case against notional content, and also to lose contact with common sense. It is clear that there is at least a way of individuating concepts and thoughts so that we can speak of how their reference and truth-value might vary in this way depending on how the actual world turns out; the very fact that we have solid intuitions about how we would describe various potential actual-world scenarios indicates this. To ignore this fact is to ignore a central aspect of our conceptual structure. Even if there are other ways of individuating concepts that yield different results, the question of which of these is the one true "concept" is not a question that needs to be answered.

Stalnaker's second objection is the following:

Even if these questions receive satisfactory answers, it will remain true that the narrow content or realization conditions of a thought, explained as I have explained them, will be defined only relative to a very limited set of possible worlds: specifically, only for possible worlds containing the thought token. The realization conditions for the thought are satisfied in a given possible world if and only if the proposition expressed by the thought in that possible world is true. Suppose the thought I am thinking could be naturally expressed as follows: "There is a hole in the ozone layer". If I focus on the wide content, then I can consider not only whether this thought is true in the actual world, where I am thinking it, but also whether it would be true if, say, human beings had never existed to pollute the atmosphere. But we can't evaluate the realization conditions in such a possible world, since the thought won't exist there. We might try to extend the procedure to apply to possible worlds not containing the thought by asking a counterfactual question about the thought: what would the content of the thought be if it were thought there? This would work in some cases, but it is likely to leave a large amount of indeterminacy in the narrow content of our thoughts. Consider a version of another one of our stories: Bert, who is a little confused about arthritis, thinks his father has this disease in his thigh. [...] Now consider a possible world in which both the language and the state of medical knowledge are quite different. In this world, there is no word like arthritis', in Bert's language, and Bert has no thoughts about his father's health. Are the realization conditions for Bert's actual thought satisfied in this counterfactual world? Bert didn't have the belief there, but if he had, would it have been true? So far as I can see, there is no way to tell. (Stalnaker 1990, pp. 136-7.)

In language of this paper, this comes to the objection that the primary intension of a concept and the notional content of a thought will be indeterminate when evaluated at many centered worlds. There are a number of things to say to this. First, as Stalnaker observes, the truth-value of a thought in a centered world will be most straightforward when the centered world contains the thought at its center, but we have seen that this is not required. For example, a world with an artichoke at its center is precisely the sort of actual-world candidate that is endorsed by my thought "I am an artichoke", even if the artichoke is not thinking. In these cases we can retain the thought from the real actual world and simultaneously ask evaluate its truth-value in other actual-world candidates without any loss of coherence.[*]

We can handle Stalnaker's second example in a similar way. If Bert's actual world turned out to be a world in which no-one used any terms like "arthritis", then to what would his semantically deferential concept "arthritis" refer? It seems most natural to say that it would refer to nothing at all. This would be a world about which his background assumptions would be very mistaken. The use of many concepts depends on background assumptions, as Russell's example "The present King of France" shows. If those assumptions do not hold in the actual world, it is reasonable to say that thoughts involving these concepts lack truth-value. When Bert uses a concept such as "arthritis" with semantic deference, he makes a background assumption that people in the community around him use the word or something like it. If they do not, then all bets are off.

In any case, Bert's thoughts involving "arthritis" still have a significant notional content. They rule in and rule out certain centered worlds in which the background assumptions are satisfied. They take no stand on worlds in which the background assumptions are not satisfied, but that was never their purpose. For the usual explanatory purposes, the inclusion and exclusion of worlds relative to those assumptions will suffice. Centered worlds in which those assumptions fail will usually be ruled out by other beliefs, such as Bert's metalinguistic beliefs in these very assumptions (for example, his belief that the term "arthritis" is used by the community around him), so that his attitude toward these worlds can be handled in other ways. For the usual explanatory purposes, however, a belief ascriber will be concerned with a thinker's attitude toward worlds that are closer to home, so it is not a problem that notional content and primary intensions are only partial functions.

Another class of concepts whose primary intensions have a limited domain of definition are perceptual demonstratives. When I think something like "That is pretty", the referent of my demonstrative is often picked out (very roughly) as the cause of such-and-such experience.[*] In a centered world in which a pretty thing is appropriately responsible for the relevant experience at the center, the thought will be true; in a world in which an ugly thing is responsible, the thought is false; but in a world in which there is no appropriate experience at the center, the thought may lack truth-value. In this case fixation of reference relies on the fact that such an experience is present, just as fixation on reference in the "arthritis" case relies on the existence of a surrounding community using the term. Again, it is not a problem that worlds are ruled in and ruled out only relative to a background condition. If for some purpose we wish to invoke the thinker's attitudes to other worlds (a world where the experience is absent, for instance), we can rely on the notional content of other thoughts in the vicinity, such as "The object in front of me is pretty".

*[[This raises another subtlety: to capture the content of certain perceptual demonstratives, one may need to build in a "marked" experience to the center of the class of actual-world candidates, as one builds in a marked individual and time. This is reflected in characterizations such as "cause of this experience", which may be irreducible in a way analogous to "next to me". (This parallels Russell's idea that reference to our experiences and to ourselves is irreducibly direct.) Building in this property of a center may secure reference to otherwise indistinguishable experiences and their perceptual objects, as with (perhaps) a speckle in a large field, or one of the red spots in Austin's (1990) "Two Tubes" puzzle (to which the present framework then provides a solution). In certain cases, centers may also require a marked thought ("this very thought"), further marked experiences, and perhaps marked orientations (e.g. to distinguish left and right). In general, what is built into a center corresponds to the things to which one can intuitively make "unmediated" reference: one's world, oneself, the present moment, the current thought, and perhaps certain experiences and orientations (though some of these might be seen as derivative on others). This is a matter I hope to explore elsewhere.]]

The precise domain of definition for the notional contents of particular thoughts is an important issue, for which there will be different answers depending on the thoughts in question. Some concepts, such as pure indexicals ("I", "here", and "now"), have primary intensions that are defined across all centered worlds. Pure non-indexicals - concepts whose referent at a centered world does not depend on the position of the center - will also have a wide domain of definition. It is concepts in between, for which the existence of a referent depends on background assumptions about how things are around the center of a world - as with semantically deferential concepts and certain demonstratives - that will have a restricted domain. This is a deep issue that deserves a detailed treatment of its own, but for now it suffices to note it is no objection to this account to note that the relevant functions are often partial.

It is occasionally suggested that there is something odd about the idea of evaluating a thought in an actual-world candidate that does not contain a copy of the thought itself. After all, we are considering the centered world as actual, but still retaining the thought from the actual world (the real actual world). But this seems simply to reflect how our thoughts work: they can endorse certain centered worlds as potential environments (that is, as actual-world candidates) without requiring those worlds to contain specific thoughts at the center. The thought "I am comatose" provides a clear example, as does a thought such as "Julius was a genius". Certainly it seems mistaken to require that a thinker's notional world-model contains a perfect copy of all of his or her thoughts.

This reflects itself in the fact that we have solid intuitions about how to (notionally) describe actual-world candidates even when those candidates do not contain the relevant thoughts. Consider a centered world in which I am at the center thinking about watermelons, and in which the inventor of the zip is not the actual-world inventor (who died at birth here) but Albert Einstein (who is as smart as ever). Then I can say: if that world turned out to be actual, it would turn out that Julius was a genius (using the "turns out" locution in the usual notional way). Correspondingly, this world is among the actual-world candidates that my thought "Julius was a genius" endorses. (Of course it is not among the worlds that the relational content of my thought endorses.) The very fact that we have these solid intuitions is evidence that something is going on. Any semantic theory is grounded in the evidence of our intuitions, so these basic data should not be ignored.

The alternative would be to require a copy of the thought or the concept at the center of every world, but this would be to greatly limit the value of the framework in accounting for the contents of our thoughts, as it ignores the fact that our thoughts are involved in taking attitudes to notional worlds in which the thoughts are absent. This would also raise the problem of just what we would have to "hold constant" in copying a thought between centered worlds: a problem raised for Fodor's account by Block (1991) and Stalnaker (1991), but which the current framework avoids entirely. It seems much more satisfactory not to involve a thought itself in its conditions of application, even to actual-world candidates.[*]

*[[Of course, the application-conditions of some thoughts will involve the presence of a thought (although usually not presence of the thought). In these cases we can build in the presence of a thought as a background condition. "This thought" provides an example: it is a background condition that there is a "marked" thought at the center. Perhaps a semantically deferential concept such as my concept "vanadium" gains its link to the community by picking out whatever is causally responsible for my own use of the concept; if so, it may be a background condition that there is a marked concept labeled "vanadium" at the center. In these cases, evaluation in centered worlds in which relevant concepts are not present at the center will be indeterminate. As before, if we want to explain our attitude to those worlds, we will have to use other concepts.]]

Finally, Stalnaker suggests:

The source of all these problems with this procedure for defining narrow content is the fact that according to this account, narrow content is derivative from (actual and possible) wide content. The explanation of realization conditions takes for granted that somehow, the external and internal facts about a mental event or state that we have identified determine a content (in the ordinary sense) for that state. Then from the actual wide content, together with the facts about what the wide content would be under various counterfactual circumstances, we extract the narrow content. Narrow content, as defined by this procedure, presupposes rather than explains wide content. (Stalnaker 1990, p. 137.)

This, it seems to me, is false and importantly so. Perhaps narrow content is derivative on wide content when it is indirectly defined by Stalnaker's "diagonal" construction, but as I have characterized notional content, it is in no way derivative. There are two basic notions - what it is for a thought to be true in a world and what it is for a thought to be true of a world - and neither of these is obviously derivative on the other. Only if we have already adopted a framework in which relational content is primary will we determine the notional content of a thought by first determining its relational content in centered world and then evaluating that relational content in the same world. It is in many ways more natural to determine notional content directly, and to directly evaluate the truth of a thought in a world.

Indeed, in many ways relational content seems to be derivative on notional content. We can see this most clearly by looking at concepts rather than complete thoughts. We have already seen that the secondary intension of most concepts generally depends on the primary intension. In some cases it is a near-copy of the primary intension, as for simple descriptive concepts, and in other cases it is determined by rigidifying the actual-world evaluation of the primary intension. By contrast, we can tell the entire story about the primary intension without ever involving the secondary intension. It therefore seems that if either intension is to be fundamental, it is the primary intension. If we see notional and relational content as composed from primary and secondary intensions respectively, and if we see secondary intensions as derivative on primary intensions, then it seems that narrow content may explain wide content rather than vice versa.[*]

*[[This suggests that in order to have a naturalistic theory of wide content, for example, we will probably need a naturalistic theory of notional content first. Arguably, the reason that contemporary causal theories of content have been unsuccessful is that all these attempt to account for relational content without first accounting for notional content.]]

It is unclear why the assumption that relational content is primary is so common in the recent literature. One reason is no doubt a concern with language: relational content is often more stably associated with a term than is notional content. Perhaps a second reason is an aversion to indexical accounts of content, grounded in Frege's insistence that the truth-value of a thought cannot depend on a thinker's location in a world. A third reason is that the structure of relational content is more naturally described in language than that of notional content, making notional content more difficult to discuss.[*]

*[[A vulgar psychohistory: since Frege it has been recognized that intensions are central to the analysis of content, to deal with cognitive puzzles, the fixation of reference, and the like. For a long time, the intensionality of reference-fixing was not clearly distinguished from that of modal contexts, so it was natural to characterize the relevant intensions with modal contexts such as "what is water in w?". After Kripke separated the two sorts of intensionality, philosophers continued to concentrate on the latter sort, even though it is ill-suited to play the main roles that intensionality was introduced into semantic theories to play. The deepest sort of intensionality lies in the fixation of reference; the sort that governs description of counterfactual scenarios is much less fundamental.]]

Whatever the reasons, the emphasis on relational content has been misplaced. In many ways, notional content is more central to thought than relational content: it is cognitively accessible, it governs the cognitive and rational relations between thoughts, and it governs behavior. But we need not dismiss relational content entirely. Its utility is still an open question, and it may have a central role at least in a theory of communication. The most satisfactory overall picture will emerge if we allow the two kinds of content to co-exist in a two-dimensional conception of meaning.

### 6 Conclusion

What of the six puzzles at the start? To summarize:

(1) A thought's content decomposes into notional and relational content, given by its associated primary and secondary propositions respectively. My twin and I differ in the relational contents of our thoughts, but our notional contents are the same.

(2) The thoughts that Hesperus is Hesperus and that Hesperus is Phosphorus have the same associated secondary proposition but distinct associated primary propositions, as the "Hesperus" and "Phosphorus" concepts have different primary intensions. The triviality of the former does not imply the triviality of the latter, as it is notional content that governs rational relations.

(3) Pierre's two beliefs have contradictory secondary propositions but compatible primary propositions, as his two concepts of London have different primary intensions, although they are both the sort of intension that can make "London"-involving belief ascriptions true. It is only contradictory primary propositions that imply irrationality.

(4) The essential indexicality of belief reflects the fact that notional content, not relational content, governs action, and that notional content, unlike relational content, is a centered proposition.

(5) The modes of presentation central to a theory of belief ascription are primary intensions and primary propositions. Belief ascriptions constrain not just the relational content but the notional content of the believer.

(6) Instances of the contingent a priori have a necessary primary proposition but a contingent secondary proposition. It is notional content that constrains one's world-model, so a contingent secondary proposition does not indicate a cognitive achievement.

There are many problems about the contents of thought that are not resolved by this framework. Most notable are problems with hyperintensionality: how do we accommodate cognitive differences between thoughts that have the same notional and relational contents, such as beliefs in different mathematical truths? That may require a new, refined kind of content, perhaps one that lies behind notional content and determines it in turn. There is also much work to be done in providing a full account of the semantics of belief ascription; and I have left the project of providing a naturalistic reduction of this sort of content almost entirely untouched. Some of these matters are likely to be much more difficult than the puzzles at issue in this paper, but the two-dimensional framework at least clarifies the lay of the land.

### Acknowledgments

Thanks to Ned Block, Frank Jackson, David Kaplan, David Lewis, Andrew Milne, Gideon Rosen, Jerry Seligman, and Robert Stalnaker, to audiences at Cornell University, Princeton University, Rice University, UCLA, University of Memphis, and Washington University, and to two referees for Mind.

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