Eric Lormand, University of Michigan
If the arguments of chapter 1 are correct, associationist connectionist models (such as ultralocal ones) yield the clearest alternatives to the LOT hypothesis. While it may be that such models cannot provide a general account of cognition, they may account for important aspects of cognition, such as low-level perception (e.g., with the interactive activation model of reading) or the mechanisms which distinguish experts from novices at a given skill (e.g., with dependency-network models). Since these models stand a fighting chance of being applicable to some aspects of cognition, it is important from a philosophical standpoint that we have appropriate tools for understanding such models. In particular, we want to have a theory of the semantic content of representations in certain connectionist models. In this chapter, I want to consider the prospects for applying a specific sort of "fine-grained" theory of content to such models.
According to the fine-grained theory I will consider, contents admit of degrees of complexity. Even the simplest propositions (e.g., the proposition that a is F) are thought to be complexes of constituent concepts (e.g., the concepts a and F). What is required for a representation r to have a complex content, say, the proposition that a is F? On a fairly standard fine-grained conception, r must display "semantic dependence" on other representations which represent the concepts a and F, i.e., the constituent concepts of the proposition. What sort of relation between representations counts as semantic dependence? The most familiar examples are syntactic relations: the content of the English sentence "sugar is white" depends on the content of its syntactic parts "sugar" and "white". Another example of semantic dependence might loosely be termed "abbreviation": a syntactically simple symbol "p" in a logical formalism may have a complex, propositional content in virtue of being treated (by convention or otherwise) as "standing in place of" a sentence such as "sugar is white", and so depending semantically on the parts of that sentence.
Although virtually all nonconnectionist models in cognitive science, as well as many connectionist models, postulate relations such as syntactic complexity and abbreviation, many connectionist models appear not to support these relations. The best examples are the associationist (e.g., ultralocal) models. Nevertheless, for reasons I will describe there is at least an appearance that representations in these models do have propositional contents. This generates a philosophical puzzle, at least for those sympathetic to the relevant fine-grained theories of content: how it is possible for a representation to have propositional content without displaying semantic dependence on other representations (e.g., without being either syntactically complex or an abbreviation)? My goal in this chapter is to explain how.
I will begin in section 2.1 by describing the intuitive idea of fine-grained theories, and the puzzle which certain connectionist models present for them. Then in section 2.2 I will attempt to show how the troublesome connectionist representations, even individual nodes, can have propositional content, and will discuss how this propositional content can even be explicit content. In the final section, I will briefly discuss some of the metaphysical commitments of the theory I propose.
Philosophers explore many distinct conceptions of content, and many distinct purposes for being concerned with content. One reason the contemporary literature is difficult is that it is unclear which conceptions of content are genuine competitors, and which conceptions are simply addressed to different, but equally legitimate, purposes.<1> To help fix ideas, then, discussions of theories of content should begin with a specification of some guiding reasons for wanting a conception of content. Since I will be addressing a puzzle which arises out of certain connectionist models, I want to focus on a notion of content which is suitable for use in cognitive science, as it might (or might not) be opposed to common sense, for example. I will therefore be concerned with the content of mental representations of the sort which are postulated in cognitive-scientific models (e.g., physical tokens of functionally-specified propositional-attitude types--see section 0.1.1). I take it that, at a minimum, cognitive science appeals to content to specify these mental representations, and to express generalizations about their functional role--generalizations relating mental symbols not only to external conditions, via perception and action, but also to other mental representations, via inference.
In this section I want to describe two sorts of theories of content which seek to respect these constraints, one which treats contents as coarse-grained, and one which treats them as fine-grained. After introducing the notion of reference conditions which is central to both theories (section 2.1.1), I will focus primarily on the notion of semantic structure which figures in the fine-grained theories (section 2.1.2). Then it will be possible to present the connectionist puzzle for these fine-grained theories (section 2.1.3).
In discussing content it is common to begin with the relation between the content of a representation and its referent, or the existing entity, if any, that it is about. There is a close connection between content and reference, as is shown by the fact that no entity can have reference unless it has content, i.e., is a representation. I will assume that the referents of mental representations are existing objects, properties, and facts (which, I will also assume, are typically instantiations of existing properties by existing objects). An idea of Paris refers to, or is about, a certain existing city, an idea of prettiness refers to, or is about, a certain existing property, and a belief that Paris is pretty refers to, or is about, the existing fact that this city has this property.<2> I will limit my attention to representations which refer (or purport to refer) in these ways, and I will call these "referential" representations.
It might be tempting to begin to specify the content of a referential representation by specifying its referent. However, referents are not the whole of content, as is indicated by the familiar fact that not every referential representation even has a referent. An idea of my pet caterpillar does not refer, since there is no such thing; nor does a belief that Paris is in Germany refer, since there is no such fact.<3> Furthermore, there is sufficient reason to deny that referents are even parts of contents, at least in the case of many successfully referring representations. Suppose that tomorrow I will obtain a pet caterpillar, Crawlette. As a result, the idea of my pet caterpillar will undergo a change in reference, from having no referent today to having Crawlette as a referent tomorrow. Since the phrase will not undergo a change in content, this shows that even for many successfully referring representations, content is not to be specified even in part by specifying referents themselves.<4>
Since objects, properties, and facts do not in general serve as the contents of (mental) representations, I want to adopt the standard philosophical terms "propositions" and "concepts" for whatever things do fit this bill.<5> One pressing question, of course, is: what are propositions and concepts, that they may serve as contents? While a full answer to this question requires consideration of a number of competing philosophical positions, I think we can place three weak, and so uncontroversial, constraints on them, given the discussion so far:
Before searching for other constraints, a reasonable strategy is to try to find something which fits these three.
To satisfy these constraints, we should focus not on the referent of a representation but on its reference condition, or the way the world has to be in order for the representation to be about some existing entity (fact, object, or property). For instance, the reference condition of an idea of my pet caterpillar is that I have a pet caterpillar; if I have a pet caterpillar x, the idea refers to x, otherwise the idea fails to refer. Similarly, a belief that Paris is in Germany has the reference condition that Paris is in Germany.<6> Reference conditions meet constraints (1)-(3) on propositions and concepts: nothing can refer unless it has a reference condition; representations can have reference conditions
without having referents; and representations can retain the same reference conditions even through changes in reference.
Because of these explanatory virtues of reference conditions, it is tempting to identify propositions and concepts with reference conditions.<7> On the most natural development of this idea, when we use a phrase or sentence e (in English, say) to identify the content of a representation r, we are saying that r has the same reference condition as e.<8> To say that r has as content the proposition that checkerboards are squares is to say that r has the same reference condition as the sentence "checkerboards are squares", while to say that r has as content the concept being a checkerboard is to say that r has the same reference condition as the phrase "being a checkerboard". It follows, on this theory, that if the two English sentences e1 and e2 have the same reference conditions, then the belief that e1 and the belief that e2 have the same content.
Many philosophers resist the identification of contents with reference conditions on the grounds that propositions and concepts must be individuated more finely than reference conditions. The familiar argument for this is that sameness of reference conditions appears not to insure sameness of content. On widespread assumptions, for example, it is logically impossible for the following two mental representations to differ in reference:
No matter what way the world is, either both are true or neither are, so they have the same reference conditions. Despite this, there is clear intuitive resistance to the idea that B1 and B2 are the same belief.
In ordinary cases, we are careful to distinguish B1 from B2. We suppose that people without mathematical training do not have belief B2, even if they do have belief B1. And we suppose that someone could have B2 even if they did not have B1, say, if they failed to realize that equilateral, right-angled, blahblahblahs are squares. Since reference conditions are not individuated finely enough to reflect these differences among mental states, some philosophers have sought more finely individuated entities which do reflect these differences. The results are versions of what I will call "fine-grained" theories of content--theories according to which representations can differ in content even though they have the same reference condition, as this notion is normally construed (see, for example, Lewis, 1972; Evans, 1982; Cresswell, 1985). These theories are opposed, naturally, to "coarse-grained" theories according to which representations have the same content if they have the same reference condition (the theory that contents are reference conditions is, of course, one such theory).<9>
Intuitively, we have some idea of the respect in which the two beliefs differ: they are somehow "structured" out of different ideas.<10> There is some temptation to read this as a claim about the syntactic structure of the physical representations which help to realize the attitudes and ideas--i.e., as the claim that these representations stand in literal whole/part relations. However, the claim is best taken as one about semantic structure, where this is to be explained in a nonsyntactic fashion. The reason is that it seems possible for there to be syntactically simple representations--ones without other representations as parts-- which nonetheless are "structured" in the relevant sense. One way for this to happen is for a syntactically simple representation to be introduced as an "abbreviation" of a syntactically complex representation. It is best, then, to look for a nonsyntactic way of explaining semantic structure.
Philosophers sympathetic to fine-grained theories standardly express the difference between the two beliefs about checkerboards as follows: one can't have belief B2 unless one has ideas of cube roots, polygons, etc., but one can have belief B1 even without having these ideas. In other words, the two beliefs are in some sense dependent on the availability of different mental representations. Intuitively, the latter belief, unlike the former one, depends on the availability of a representation with the content being a square root, for instance. Also intuitively, it should be possible for a representation to depend on representations which are not its parts, perhaps as a building "depends" on the ground below it. Therefore, dependence may be a first step toward understanding the notion of semantic structure without relying on claims of syntactic structure.
Of course, these intuitive appeals are no substitute for a philosophical account of what it is for one representation to be dependent on another, in the relevant sense. Although the connectionist puzzle for fine-grained theories is somewhat independent of the particular account adopted, it is necessary to have one on the table in order to describe the puzzle. Perhaps the foremost task of an account of dependence is that of avoiding a certain extremely "holistic" conclusion. Much of human inference appears to be holistic, in the sense that virtually any two premises can be combined in some rational inference or other. Given this sort of psychological holism, (virtually) every representation is such that its "functional role" depends on (virtually) every other representation (available to the thinker). The functional role of belief B1 that checkerboards are squares depends, in this way, on whether or not the thinker has representations for Aristotle, for being polygonal, etc. If this is the relevant kind of dependence, then fine-grained theories cannot distinguish representations (such as the two beliefs about checkerboards) in terms of their dependence relations. They would depend on the same set of representations, namely, (virtually) every one.
As a first step towards avoiding this result, I want to try to get clearer about what it is about a representation r which must be dependent on the availability of other representations, in order for r to be semantically structured. While psychological holism might show that some facts about a representation--such as its functional role--are dependent on (virtually) every other representation, it may be possible to identify some content-relevant facts which are not subject to extreme holism. A natural idea is that r is semantically structured iff r's content (rather than its functional role) is dependent on that of representations with other contents. Since semantic structure is taken to be a determinant of content, this is indeed a claim which the fine-grained theorist wants to make. However, given that the fine-grained theorist is trying to explain content (at least partially) in terms of semantic structure, it is circular to explain semantic structure in terms of content. In specifying the relata of the relevant dependence relation, the fine-grained theorist needs to specify facts which, though relevant to content, are identifiable independently of content. Here the most natural strategy is to appeal to reference conditions.<11> On fine-grained theories, although reference conditions are clearly relevant to content, one can specify a representation's reference condition independently of its content. How might this suggestion be spelled out so as to avoid the holism problem?
There is one preliminary to spelling out this suggestion. While the fine-grained theories under consideration maintain that the reference condition of a semantically structured mental representation r depends on the subject's having some or other representation with a different reference condition C, they do not necessarily maintain (and probably should not maintain) that r's reference condition depends on the availability of any particular token representation with reference condition C. It will help, then, to introduce a notation for grouping representations according to their reference condition. If a mental representation has reference condition C (whatever C may be), call it an C-referrer. The suggestion on behalf of fine-grained theories, then, is that a thinker's mental representation r is semantically structured out of C-referrers iff r's reference condition is dependent on some C-referrer or other's being available to the thinker. In this case, I will say that the representation is "semantically dependent" on C-referrers. On the fine-grained theories I will consider, the content of a representation not only reflects its own reference condition, but also reflects the reference conditions of other representations on which its reference condition depends.
As for holism, while the precise functional role of a representation may depend on that of (virtually) every other representation, its reference condition may depend on that of only a restricted set of other representations. We can display this possibility more clearly by explaining the relevant kind of dependence in terms of a certain kind of counterfactual claim. In speaking of a representation r's reference condition as being dependent on C-referrers, I mean: were the C-referrers actually available to the thinker to have a different reference condition, then (as a result) r would have a different reference condition (holding fixed the actual functional relations between r and these C-referrers). Imagine someone with a mental representation B1, the realization of a belief that checkerboards are square. Suppose he also has available to him mental representations for checkerboards, for being square, for Aristotle, and for being polygonal. Intuitively, if the checkerboard-referrers or the squareness-referrers were to have different reference conditions--e.g., by being the effect of different perceptual states, of different phenomena in the world, etc.--then (holding fixed the functional relations between these representations and B1) B1 would also have a different reference condition. However, intuitively, even if the Aristotle-referrers and the polygonality-referrers were to have different reference conditions, B1 might still have the same reference condition (holding fixed any functional relations between B1 and these representations).
Of course, these intuitive assessments of the counterfactuals might not be borne out by a proper philosophical theory of reference conditions: a theory which determines which particular representations have which particular reference conditions. Philosophers differ over what factors help to determine the reference conditions of a representation--its covariation with certain conditions, its functional role, its adaptational role, etc. This is a widely discussed and widely open question which would take considerable resources to address properly. I will not even begin to do so here, since the question does not appear relevant to the choice between fine-grained and coarse-grained theories of content. Defenders of coarse-grained theories have to address this question as well, since they, too, use the notion of reference conditions in understanding content. What I am concerned to show is that, contrary to a common opinion, holism does not raise more of a problem for fine-grained theories than it does for coarse-grained theories.
Suppose that (contrary to intuitive judgements) reference conditions turn out to be subject to an extreme holism, in that which reference condition a given representation has depends on which reference conditions (virtually) every other representation has. If so, then reference conditions would themselves be "fine-grained" in the sense which matters to defenders of fine-grained theories. For example, suppose that B1--a belief intuitively specified as the belief that checkerboards are squares--is held by someone without special mathematical training, and that B2--a belief intuitively specified as the belief that checkerboards are equilateral, right-angled polygons with a number of sides equal to the cube root of sixty-four--is held by someone with special mathematical training. If reference conditions are holistic, then (contrary to intuitive appearances) these beliefs have different reference conditions, as fine-grained theories would have it. On the other hand, if reference conditions are not subject to extreme holism, then we can make fine-grained distinctions among the two beliefs in terms of which representations their reference conditions depend on.<12>
To avoid extreme holism is not yet to claim that there can be simple representations, i.e., representations which are not semantically dependent on representations with other reference conditions. Even if a representation does not depend on every other representation, every representation might still depend semantically on some other representations. Every representation might be part of some (small or middle-sized) circle of mutually dependent representations, which would make a sort of "local holism" true. Perhaps the simplest representations are not, for this reason, absolutely simple. The connectionist puzzle arises independently of whether or not a fine-grained theory is committed to (absolutely) simple representations. It also arises independently of which sorts of representations are thought to be "simplest". Are some ideas in cognitively central systems (such as "checker" and "board") as simple as representations get, or are they in turn semantically structured out of representations in cognitively peripheral systems (e.g., the initial stages of vision)?<13> Since in presenting and addressing the puzzle I will mainly use examples of extremely "peripheral" connectionist representations, I will leave open this question about "central" representations.<14>
To frame the connectionist puzzle, the most important point about semantic structure (however it is ultimately to be construed) is its relevance to content ascriptions. In the previous section, I described a coarse-grained theory which claims that when we identify the content of a representation r by using an English phrase or sentence e, we commit ourselves to the claim that r has the same reference conditions as e. On the most natural development of the present fine-grained theory, we commit ourselves to more than sameness of reference conditions. We also commit ourselves to the claim that r and e have the same semantic structure-- i.e., that r's reference condition semantically depends on the availability of representations with the same reference conditions as those on which e's reference condition depends.<15> For example, suppose "A B C" is a syntactically complex sentence which is semantically dependent (only) on the representations "A", "B", and "C".<16> Then for r to have the content that A B C, not only must r have the reference condition of "A B C", but this fact must depend (only) on representations with the same reference conditions as "A", "B", and "C". On this account, even if the sentences "A B C" and "D E F" have the same reference conditions, the belief that A B C and the belief that D E F might have different contents.
Fortunately, the puzzle which connectionism presents for fine-grained theories of content can be described without focusing on intricate details of connectionist networks. We can display the problem by returning to the interactive activation model of reading (see section 0.2.1).<17> If nodes in connectionist networks are to be genuine representations, they must have semantic contents. For example, consider a particular node in the reading model, a feature node f the role of which is to become activated as a result of visual presentations, in word-initial position, of shapes like that of the top half of a circle, such as form the top of the letters "C", "G", "O", "Q", and "S". If f is a representation, it must have content, and a natural idea is that it has the content that a top-half-of-a-circle-shaped figure is being visually presented in word-initial position. What does it mean to say that f has this content? Well, on the coarse-grained theory of content presented in section 2.1.1, it means that f has (at least nearly) the same reference conditions as the English sentence "A top-half-of-a-circle-shaped figure is being visually presented in word-initial position". Call this sentence e. Then, on the coarse-grained theory, the claim is that sentence e and node f are true (or "veridical", or "faithful to the input", etc.) under the same conditions. The situation is quite different for fine-grained theories, however.
On any fine-grained theory, specifying reference conditions is not sufficient for specifying content, since two representations may differ in content even if they share reference conditions. Furthermore, on any fine-grained theory, even if the English sentence e does adequately express the reference conditions of the feature node f, it is completely inappropriate to take e seriously as a specification of f's content. On the fine-grained conception of content ascriptions I mentioned in the previous section, to say that f has the content that a top-half-of-a-circle-shaped figure is being visually presented in word-initial position is (at least) to say that f is semantically dependent on representations for halfness, circularity, etc. However, f is simply triggered by an array of visual stimulations, independently of the influence of general knowledge about halfness, circularity, etc. In fact, the interactive-activation model has no knowledge of circles at all, and does not in any sense have a representation for being a circle. Therefore, on the fine-grained theory, f can't represent presented figures as being top-half-of-a-circle-shaped. Of course, it might simply be suggested that we have misidentified the content of f. To avoid wrongly attributing ideas of being half, being a circle, etc, we might even draw what we mean, saying that f represents visually presented figures in word-initial position as being -shaped. But this still leaves the problem. The revised suggestion is that f has the content that a -shaped figure is being visually presented in word-initial position. Even this content ascription requires the system to represent the (rather sophisticated) general concepts of shape, vision, etc. How can f have this content if the system lacks representations of these concepts? And if we can't take such ascriptions seriously, what ascriptions can we take seriously?
A defender of a fine-grained theory might simply respond that there aren't any ascriptions which we can take seriously. If verificationism is correct, it might follow from this response that such nodes have no content at all. Since it is established practice in cognitive science to treat such nodes as representations, however, this conclusion would weigh heavily against fine-grained theories of content. Even if verificationism is incorrect, and no such strong conclusion follows, the resulting notion of content would be unsuitable in connectionist theorizing. If there aren't any fine-grained ascriptions which we can take seriously, then there aren't any descriptions or generalizations involving fine-grained contents which we can take seriously, at least where certain individual nodes are concerned. This situation would be an embarrassment to any philosopher who has sympathy with the project of developing a notion of content which is suitable for use in cognitive science. To fulfill this project, it might seem that we need to abandon fine-grained theories in favor of coarse-grained theories, at least in the case of the troublesome connectionist representations. I hope to show how a fine-grained theorist can solve the connectionist puzzle without conceding ground in this fashion.<18>
It is possible that a defender of a fine-grained theory would show no surprise at the unavailability of serious content ascriptions for connectionist nodes such as feature nodes in the interactive-activation model. This might be explained by appeal to a familiar theoretical construct of fine-grained theories, namely, simple concepts. On many fine-grained theories of content, propositions are complexes of concepts, and these concepts are, in turn, either simple or else themselves complexes of simpler concepts. Opinions differ about which concepts are the simple ones. Some think many syntactically simple words in natural languages--words such as "caterpillar" and "board"--express simple concepts. Others think that simple concepts are expressed only by more purely observational representations, such as might be involved in early visual processing. We can abstract away from such disagreements of detail to isolate a relevant feature which is supposed to be shared by all representations which express simple concepts.
In ascribing content to such a representation, often the best we can do is to describe the referents of the representation. However, in doing so we generate the same kind of puzzle as that generated by the connectionist nodes: we normally employ concepts which need not be expressed by someone who grasps the target concept. Suppose, for illustration purposes only, that "caterpillar" in fact expresses a simple concept. If asked to say what "caterpillar" means, we might say that it picks out some furry worm-like animals which turn into butterflies. Given fine-grained strictures on content ascription, however, this would not be a serious specification of the concept expressed by "caterpillar", since (we are supposing) a representation could express that concept even in the absence of representations for worm, animal, butterfly, and so on. In such a case, the best we can do by way of a serious specification of fine-grained content is to repeat the representation: hence those inclined to think of "caterpillar" as expressing a simple concept often identify this concept as "the concept caterpillar". Given that at least some fine-grained theories are already prepared to countenance simple concepts, this device might be used to account for the similar difficulties arising with respect to representations in early perceptual processing. (In fact, even someone who does not think that high-level representations such as "caterpillar" express simple concepts might be tempted to accept this idea for some nodes in connectionist models of low-level perceptual processing.)
The problem with this strategy is that some--in fact, most--contentful nodes in connectionist networks are interpreted propositionally. This precludes the general strategy of attributing to individual nodes the sorts of contents--namely, simple concepts--which some assume to be possessed by familiar syntactically simple words. If we are to find precedents for individual nodes with propositional content, we must look elsewhere. There are familiar syntactically simple representations which are propositional, as Robert Cummins notices:
Examples of propositional but syntactically simple symbols which are parts of public language are the words "Mayday" and "Roger", familiar from telecommunications, or the symbol "p", which might in a particular logical notation be used to mean that Paris is pretty. Even without assuming that all public symbols semantically depend on mental representations, however, it is at least intuitively plausible that all of these symbols are semantically dependent on other representations (whether mental or linguistic) in a way which reflects our complex specifications of their content. Intuitively, if Paul Revere's word "land" (or corresponding idea) had referred to helicopters, then the flashing of a single lantern would have been true if and only if the British soldiers were moving by helicopter, rather than by land (holding fixed the functional relations between his word and the lanterns, including in particular those which resulted from his conventions). As far as I know, every propositional representation in natural language--or in any form of public communication, for that matter--is semantically dependent on other representations in a similar fashion. This is the sense in which the commitment to connectionist nodes which are propositional without standing in semantic dependence relations is without obvious precedent. The philosophical challenge for fine-grained theories is to show how it is possible for syntactically simple representations without semantic dependencies to be propositional, or else to show why this is impossible.<19>
To meet this challenge, I want to show how a fine-grained theory of content can appeal to simple propositions. This can and should be done without prejudging the issue of which particular representations (if any) express simple propositions, just as we can abstract from disagreements over which representations (if any) express simple concepts (see section 2.1.2). If some propositions are simple, presumably this is because they share certain features with those concepts which are simple. A natural idea, given fine-grained theories' appeal to semantic dependence, is that simple concepts are those which may be represented by representations without semantic dependence on other representations. To return to an example from the previous section, it is sometimes held that "caterpillar" can mean caterpillar even if it were to become dissociated from other concepts such as animal, butterfly, and so on. Perhaps there are no other representations in particular on which the reference condition of "caterpillar" semantically depends. If so (and we are only imagining this for sake of illustration), on the present theory, this would mean that "caterpillar" has as content a simple concept. I suggest that we extend this general idea to the case of propositions, so that simple propositions are those which may be represented by representations which do not semantically depend on any representations with other contents. On this account, any connectionist node or other representation which satisfies this condition represents a simple proposition (again, the question of which ones do and which ones don't depends on the operative notion of semantic dependence).<20>
Although this idea is simple to state, it must be defended against several objections. Providing this defense will occupy me in this part of the chapter. My first aim is to show that simple propositions are consistent with the distinction between propositions and concepts (section 2.2.1). Then I want to distinguish the present proposal from one based on de re attributions of content (section 2.2.2). Finally, I will try to show how simple propositions can be represented explicitly by connectionist nodes (section 2.2.3).
One potential worry about countenancing simple propositions is that doing so threatens the distinction between propositions and concepts. While not much seems to have been written about the distinction, it is at least initially plausible that propositions are to be distinguished from concepts by virtue of distinctive facts about their structure. If some propositions are taken to be simple, then, what would distinguish them from simple concepts? I will approach this question indirectly, by asking the question: which representations are supposed to have propositional content, and which representations are supposed to have merely conceptual content? It is easy to distinguish propositional representations from merely conceptual representations, case by case. The belief that Paris is pretty--or the wish that it were--has propositional content. By contrast, the idea of Paris, or of being pretty, has merely conceptual content. It is more difficult to formulate a semantically interesting principle by which the cases are to be distinguished.
A first stab at it is to say that propositional mental representations are those, like beliefs, which have a truth value (truth, falsity, and, if possible, undefined truth value). However, there are other sorts of propositional mental representations--desires, emotions, etc.--which have no truth value. To cover these cases, one might try to use some more general notion instead of truth value, such as "success value": beliefs are successful if true, desires if satisfied, joy if appropriate, etc. It might then be said that propositional representations are those with success values. Without some principle of generalization from truth to success, however, this suggestion leaves unclear why the "reference values" of ideas aren't also success values: why isn't the idea of Paris successful since it refers to an existing object, and the idea of Atlantis unsuccessful since it fails to refer to one? A different suggestion might be that propositional representations are (or at least purport to be) about facts, as opposed to mere objects and properties. This also is inadequate. The idea of my favorite fact does purport to be about a fact; however, it is not a propositional representation but instead a conceptual one.
It is a striking fact that ideas are the only apparent examples of merely conceptual mental representations. However, it would not be correct simply to say that ideas have conceptual content while other mental representations--the propositional attitudes--have propositional content. As I argued in section 0.1.2, representationalism is committed to the existence of propositional ideas (and what I called propositional "symbols"--for present purposes these can be lumped with ideas). Nevertheless, by first characterizing the difference between attitudes and ideas, as I will show, we can go on to distinguish propositional ideas from merely conceptual ideas. So the strategy I adopt will be undertaken in two steps.
As I suggested in section 0.1.2, propositional attitudes are those mental representations which, unlike ideas, standardly function as units of reasoning. Such representations have rationality values, i.e., degrees of rationality or irrationality, which can influence the rationality values of other representations or actions, or at least be influenced by other representations or perceptions. A belief that Paris is pretty--or a wish that it were--has a rationality value. By contrast, a mere idea of Paris--or of prettiness or the present time--is neither rational nor irrational. Nor is a propositional idea (e.g., that Paris is pretty) itself rational or irrational. It is hard to see how it could have a rationality value, since (by representationalism) it plays the same role in the belief that Paris is pretty that it does in the doubt that Paris is pretty, the same role in the hope that Paris is pretty that it does in the fear that Paris is pretty. Beyond drawing this connection between propositional attitudes and rationality values, I have very little to say about the proper conception of rationality values. I imagine that, at a minimum, having rationality values is corequisite with having a role as a (potential) premise or conclusion of inference.<21>,<22>
On, then, to the second step: distinguishing propositional ideas from merely conceptual ones. Here we can simply say that propositional ideas are those ideas which help to realize propositional attitudes without combining with other ideas. An idea that Paris is pretty, taken alone (i.e., without other ideas), can help to realize a propositional attitude (e.g., the belief that Paris is pretty). But an idea of Paris--or of prettiness, or my favorite fact--must cooperate with other ideas to realize a propositional attitude.
These results can easily be turned into an account of the difference between concepts and propositions which is fully compatible with the postulation of simple propositions. Propositions are those contents which are possessed either by representations (e.g., beliefs) with rationality values, or else by representations (i.e., propositional ideas or propositional symbols) which taken alone can help to realize them. Concepts are those contents which are possessed by representations (e.g., ideas) which must cooperate with other ideas to realize representations with rationality values. This is, I submit, all that is essential to a content's being a proposition rather than a concept, or a concept rather than a proposition. In particular, structure is inessential to the distinction. Since we can draw this distinction (at least in theory) even in the case of simple contents, we can postulate simple propositions while maintaining a distinction between them and simple concepts.
Another potential worry about countenancing simple propositions is that doing so would introduce an element of coarse-grainedness into fine-grained theories. A natural question to ask is: if there are simple propositions, how are they to be expressed? Any that-clause we use will misleadingly commit us to postulating semantic dependencies where there are none. Recall the example of the interactive-activation model of reading, and in particular the feature node f (see section 2.1.3). One temptation was to say that f has as content the proposition that a top-half-of-a-circle-shaped figure is being visually presented in word-initial position. The trouble is that this erroneously attributes to the network representations which represent the concepts of being a half, of vision, etc. While it is possible to use such that-clauses along with disclaimers--e.g., "I hereby disavow the offensive commitments which normally attach to the claims I am making"--there is something vaguely dissatisfying about doing so.
One way to express this dissatisfaction is with the following question: what is the difference between using a complex that-clause along with a disclaimer, and simply engaging in what philosophers call de re attribution? Even defenders of fine-grained theories admit that there are some cases of content attribution for which reference conditions are all that are relevant. Suppose, for example, that you and I are making dessert in my kitchen, and I think to tell you about my mother's belief that sugar is bad for the teeth. Pointing to the sugar jar, I might say "You, know, Mom thinks the stuff in this jar is bad for the teeth". Since I know that my Mom has never even heard of the jar I am pointing to, however, I only intend my content ascription as a de re specification of the reference conditions of her thought. Similarly, someone can use the apparatus of de re attribution to describe the feature node f as "meaning that a top-half-of-a-circle-shaped figure is being visually presented in word-initial position". Since defenders of fine-grained theories do not take de re attributions seriously as specifications of content, however, this would not be taken as a genuine answer to the question: what is f's content? But by the same token, the postulation of simple propositions may seem to add nothing to the arsenal of fine-grained theories if we cannot express them without invoking de re disclaimers.
It may well be impossible for us to express simple propositions with ordinary complex that-clauses. But this would not prevent us from specifying or describing such a proposition, simply as the (unique) simple proposition associated with such-and-such reference condition. This strategy is importantly different from employing de re attribution. It will help us to see the difference if we employ a notational device for shortening this sort of specification to take the form of a that-clause, while marking disclaimers of normal commitments to semantic dependence.
As I mentioned in section 2.1.2, saying that a representation r has the content that A B C normally carries the implication that r is semantically dependent on representations with contents A, B, and C.<23> To bracket this implication, we might bracket the representations used to specify the content. Thus, we might say that a representation r has as content the simple proposition that [A B C]. This would mean that r has the reference conditions of "A B C", without having the same content, i.e., without having the same set of semantic dependencies. To return to the feature-node example, we can express the content of f by saying that it means that [a top-half-of-a-circle-shaped figure is being visually presented in word-initial position]. This is merely a notational shorthand for saying that f has as content the proposition specified by (i) the reference condition of "a top-half-of-a-circle-shaped figure is being presented in word-initial position" and (ii) the null set of semantic dependencies.<24>
The brackets do signify a sort of attribution similar to de re attribution, in the sense that expressions with the same reference conditions may be substituted within brackets without a change in attributed content. However, such attributions differ from de re attributions in an important way: rather than signifying that r has some content or other associated with the reference conditions of "A B C", the brackets signify that r has a quite specific such content, namely, the unique simple one. Unlike ordinary de re attributions, therefore, we can take such attributions seriously, and literally, as precise specifications of fine-grained content. Moreover, the content so specified is genuinely fine-grained. It is true that any two representations with simple content have the same content if and only if they have the same reference condition. This is not a violation of fine-grainedness, however, since it does not mean that every pair of representations with the same reference condition have the same content. In particular, representations with simple contents do not have the same content as representations with complex contents. By contrast, countenancing simple propositions furthers the aims motivating fine-grained theories of content. Doing so increases fine-grainedness, by increasing the stock of contents which may be specified.<25>
There is another objection available to someone who wishes to deny the existence, or at least the utility, of simple propositions. It is reasonable to require that, to be a representation, an entity must have a content explicitly.<26> For a simple proposition to be the content of a connectionist node, then, sense must be made of the notion of representing such propositions explicitly. On some views, this is not possible. Dan Dennett, for example, has suggested that syntactic complexity is necessary for explicit representation:
If Dennett is right, then there can be no connectionist nodes which represent propositions explicitly. But that would mean that fine-grained theories, even with simple propositions, fail to furnish a conception of content suitable for (many) cognitive scientific models.
Although I admit that Dennett's view is seductive, I think it is a mistake. The best way to see this is to focus on the role of the word "explicit". What does it serve to exclude? Since its clearest opposite is "implicit", we can begin by getting a grip on that notion. Dennett characterizes implicitness admirably in the next paragraph: "for information to be expressed implicitly, we shall mean that it is implied logically by something that is stored explicitly" (Dennett, 1987, p. 216).<28> This definition has more plausibility; unlike his definition of "explicit", it might have been lifted straight out of any dictionary.<29>
So where's the problem for Dennett's requirement of syntactic complexity? The problem is that there is no appropriate connection between syntactic complexity and the explicit/implicit distinction. There is an appearance of a connection, and this appearance probably explains the initial seductiveness of the requirement, but the appearance is illusory. Specifically, it might appear that syntactic complexity is necessary for there to be a distinction between explicit and implicit content. Consider the following train of thought:
The proper response is: easily. All that is needed for a representation to have some content explicitly and others implicitly is for it to have content at all.
Suppose that one (explicit or implicit) content of a connectionist node is that [one is seeing shape S]. Interestingly, no matter whether this content is explicitly or implicitly represented, it follows that there are other contents which are merely implicitly represented: that [someone is seeing shape S], that [one is seeing or smelling some shape], and so on. We know that these contents are merely implicitly represented, because they are less specific than another (implicit or explicit) content of the representation.<30> This suggests that an explicit content of a propositional representation is a content which is maximally specific (relative to its other contents). This is why the sentence "Paris is pretty" explicitly represents the fact that Paris is pretty but only implicitly represents the fact there is at least one pretty object. Although this account would undoubtedly have to be sharpened for technical reasons, I have said enough for us to see why it is preferable to Dennett's account in terms of syntactic complexity. The specificity account is potentially applicable in a uniform manner to any representation, including individual connectionist nodes, and makes manifest the relationship between explicitness and implication. The syntactic complexity requirement on explicit representation fails on both of these scores, and should not be enforced. There is no reason, then, why simple propositions cannot be represented explicitly.
Since simple propositions are unfamiliar, it is necessary to motivate belief in them. How should this be done? Consider an analogous case from arithmetic, namely, the "discovery" of the number zero, or of the negative numbers. Suppose we meet someone who is familiar only with the positive numbers, and we want to convince him that zero is a number. To motivate the belief that zero is in the running to be a genuine number, it would presumably be necessary to show that it would be "continuous" with the recognized numbers, in that it would share enough of their important features and relations. To motivate the belief that zero exists, furthermore, it would presumably be necessary to show that this belief serves a useful arithmetical purpose. I suppose that belief in simple propositions can be motivated in an analogous way--by showing that they are continuous with familiar fine-grained propositions, and that they serve a useful semantic purpose.
I hope it is clear in what important respects simple propositions are continuous with other more familiar fine-grained contents. Like other contents, these propositions are individuated by associated reference conditions, by a set of associated commitments to semantic dependence relations (in this case, the null set), and by the presence of rationality values (to determine whether a content is a concept or a proposition). Like other contents, they may be explicitly represented. Furthermore, simple propositions may themselves be presupposed by other, more complex contents: for example, if one representation has the content that [A B C] and another representation has the content that [D E F], a suitable syntactic combination of the two representations might have the content that [A B C] and [D E F].<31> Finally, postulating simple propositions furthers the aims motivating fine-grained theories of content.
While these are reasons for considering simple propositions, specified as I have specified them, to be in the running to be contents, more reason may be demanded for postulating them in the first place. It seems to me that we have as much reason to postulate simple propositions as we have to postulate more familiar fine-grained contents; the main reason is that these contents figure in cognitive-scientific explanations. I suppose that connectionist nodes without semantic dependencies--more generally, but more roughly, all syntactically simple representations which are not abbreviations--have simple contents. Since simple propositions may serve as contents of connectionist nodes, and since such representations seem to be required by research programs which show some promise of yielding true theories of at least some cognitive phenomena, good methodology dictates that we should believe in simple propositions, if we want a fine-grained theory of content at all.
In this final section of the chapter, I would like to address the question of what sorts of entities we are committing ourselves to when we commit ourselves to fine-grained propositions and concepts which admit of degrees of complexity. First I give a rough description of what I take to be the standard conception of such contents, namely as mathematical trees of a certain sort (section 2.3.1). Then I attempt to express some rather elusive metaphysical worries about such a view (section 2.3.2). Finally, I present an alternative account according to which contents and propositions are certain sorts of properties of representations (section 2.3.3). I hasten to express my belief that the conclusions reached in sections 2.1 and 2.2 in no way depend upon the metaphysical conclusions in this section.
On fine-grained theories of content, as I have described them, propositions and concepts cannot be identified with reference conditions. Instead, they must be identified with entities which admit of degrees of complexity, to reflect the semantic-dependence relations among representations. What precisely might these entities be? The relation between complex contents and simpler contents is most naturally treated as an abstract correlative to the relation between wholes and parts, perhaps the relation between (mathematical) trees and subtrees.<32>
Although there are different ways to pursue this idea, to a first approximation a content C might be taken to be a tree structure whose nodes are "filled" by reference conditions. The reference condition at the root node would be the reference condition of representations with content C. If C is a simple concept or proposition, then the tree consists only of the root node. If C is a complex concept or proposition, however, the root node has descendant nodes. In this case, the relation of ancestry in the tree corresponds to the relation of semantic dependence: every node in the tree is be filled with a reference condition such that representing C requires semantic dependence on representations with that reference condition. Since some dependencies are mediated by others (e.g., "checkerboards are square" depends on "boards" only through depending on "checkerboards"), some nodes would be mediate descendants of the root, others immediate descendants.
The entire structure would then be reduced, in the way of mathematical trees generally, to complex set-theoretic objects whose members, ultimately, are the reference conditions which fill the nodes of the tree. Contents, on this view, simply are such set-theoretic trees. To have a handy name, then, I will call this version of the fine-grained theory the "tree theory" of content.
Metaphysical worries form one source of resistance to the tree theory, although these worries are very difficult to pin down. We can certainly imagine philosophers who would object to the tree theory on the grounds that it postulates abstract entities. However, such philosophers would object equally to a coarse-grained theory of content which postulates reference conditions. Like trees, reference conditions are supposed to be abstract objects. They are possible ways for the world to be; in other words, they are properties which may or may not be instantiated by the world. For the purposes of choosing between the tree theory and the coarse-grained theory, then, we can ignore this metaphysical worry.
A more subtle worry arises in its place, however. In section 2.1.1, I described my assumption that contents are used in cognitive science to specify mental representations and to express generalizations about the functional roles of these representations. Along with a smattering of philosophers, I am inclined to go one step further, assuming that cognitive science appeals to the content of mental representations not only to express generalizations about functional role, but also to provide causal explanations of these generalizations.<33> Crudely put, then, I am interested in conceptions of content which at least leave open the possibility that content has causal powers. Given this, there is a tension between the tree theory and a certain general naturalistic conception of the sorts of things which have causal powers.
Although a fair amount of mystery surrounds the notion of causation itself, we can take as relatively unproblematic the notion of a concrete (i.e., "physical") object's having causal powers. Intuitively, a concrete object has causal powers just in case some fact about the object has causes or effects. Furthermore, there are developing theories which seek to explain how (first-order and higher-order) properties of (and relations among) concrete objects, despite being abstract, play a role in natural laws, and in natural-world cause-effect relations.<34> By comparison, we have no understanding of how set-theoretic objects play any sort of causal role. Sets are not standardly thought to be concrete objects, and they are not standardly thought to be properties or relations (of whatever order) involving concrete objects. Set-theoretic descriptions can, of course, be used to classify causally active objects, properties, and facts, but this is not the same as the sets' being causally active. If contents are set-theoretic objects, then, it is unclear that there is any room for them to have genuine causal powers, and so unclear that they can underwrite causal explanations in virtue of content.<35>
A final metaphysical worry about the tree theory is that it is in a crucial respect stipulative. Given a fine-grained theory of content, there are many different families of mathematical tree structures which can equally effectively be identified with contents. Furthermore, there are many equally effective ways to reduce mathematical trees to sets. Given this, it is natural to wonder which of the many suitable set-theoretic objects is identical to a given content. While it is true that this question may be brushed aside with a stipulation, we should in a naturalistic spirit favor a theory which gives an objective answer to the question of what contents are.<36>
I think that a more defensible fine-grained theory of content can be developed, one which treats propositions and concepts not as set-theoretic trees but as properties, properties which are (potentially, anyway) causally active. Which properties are supposed to be identified with propositions and concepts? I want to identify contents with certain properties of representations. Before discussing which properties of representations I mean, it is best to describe in general terms how this strategy is supposed to work. On a view of content common to the tree theory and most coarse-grained theories, concepts and propositions are thought to be objects related to representations, typically by the expression relation. An alternative is that contents are types of representations--in particular, semantic types. Any token object belongs to many types: my desk is a token of the type of thing made of wood, the type of thing I own, the type of thing in Massachusetts, and so on. To say this is simply to say that any token object has many properties: my desk has the property of being made of wood, the property of being owned by me, the property of being in Massachusetts, and so on. Indeed, the natural view is that types are properties. On the view I propose, then, when we say that a representation has a certain content, we are saying that the representation belongs to a certain semantic type, or, what is the same thing, that the representation has a certain property. This is what enables the identification of contents with properties of representations. In turn, this will enable a fine-grained theory to avoid the metaphysical worries associated with set-theoretic objects, and to leave room for a genuine role for content in causal explanations.<37>
If we identify the content of a representation with the property of having a certain reference condition, unfortunately, the result is a coarse-grained theory of content. Nevertheless, as I explained in section 2.1.1, reference conditions do fulfill some of the constraints on contents, and so it is appealing to identify contents with properties which are specified at least partially in terms of reference conditions. We can come near enough to a complete specification by exploiting the semantic dependence requirement, as I described it in section 2.1.2. This yields the following first approximation (which, coincidentally and thankfully, is also my final approximation):
Ignoring subtleties,<38> a content is fully specified once the reference conditions in (i) and (ii) are specified. Simple propositions and concepts, naturally enough, are those properties specified by the null set of reference conditions in (ii).
<1>Of course, the fact that contents serve different purposes (even apparently antagonistic ones) does not mean that a representation has different "kinds" of content, as many philosophers are quick to suppose. Often, the urge to postulate different kinds of content is merely a vestige of verificationism. We don't postulate that an object has different kinds of shapes simply because we are interested in shape for various reasons and have various methods (even apparently antagonistic ones) for amassing evidence about shape.
<2>See Barwise and Perry, 1981, for a defense of this conception of reference against the Fregean argument that sentences (and so, presumably, beliefs) refer not to facts but to (something like) truth values. What I call facts they call "situations" (which are not to be confused with their "abstract situations"). While the Fregean position is viable, the appeal to facts is more interesting for my present purposes. I will be considering (and rejecting) the position that contents are identical to referents, and this identification is not even initially tempting on the Fregean view. (In a moment, I will also consider the view that predicative ideas refer not to properties but to groups of objects.)
<3>What about predicative ideas, such as the idea of being pretty? Does this idea refer even if there are no pretty things--refer, say, to the property of being pretty? This raises controversial issues. Can properties exist without being instantiated? What about properties which are logically impossible to instantiate? Since my present point is independent of the proper answer to these questions, I will not to take a stand on them here. It would even be okay for my present purposes if these issues were sidestepped by taking the idea of being pretty to refer, not to a property, but to all and only the pretty things.
<4>This is compatible with there being some referential symbols for which content is partly or wholly constituted by referents themselves. It would take us too far afield to enter the debate over whether or not there are such cases, however. My opinion is that even what philosophers sometimes call "wide content" need not be specified by referents, but may be specified by reference conditions, of the sort to be described below.
<5>It is necessary to ward off certain associations from the psychological usage of the terms "concept" and "proposition". Often these terms are used to mean, not contents, but certain mental representations themselves. Although, as I will explain in section 2.3.3, there are ways to reconcile the psychological use of the terms with their semantic use, it should not be assumed from the start that the two uses coincide.
<6>Of course, in the case of beliefs and other symbols with truth value, reference conditions are commonly called "truth conditions". On the matter of terminology, it is perhaps useful to indicate that the distinction between referents and reference conditions is for all practical purposes the same as Carnap's distinction between "extensions" and "intensions" (Carnap, 1947). I shy away from this terminology, however, because I think "intension" is often also used for something more akin to Fregean senses (certain entities which are more finely grained than reference conditions).
<7>See Stalnaker, 1984 for a defense of a conception of propositions as functions from "possible worlds", or possible ways for the world to be, to truth values. Concepts might be treated in a similar fashion, as functions from possible worlds to reference values (or perhaps to referents themselves).
<8>In everyday attribution, we are satisfied if the reference conditions are nearly the same. However, even in everyday attribution we are aware that attributions are more accurate the nearer the reference conditions are. When we mean to speak strictly and accurately, as we might for purposes of doing cognitive science, the ideal is sameness of reference condition.
<9>I am not pretending that the reflections motivating fine-grained theories suffice to eliminate coarse-grained theories of content. To save a coarse-grained theory--e.g., to maintain the identification of content with reference conditions--one option is to insist that beliefs such as B1 and B2 do have the same content, but differ with respect to some other dimension. I will have a little to say in section 2.2.1 about why the sorts of differences among mental states exemplified here may legitimately be reflected in content. For now, however, I am willing simply to assume and develop a fine-grained theory, for the sake of expressing the puzzle presented by connectionism. Of course, this dispute about what should and should not count as part of content may in the end be no more than a terminological issue, or else one to be finessed by adopting the verificationist's trick of treating the word "content" as referring ambiguously to various "kinds" of content.
<10>It is possible to adopt a fine-grained theory of content without appealing to a notion of semantic structure (Block, 1986). Such a view would not be faced with the connectionist puzzle to be described below. I will give fleeting attention to the view in section 2.3.2.
<11>Carnap's (1947) notion of intensional isomorphism also embodies dependence relations among reference conditions (i.e., his "intensions"). Similar positions are defended by Lewis (1972) and Cresswell (1985). In section 2.3 I will attempt to develop a metaphysical account of contents which is different from the account offered by these later authors.
<12>Although I have tried to sketch a particular strategy for avoiding the extremely holistic conclusion, it is enough for my present purposes simply to proceed on the assumption that there is some way of doing so. Neither the connectionist puzzle nor my solution to it depends on the particular strategy adopted.
<13>There may be some question as to how "central" and even partially "theoretical" ideas such as those referring to boards (or to caterpillars, or to quarks) could turn out to be simple, given their functional dependencies on peripheral and observational symbols. The reason they can (at least in principle) be simple is that their reference conditions might not depend on the reference conditions of particular types of peripheral symbols, where these types are individuated according to reference condition. Suppose a thinker's mental symbol "board" is triggered in part by certain symbols in his visual system which respond to rectangles presented under certain conditions. Even if these symbols were to have a different reference condition--e.g., even if they were to respond to circles instead of rectangles--it could be that "board" would have the same reference condition, if it has sufficiently strong causal connections to other, independently triggered, symbols (such as those responding to certain kinds of tactile pressure, or certain kinds of spoken communications from other people). (Again, this intuitive result might or might not be borne out by a philosophical theory of reference conditions.)
<14>Eventually, I will also have to say something about what sorts of entities propositions and concepts are, on the fine-grained theory (see section 2.3).
<15>At least, this is so when we mean to speak strictly. See note <8>.
<18>Similar worries have appeared in other guises in philosophy, so the present puzzle may be better understood once these connections are drawn. I have in mind Donald Davidson's worries about content ascriptions to non-human animals, and Stephen Stich's worries about content ascriptions to small children and the mentally infirm (Davidson, 1984; Stich, 1984). While we have some inclination to treat animals of other species as having thoughts, we are easily persuaded that our content ascriptions are inaccurate. It is natural to suppose that a dog is capable of thinking that the person who normally feeds it is nearby. But at best, this specifies the reference condition of the thought, not its fine-grained content--is it so natural to suppose that the dog also has ideas of personhood, or of normality? Further attempts to hone in on the content by making substitutions for "person" and "normally" only make the problem worse, eventually appealing to general ideas of perception, or time, etc. As Stich emphasizes, the situation is the same for a child or a severely mentally handicapped person--consider their apparent thoughts about the people who normally feed them, and the bulk of their other thoughts. Both Davidson and Stich favor the conclusion that these apparent thoughts have no contents at all, except perhaps as a matter of our conventions. Even if we resist this extreme conclusion, however, the fine-grained theories under consideration are in the embarrassing situation of being unable to specify the content of the thoughts. My solution to the connectionist puzzle will also apply to these problems, although I won't trace out the connections.
<19>The challenge is made more important by the fact that it is not restricted to individual nodes in connectionist networks. Many other connectionist models treat groups of nodes as symbols, but also do not admit of syntactic complexity or any similar relation of semantic dependence. Symbols in these models give rise to the same difficulty. Also, given that the puzzle arises from lack of semantic dependence, we can see why many features of connectionist networks are irrelevant. For example, their being "hardwired" drops out. The problem would arise in the same way for models of cognition which, for example, postulated tiny people who read (only) syntactically simple symbols off of tiny monitors, compare them with similar patterns--rules?--in tiny library books, and write new ones onto the monitors according to what they find in the books. Most of the discussion, therefore, will be applicable not only to connectionist nodes but also to any symbols which appear to be propositional despite the lack of semantic-dependency relations.
<20>Toward the end of this section I will show how to extend a similar treatment to nodes which, though not genuinely simple (due to their involvement in local holisms), also give rise to the puzzle for fine-grained theories.
<21>What is less clear is whether there is any way to distinguish inferential relations from non-inferential relations among symbols (e.g., association of ideas), short of appealing to the rationality values of the symbols. Nevertheless, and incidentally, we can use these ideas to defend the claim that some symbolic nodes in connectionist networks have propositional contents, rather than merely conceptual contents. This claim does not rest solely on the (legitimate enough) grounds that it is established scientific practice to interpret nodes propositionally. If a node is thought to be a symbol at all, it must have either propositional content or merely conceptual content. Now, suppose I am right that if a symbol has a rationality value, or figures as a premise or conclusion of inference, then it has propositional content. Therefore, if connectionist networks are to fulfill their appointed task of helping to explain certain rationally evaluable mental processes--e.g., the "tacit inference" involved in perception--they must contain some units of reasoning, i.e., some propositional symbols. Therefore, the only way for all symbolic nodes to be merely conceptual would be for them to combine to form propositional symbols. Not any methods of combination will do, however: just as not all collections of words are sentences, so not all collections of conceptual symbols are propositional symbols. A mechanism of syntactic combination, or something close, seems to be required. However, many connectionist models do not contain suitable mechanisms of combination. Given this, at least some of the nodes in these models must have propositional content if they are to be symbols at all.
<22>Incidentally, the present conception of the difference between propositions and concepts can be used by defenders of fine-grained theories to respond to a certain kind of objection on behalf of coarse-grained theories. A defender of a coarse-grained theory can reasonably ask why features of functional role--such as those which distinguish the two beliefs about checkerboards in section 2.1.2--should be reflected in content. After all, not every difference in inferential role counts as a difference in content. For example, the inferential role of a belief may change as it becomes more strongly held, but its content does not. Nevertheless, there are things which can be said in defense of considering functional role as being relevant to content. For one thing, some elements of functional role are already built into content, even on coarse-grained theories. Suppose my account of the difference between propositional symbols and merely conceptual symbols is even roughly right. If so, then the very difference between having propositional content and having merely conceptual content tracks a rather important difference in functional role: only symbols with propositional content have rationality values at all, so only they can figure as premises or conclusions of rational inference. Given this, there can be no general prohibition against building into content differences in functional role.
<24>The proposed reference condition of f is intended simply as an illustration. The claim being illustrated is compatible with any of the main philosophical theories of reference conditions, which may assign different reference conditions to symbols such as f. The present claim may be put as follows: whatever the reference condition of f, the content of f is the simple proposition associated with that reference condition.
<25>Given the bracketing convention, and the theoretical apparatus for which it is a shorthand, we are equipped to deal with symbols which exhibit the connectionist puzzle, but which are not absolutely simple (perhaps because they enter into a locally holistic circle of symbols). We can use the bracketing convention to describe the content of many such symbols, specifying propositions which are not absolutely simple, but which nevertheless are not expressed by an unbracketed that-clause. To do this, we might place brackets around only part of a content-specification, saying for instance that a symbol s has as content the proposition that [A B] C. Since "C" is unbracketed, this means that s does depend on a symbol with the same content as "C", and so is not absolutely simple. However, it means that s does not share the dependencies of "A B", namely, dependencies on symbols with the same content as "A" and "B". Instead, it would mean that s depends on a symbol with the same reference condition (but not the same content) as "A B". In the same vein, we might attribute the content that [A B] [C], where the brackets around "C" signify that s depends on a symbol with the same reference condition as "C", but does not also depend on the symbols which "C" depends on. (In all these cases, as usual, it is being said that s has the reference condition of "A B C".) This strategy of using the bracketing convention may not always be applicable, since there may not always be a specification of a symbol's reference condition which admits of a pattern of bracketing reflecting the symbol's systematic dependencies. In these cases, however, we can always resort to a direct listing of these dependencies.
<26>Sometimes, it is said that symbols themselves must be explicit. As natural as this sounds, however, it involves a category mistake, at best. "Explicit" is properly used to describe the relation between a symbol and its content. It makes sense to ask whether a symbol represents a proposition explicitly or only implicitly; but it makes no sense to say, strictly and literally, that a symbol is explicit, just as it makes no sense to say that a symbol itself is implicit.
<28>What is it for some information--some potential condition--to be "implied logically" by other information--another potential condition? It is, I suppose, for it to be logically necessary for the first condition to hold given that the second one does.
<29>More generally, there are the various forms of what Cummins, 1989, calls "inexplicit" content. There are two varieties. First, there are conditions which are logically necessary given explicitly represented conditions plus some other conditions (e.g., facts about the domain). Second, there are conditions which are logically necessary given only conditions not represented explicitly (e.g., the state of control, the form of the representation, or the medium of representation), independently of what is explicitly represented. Since my subsequent remarks about implicit content will depend only on the notion of logical necessity common to all of these types of inexplicit content, my remarks can easily be expanded to take these into account.
<31>This is an advantage of the present theory over any attempt to draw Gareth Evans' intuitive distinction between "conceptual content" and "nonconceptual content" (Evans, 1983). If it were true that connectionist nodes had contents of a "new", nonconceptual, kind, it would be mysterious how these contents could figure in contents of the "old", conceptually structured, kind.
<32>See Lewis (1972) and Cresswell (1985) for illustrations of the tree theory. These authors credit Carnap (1947) with inspiration for their views, although I am not sure that Carnap would have much sympathy with the search for objects to identify with contents.
<33>Incidentally, this provides a source of resistance to fine-grained theories of content which simply specify contents in terms of functional role (see, for example, Block, 1986). By building a symbol's functional role into the specification of its content, such theories remove the possibility of causal laws which help explain functional role in terms of content.
<35>Although some properties have causal powers, the situation for the tree theory is not improved by focusing on a symbol's (alleged) property of having a particular tree as content. It is only (nth-order) properties and relations involving physical objects which lend themselves to our naturalistic understanding of causality. If there are such entities as sets and trees, presumably their properties do not have causal powers any more than they themselves do. In particular, relations between symbols and trees, such as the "expression" relation postulated by the tree theory, would be causally inert.
The objection does bother me, although in the next section I try to do better than postulating sui generis contents.
Incidentally, the "general objection" to set-theoretic identifications which Lewis mentions was first cast by Paul Benacerraf (1965) against the theory that numbers are sets of a certain sort. I think that my treatment of contents has an analog for numbers, although I am not yet prepared to defend such a treatment.
<37>By identifying contents with properties, or types, of symbols, we go some way toward adjudicating certain theoretical differences between philosophers and psychologists. Philosophers, by and large, think of concepts and propositions as abstract objects, while psychologists often think of concepts and propositions as concrete, mental representations. On the rare occasions when one side chooses to admit the sensibility of the other side's conception, it is normally supposed that the other side "means a different thing". However, we can unify both conceptions in a sensible way. Since concepts and propositions are types, they are, strictly speaking, abstract. But since they are types of symbols, we can at least speak of mental representations as instances or tokens of concepts and propositions. Concept tokens and proposition tokens are psychological entities in people's heads in precisely the same (useful) sense that word tokens and sentence tokens are on pieces of paper, even though word, sentence, concept, and proposition types are abstract.
<38>For example, a third clause is needed to distinguish properties which are propositions from those which are concepts (see section 2.2.1).