Predication as Structural Representation; Concepts as Information Compression-Decompression Hubs
Johan Heemskerk and Gualtiero Piccinini
Shea’s new book, Concepts at the Interface, is a trove of important ideas. To give just a few examples: Shea draws several important distinctions that criss-cross existing categories though arguably cutting deeper – such as the distinction between varieties of content-respecting transition; he suggests that cognizers use concepts to partly solve and partly circumvent the frame problem; he sketches a compelling answer to how agency relates to simulation; he collects a significant body of empirical literature and shows its relevance to an account of concepts.
The central theme of the book is that concepts mediate between propositional thought and sensorimotor simulation. In propositional thought, language-like representations bind subjects and predicates and feature in logical reasoning “involving conjunction, negation, and disjunction” (45). Shea suggests that subject-predicate binding and logical reasoning typically go together, so we follow him in focusing on propositional representations insofar as they involve subject-predicate structure (45).
In sensorimotor simulation, representations in dedicated sub-systems are activated. Distributed representations with sensory content combine to form, for example, image-like representations. Running a simulation can be modelled as navigating a path through a high-dimensional state space, in which proximity in the state space represents dimensions of similarity between the contents represented.
Shea argues that concepts act as an interface between these two representational systems. As Butterfill and Sinigaglia (2014) suggested when they introduced the interface problem for action, there is a prima facie puzzle surrounding how representations with differing formats can interact. In this original interface problem, the puzzle involved how intentions, which have a “propositional format”, can interface with motor representations, which have a “motoric format”, leading to successful action.
Shea focuses on a more general interface problem that involves offline thought. The relevant difference, for Shea, is structural representation versus predication. As Shea writes, there is “an important difference between the content-specific way representations combine in a structural representation and the content-general way representations combine in language and conceptual thought” (52). Specifically, argues Shea, predication is not a kind of structural representation; it is a sui generis, general-purpose kind of representation. The difference between predication and structural representation raises a puzzle about how the relatively unconstrained combination of conceptual thoughts can nonetheless activate relatively more constrained sensorimotor simulations. Shea’s answer is that concepts, temporary labels in working memory, combine to form propositional thoughts while also connecting to bodies of sensorimotor information.
There is a lot to say about Shea’s book (cf. our review of the book, hopefully forthcoming in a major journal). In this commentary, we investigate whether there is a stark difference in kind between sensorimotor simulations and propositional representations. We will argue that predication is a form of structural representation, so both sensorimotor and propositional representations are ultimately forms of structural representation. If both predication and sensorimotor simulation are structural representations, the need to mediate between them may seem less puzzling (cf. Ferretti and Caiani 2019). Nevertheless, there may be enough differences between them that concepts are still needed to mediate. At the same time, recognizing that all mental representation is structural gains us something very valuable: a more unified account of how the mind represents.
Structural Representation versus Predication
What are structural representations, and how do they allegedly differ from predication? Shea defines structural representation as a “complex representation in which a relation on representational vehicles v1, . . . , vn represents a relation on the entities represented by v1, . . . , vn” (38). In sensorimotor simulation, individual representations may have something like a pictorial format (e.g. Barsalou 1999). To take an analogous example from public representations, a map can represent the gradient of an incline using contour lines, with increasing density of contour lines representing increasing gradient. A relation on the vehicles – closeness of lines – represents a relation on parts of the land – the gradient of incline between them.
As Shea points out, once a convention has been established, this constrains what the vehicle can represent. Since proximity of contour lines to each other itself represents gradient, it cannot now be co-opted to represent something entirely distinct – it already has a semantic value (49).
Unlike sensorimotor simulation, Shea argues that the mode of combination of elements in a propositional representation “does not place strong constraints on what relations can be represented of the singular terms that are combined into a complete content” (49). In language-like thought, for example, Evans’ generality constraint (Evans 1982) suggests the very unconstrained ability to concatenate any subject with any predicate.
Before we get into Shea’s arguments against propositional representations being structural, let’s ask why Shea defines structural representation as he does. In the literature, there are several notions of ‘structural representation’ (for overviews see e.g. Artiga 2023, Facchin 2024). Virtually all of them build on key insights from theorists such as Cummins (1989) and Gallistel (1990), who take structural representation to be a certain kind of “isomorphism” or “homomorphism” in which “entities, relations, and operations in the represented system” are mapped onto “entities, relations, and operations in the representing system” so that for all relations between entities in the represented system there is “a corresponding relation between their representatives in the representing system” (Gallistel 1990, 16). The key difference between this definition and Shea’s is that while there must be a relation between entities which is mirrored, the relation itself need not carry semantic content.
While Shea’s more restrictive definition might be helpful in some contexts, we wonder what motivates its employment in the current context. In particular, we worry that Shea’s usage may be at odds with the dominant view of representation in the mind sciences (Thomson and Piccinini 2018). At any rate, the question we are asking – whether predication is a form of structural representation – can be answered under either notion of structural representation, so let’s proceed either way.
Shea provides two arguments that either propositional representations are not structural, or if they are, they are a special kind of structural representation. The latter case nonetheless supports the central argument of the book, since propositional representation would still require mediation by concepts when appropriate sensorimotor simulations need to be processed.
Shea’s Argument from Bradley’s Regress
The first argument is that propositional representations are not structural. Shea argues that treating subject-predicate binding as a case of structural representation requires the relation between subjects and predicates itself to represent the relation between objects and properties. Shea maintains that the candidate relation that would have to be represented is that of property “instantiation”. He argues that this runs into Bradley’s regress:
“If instantiation is a substantive relation that unites object and property, then presumably the object, the property, and the relation of instantiation can all exist without the object and the property being related by the relation of instantiation. So it looks like we need the relation of instantiation to come in again to unite them. And so on up a potentially infinite hierarchy.” (48)
To avoid running into Bradley’s regress, Shea proposes that predication is not structural representation, and because of that the relation between subjects and predicates need not represent instantiation.
Our Reply: Predication Is a form of Structural Representation
For starters, whether Bradley’s regress occurs and whether it is a problem are contentious matters in the metaphysics of properties and relations. Luckily, we don’t need to solve the metaphysics of properties and relations while we investigate mental representation. Whatever solution works had better be compatible with the structure and semantics of mental representations.
The question that is relevant here is whether the relation between a subject and a predicate can either represent (per Shea) or be homomorphic to (per Gallistel) the relation between the represented targets. We see no obstacle.
Consider whether that orange is round. The relation between “that orange” and “is round” may either represent or be homomorphic to the relation between that orange and its roundness. Substitute any other subject for “that orange” or any other monadic predicate for “is round” and the representation relation/homomorphism holds. Specifically, the sentence formed by concatenating the subject and the predicate gets evaluated as true if and only if the targeted object has the targeted property, false otherwise. Or consider whether Alice loves Bob. The relation between “Alice”, “loves”, and “Bob” may either represent or be homomorphic to the relation between Alice (as subject), love (as a relation between a lover and a beloved), and Bob (as object). Substitute any other grammatical subject for “Alice”, grammatical object for “Bob”, or transitive predicate for “love”; the representation relation/homomorphism holds. Specifically, the sentence formed by concatenating the subject, predicate, and object gets evaluated as true if and only if the object targeted by the grammatical subject stands in the predicated relation to the object targeted by the grammatical object, false otherwise.
More could be done to flesh out this idea. The basic point is that truth-conditional predication relies on an underlying structural mapping. Provided there is a relation between the target of a subject and the target of its predicate, and regardless of the metaphysics of that relation, the propositional subject-predicate representation will represent (or at least be homomorphic to) that relation, even if implicitly, in the concatenation of the subject and its predicate. If there is a metaphysical problem on some understanding of the relation between objects and their properties and relations, this is irrelevant to the semantics of the representation.
Shea’s Argument from Generality
Shea’s second argument concedes that propositional representation might be structural but maintains that it’s a special kind. Again, quoting Shea:
“If predication refers to instantiation, this places very little constraint on what can be represented by the structure. It is an extremely general scheme of concatenation. The simpler view, it seems to me, is that predication is not a case of structural representation, but even if it is, there is still a clear difference in generality” (50)
This concession aims to retain a computationally relevant distinction between simulation and predication, one which supports the need for an interface via concepts. The argument is that the constraints of the conceptual system set it apart from the simulation system, in that the former is highly unconstrained. We need some way to mediate between highly constrained representations on the one side, and liberally constrained representations on the other.
Our Reply: Concepts as Information Compression-Decompression Hubs
Constraints come in degrees. Coelho Mollo and Vernazzani (2023) suggest that we should understand differences in formats in terms of differences in the articulation of the vehicles of representation. Some representational vehicles place strong constraints on possibilities for co-representation. For example, in the map example above, using contour lines to represent gradients places strong constraints on what two lines being close together can represent – i.e. what else can be represented by the vehicle (perhaps the vertical distance between points, but not the colour of the terrain).
Nonetheless, Coelho Mollo and Vernazzani suggest that this notion of format difference is best understood as one of computational constraints, with higher degrees of freedom corresponding to fewer computational constraints, and that we should measure constraints as a range across different representations (14). We agree and suggest that propositional representations can interface with sensorimotor simulations in the way representations of different formats are thought to interface on the computational view of formats: by “a process of lossy compression followed by a process of decompression that includes generative elements” (14). If this is the case, more can be said about how concepts mediate between predication and simulation.
Concepts – more precisely, the memory traces of concepts – may be representational hubs that link generative resources usable for simulation in various modalities with representations of natural language words that can be recombined relatively freely (subject to grammatical constraints). When activated within working memory, what Shea calls “labels” may be neural encodings of natural language words, or perhaps neural representations that are few neurocomputational steps away from neural representations of words. In the simulation-to-predication direction, activating such concepts may allow cognizers to compress some of the information contained within a sensorimotor simulation to yield a linguistically encoded propositional representation that captures one aspect of what was simulated. In the predication-to-simulation direction, concepts may activate generative resources that, in turn, can form simulations that expand on what was propositionally represented (cf. Piccinini and Hetherington 2025).
This suggestion has similarities with Eliasmith’s “semantic pointer architecture” view (Eliasmith 2013). According to this view, compressed sensorimotor information is represented in concepts. Shea distinguishes his view from Eliasmith’s, arguing that any information encoded in concepts “need not be an abstract version or compression of the special-purpose information pointed to by a concept” (136). We are not suggesting that the only role for concepts is to encode compressed sensorimotor information. However, if propositional representations are structural representations with fewer constraints, one of the roles concepts may play is to encode a lossy compression of sensorimotor information. If some of the specificity of the sensorimotor information is lost, there are going to be fewer constraints on what can be co-represented propositionally.
The upshot is that propositional representations are merely one extreme of the constraint range, with sensorimotor simulations on the other. To provide some intuitive support for this, consider the following types of relation, each of which impose more or fewer constraints on what can be co-represented: being above is a relation which is more liberal with respect to what can be co-represented than being inside; everything in space can be above something else, but some things prohibit other things being inside them due to their density or size. However, being above is less liberal than being near along at least one dimension, since near things can be above, below, left to, or right to one another. There are clearly degrees of freedom of representation within structures containing these relations. Concatenating subjects and predicates is relatively liberal, but lies on a continuum with other relations with respect to degrees of freedom of what can be co-represented.
Conclusion
We have argued that, pace Shea, predication is a form of structural representation, and this gives us a unifited account of mental representation. We have also sketched a neurocomputational account of the role of concepts as mediators, which may yield a refinement of Shea’s account. These are just two examples of the many ways in which Shea’s brilliant work is sure to inspire further developments in our understanding of concepts.
Acknowledgments
Thanks to Lauren Graf for editorial assistance.
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