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Crossing the associative/inferential divide:

ad hoc concepts and the inferential power of schemata*

Abstract: How do we construct ad hoc concepts, especially those characterised by

emergent properties? A reasonable hypothesis, suggested both in psychology and in

pragmatics (Relevance Theory), is that some sort of inferential processing must be

involved. I argue that this inferential processing can be accounted for in associative

terms. My argument is based on the notion of inference as associative pattern

completion based on schemata, with schemata being conceived in turn as patterns

of concepts and their relationships. The possible role of conscious attention in

inferential processes of this sort is also addressed.

Keywords: concept; ad hoc concept; conceptual combination; inference;

associative process; working memory; Relevance Theory

* A previous version of this paper was presented at the workshop “Ad hoc concepts in Relevance Theory” organized by Agustin Vicente at the University of Basque Country in Vitoria (September 2013). I have to thank Agustin, and all the participant to the workshop (Nicholas Allott, Robyn Carston, Alison Hall, Mark Jary, Elisabetta Lalumera, Fernando Martinez Manrique, Tim Pritchard, Mark Textor) for the precious discussion we had. I also have to thank James Hampton, who in a day-long conversation has generously helped me in focussing some crucial issues of this paper, and also for encouraging comments to a second version. Finally, many thanks are due to the insightful comments of three anonymous reviewers, which have importantly improved the final version.

1. Introduction

Ad hoc concepts can been defined as temporary concepts constructed spontaneously in order

to achieve a goal that is relevant in the current situation (Barsalou 2010). The notion has been

introduced in psychology by Barsalou (1983) in the context of a discussion of the dynamic nature of

concepts and it has recently been the focus of some research in cognitive pragmatics, under the

assumption that understanding utterances requires that concepts are not simply activated but rather

modulated and adjusted in order to fit specific linguistic and non-linguistic contexts. One of the

most interesting view of such modulation of concepts during language comprehension has been

provided by Relevance Theory (from now on, RT), whose account assigns a crucial role to

inferences. My purpose in the present paper is to elaborate on this idea, specifically by arguing that

the inferences involved in the construction of ad hoc concepts, even in difficult cases characterised

by emergent properties, can be performed by associative processing.

This claim is far from obvious, since psychologists mostly think of associative processing as

a specific kind of learning mechanism (and its counterpart for the recovery of information), which

should be distinguished from other mechanisms of knowledge acquisition and exploitation usually

referred to as inferential (see Shanks 2010 for a review). In most cases, a distinctive feature is held

to consist in the latter – but not the former – processes being accompanied by conscious attention.

More generally, the crucial point is that associative processing is conceived of as insufficient to

provide motivated transitions from one mental content to another. In slightly different words,

associative processing is thought to allow at most the recognition of previously encoded perceptual

patterns, but not any form of inferential reasoning. Examples of this restricted view of associative

processing are legions. For instance, Wood et al. (2007) have conducted a study on nonhuman

primates' ability to perceive actions as goal-directed. Specifically, they have showed that different

kinds of nonhuman primates understand a pointing gesture produced with the elbow as goal-

directed only in case the experimenter's hands are not free to move. Their conclusion is that the

ability of those animals to understand goal-directed actions “extends beyond […] associative

mechanisms, drawing upon inferences about an agent's goals in the context of particular

environmental constraints” (Wood et al. 2007: 1405).

Even in RT, as I will show, there is some reason to suspect that associative mechanisms and

inferences are put in opposition to each other. As a matter of fact, relevance theorists explicitly

differentiate their inferential account from associative ones such as that proposed by Recanati

(2004), according to which “'dumb' processes of activation and association may well mimic the

smart, inferential processes posited by Relevance Theory” (Recanati 2007: 52). It should also be

noted that, in spite of his defence of associative processing as apt to deliver inferential effects,

Recanati himself draws a distinction between associative, inferential-like pragmatic processes and

genuinely inferential pragmatic processes. In recent works (Mazzone 2011; 2013; 2014) I have tried

to expand Recanati's associative approach by arguing that it can be applied to any kind of pragmatic

processing. Once we admit that inferences can be licensed by associative processing, I suggest,

there is no room left for a non-associative notion of inferential processing in pragmatics.

A general demonstration that inferential reasoning can be implemented by associative

processing is largely beyond the scope of this paper. My far more modest aim is to suggest that this

might be the case in the construction of ad hoc concepts. To that effect, I will firstly analyse how the

associative/inferential issue has been framed in pragmatics (section 2) and, specifically, I will

consider an argument against associative accounts of inferences that is indicative of the general

attitude towards this issue. The point of the argument is that associative relations are too poor to

license motivated transitions between concepts. On the contrary, I will show (in section 3) that

simple associative relationships are maintained to allow inferences by otherwise very different

approaches to concepts such as semantic network models and Barsalou's theory. What is common to

them is the idea that concepts are connected to each other by different kinds of associative patterns

which allow, thanks to a simple mechanism of pattern completion, different kinds of inferences. In

section 4, I will frame this idea of associative patterns in terms of the notion of schema, that is, a

structure of representation constituted by a certain number of components and their relationship(s),

and I will argue – following Barsalou – that also sensorimotor representations have such a

schematic organization. In section 5 I will consider the possibility that inferential processing in

general and ad hoc concept construction in particular require conscious attention. I will argue

instead that consciousness and working memory just add stability to the associative construction of

ad hoc concepts, which can occur automatically as well. Finally (section 6), I will illustrate how

difficult cases of ad hoc concepts – that is, cases involving emergent properties – can be accounted

for by an associative account.

2. The associative/inferential issue in pragmatics and the argument of Wilson and Carston (2007)

According to Relevance Theory, ad hoc concept construction would not require any special

explanation. It is rather claimed to be a product of the very same pragmatic process by which both

explicit and implicit content of utterances are determined. This process is supposed to consist in an

inferential derivation thanks to which the implicit content (and other contextual conclusions) are

drawn from explicit content and a number of contextual assumptions. Consider, for example, the

following exchange:

(1) Peter: Will Sally look after the children if we get ill?

Mary: Sally is an angel.

Apparently the implicit content conveyed by Mary's utterance is an affirmative answer to the

question raised by Peter – something like SALLY WILL LOOK AFTER THE CHILDREN IF WE

GET ILL. This content is supposed to be the conclusion of an inference having as its premises the

explicit content of Mary's utterance and possibly other contextual assumptions. As to the explicit

content, however, the concept that the word “angel” contributes to it cannot be the encoded concept

ANGEL which has as its logical property SUPERNATURAL BEING OF A CERTAIN KIND. It is

thought instead to be a different concept – let us call it ANGEL* – obtained by modulating the

encoded concept in accordance with the context.

One might be tempted to think that the construction of such modulated concepts, insofar as

they are components of explicit content, precedes the inferential process proper: ad hoc concepts

such as ANGEL* might be activated by a simple associative dynamic – based on the rank of

accessibility of their properties – and then fed into the explicit content which provides one of the

premises for the inferential process. However, this is not the way in which relevance theorists

conceive of ad hoc concept construction. In their view, the inferential pragmatic process does not

proceed linearly from premises to conclusions; there is, instead, a mutual adjustment of explicit

content, contextual assumptions and contextual conclusions due to both forward and backward

inferences. In practice, not only are conclusions drawn forwards from premises, but also premises

may be adjusted backwards as a result of contextual expectations about the conclusions to be

inferred. But then, backward adjustment may affect explicit content and thus the ad hoc concepts

which constitute it. In our example, Peter's question, insofar as it requires a yes/no answer, can be

thought to raise the expectation that Mary intends to claim either SALLY WILL LOOK AFTER

THE CHILDREN IF WE GET ILL or its negation, and this expectation in turn licences a backward

inference towards the explicit content, which has to be coherent with either the affirmative or the

negative claim. Thus, the concept ANGEL has to be modulated until the explicit content provides a

premise which has either the affirmative or the negative claim as its conclusion.

In sum, according to RT ad hoc concepts may be provisionally activated as a result of a

simple associative dynamic of accessibility, but it is the inferential pragmatic process which

eventually determines the explicit content and the ad hoc concepts that are accepted by the hearer as

part of the contextually appropriate interpretation. That this view implies an opposition between

associative and inferential processing is suggested by a number of papers (Carston 2007; Wilson

and Carston 2006; 2007; Sperber and Wilson 2008) in which relevance theorists argue for their

inferential account in the face of associative alternatives, the most explicit of which has been

proposed by Recanati (2004). It is important to note, however, that Recanati's associative account is

limited to what he calls “primary pragmatic processes”, which include the mechanisms by which

word meanings are contextually modulated so as to provide the explicit content of utterances. In

line with the Gricean approach, Recanati maintains that the further transition from the explicit

content to what is implicitly conveyed by it in a context has to be conceived instead in terms of

genuinely inferential (as opposed to merely associative) processes.

In practice, Recanati conceives of primary pragmatic processes as local associative

processes, based on the spreading of activation within conceptual networks and the consequent

degree of activation of concepts. A concept would be contributed to the explicit content of the

utterance insofar as that concept is the most accessible (i.e. the most activated) for the system given

the situation. There is thus a competition between concepts, which is also affected by what Recanati

calls “accessibility shifts”: the context may enhance (or reduce) the activations induced by isolated

linguistic items, thus subverting the initial patterns of accessibility. For one example, even if the

most accessible meaning for the word “bank” (for an addressee) were FINANCIAL

INSTITUTION, the context might provide other sources of activation which enhance the

accessibility of the alternative concept RIVER SIDE.

An important role is played here by the notion of schema, which can be defined as a representation

tying two or more concepts together into a structured whole. In practice, any concept may activate

schemata which in turn spread the activation to their other components. Schemata are appealed to

by Recanati in order to explain how accessibility shifts may promote the search for coherence in

primary pragmatic processes: the initial advantage of a given interpretation may be overridden due

to the fact that a less accessible concept has a better fit with – and therefore receives further

activation by – some contextual piece of information via schemata of which they are both

components. In this way, concepts that are more coherent with other pieces of information in the

context come to be preferred over initially more accessible but less coherent ones.

In recent papers (especially Mazzone 2011; 2013; 2014) a sort of mediation between RT and

Recanati's approach has been proposed. Recanati (2007: 52) has claimed that, thanks to the role

played by schemata in ensuring motivated transitions between contents, associative processes can

“mimic the smart, inferential processes posited by Relevance Theory”. But then, one is tempted to

extend his approach beyond the explanation of explicit content and apply it to implicit content as

well. This would dissolve Recanati's distinction between primary (i.e., associative and inferential-

like) pragmatic processes and secondary (i.e., genuinely inferential) pragmatic processes, in line

with RT's claim that a single inferential process is responsible for the comprehension of both the

explicit and the implicit content of utterances. There would be, though, a price to pay for relevance

theorists as well: they should accept that not only is associative processing responsible for

delivering the interpretative hypotheses which are then involved in forward and backward

inferences, but also those inferences are in fact performed by associative processes. This would

make no difference for the above explanation of how the ad hoc concept ANGEL* is recovered in

the example (1), that is, by means of a combination of forward and backward inferences. What is

put in doubt is the independent assumption that such inferential mechanism cannot be implemented

by associative processes.

As a matter of fact – although there are interesting points of convergence between RT and

associative accounts – relevance theorists have explicitly contrasted associative explanations with

their own approach in a number of papers (Carston 2007; Wilson and Carston 2006; 2007; Sperber

and Wilson 2008).1 The most extensive argument against the associative account is provided by

Wilson and Carston (2007), and it is interesting to analyse it as indicative of a more general attitude

towards this issue. Wilson and Carston (2007: 243) claim that statistical associations “provide no

basis for drawing warranted conclusions”. The argument is based on considerations of statistical

associations among lexical items in a corpus, as they are represented in the connectionist model

discussed by Kintsch (2000; 2001). Wilson and Carston presume that there is a general cognitive

lesson to be learned from the discussion of this model, and it is that although all inferential

1 It might also be argued that an associative account of inferences is not compatible with RT's modularism. This point, however, is beyond the scope of this paper.

relationships are also associations, not all associations are inferential:

In the minds of many speakers of English, for instance, “shark” is non-inferentially associated with “diver”, “salt” with “pepper”, “love” with “hate”, and so on. (Wilson and Carston 2007: 244)

As a consequence, we are told that associative processes “will vastly overgenerate, and some

method of filtering out unwanted associations will be required’’ (Wilson and Carston 2007: 252). In

this sense, associative processes are unconstrained with respect to drawing warranted conclusions.

I can see two related problems in this argument.

In the first place, by saying that “shark” is non-inferentially associated with “diver”, the

authors apparently mean that only a specific class of associative relationships can properly be

considered inferential. For instance, they observe that, based on co-occurrences in the corpus, the

word “shark” can be expected to have the words “fins”, “dolphin”, “diver” and “fish” as its close

associates, but while “x is a shark” entails “x is a fish” it is not the case that it also entails “x is a

diver” or “x is a dolphin”. They conclude therefore that not all associations are inferential.

However, it is disputable that the domain of inferences should be delimited in such way.

Specifically, it can be doubted that inferences have to be equated to logical entailments based on

category inclusion. In pragmatics as well as in other cognitive domains a variety of probabilistic

inferences can be drawn on the basis of regularities of different sorts. For one example, on the basis

of regularities concerning sharks, from “x is a shark” we can infer “x has fins”.

Here is where the second problem comes in. In order for a cognitive system to license in

different circumstances either the inference from “x is a shark” to “x is a fish” or the inference from

“x is a shark” to “x has fins”, that system has to encode more information than the simple fact that

“fish” and “fins” are both associated to “shark”. If fact, insofar as the nature of the relationships is

not represented, we can only have an indiscriminate activation of all the associates without any

chance to pick up the one which is required by the current cognitive task (either “fish” or “fins”)

and, relatedly, without any chance to grasp the reason why that one is required by the current task

(based on the task, either the “is” or the “has” relationship might be relevant). But then, relevance

theorists' conclusion depends on their specific choice to consider associative representations which

convey very poor or no information. Such a choice – it should be added – is in line with the

widespread (but disputable) assumption that associative relationships may capture at most simple

perceptual configurations or even mere co-occurrences, without any other information than the

probability of their co-occurring.

As I will show in the next section, this assumption is at odds with a claim which is

commonplace in the psychological literature on concepts (for instance, see Murphy 2002), that is,

the claim that our conceptual system is held together by an information-rich network of associative

relations – which also encode information on the relationships among concepts – and that, as a

consequence, those associations license inferences. It might be objected (some referees actually

raised this point) that the notions of association respectively employed in arguments against

associative accounts and in the literature on concepts are different, and therefore that my dispute

with RT is purely verbal. I partially agree on the premise, but not on the conclusion. In many cases,

when inferential processes are distinguished by associative ones the focus is on the kind of

cognitive abilities which appear to be involved at the behavioural level. From this perspective, one

can legitimately claim that certain processes are inferential, not associative, at the behavioural level,

even if it turned out that, at the implementation level, the inferences involved are in fact performed

by associative processing. The point is that, just as it seems to be the case for RT's position, the two

different conceptions of “associative” may be mixed up so that from the fact that inferential (i.e.,

non-associative in the behavioural sense) abilities are at play the conclusion is drawn that those

inferences cannot be processed associatively (in the “implementation” sense).

There are two reasons why I incline to think that this is what happens in RT: first, because

its proponents explicitly reject Recanati's proposal that inferential-like effects can be obtained by

associative processes and, second, because Wilson and Carston's (2007) argument appears to focus

on the implementation level, not on the kind of ability at play. The clarification that I propose is

useful, in my opinion, in order to avoid precisely that sort of conceptual confusions. Similarly, I

have nothing to object to Wood et al.'s (2007) view – see section 1 – that nonhuman primates might

exhibit abilities that are better thought of as inferential rather than associative (behavioural level), to

the extent that no conclusion is drawn as to the possibility that these abilities are implemented by

associative processes.

3. Inference as statistical pattern completion

In the previous section I observed that in pragmatics as well as in other cognitive domains a

variety of probabilistic inferences can be drawn on the basis of regularities of different sorts.

Cognitive science is therefore interested in a less restricted notion of inference than mere logical

entailment based on category inclusion. Moreover, inferences in this wide sense might be performed

by associative processing, provided that sufficient information about the nature of associative

relationships is encoded. In practice, any such association licences inferences of some kind, and

precisely of the kind that the nature of its represented relationship allows it to licence. For instance,

spatial relationships allow spatial inferences, and so on and so forth.

That information-rich associative relationships allow inferences has been claimed by

otherwise very different psychological approaches to concepts such as semantic network models

and Barsalou's theory.

To start with, one of the key intuitions underlying the development of semantic network

models in the 70's was precisely that concepts can be connected by different types of relationships

licensing different types of inferences. To the extent that the node SHARK is connected to the node

FISH by means of a ISA (a category inclusion) link, the semantic network licenses the inference

from SHARK to (ISA) FISH. But with equal right, provided that the node SHARK is connected to

the node FINS by means of a HAS link, the semantic network licenses the inference from SHARK

to (HAS) FINS and so on and so forth. As previously noted, there is no reason why one should only

consider statistical associations between lexical items in texts when posing the question of whether

inferences can be performed by associative processing: conceptual associations of the above sort

should also be considered.

The connection between associative relationships and inferences is also recognised by

Barsalou, in a paper where semantic network models are nevertheless criticised for conceiving

concepts as amodal symbols and as decontextualised entities (Barsalou 2005: 221-222).

Specifically, the inferences enabled by the conceptual system are described by Barsalou (2005) in

terms of statistical pattern completion.

In his view, concepts are not isolated and context-independent entities, detached from

information on settings in which objects appear. Against this view, he proposes the notion of

situated conceptualization according to which concepts are encoded as components of specific

settings to which they are specifically tuned. Situated conceptualizations are maintained to play a

key role in drawing inferences:

The situated conceptualization that becomes active constitutes a rich source of inference. The conceptualization is essentially a pattern, namely, a complex configuration of multimodal components that represent the situation. When a component of this pattern matched the situation, the larger pattern became active in memory. The remaining pattern components-not yet observed-constitute inferences, that is, educated guesses about what might occur next. Because the remaining components co-occurred frequently with the perceived components in previous situations, inferring the remaining components is justified.

Let me focus on a couple of points touched in this quotation.

First, patterns are suggested here to play the same role that Recanati (2004) assigns to

schemata. According to Recanati, a schema receives activation from any of its components and,

once activated, it raises in turn the accessibility of its other components. In short, a schema enables

inferences – i.e., schematically motivated transitions – from any of its components to the other

components. This is also the kind of mechanism described in semantic network models. For

instance, thanks to the labelled link HAS the nodes SHARK and FINS enter into a pattern (a

schema) such that whenever SHARK is activated FINS can be inferred via that pattern. I find it

important to note that this mechanism has the structure of modus ponens: given the pattern IF A

THEN B, and given A we are justified in concluding B. In practice, the mechanism we are

describing is a generalised form of modus ponens, in various senses: because inferences are

probabilistic, because As and Bs can be connected by a number of different patterns besides

material implication (IF-THEN), and because more than two entities can be connected within a

given pattern.

Second, the above quotation not only establishes a direct link between inferences and

frequency of co-occurrence in experience, thus emphasizing the statistical character of inferences 2,

but it even suggests that frequency of co-occurrence is the reason why one is justified to infer the

remaining components of patterns. In a sense, this is an appeal to induction as a form of

justification. For instance, it is the frequency with which sharks and having fins co-occur in our

experience that justifies the inference form SHARK to (HAS) FINS. It should be kept in mind,

however, that in another sense once a schema is encoded in our conceptual system, it is this schema

that justifies the transition from one to another of its components. In this sense, what properly

justifies the inference from SHARK to FINS is the pattern SHARK HAS FINS.3 An interesting

2 “Everything about the production of inferences via pattern completion has a statistical character” (Barsalou 2005: 629).

3 One of the referees has argued that, since I am concerned with a descriptive enterprise, questions of justification had better be left aside. His/her suspicion is that “justifies” here is ultimately just a placeholder for “causes”. To be sure, I am not concerned here with normative epistemological issues. However, there is a cognitive reason for speaking of justification and not of cause: while associations in a restrictive sense can only be causes of concept activation, schematic associations in my sense can be thought to justify concept activation, to the extent that they can act as premises in rules of inference having certain concepts as their conclusions. I have described these rules of inference in terms of generalised modus ponens. (Thus, to be precise, it is the use of schemata in these rules of inference, not schemata in themselves, that justifies the conclusion.) If this is a special, cognitive use of “justification”, so be it.

The referee has two further objections to these considerations. One is that only sentential entities can act as inferential premises and conclusions. However, section 4 is precisely devoted to explaining why my generalised notion of modus ponens is thought to apply to non-sentential entities as well. The general idea is that sensorimotor representations have structure and can be combined productively in a way that is largely isomorphic to linguistic productivity. This is sufficient for sensorimotor representations to be subject to normative considerations, although this is not my concern here. The other objection is that my non-normative use of “justified” is scarcely clear. Does it mean “seems justified”? “This seems implausible – the referee says – since it would presuppose conscious awareness of the transition”. I agree that conscious awareness cannot be a general requirement for the kind of associative processes described here. As a matter of fact, in section 5 I propose that conscious awareness adds stability to the processes at issue, but the inferential structure is already provided by the schematic organization of associative knowledge. I insist that there is a clear distinction between the claim that associations are mere representations of co-occurrences and the claim that associations have schematic organization: in the latter case, but not in the former, activations can provide motivated transitions, that is, transitions from one content (p) to another (q) by means of a schema (if p then q), even when these transitions are not accompanied by conscious awareness.

application – that I will address below – of this distinction between inductive and schematic

justification is that the transition from one mental content to another can be justified even in the

absence of direct inductive evidence of the correlation, provided that there are schemata justifying

that transition.

To sum up, cognitive inferences can be conceived as a form of statistical pattern completion

and, in a sense, as a generalised form of modus ponens.

4. Schemata as sensorimotor representations

Another point raised by Barsalou is that concepts are neither amodal symbols nor

decontextualised entities. This view implies that concepts are richer in information than they are

presumed to be by semantic network models. Let me focus on the first point, the criticism of

concepts as amodal symbols.

Barsalou has famously insisted on the thesis that concepts are based on sensorimotor

representations. This is not intended to mean that our conceptual system is “a collection of holistic

images like those in a camera, video recorder, or audio recorder” (Barsalou 2005: 621). On the

contrary, in Barsalou's view situations and objects are analysed in components and features whose

sensorimotor representations are organised hierarchically in the brain, so that those components

“can be combined productively to produce infinite conceptual combinations” (Barsalou 2005: 625).

In other words, the idea is that structural (or schematic) organization and sensorimotor format of

representations can coexist. I now propose to analyse further this idea by connecting it to the notion

of schema.

Schemata or patterns, as I have described them above, are structures of representation

constituted by a certain number of components and their relationship(s). Recanati (2004) has

adopted a notation for schemata an example of which is STEAL (x) → IS ARRESTED (x). This

notation, although very abstract and simplistic from a cognitive point of view, can be a useful

approximation for certain purposes. One of its merits is that a schema is represented as a

relationship between concepts, and concepts are represented in turn as predicates with slots for

variables. This notation is reminiscent of Frege's (1952a; b) theory according to which concepts are

functions which take individuals as arguments and return truth values. For instance, the concept

DOG (x) is a function that gives the truth value TRUE by substituting for “x” the name of any

individual which is an actual dog.

My suggestion is that schemata have this general structure, that is, they are constituted by

relationships between nodes which have slots that must be filled by selecting a single item from a

range of possible arguments. However, I also propose that a cognitively plausible notion of schema

has to be richer than the above notation suggests, in two senses.

In the first place, schemata must specify the nature of the relationship(s) between their

components. As we saw above, this is required in order for schemata to enable inferences, but it is

also what one expects from all we know about learning. We do not apparently encode concepts such

as SHARK, FISH, FINS, DIVER without encoding at the same time information about how these

concepts are connected with each other – and presumably with other concepts as well. For example,

that sharks have fins – and markedly, that between sharks and fins there is a part-whole relationship

– is something that we come to represent as a simple result of their experiential co-occurrence. In

fact, one could go even further and observe that not only do we encode SHARK and FINS as

involved in a part-whole relationship, but we also represent this as a specific spatial relationship

such that fins are located on sharks in certain positions. It is not difficult to see that this allows

much more specific inferences than that from SHARK to (HAS) FINS alone.

In the second place, the “(x)” in Frege's notation is a very poor instrument for representing

the variability within concepts. It just stands for possible arguments without providing any specific

representation of the range of values within which the arguments may lie.4 However, in the history

of the notion of schema stemming from Bartlett (1932) (and including Mandler 1979; Rumelhart

and Ortony 1977; Schank and Abelson 1977; Smith 1989), there is a different approach which

4 Incidentally, that notation may be used for co-indexing of arguments (as Recanati 2004 has shown), but for our purposes we can leave this issue aside.

allows for a more concrete representation of variability. In practice, psychology and artificial

intelligence have described schemata as containing specification of the possible values for any of

their slots. This specification may include defaults for the most typical values but also other

possible values, whose relative probability can be itself specified. To be sure, these values, just as

any other component of schemata, have been traditionally represented by means of amodal symbols

(propositional labels). However, one can legitimately presume that sensorimotor representations

might also account for variability within schemata. For example, since sharks differ from one

another to some extent, in order to apply their concept to actual instances of the species, this

representation must specify not one single shape but instead a range of variability for possible

shapes. And the same holds for fins and other parts. Thus, the schema SHARK HAS FINS can be

thought to contain a sensorimotor representation of sharks and a sensorimotor representation of fins

with their respective ranges of variability.

To sum up, structural (or schematic) organization and sensorimotor format of representation

can coexist, and the schematic structure appears to consist in relationships between concepts which

have slots to be filled by selecting a single sensorimotor representation from a range of possible

ones.

5. Meaning construction

Up to this point we have been analysing the notions of inference and schema, in order to

assess whether it is the case that associative relationships between concepts are too unconstrained to

play a role in the explanation of inferential processing. Our considerations suggest instead that

associative schemata are information-rich structures of representation enabling inferences

conceived in terms of statistical pattern completion.

However, even assuming that the notion of inference as pattern completion is accepted, and

therefore that contextually modulated concepts can be arrived at justifiedly as the result of

activation spreading through schemata, the issue remains as to whether simple associative activation

can wholly account for what one can call the constructive aspect of pragmatic (and conceptual)

processes. In this vein, Carston (2007) observes that associations might suffice insofar as what is at

issue is activation and deactivation of already encoded concepts (or their parts), but they are not

sufficient in order to understand genuinely constructive processes, that is, processes in which new

patterns of features – including properties that are not directly accessible from the initial concepts –

are constructed on purpose, for instance as a result of fresh metaphor comprehension or cases of

conceptual combination. In other words, we have to deal here with the most difficult and interesting

cases of ad hoc concept construction, that is, those involving emergent properties. For instance,

Carston observes that the utterance

(2) Mary is a bulldozer

requires the construction of the ad hoc concept BULLDOZER* which can be paraphrased as being

“obstinate, insensitive, uninterested in other people's opinions and feelings”, a concept which is not

going to be found in the encyclopaedic entry or the schemata attached to the linguistically encoded

concept BULLDOZER5. Therefore, she concludes, “some process or mechanism other than, or

additional to, the activation (and deactivation) of existing concepts or parts of schemas is required”

(Carston 2007: 29).

In the next section I will show how the account based on associative schemata might explain

cases of ad hoc concepts with emergent properties. The general idea is the following: it is not

necessary a direct connection with the appropriate ad hoc concept, insofar as there is a chain of

schemata providing an indirect route to it. Before turning to that, however, there is another issue

that is worth discussing briefly. The insistence on the constructive nature of these cases might be

motivated by the intuition that concepts can not only be activated one after the other, but they can

5 At least if we suppose that the metaphor is fresh and BULLDOZER* is not lexicalised. Otherwise, one should substitute an actual fresh metaphor for this example.

also combine with each other so as to form temporarily stable configurations. This is interesting

because, as we saw in section 1, some scholars assume that conscious attention and working

memory are distinctive features of inferential (versus associative) processing.

As a matter of fact, relevance theorists have recently explored the possible contribution of

attentional processes to fresh metaphor comprehension. With reference to experimental data on

metaphor comprehension, Rubio Fernandez (2007) analyses a pattern of late suppression of

irrelevant meanings and proposes to interpret this as a case of meaning construction, a process that

would differ from simple meaning selection in that the former but not the latter would involve the

intervention of effortful attentional processes. Specifically, while in interpreting homonyms

irrelevant meanings appear to be suppressed early and in an automatic manner, on the other hand

“suppressing the literal meaning of a novel metaphor would require the operation of later,

attentional processes”, and this is why “we are usually aware of figurative language use” (Rubio

Fernandez 2007: 364). In the same line, Carston (2010) proposes that complex and extended

metaphors might involve a more controlled and reflective mode of processing than conventional

ones.

I agree that conscious attention may have a role to play in these and other cases of

comprehension (see Mazzone 2013). However, this does not prove that complex conceptual

combinations cannot be implemented by simple associative processing, with no intervention of

attentional processes.6 My suggestion is that conscious attention adds stability to such constructive

processes, but it is the schematic organization that I described earlier what makes them possible in

the first place. This claim would require a more detailed examination, but for the present purposes a

couple of considerations will suffice.

In the first place, there are reasons to think that sophisticated cognitive processes can occur

even without the intervention of conscious working memory, although working memory is crucial

in order to ensure stability over time to those processes. An interesting case in point is evidence

6 It has even been suggested that attentional processing emerges itself “from the operations and interactions of very elementary processing units” (Shanks 2010: 275), that is, from basic associative mechanisms. However, for the present purposes we can leave this aside.

from goal pursuit. Although the traditional view conceived goal pursuit essentially as a conscious

and effortful process, decades of research in social psychology starting with Bargh (1989; 1990)

have shown that goal pursuit can be automatic and unconscious. Our previous experience shapes

“associative networks that include contexts, goals that are regularly pursued in these contexts, and

means that one usually uses to attain these goals” (Hassin, Aarts, Eitam, Kusters and Kleiman 2009:

550-551). But then, these associative networks allow for goal pursuit via simple spreading of

activation. In this line, Huang and Bargh (in press) have recently insisted on the existence of deep

similarities between conscious (controlled) and unconscious (automatic) processing of goal-directed

behaviour. In practice, conscious and unconscious action control seem to differ from each other

only in their respective dynamics of activation, with the former being more stable over time than the

latter.

Another line of argument comes from Miller and Cohen's (2001) influential model of

executive functions. According to that model, working memory, conscious attention and cognitive

control are just different facets of a dynamic based in our prefrontal cortex (PFC). Now, the role of

the PFC is described as essentially “modulatory” (Miller and Cohen 2001: 183), in the sense that it

does not perform some proprietary kind of elaboration, it rather ensures that some already occurring

cognitive elaboration is maintained and shielded from distracting and competing processing.

These considerations are easily applied to a simple case of conceptual combination.

Assuming that SHARK and FINS are linked by a spatial part-whole schema, then the activation of

this schema together with its components can be seen as a temporary conceptual configuration

which is able in turn to cause further activations in the network. Whenever such a configuration

succeeds in entering working memory, it reaches a (relatively) stable activation thus activating the

related representations for all the time needed for task execution. But even when the conceptual

configuration is activated without gaining access to conscious working memory, it nevertheless may

play a role in further processing by affecting the activation of related information.

In sum, if our previous considerations are correct, there is no reason to assume that

conceptual combinations necessarily require conscious attention and working memory, although in

the normal case these are present. Specifically, my suggestion is that they give stability to schematic

associative processing. Let us finally turn to the case of emergent properties.

6. Ad hoc concepts with emergent properties

Within the pragmatic literature concerning ad hoc concept construction, emergent properties

– i.e., properties that are not present in the concepts presumed to provide the lexical meaning of

words – have been recognised as an especially difficult issue (e.g., Wilson and Carston 2006; 2007).

This issue is also addressed in psychological literature on concept combination. Hampton and

Jonsson (2012) for instance raise the issue of how, when the concepts BIRD and PET are combined

together in the complex concept PET BIRD, the emergent property LIVES IN CAGES – which is

not present in either of the constituent concepts – can be formed.7 They propose two routes by

which this might occur. One route is what they call extensional feedback: “The attribute is clearly

made available by people recalling visits to pet shops or to friends' homes where they have seen pet

birds”. This amounts to the inductive justification for inferences we spoke of earlier. Through

experience a schema is formed such as PET BIRD LIVES IN CAGES, which then justifies the

inference from the complex concept PET BIRD to the property LIVES IN CAGES. But Hampton

and Jonsson also mention another possibility: “Alternatively people might use their 'background

theories' to guess that if a bird was not kept in a cage, it would not remain a pet for very long”. The

question is, what does it mean that people use background theories and how do these theories

provide non-inductive justification for inferences such as that from PET BIRD to LIVES IN

CAGES?

In my view, the answer can be found in the notion of schema. This is the direction suggested

by Hampton himself when he describes how background theories could be incorporated into

7 In Barsalou's account, ad hoc concepts are expressed by phrasal structures such as, for instance, “things to pack in a suitcase”. However, a concept combination such as PET BIRDS can be re-described in terms of the phrasal structure “birds which are also pets”.

prototype representations (Hampton 2006: 4):

The crucial difference is that similarity to prototype is not a simple function of matching attributes, but involves deeper causal information. One way to think of this is to suppose that in addition to having a set of features, a theory-based prototype has a set of information about the relations between those features. If an item has the features, but does not have them in the right relations to each other [...], then its similarity to the prototype will be poor.

As in the notion of schema we considered earlier, the crucial idea is that the conceptual system must

encode the relationships between its components. We have already seen that this is essential in order

to have inferences conceived as pattern completions. In addition, Hampton and Jonsson suggest that

background theories – and therefore, according to Hampton (2006), relations between features – are

key to the explanation of emergent properties. My proposal is that this might occur as a form of

complex pattern completion based on chains of patterns.

An interesting indication of how this mechanism could work is found again in semantic

network models, an important feature of which was inheritance of properties from superordinate to

subordinate categories. For one example, if BIRD is a superordinate category with respect to

ROBIN and if (HAS) WINGS is encoded as a property of BIRD, then the network licences the

conclusion that that property applies to ROBIN as well. In such a case, there is no encoded pattern

directly connecting ROBIN and (HAS) WINGS and therefore no pattern completion in the sense we

considered earlier. Nevertheless, there is a chain of two patterns – ROBIN ISA BIRD and BIRD

HAS WINGS – such that ROBIN is indirectly connected to HAS WINGS thanks to that chain: this

can be called a case of complex pattern completion.

It should be noticed, however, that inheritance in semantic networks is dependent on the

specific labelled links involved: properties can only be transferred downwards along ISA links. Can

this be explained on the basis of simple spreading of activation along the network? Although a

complete account is beyond the scope of this paper, we should keep in mind the possibility of a

more complex dynamic than activation simply spreading in all directions. Specifically, we should

consider the possibility of a rich network involving inhibitory as well as excitatory links (e.g., see

Waltz and Pollack 1985). For example, superordinate categories might have inhibitory links with

properties that are specific of subordinate categories, so that those properties cannot be transferred

upwards along ISA links. For another example, the inference from ROBIN to (IS NOT) DOVE

might be licensed by lateral inhibitory links between concepts at the same hierarchical level.

To be sure, the transfer of activation from ROBIN to (HAS) WINGS does not amount to the

explicit proposition ROBIN HAS WINGS. Even more so, the inhibition of DOVE as caused by the

activation of ROBIN does not amount to the explicit proposition ROBIN IS NOT DOVE. However,

my suggestion is, first, that the dynamic of activation and inhibition together with the schematic

organization of conceptual networks can explain implicit inferential processing and, second, that

conscious working memory adds stability to this inferential process. In other words, our cognitive

system can make assessments of consistency between conceptual contents on the basis of schematic

relationships which are at its disposal also in automatic associative processing. When conscious

working memory enters into the picture, assessments of consistency become explicit since the

subject focusses attentively on schemata and chains of schemata connecting the contents at issue. It

is also possible that occasional schemata are formed in working memory as a result of contents

being connected by means of chains of encoded schemata. For instance, when the subject focusses

attentively on the sequence of two schemata ROBIN ISA BIRD and BIRD HAS WINGS, she might

form the occasional schema ROBIN HAS WINGS as a result of their combination. For another

example, by attentively focussing on the schemata ROBIN ISA BIRD and DOVE ISA BIRD the

subject might form the occasional schema ROBIN IS NOT DOVE in working memory.

With all this in mind, we can sketch an explanation of how the emergent property LIVES IN

CAGES can be inferred starting from the combination of the concepts PET and BIRD. Let me

emphasise that what follows is just a sketch, intended to give a general idea of how complex pattern

completion might work in a case like this. We should also keep in mind that any attempt to provide

explicit representations of our conceptual systems suffers from the difficulty of doing this in a non-

arbitrary way. For the sake of simplicity I will use the sketchy notation adopted by Recanati (2004),

in which there is no explicit representation of the relationships between concepts.

I propose to consider two chains of schemata, one starting from the concept BIRD, the other

from the concept PET:

(1) a BIRD (x) → FLY (x)

b FLY (x) → FREE TO GO AWAY (x)

(2) a PET (x) → PEOPLE WANT TO PREVENT (FREE TO GO AWAY (x))

b PEOPLE WANT TO PREVENT (FREE TO GO AWAY (x)) → PEOPLE KEEP

(PRISONER (x))

c PRISONER (x) → IN CAGE (x)

By way of complex pattern completion, the concept BIRD allows one to infer FREE TO GO AWAY,

which is also a component of the property PEOPLE WANT TO PREVENT (FREE TO GO AWAY

(x)) associated to the concept PET. Thus, the activation of both PET and BIRD can be expected to

cause strong activation of this property, which in turn activates the sequence ending with the

concept IN CAGE.

To be sure, as a result of the activation of the concepts PET and BIRD, other properties than

(LIVES) IN CAGES can be activated as well. As a matter of fact, in free property listing tasks a

variety of sparsely related properties is supplied by subjects. However, this appears to depend on the

specific nature of the task: free property listing is a very special cognitive task in which there is no

specific goal to be pursued except listing properties itself. Thus, it is no surprise that subjects supply

scarcely systematic lists of properties. On the contrary, in normal cases linguistic and non-linguistic

contexts can be expected to constrain concept construction in a number of ways, which include

evidence of the specific goals pursued by others – for instance, the goal pursued by a speaker when

she speaks of “pet birds” on a particular occasion. In accordance with RT's view exposed in section

2, contextual evidence about communicative goals presumably affects concept construction by

means of backward inferences to the explicit content of utterances. In other words, goals put a

rational constraint on the interpretation, by triggering a search for the concepts apt to figure in the

explicit content if this has to act as a premise drawing to the contextually expected conclusion(s).

To sum up, my general point is that such backward and forward inferences can be explained

as cases of pattern completion based on the schematic structure of associative networks of concepts.

Let me insist: this is not to say that the spreading of activation forwards and backwards in

associative networks is all there is to conceptual processing. On the contrary, my suggestion is that

most of the times conscious working memory interact with automatic activation adding stability to

the inferential process. As a consequence, (some of) the inferential relationships might be grasped

consciously.

7. Conclusions

Relevance theorists have suggested that associative relationships are not sufficient to explain

pragmatic inferences, in that associations are too unconstrained to licence warranted conclusions.

On the contrary, I have claimed that associative relationships have enough structure to drive and

constrain inferential processing. Specifically, I have tried to provide an associative account of the

inferences by which ad hoc concepts involving emergent properties could be constructed.

My proposal is based on the claim, that is widespread in psychology, that our conceptual

system contains rich representations and that those representations license inferences. More

specifically, I have analysed the notion of inference in terms of statistical pattern completion based

on schemata. In turn, schemata have been analysed as patterns constituted by concepts and the

specific relationships between them, with concepts specifying ranges of variability for their

application. Finally, I have argued that those inferential processes may occur automatically and that,

although conscious attention normally cooperates with them, it does not change drastically their

nature but only adds stability to the process.

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