The geometry of predication: a configurational derivation of the defining property of clause structure

Abstract

Predication is the fundamental grammatical relation defining clausal structures in all (and only) human languages. This notion is by definition compositional, since it consists of a link between a subject and a predicate. The central question addressed here is whether this traditional notion, which has never been dismissed ever since the canonical models of Ancient Greek linguistics, can be derived at a formal level from more abstract compositional algorithms. Capitalizing on predication in copular sentences, which allow factoring out non-essential aspects of this phenomenon, such as the morphological asymmetry between verbs and nouns, I propose a configurational approach to predication. This new approach is based on the notion of symmetry as derived by purely compositional mechanisms. Finally, I address some theoretical and empirical consequences of this generalization including those pertaining to neurolinguistics.

This article is part of the theme issue ‘Towards mechanistic models of meaning composition’.

1. Predication: a configurational definition

Predication is a prototypical compositional notion since it is defined by the combination of two distinct and diverse elements, a subject and a predicate, in the proper configuration. The term ‘composition’ is obviously pervasive in science for it refers to the generation of a novel structure by assembling smaller parts but, in fact, the term was originally used in linguistics; etymologically, composition derives from the Latin translation of the Ancient Greek term ‘syntax’ which was introduced to refer to the harmonic composition of words in a sequence.¹ The term ‘configuration’, instead, refers to the fact that syntactic relations cannot be represented on a single linear dimension despite the fact that the physical stimulus is indeed linear: they require at least two dimensions which are normally represented as graphs on a plane (see [2]). This is very easy to detect but it is often neglected. To illustrate the configurational properties of syntax, a simple sentence like The war which destroyed these countries was not unexpected is sufficient. The number features of the singular noun war cannot be conveyed along the sequence of words to trigger agreement on the verb is; a second dimension must be introduced, which gives rise to a configuration. Thus, the question addressed here is whether this compositional notion can be selectively derived in a configurational way.

Predication constitutes the defining property of clause structures in all (but only) human languages and is one that has never been dismissed since it was established in the canonical models of Ancient Greek linguistics. The definition of sentence is one of the most studied issues in linguistics: Giorgio Graffi noticed that among the 150 different definitions of sentence in Ries [3] only 15 were established before the nineteenth century, testifying to ‘the great theoretical excitement which characterized syntactic research […] but it also demonstrates the lack of a new dominant paradigm’ [4, p. 115]. Possibly, the most cited definition of clausal predication can be traced back to Aristotle's own work who, being aware that with his definition he could only capture the notion of declarative sentence, thus excluding for example prayers or sentences in the future tense, defined it as a sequence of words of which you can tell if ‘there is truth or falsity’ (De Int. 4, 17a, 3–6). This indissoluble link with the notion of ‘truth (value)’ has turned predication and clause structure into the fingerprint of human language. Although intuitively clear, the notion of predication is not easy to capture. The following example contrasts a case of predication in (1)b versus a noun phrase in (1)a:

• (1)a The run.

•  b They run.

The notion of predication as implemented in (1)b must be kept distinct from other forms of predication which are employed in linguistics, such as the predication which is ‘hidden’ in noun phrases. Stemming from the Fregean tradition, formal semantics exploits the notion of predication to describe the interpretation of noun phrases (e.g. [5]). For example, a noun phrase like a run in a sentence Mary saw a run is interpreted as ‘(∃ x) (run (x) & see (m, x)’ which explicitly contains the predicate run as applied to the individual denoted by the variable name ‘x’ as in ‘run (x)’, being m the constant denoting Mary. However, that this predicative structure is different from the predicative link defining clausal structures can be easily proved by observing the following contrast:

• (2)a * John says the run.

•  b John says they run.

In fact, the notion of clause structure has been captured in formal linguistics by the simple formula describing any sentence (S) as the link between a noun phrase (NP) and a verb phrase (VP) ‘S → NP VP’ which underlies (1)b where the notion of subject is unambiguously assigned to the NP and that of predicate to the VP. Notably, ‘This idea of defining functional notions in configurational terms has been a constant within the developing of Chomsky's theories and one of the great contributions he has given to syntactic theory’ [6, p. 88].

In this paper I will propose that predication can be derived from purely configurational factors as generated on a simple binary combinatorial operation.

2. Two minimal layers of clause structure plus one

Clause structures must be able to carry different kinds of information compositionally which cannot be expressed by the lexicon. One type is the assignment of thematic roles such as agent and patient, as in the following contrast where John and Mary interchange their roles:

• (2)a Mary portrayed John.

•  b John portrayed Mary.

The same lexical entries yield completely different meanings as the result of the different configurations where they are inserted as suggested in Hale & Keyser [7].²

Clause structures, on the other hand, not only express theta-role assignment: another kind of information pertaining to scope-discourse properties is provided by them, such as the definition of quantificational domains in interrogative sentences like the following:

• (3) Whom did Mary portray t?

Here, the wh-operator whom, the object of the verb, moves out of the internal layer where thematic roles (here, patient) and Case (here, Accusative) are assigned to reach the external layer leaving an empty category, traditionally represented as ‘t’: this is required to implement the proper configuration associated to variable binding and define the scope of the operator. As a first approximation, (3) may be paraphrased as ‘for which x is it true that Mary portrayed x?’.

Clauses must then minimally contain at least two layers: a thematic layer and a quantificational one, hierarchically organized (see figure 1).³ This twofold structure is also considered to reflect the so-called ‘duality of semantic interpretation’: prototypically, argument structure, on the one hand, discourse properties, on the other [9]. This minimal structure, however, is not empirically sufficient to describe clause structures, and more specifically to implement predication. There are at least two reasons. First, thematic assignment is independent of predication, witness the distinct diathesis in the following contrast:

• (4)a Mary portrayed John.

•  b John was portrayed by Mary.

The subject changes in the two examples, which have identical thematic role assignments, and, of course, it cannot be considered as involving the upper layer; apparently, a third intermediate layer is needed.

Figure 1.

Two independent layers of clause structure. (Online version in colour.)

Interestingly, there is independent evidence that a specific extra layer is needed. Consider the two following examples:

• (5)a Mary portrayed John.

•  b Mary's portrait of John.

Mary and John receive the same thematic roles in (5)a-b, respectively agent and patient, despite the fact that (5)a is a clause structure whereas (5)b is a noun phrase. In other words, predication can carry thematic information but the identification of subject and predicate cannot be derived from it (see [10] for an extended discussion).

The second reason for the necessity of an extra layer comes from a clause involving the copula, which will be discussed separately in §4. Consider first the following case:

• (6) This is [_NP Mary's portrait of John].

The thematic roles of agent and patient pertaining to the predicative head portrait are assigned within the noun phrase but, crucially, not to the subject of predication, namely this. Clearly, the possibility of two diatheses as in (4)a-b and copular constructions such as (6) force us to assume another layer for clause structures, for purely empirical reasons related to predication (see figure 2). Notably, necessity of a dedicated layer for predication has been traditionally also supported by cases like:

• (7)a A man is in the room.

•  b There is a man (in the room).

Traditionally, the insertion of a preverbal NP there, an alleged semantically null element referred to as an ‘expletive’, is considered as a consequence of the requirement that a sentence contains a subject. An influential interpretation is offered by Chomsky [11] following Rothstein [12] in ‘roughly the Fregean sense’: the NP there is allegedly required as a subject to ‘saturate’ the function expressed by the VP predicate. This view and the corresponding analysis is contrasted empirically and theoretically in Moro [13] where it is suggested that the noun phrase there plays the opposite role of predicate within an alternative interpretation of the NP VP sequence explained in the next section.

Figure 2.

A three layer minimal model of clause structure. (Online version in colour.)

In the last decades, the analysis of clause structure has developed arriving at a ‘polymeric’ analysis where the same schema is recursively repeated across the three domains: each and every element entering in the computation is assembled by means of a binary operation, technically referred to as ‘Merge’ which recursively⁴ generates hierarchical structures [15,16]. The typical schema includes an obligatory head (X°) and two optional phrases, namely a complement (YP) and a specifier (ZP), and is represented as follows:

• (8) … [_XP ZP [X° YP]] …

In this construction, which in the Bloomfieldian tradition was dubbed ‘endocentric’ for the X is ‘the centre’ of the phrase, X, Y and Z are variables on the domain of morphemes. Clausal morphemes, in particular, include C°, I° and V°; these three morphemes constitute the spinal cord of clause structure acting as hubs of the three layers represented in figure 2. For empirical and theoretical reasons, the syncretic morphemic content of these three heads was expanded into more fine grained entities. The first proposal refers to I° and it was to split I° (inflection) into the T° (tense) and the Agr° (agreement) components ([17,18], with independent and different motivations; see also [19] for distinguishing Agr°-S and Agr°-O for subject and verb agreement, respectively); V° also underwent a similar treatment arriving at the identification of an abstract ‘light verb’ ‘v°’ along with ‘V°’ [7,20–22]; finally C° was also examined through the linguistic magnifying glass and turned out to be articulated in several smaller sub-domains, including many other functional heads such as Foc°, Top°, Fin°, Force°, Voc°, and so on (e.g. [23–25]) yielding to the so-called cartographic project [26].

3. The loss of specificity of predication structure

The predicative layer turned out to be identified with TP (the Tense Phrase, projected by T°). The traditional representation of a sentence as (9)a, associating the grammatical function of subject to the NP and that of predicate to the VP, was just isomorphically translated as (9)b which reproduces the configuration of any other phrase, for example, NP (9)c underlying (5)b, i.e. Mary's portrait of John:

• (9)a S → NP VP

•  b [_TP NP [T VP]].

•  c [_NP NP [N PP]].

The specificity of the configurational definition of predication as it was in S → NP VP seems to have been lost throughout the development of the analysis of clause structure. Predication is still associated to a configuration, i.e. (9)b, but this configuration cannot be differentiated from any other phrase; as a consequence, a compositional derivation of predication also seems to be lost.⁵

Given this scenario, the same original question, namely whether there is any compositional, qua configurational, algorithm to derive the special relation of predication, still persists.

4. Factoring out irrelevant features in predication

What remained constant across the development of clause structure analysis, from S → NP VP to [_TPNP [T VP]], is the assumption that the preverbal NP is the subject of predication and the VP is the predicate. This ‘dogma’ which has persisted across the different analyses is due to a single fact: that the noun phrases occurring with the verb are its arguments. A radical departure from this schema imposes itself when non-argumental noun phrases are considered, i.e. noun phrases which can play the role of a predicate. The simplest and more frequent case is copular sentences, that is sentences involving the verb to be and its equivalents across languages. I will summarize here the analysis given in Moro [13,17] in two steps. First step: consider for example the following sentences:

• (10)a This is [Mary's portrait of John].

•   b I consider this [Mary's portrait of John].

•   c This is considered [Mary's portrait of John].

•   d I bought [Mary's portrait of John].

Clearly, the thematic roles of agent and patient assigned by the predicate portrait to Mary and John do not target the preverbal NP which is clearly subject of the sentence and this supports a first important result: thematic assignment can be manifested in a predicative link but it is not necessary. Moreover, (10)d clearly shows that a predicative noun phrase does not necessarily play this role: it can be an argument as well. More generally, whether or not a noun phrase plays the role of a predicate or an argument depends on the syntactic structure, where it occurs, and cannot be predicted by intrinsic lexical properties.

Second step: consider a sentence like A picture of the wall caused the riot. A synonymous paraphrasis of this sentence is A picture of the wall was the cause of the riot (11)a. The latter is synonymous with (11)b:

• (11)a A picture of the wall was the cause of the riot.

•   b The cause of the riot was a picture of the wall.

Despite the fact that the sequence is the same, i.e. it is NP V NP in either case, the two sentences have a very different structure. Many empirical tests support this conclusion, for example, the following contrast:

• (12)a Which riot do you think that a picture of the wall was the cause of?

•   b * Which wall do you think that the cause of the riot was a picture of t?

More generally, a subset of the set of copular sentences of the type NP V NP allows this symmetric alternation. The explanation of this and many other contrasts is based on the hypothesis that, along with the canonical structure where the subject is raised to the preverbal position (adopted since [28]; see [29] for a detailed account and a full list of references), an inverse structure can also be derived from the same base generated structure by raising the predicative NP to the preverbal position:⁶

• (13)a NP copula [_SC t NP ] canonical copular sentence

•   b NP copula [_SC NP t ] inverse copular sentence

This provides the second fundamental result: the rigid association of the function of subject and predicate to the NP and VP surfacing in (9) cannot be maintained. A sentence can still be minimally considered as a combination of an NP and a VP but the former may be a predicate and the subject may be embedded in the VP. This result has as a consequence that preverbal there must not be necessarily interpreted as a subject expletive; in fact, it can be proved that it is a predicate expletive allowing the derivation of many otherwise recalcitrant properties of there-sentences.

Combining these two results and summarizing, we can conclude that, once the morphological asymmetries canonically distinguishing between a subject and a predicate, prototypically realized as NP and VP, are factored out, the only surviving requirement of the traditional representation of clause structure as adopted in (9)a-b is that a phrase is constituted by an NP and a VP. The configurational characterization of grammatical functions associated to these two phrases is lost: more specifically, the preverbal NP does not need to be the subject. The preverbal NP may well be the predicate exactly when the post verbal NP is the subject occupying a position embedded in the VP as in (13)b. In other words, copular sentences ultimately prove that the intermediate clausal field cannot be associated to predicative functions. On the other hand, the peculiar structure of these sentences provides us with new empirical reasons to formulate an alternative perspective and offer a positive answer to the central question addressed here, namely whether there can be a way to derive predication from compositional algorithms.

5. A conjecture and its implication for the theory of syntax

Consider again the abstract structures in (13)a-b and the following examples where (14)c is a canonical sentence, whereas (14)d is an inverse one:

• (14)a * pro sono [molte foto la causa].

•    (pro are many pictures the cause)

•   b * Ci sono [molte foto la causa].

•    (there are many pictures the cause)

•   c Molte foto sono [t la causa].

•    (many pictures are the cause)

•   d La causa sono [molte foto t].

•    (the cause are many pictures)

There are two logical possibilities to explain these facts: either something is required in that higher position that attracts either NP—as assumed by the so-called ‘Extended Projection Principle’ based theories, corresponding to the standard theory [19]—or rather something must be avoided in the lower one that expels either NP. That the first hypothesis must be excluded is proved by cases like (14)a-b showing that raising is also obligatory in those languages where silent pronouns (pro) or overt expletives (ci) are available which allow the lexical subjects to stay in situ.

In fact, an explanation for movement was based on the fact that the small clause complement of the copula is generated by merging two determiner phrases, the predicate and the subject, without the intervention of a head. The resulting phrase, which (again referring to the structuralist tradition) can be considered as exocentric, is symmetric. This fact has a consequence on syntax since we know, for independent reasons, that symmetry blocks the derivation of clauses. Movement must then intervene to rescue the structure: it breaks the symmetry by displacing either NP ([16,31] principle of Dynamic Antisymmetry).⁷ More explicitly, copular constructions show that predication is encoded in syntax by means of a symmetric configuration.

To capture the structural condition of predication, I propose to generalize this condition implemented by copular constructions to all types of sentences by formulating the following conjecture:

• A conjecture: all and only predicative structures are codified in syntax by symmetrical constructions.

If this proves tenable, it would constitute a positive answer to the possibility of identifying this core relation in terms of purely compositional, qua configurational, algorithms. Predication is encoded in syntax by the merging of two symmetrical phrases, whether or not a thematic assignment is performed.⁸ One of the consequences is that the intermediate level represented in figure 2 is not the one where predication is encoded but that it is rather necessary for predication for independent structural reasons imposed by the compositional mechanisms provided by grammar.

The representation of clause structure architecture can then be refined as shown in figure 3, where by ‘splitting field’ I mean the minimal portion of clause structure needed to break the symmetry generated by a predicative structure. In Indo-European languages, the splitting field is construed by exploiting tense morphemes, which are either expressed syncretically on verbs other than the copula or by the copula itself when the predicate is nominal; this lexical choice is of course not necessary and in other languages the splitting field may be realized by different strategies. Since predication can take place without thematic assignment as in (10)a or in an even more minimal case such as this is so, the internal layer indicates this option by brackets with the possibility that argument structure may occupy a separate optional more nuclear layer.

Figure 3.

Revising clause structure. (Online version in colour.)

As usual, the evaluation of a specific proposal in human grammar must proceed on global grounds and it must take into account a full range of empirical facts which cannot be examined here.⁹ Nevertheless, from a purely theoretical point of view, this approach has some interesting immediate consequences, beside those related to the derivation of predication in compositional terms. First, it explains why clause structure needs an extra layer beside the thematic and the scope-discourse related ones: some structural space is needed to solve the symmetry-breaking function of movement. The phrase formed by merging two maximal projections must be split in order to neutralize the symmetry and make the structure accessible to further computation; the landing site of the element moved cannot invade the space of the external layer—for the sake of simplicity, this intermediate layer can be referred to as the ‘splitting field’ of clause structure. Second, because the scope-discourse layer is universally hierarchically superior to the thematic one it implies that the splitting field is universally intermediate between the two, since it is immediately generated after the thematic assignment has taken place (if there is any). Third, it implies that there must be at least one splitting field per clause structure, as otherwise there would be no predication and thus no clause structure. If we limit the observation to sentences which are not embedded, this also implies that there must be at most one or, in other terms, that there is exactly one splitting field per clause structure.¹⁰

6. Symmetry-breaking phenomena and the electrophysiological code for syntax: some speculations

I have so far proposed an argument which clearly pertains to a computational and representational level, by adopting Marr's [39] trifold taxonomy: grammar must generate a specific structure to implement predication—which is independent from thematic assignment and discourse related functions—and it does so by exploiting the basic independently activated formal tools, such as Merge: symmetry is the selective algorithmic tool that carries out this fundamental task. Of course, syntactic formal operations are physically computed by neuronal networks but at the moment it seems difficult to establish a systematic correspondence between the formal and the neurobiological levels of representation, because the building blocks of linguistic structure cannot be (immediately) translated into neurobiological mechanisms. There is indeed empirical evidence, though, that these two levels of representation must be isomorphic or, more specifically, that language structure is biologically driven. For example, learning and manipulating an artificial syntactic rule which does not rely on recursive hierarchical structures but rather on linear sequences—call them ‘impossible languages’—does not activate the typical neural networks pertaining to language ([40,41]; see [2,30] for an extensive illustration and a critical discussion). This allows us to exclude that syntax is just based on ‘arbitrary and cultural conventions’, to put it in Eric Lenneberg's words, for neuronal networks cannot be conventionally activated ([42]; see also [30,43–45] for updated discussion at this level). On the other hand, beside the modulation of neural networks reflecting the existence of impossible languages (call it the where-problem) there is no real understanding of the electrophysiological mechanism underlying syntax (call it the what-problem).

It has been suggested that what constitutes a negative factor in the search for the fundamental foundations of language is the high level of abstraction of linguistics as opposed to the concrete level of neurobiology. However, this assumption seems to be ideological rather than empirical. In fact, the issue of ‘granularity’, adopting Poeppel [46]'s terminology, cannot and should not be raised with respect to the sole domain of linguistics. Nothing guarantees that neurobiology is at a better stage on the way of decomposing the observed phenomena in the interaction of simpler facts. It may well be the case that any convergence between these two empirical perspectives, not to speak of a unification, must first go through a deep reanalysis and a search for the relevant levels of granularity within both these disciplines, if not a radical rethinking as has always happened in unification processes in science (see [47]). The question of granularity in linguistics is indeed real but it simply coincides with a general tension which characterizes any field of modern science, much in the sense expressed by Jean-Baptiste Perrin, that the essential of science is ‘to explain what is visible and complicated by means of what is simple and invisible’ (quoted in [48])—the prototypical example is of course Mendeleev's periodic table for physical science—but that should not be an exclusive goal of this field. Ideally, both linguistics and neurolinguistics share what we may call ‘Turing's program’ [49] who envisaged the possibility of applying the same reductionist and minimalist approach to the life sciences. More specifically, Turing was trying to capture the chemical basis of morphogenesis in biological organisms, i.e. the biological instructions that may determine the anatomical structure of a resulting organism: ‘It is suggested that a system […] although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances.[…] The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take’ [49, p. 5]. Possible languages and possible organisms alike should then be considered as the result of an intricate instable computation of simpler elements.

Finally, although I do think that the configurational approach to predication illustrated here pertains to the computational and representational level, I would like to address a final remark concerning its potential role for the understanding of the implementational level. The what-problem consists of deciphering the electrophysiological code of syntax. We do not yet know how syntactic units are encoded although we are beginning to understand some aspects of the code. For example, an increase of electrophysiological activity in language networks has been observed by a progressive augmentation of syntactically merged words [50], or the presence of sound representations was detected during inner speech in non-acoustic areas preceding motor planning [51]. If the compositional derivation of predication proposed here is correct, it implies that the neuronal structures underlying syntax must be sensitive to the computation of symmetries; since symmetries are in fact one of the basic phenomena from both a physical and a cognitive point of view, it is not inconceivable that symmetry and symmetry-breaking phenomena may be encoded and computed in a physical medium. All in all, if the core of human language, namely the capacity to produce a sequence of words of which you can tell if ‘there is truth or falsity’, could be linked to the capacity of neuronal networks to recognize and manipulate symmetry our hope to decipher the electrophysiological equivalent of this extraordinary capacity may not be only a dream.

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Competing interests

We declare we have no competing interests.

Funding

We received no funding for this study.