1.1 On definitions and definitional sentences

By a definition or a definitional sentence in this work we refer to a sentence that explains the meaning of a lexical item, in other words, the answer to the question ‘What is X?’ or ‘What does X mean/refer to?’. Definitions are found everywhere, in dictionaries, encyclopedias and textbooks, but also in speech contexts for pedagogical and practical purposes, whether academic or non-academic. They are significant for human cognition as they let speakers reveal the lexical meaning of a concept in terms of language, and they play an important role in language acquisition as well (Krifka 2013a).

Definitions constitute a form of meta-language that facilitates the use and understanding of lexical items. In this sense they are different from other types of sentences as they communicate not about the world but about the language being used by participants in a linguistic interaction. They introduce a new term or impose a particular understanding on an existing term.

According to what has been said in the previous paragraph, definitional sentences represent a clear-cut manifestation of genericity. On the one hand, the term to be defined is expressed by means of a nominal expression that does not have a specific referent in the real world but is the name of a kind (an entity that is not spatiotemporally localized), thus introducing a case of D-genericity (Gerstner-Link & Krifka 1993). In addition, the term to be defined introduces a concept. Regarding the relation between kinds and concepts, it has been postulated that concepts describe kinds/categories, and kinds are reifications of conceptual descriptions (Mueller-Reichau 2011: 46–47).⁵

On the other hand, definitions are expressions of I-genericity, as they are characterizing statements about kinds (Krifka et al. 1995). Since such sentences are not bound to specific times or worlds, they can be claimed to be atemporal (Greenberg 2002); they represent regulations (Cohen 2001) because they describe general truths and are law-like.

Unfortunately, although definitions have received the attention of philosophers since ancient times (Gupta 2015), they have been understudied in formal linguistics, with the exceptions we will comment on below. From a linguistic perspective they have been studied mainly in lexicography, in order to establish what a good and valid definition of a lexical entry is, aiming at precision and clarity. However, the syntactic and semantic characteristics of definitions in different languages have been largely neglected within linguistic theory.

In the next section we consider two major distinctions that have been proposed in relation to the status of definitions.

1.2 Definitional generics vs. descriptive generics

Krifka (2013a), following Lawler (1973), Burton-Roberts (1977) and Cohen (2001), claims that definitional sentences are fundamentally different from descriptive sentences, even though both types of sentences are generic. Definitions communicate about the language used to describe the world, while descriptions communicate about patterns that appear in the world, presupposing that the language is fixed and the same for all participants in the interaction. This difference is illustrated by the well-known examples from Lawler (1973) presented in (4) and (5).

Sentence (4) explains what madrigals are, providing their principled characteristics, their “essence” (in Aristotle’s terms), while sentence (5) asserts something about the world in which madrigals are found. Considering their analytic status, Burton-Roberts (1977) claims that definitions are meta-predications, for they involve concepts (in the sense used by Frege): the polyphonic concept is predicated of the madrigal concept. Furthermore, we can rephrase (4) as ‘to be a madrigal is to be polyphonic’, but we cannot rephrase (5) as ‘to be a madrigal is to be popular’.⁶

Note, furthermore, that definitions of the type illustrated in (4) are partial (Krifka 2013a: 381) precisely because they are predicational, introducing adjectival properties. In contrast, those definitions of the type illustrated in (1) involve either an identity/identification between kind-referring expressions, which indicates that the type of definitional generics addressed in this paper are not partial, but full, classical definitions.

1.3 Definiendum and definiens

Definitions are not a uniform class of sentences. Different sources (e.g., dictionaries, encyclopedias, speakers, etc.) may give different bits of information and still be effective in providing the meaning of a lexical item. Moreover, definitions may be expressed with the help of various types of sentences, among which binominal copular sentences of the type ‘NP1 is NP2’ are common. Such sentences represent potential answers to the questions ‘What is X?’ or ‘What does X mean/refer to?’, which are canonical ways of requesting a definition (Burton-Roberts 1986) and establishing what can be called the definitional mode of speaking. The response to this question presupposes knowledge of X and consequently knowledge of the existence of the kind entity X.

According to Aristotle, a definition is a statement that gives the essence of a thing (Topics, I.5, see also Cohen 2001: 14).⁷ Classical or canonical definitions consist of a name of the object to be defined followed by a list of the most salient characteristics of the prototypical object. In canonical definitions, which typically have the form of a copular sentence, the term that is defined is called the definiendum, and it is the pre-copular part of the sentence. The postcopular part defines the precopular NP and is called the definiens. The definiens consists of the head noun, representing the genus (class, species) and, possibly, additional properties (differentia) that distinguish the definiendum from other possible subdivisions (subclasses) of the genus (see Eringa 1981; Cormack 1998). From a linguistic perspective these additional elements of the definiens are commonly expressed by means of adjectives, prepositional phrases, and subordinate clauses, as illustrated also in (6). In the postcopular part, mammal is the genus, and aquatic and terrestrial correspond to the differentia.

It is also important to bear in mind that different types of relationships can be postulated between the definiendum and the definiens. In terms of Cormack (1998: 184), according to whom the denotation of a noun is a set, the English definition in (7a) represents a case of set-identity while (7b) is a case of set-inclusion: the former introduces a relation of identity between the denotation of the two nominal expressions, and the latter claims that the individual having the property of being a rabbit is a member of the set of individuals having the property of being an animal.

In our terms, (7a), like previous example (1a), introduces an identity relationship between two kind expressions, the one corresponding to the definiendum and the one corresponding to the genus of the definiens. It could be rephrased as ‘As for the kind named by the noun oculist, it is identical to/identified with the kind named by the noun eye-doctor, and the other way around’. However, example (7b), like previous example (1b), introduces an identification relationship between two kind expressions, the one corresponding to the definiendum and the one corresponding to the genus part of the definiens. In this case it could be rephrased as ‘As for the kind named by the noun rabbit, it is identified with the kind named by the noun animal, but not the other way around’.

From a discourse perspective, and with specific reference to the sentences of interest in this study, a reviewer has suggested that Russian definitional generic sentences may be viewed as contractions of a specific type of question-answer pair. Thus, the definiendum can be considered a short form of a question and the definiens a short form of an answer. Consider (8) for (1a, b).

Under this perspective the dash used in (1a, b) is a reflection of the sentence border between the Q-A pair, and the neuter pronoun èto would have a propositional discourse referent (see Krifka 2013b). We will refine this intuition in Section 3, where we claim that NP1 is an aboutness topic, and èto a presentational pronoun.

In the next section we move to Russian definitional sentences that define nominal concepts, which are identified with kinds (Krifka 1995; Mueller-Reichau 2011). We support the hypothesis that they are non-predicational, similar to equatives and identificational and specificational copular sentences.

2.1 A brief overview of copular sentences: NP1 is NP2

Copular sentences are traditionally divided into predicational (9) and non-predicational ones. The latter include equative (i.e., identity) (10), identificational (11) and specificational sentences (12).⁸ The main difference between these sentences is that in (9) NP2 is non-referential, while it is referential in the others (10)–(12). By contrast, NP1 is referential in (9) and (10), but it is less referential in (11) and (12). In the latter it has even been considered predicative.⁹

In relation to the latter claim the standard wisdom is that in a specificational clause the complement is focus and the subject is topic, and the reason why the subject is always topic is that this is considered a precondition for obtaining a specificational clause.¹⁰

Syntactically, in copular sentences the predication is claimed to be mediated by the projection of a functional head Pred (Bowers 1993; Svenonius 1994; Adger & Ramchand 2003; and others), as represented in (13).¹¹

In the case of predicational, equative and identificational copular sentences, it has been proposed that a referential NP subject moves to a SpecTP position. By contrast, in specificational sentences it has been suggested in the literature (Mikkelsen 2006) that a predicative NP that bears a topic feature moves to SpecTP, the output of this movement being a sort of copular inversion structure in which NP2 may show non-canonical agreement with the copula in some languages. We will come back to this issue below.

Sometimes identificational sentences have been considered a special case of specificational sentences (Mikkelsen 2004), and specificational sentences have been claimed to show different properties in different languages. Thus, Partee (2010) comes to the conclusion that specificational sentences in English and Russian differ at the syntactic level: in the former NP1 is the syntactic subject, while in the latter it is NP2. In Russian, NP2 is always in the nominative and the verb agrees with it. However, the meaning of specificational sentences is the same in both languages: NP1 expresses a property and NP2 is referential (type <e>). Their information structure is also the same: NP1 is discourse-old (i.e., the topic), while ‘is NP2’ is new information.

Semantically, it should be noted that in copular sentences referential NPs (e.g., Mark, Samuel Clemens, Mark Twain, that) refer to individual entities, and reference is achieved by means of a proper name, a definite description or a deictic demonstrative pronoun. It might well be the case, however, that referential NPs of copular sentences have kind reference, as illustrated in (14).¹² This is important because in definitions, as exemplified in (1a, b), NP1 and NP2 both have kind reference, that is, they both refer not to ordinary objects but to abstract entities (i.e., kinds conceived as abstract sortal concepts; Mueller-Reichau 2011).

Let us now look at definitional sentences in more detail. Which type of copular sentences are they? Are they predicational or not?

Declerck (1988) considers definitions to be different from predicational sentences on the grounds that the former are meant to explain the contents of the concept or its use to the hearer, while the latter are meant to ascribe some property to the subject. Roy (2013), on the other hand, views defining sentences as a subclass of predicational copular sentences, claiming that they ascribe a property that is salient enough to “define” an individual as a particular member of a class of individuals (Roy 2013: 35).¹³ However, note that Roy, as is commonly the case in the studies of copular sentences, deals with NPs that – when referential – only refer to individuals, not to abstract concepts or kind entities, as is arguably the case in definitional copular sentences, which we focus on in this article.

In the next section we move on to definitional sentences in Russian. We first discuss the issue of whether they are predicational or non-predicational, and we show that definitional sentences are non-predicational, as they differ from predicational ones not only semantically but also syntactically. We also show that definitional sentences have similarities with equative, identificational and specificational sentences, whose main common characteristic is that NP2 is referential.

2.2 Russian definitional sentences: Non-predicational copular sentences

Russian definitional sentences of nominal concepts that describe kinds/categories are normally expressed by a bi-nominative copular sentence; that is, both the precopular and the postcopular NPs are in the nominative case. Note that this is the situation no matter whether the relationship between the definiendum and the definiens is one of identity or identification. Let us consider (15) (the parallel to English (7)).

Note that in both definitions a pronominal morphosyntactically invariant element èto, originating from a demonstrative pronoun, appears to be obligatory in between the two nominals. Crucially, this pronominal element èto is excluded from predicational bi-nominative sentences (Geist 2007), as illustrated in (16).

Pereltsvaig (2001), Geist (2007) and Reeve (2010) point out that èto cannot be omitted in equative sentences either, as it provides a sort of “semantic glue” for the two co-referential NPs, which cannot combine directly.

A second syntactic difference between predicational and non-predicational sentences is the lack of a nominative vs. instrumental alternation on NP2 in non-predicationals. In relation to this issue, Matushansky (2008) claims that the nominative case may have either a predicative or a sortal/classificatory meaning, as exemplified in (18a). In contrast to this example, which is ambiguous, (18b) and (18c) are not. Note that the non-predicative reading of poet is either expressed in the nominative case without a copula (e.g., (18a), (15a)) or with a copula (e.g., (18b)), the meaning being that Puškin is identified with an individual entity that has the property denoted by the noun poet. By contrast, the predicative reading of poet is either expressed in the nominative case without a copula (e.g., (18a), (16)) or in instrumental case with a copula (e.g., (18c)).

Concerning definitional copular sentences, it should be noted that the nominative vs. instrumental case alternation is not found in them, since both NP1 and NP2 of definitional generic sentences must be in the nominative case.

Interestingly, the same pattern is attested in equative sentences (Geist 2007). Recall the example in (17). In this type of sentence the nominative case cannot alternate with the instrumental either, even if the copula is overt, as illustrated in (19).

This means that definitionals look similar to equatives, but they differ from them as in equative sentences NP1 and NP2 refer to individual entities that are assumed to be co-referential, whereas this is not the case for definitional sentences. Instead, as we show in this paper, in the latter the two NPs refer to kinds, conceived as abstract sortal concepts (Mueller-Reichau 2011; Borik & Espinal 2015; in press), and the meaning conveyed is that there is identity/identification between the two kind-referring NPs.

To sum up, an NP2 in the instrumental is a characteristic of predicational sentences (Rothstein 1986; Pereltsvaig 2001; Geist 2007; Bailyn 2012; Bogatyreva 2014), and it is ruled out of definitional sentences.

An additional syntactic characteristic of definitional sentences, which makes them different from predicational ones, is that, generally, such sentences do not contain an overt copula.¹⁴ Accordingly, in the Russian linguistic tradition (Mel’čuk 2012: 86) they are called “nominative” (imennoe predloženie). In the present tense, the copula BE is not generally overt and is never obligatory, but it may be used for stylistic purposes (e.g., in philosophical statements, mathematical definitions and poetic or biblical sources). No matter whether the copula is overt or covert, NP2 is always in the nominative case, as illustrated in (20).¹⁵

Note that only (20a) shows the neuter demonstrative pronoun followed by a copula in the present tense.¹⁶ Furthermore, note that even though the present tense copula may optionally appear in definitional and equative sentences, it is obligatorily absent in predicational ones, as illustrated in (21).

In the past or future tense, the copula BE is obligatory, as illustrated in the definitions in (22a), which is the past of (22b), and in (23a), which would turn into (23b) in the present.

Example (22a) in a past tense form further illustrates a life-time effect, since it implies that representatives of the kind dodo do not exist anymore. In other words, the meaning of (22a) is that nowadays there are no dodos, but the kind dodo is still presupposed to exist. In contrast to (22a), example (24a), where èto co-occurs with a past tense copula followed by an NP2 in instrumental case, is ungrammatical. Example (24b) is also ungrammatical because NP2 Number and Gender agreement with the copula is required in definitional sentences. See also below, section 3.3.2.

Finally, it should be noted that, beyond the copula BE, definitional sentences also allow – next to the pronoun èto – a non-copular verb (e.g., značit’ ‘to mean’, označat’ ‘to refer’), as illustrated in (25).¹⁷

Despite this possibility, in this article we are looking at the properties of definitional sentences of nominal concepts with no overt copula, like those exemplified in (1). We posit that in definitional sentences the copula is always structurally present but it may be covert. There are several pieces of evidence for this. Firstly, the overt copula may appear in some present tense sentences in Russian (as shown in (20a, c)). Secondly, the byt’ ‘to be’ copular verb is obligatory both in the past and in the future (as illustrated in (22a) and (23a)). Thirdly, the full present tense paradigm of the copular verb byt’ existed in Old Slavonic and Old Russian (and still exists in other Slavic languages) (Kondrashova 1996). For all these reasons we postulate that the structure of present tense definitional sentences in Russian contains a null BE.¹⁸

To sum up, in this section we have shown that Russian definitional sentences are non-predicational. Unlike predicational sentences, they have a pronominal element èto in between NP1 and NP2; they do not manifest the nominative vs. instrumental alternation of the postcopular NP in the presence of an overt copula; and they may admit an overt present tense copula. Considering the above-mentioned characteristics, it can be concluded that Russian definitional sentences pattern with equatives, which characteristically are non-predicational copular sentences. This is explicable if we assume that, unlike NPs in equative sentences, which show co-reference between object entities, NPs in definitional sentences show co-reference between kind entities, through either identity or identification.

3.1 The structure of definitions

As mentioned above, definitions consist of two parts, the definiendum and the definiens, a division that represents a special way of topic-comment structuring that is pervasive in human communication (Krifka 2013a).

As already mentioned in (3), we postulate the following structure for such definitions:

The definiendum (NP1) is the term whose meaning is being provided by the definiens. In Section 3.2 we argue that it corresponds to an aboutness topic, similar to the logical subject of categorical judgments. On the other hand, the definiens (the PredP projection that is merged within a TP) delivers information about the definiendum. In Section 3.3 we claim that the definiens (èto BE NP2) is a copular sentence that is structurally equivalent to an identificational sentence (see (11)). Unlike what has been postulated in the literature for specificational sentences (Heggie 1988; Moro 1997; Partee 2000; 2010; Alsina & Vigo 2014; and others), we argue that postcopular NP2 is not an inverted syntactic subject of the copular verb but rather a complement that shows non-canonical agreement (Béjar & Kahnemuyipour 2017). Èto is a presentational pronoun that connects the two NPs by means of a two-place relation of type <e^k <e^k,t>>. Finally, in Section 3.4 we defend the notion that the copula BE in definitions of nominal concepts encodes an identity function (i.e., it returns the same value that is used as its argument, the postcopular NP2).

3.2 The definiendum: NP1

In definitions NP1 denotes an abstract sortal concept; it is the name of a kind.¹⁹ We hold that the denotation of NP1 is similar to that of generic definites (Carlson 1977/1980), also known as singular generics (Chierchia 1998) and definite kinds (Borik & Espinal 2015; in press), and it corresponds to an intensional atomic integral entity (type <e^k>). It should be noted that the notion of definite kind is about language (how D-genericity and reference to kinds of things is expressed in natural languages), and is coherent with Krifka’s (2013: 375) claim that “definitional generics restrict the language used to describe the world”.

The kind denotation of NP1, similar to definite kinds, is evidenced by the fact that while definite kinds are able to appear in argument positions of kind-level predicates, as in (27a), these same definite kinds can be easily rephrased in the form of a definition, as illustrated in (27b), where iPod is the name of a kind that refers to a kind conceived as an integral entity, without any commitment to instantiations or realizations of the kind.

Similarly, NP1 in (28) refers to a kind that is identified with another kind, the denotation of NP2. Identity between kinds is found cross-linguistically and is a common process in L2 acquisition, as illustrated by the two examples in (29).

Parallel examples are presented in (30), repeated from (15a), and in (31), repeated from (22b). In (30) the NP1 okulist refers to a kind entity, whose identity is provided by a second kind entity, the NP2 glaznoj vrač, and in (31) dront refers to a kind entity, which is identified with the kind ptica.

Interestingly, it is also possible to have a generic plural term as NP1. Compare (32a, b). Note that the definiens part of both sentences remains unchanged, no matter whether the definiendum is singular or plural.

We hold that unlike the kind expression kit ‘the whale’, which refers to a kind conceived intensionally as an integral entity, the generic plural kity ‘whales’ refers to a kind conceived extensionally as a set of individuals that have the property of being whale (Borik & Espinal 2015: 183). Thus, our claim is that the kind denotation of NP1 is identified in both examples with the kind mammal, here introduced by a special lexical item, vid ‘kind’.

Beyond these semantic properties, NP1 always gets a default nominative case. Pereltsvaig (2001) posits that Russian nominative case can be found in two types of nominals, those whose nominative is licensed by a certain syntactic configuration, and those that need not be marked for case at all. We suggest that the NP1 found in definitional copular sentences is a candidate for the second type, given that NP1 is structurally outside the copular sentence and cannot obtain nominative case from Tense. Syntactically, we postulate that NP1 is generated sentence initially, at a left-peripheral sentential domain, that is in TopP (Rizzi 1997; and others). The nominative singular marking of NP1 appears to be only part of a morphophonological cluster, a default choice in the absence of a trigger of syntactic features.²⁰

Concerning the information structure conveyed by definitions, NP1 is to be considered an aboutness topic (Reinhart 1981; Krifka 2007; Roberts 2011) that the statement delivers information about. In other words, definitions are about the definiendum, as they supply information about the meaning of the term to be defined (Krifka 2013a), and NP1 refers to an “entity that a speaker identifies, about which then information, the comment, is given” (Krifka 2007: 40).

This proposal makes definitions on a par with categorical judgments (Kuroda 1972; Ladusaw 1994).²¹ The precopular NP1 looks like a logical subject (i.e., a topic) of a categorical judgment, while the rest of the sentence (the PredP, part of a TP) corresponds to the logical predicate. Like NP1s in categorical judgments, NP1s in definitional sentences are topics, which in the latter case must be interpreted generically. Moreover, both NP1s in definitional sentences and NP1s in categorical judgments have a strong reading with a presuppositional interpretation, more exactly a presupposition of existence.²² Syntactically, definitional sentences differ from other categorical judgments in that the NP1, being merged in SpecTopP, must be nominative, while the NP1 of the rest of categorical judgments may show a variety of cases after internal merge to SpecTopP.²³

To sum up this section, semantically speaking the definiendum (i.e., NP1) is interpreted generically and refers to a kind (conceived either intensionally or extensionally). Furthermore, it is interpreted as an aboutness topic similar to the logical subject of categorical judgments. This analysis of NP1 supports the claim that in a sentence such as (30) an identity is established between two kind expressions (i.e., oculist and eye doctor), and the sentence can be translated into English by saying ‘As for the kind named with the noun okulist, it is identical to/identified with the kind named with the noun glaznoj vrač’. In (31) the kind dodo is identified with the more inclusive bird kind, and can be translated into English as ‘As for the kind named by the noun dront, it is identified with the kind named by the noun ptica’. In any case, NP1 always has a default nominative case form.

3.3 The definiens: èto NP2

3.4 Back to the whole structure of definitional sentences

Let us consider once again the structure in (3), repeated here as (56).

So far we have argued that NP1 is a Topic (specifying what a statement is about), èto is a presentational pronoun, and NP2 is the constituent that provides conceptual content to define NP1 and the reference with which NP1 is associated. Recall also that the examples in (1), repeated here as (57), provide two possible readings for definitional generic sentences: the first one, (57a), that can be paraphrased as ‘As for the kind named by the noun gippopotam, it is identified with the kind named by the noun begemot’, and the second one, (57b), that can be paraphrased as ‘As for the kind named by the noun gippopotam, it is identified with the kind named by the nominal expression tolstokožee mlekopitajuščee živuščee v Afrike’.

In this section we claim that the copula of definitional sentences is associated with a type-neutral identity function for <e^k> that returns the same value that is used as its argument (i.e., f(x) = x). Other than that, the copula has no semantic effect. This identity function is responsible for the identity/identification characteristic of definitional sentences. Accordingly, the copula maps any kind entity (type <e^k>) into itself, λy.y, while èto denotes a two-place relation (type <e^k<e^k,t>>), since it takes as input the meaning of NP2 and gives as output a one-place relation that combines with the meaning of NP1 to yield a generic sentence. This is represented in (58) for sentence (57a). Sentence (57b) would have a parallel representation, since tolstokožee mlekopitajuščee živuščee v Afrike stands for a modified kind.

In this structure, NP1 is the topic that introduces a kind entity, to which a new concept, a second kind entity (NP2) is ascribed. As argued in this section, this identity/identification between NP1 and NP2 takes place in two steps. First, BE introduces a type-neutral identity function that maps kind entities to themselves. Second, èto takes as input the kind entity output of BE and gives as output a function that looks for a second kind entity with which it is identified. This is how we predict the compositional meaning of definitional generic sentences in Russian.