Volume 8 Issue 1 (2010) DOI:10.1349/PS1.1537-0852.A.346 Note: Linguistic Discovery uses Unicode characters to represent phonetic symbols. Please see Optimizing Display for requirements to accurately reproduce this page. Semantic Maps as Metrics on MeaningMichael CysouwBy using the world’s linguistic diversity, the study of meaning can be transformed from an introspective inquiry into a subject of empirical investigation. For this to be possible, the notion of meaning has to be operationalized by defining the meaning of an expression as the collection of all contexts in which the expression can be used. Under this definition, meaning can be empirically investigated by sampling contexts. A semantic map is a technique to show the relations between such sampled contextual occurrences. Or, formulated more technically, a semantic map is a visualization of a metric on contexts sampled to represent a domain of meaning. Or, put more succinctly, a semantic map is a metric on meaning. To establish such a metric, a notion of (dis)similarity is needed. The similarity between two meanings can be empirically investigated by looking at their encoding in many different languages. The more similar these encodings, in language after language, the more similar the contexts. So, to investigate the similarity between two contextualized meanings, only judgments about the similarity between expressions within the structure of individual languages are needed. As an example of this approach, data on cross-linguistic variation in inchoative/causative alternations from Haspelmath (1993) is reanalyzed. 1. Measuring MeaningMeaning is a particularly elusive property to measure. The central problem is that the meanings of linguistic expressions are variable across languages, and it is still mostly unknown how large this variability is. It does not really help to analyze the meaning of a language-specific expression (for example the English verb to walk) by saying that it expresses a general concept (like WALK). Such a change in typography still leaves open the question as to what the relation is between WALK and, for example, the meaning of the German word spazieren or the Spanish word andar. Actually, without a more explicit definition of the concept WALK, asking whether andar expresses the concept WALK is not much different from asking whether andar means the same as to walk. Yet, individual linguistic expressions across languages never convey exactly the same range of senses, making such a simplistic approach to comparing meaning across languages devoid of content. In this paper, I will defend the view that a much more profitable operationalization of cross-linguistic variability of meaning is achieved by defining the meaning of a language-specific expression as the collection of all contexts in which the expression can be used . This definition represents, to some extent, a reversal of the intuitive notion of meaning. Meaning is typically thought of as some kind of property of a linguistic expression that governs its potential appearance in a particular context. In this conventional view, the main difficulty is how to express this property called “meaning”. The approach to meaning proposed in this paper simply defines this property as the sum of all actual appearances. It is of course practically impossible to ever collect all appearances of a particular linguistic expression (be it a lexical or a grammatical item) in a living language—though this is possible for a dead language by including all documentation available—but samples of contexts can be used for any empirical question at hand (cf. Croft 2007; Wälchli & Cysouw 2008 for a similar approach to meaning). Samples of the actual occurrences of expressions in concrete contexts can be used to compare the variation in meaning between different language-specific expressions. So, instead of assuming that we know what the English expression walk means, I propose to sample its meaning by considering various contextualized occurrences of walk-like situations. To compare expressions across languages, ideally the same sample of contexts should be used for all languages investigated. The parallel collection of such occurrences across languages can take various forms. It is possible to use extra-linguistic stimuli, like pictures (e.g. Levinson & Meira 2003) or video sequences (e.g. Majid et al. 2007), and investigate the linguistic expressions used to describe them. The contexts can also be defined purely linguistically, using descriptions of situations (e.g. Dahl 1985) or examples from parallel texts (e.g. Wälchli 2005). In the practice of grammatical typology it is often impossible to collect sufficient parallel expressions because of the limited amount of material available and because of the difficulty of finding native speakers for all the languages to be investigated. So, instead of concrete occurrences of language-specific expressions in context, normally somewhat larger domains of contexts are used in which an expression can occur (e.g. Haspelmath 1997). These domains are (more or less) explicitly defined as “chunks” of meaning, large enough to be identifiable from reference grammars, and small enough to capture the main distinctions of the cross-linguistic variation.[1] Both parallel expressions in context as well as the somewhat more abstract domains of meaning as used conventionally in linguistic typology are called ANALYTICAL PRIMATIVES in Cysouw (2007).[2] One of the consequences of comparing languages on the basis of an (empirical) selection of analytical primitives is that such a selection strongly reduces the range of possible meanings that can be identified across languages. Instead of the real-world continuous variation of possible meanings, a (finite) sample of analytical primitives only allows for a restricted, point-wise, granular view on this variation. In this approach, the meaning of a language-specific expression reduces to a subset of the sampled primitives. This subset consists of those sampled contexts in which the language-specific expression occurs. From the perspective of individual languages, the semantic analysis offered on the basis of such a selection of primitives might be somewhat coarse-grained and perhaps to some extent even misleading. The most important gain of this approach, however, is that it offers a concrete operationalization of the cross-linguistic study of meaning. From this perspective, the comparison of the meanings of two expressions from two different languages consists in the comparison of the selected subsets of analytical primitives. Any deficits in the comparison arising from a biased selection of analytical primitives can easily be repaired by changing or extending the sample of primitives. To be able to make cross-linguistic comparisons between language-specific expressions from different languages, first the internal structure among the primitives must be considered. This paper deals with the empirical establishment of such structure among analytical primitives in the form of semantic maps (Section 2). The actual comparison of language-specific expressions (i.e. questions like “how similar is English walk to Spanish andar, and in which aspects to they differ?”) will not be further pursued here.[3] In a very general sense, the structure among analytical primitives amounts to establishing a metric on analytic primitives, i.e. a specification of the distances (or “dissimilarities”) between them , as will be discussed in Section 3. One way to empirically arrive at these dissimilarities between primitives is to use cross-linguistic diversity in the encoding of the primitives, as discussed in Section 4. Only language-specific analysis is necessary to establish dissimilarities between primitives—no cross-linguistic judgements are necessary. This important insight led to the establishment of semantic maps in the first place but will be generalized here in Section 5. In Section 6, I will argue that both form and behavior can be analyzed as language-specific encoding . An example of this conceptualization of the cross-linguistic study of meaning is presented in Section 7, in which data from Haspelmath (1993) on the inchoative/causative alternation is reanalyzed. 2. Semantic MapsAnaytical primitives are not just points in an unstructured cloud of semantic space. Some primitives are more similar to each other than to others. Such structure among analytical primitives is suitably analyzed by using semantic maps (cf. Haspelmath 2003). Semantic maps are a special kind of analysis and display of the internal structure of a sample of analytical primitives. My use of the terms SEMANTIC SPACE and SEMANTIC MAP is most closely related to Haspelmath’s terminology, in which “a semantic map is a geometrical representation of functions in ‘conceptual/semantic space’ ” (Haspelmath 2003:213). This is different from the terminology used by Croft (although there is no difference in content), who uses the term “conceptual space” for the geometrical representation, and “semantic map” for the language-specific instantiation (cf. Croft 2001:92ff; Croft 2003:133-139; Croft & Poole 2008:3). The different terminologies are summarized in Table 1. Differently from the received view of such semantic maps, I propose here to strictly separate the notion of a semantic map into two different aspects, namely the STRUCTURE among the primitives and the DISPLAY of this structure. The structure itself will be formulated as a metric on the primitives; the display of the structure is the semantic map proper. Given a particular set of data, there will both be different ways to establish the structure among the primitives, and there will be different ways to display any structure attested. Because of the multitude of possibilities, it is particularly important to separate effects stemming from the decision on how to measure the structure from effects resulting from the specific method of visualizing the structure. In this paper, I will only discuss approaches to the establishment of the structure among primitives. The discussion of the various possible visualizations will be left for another occasion.
Table 1: Terminological clarification
3. Metrics and Distance MatricesA METRIC is the mathematical explication of a notion of distance (or dissimilarity, i.e. the opposite of similarity). In our daily world, the most natural notion of distance is the Euclidean distance, i.e. the distance “as the crow flies”. However, when moving from point A to B it is often not possible to take the direct route (if you are not a crow), so another natural metric is the ground travel distance. This notion of distance can widely deviate from the straight-line Euclidean distance, namely when there is no (approximately) direct route to get from A to B while staying on the ground. Still another way to measure distance in daily life is to take the time it takes to get from A to B. Again, this notion of distance might give a rather different perspective on our surroundings depending on transportation possibilities. These different ways of measuring distance illustrate that any notion of distance is a question of perspective and is not in any sense pre-established by the nature of the objects investigated. This holds also for metrics on meaning: what counts as similar in meaning depends on which perspective one wants to take.[4] The result of applying a metric on some data is a table of pairwise distances for all pairs of objects investigated: a DISTANCE MATRIX. So, given some data and a decision on how to interpret the data (the metric), distances between pairs of objects can be computed. Normally, such pairwise distances are expressed as a (fractional) number between zero and one. At the one extreme “0” indicates “no distance”, i.e. the two objects are the same, and at the other extreme “1” indicates “maximal distance”, i.e. the objects are completely different. It is not necessary to normalize distances to this zero-one interval, but it makes it easier to combine distance matrices. Also, decimally written values between zero and one can intuitively be taken to represent percentages. For example, a distance of 0.54733 can be interpreted as “almost 55% of the maximal distance”. And, finally, the distances between zero and one are easily switched to similarities, because when two objects have a distance of d, then they have a similarity of 1− d. Distance matrices can become bewilderingly large and difficult to interpret for a human being. For example, with only 10 analytical primitives there are already 10×9÷2=45 distances between pairs of primitives. Just looking at such a long list of numbers will normally not result in very revealing insights because it is difficult to identify meaningful distinctions amid the wealth of available information. There are many ways to help a human being make sense of what would otherwise be categorized as information overload, but this is an extensive topic which I will not discuss in detail here. Suffice it to say that visualization is a highly powerful technique, though it can also be deceptive because human eyes (and brains) tend to see patterns even when there are none. For this reason it is advisable never to rely on just one visualization and to always determine afterwards whether any patterns perceived are really statistically significant. Finally, it is important to recognize that every visualization is always an abstraction of the underlying data, or, put more bluntly, many details are necessarily ignored, or intentionally misrepresented, in the process of making a visually pleasing graphic display. The network-like graph used for traditional semantic maps (cf. Haspelmath 2003) is an example of such a pleasing graphic display for which various fundamental abstractions of the available data are made (cf. Cysouw 2007 for a detailed criticism). 4. Using Linguistic DiversityThe basic intuition behind the semantic map approach to meaning is that cross-linguistic variation in the expression of meaning can be used as a proxy to the investigation of meaning itself . Concretely, recurrent similarity in form reflects similarity in meaning, or, as Haiman (1985:19) puts it: “recurrent identity of form between different grammatical categories will always reflect some perceived similarity in communicative function.” Thus, the assumption is that when the expression of two meanings is similar in language after language, then the two meanings themselves are similar. Individual languages might (and will) deviate from any general pattern, but when combining many languages, overall the cross-linguistic regularities will overshadow such aberrant cases.[5] Formulated within the framework set up in the previous sections, this basic intuition can be formalized as follows. To start off, a sample of analytical primitives has to be established, and expressions of these primitives must be collected for a sample of the world’s languages. Then, for each language individually, the similarity between these expressions can be established within the structure of the language (i.e. only language-specific constructions and language-internal form-similarities are investigated). Technically formulated, this means that a language-specific metric on the expressions will be set up—a different one for each language (see Section 7.2 for a concrete example of how this might work). Then, the cross-linguistic metric on the analytical primitives (“semantic map”) is the average of the language-specific metrics on the expressions collected. This simple statement represents a big step forward for any empirical investigation of meaning (cf. Haspelmath 2003:230-233). Instead of requiring elusive judgments about the similarities between meanings, all that is needed now are very concrete judgments about the similarity between language-specific expressions within one and the same language. So, to establish a cross-linguistically viable metric on meaning, it is not necessary to perform cross-linguistic comparisons of expressions from different languages. Purely on the basis of many language-specific analyses, it is possible to arrive at general results. 5. Constructions and StrategiesTo establish a metric on expressions, a notion of (dis)similarity between expressions is needed. There are basically two different kinds of (dis)similarity. The first possibility is to compare the amount of shared morphophonological material between expressions. Such similarity is purely language-specific and cannot be used to directly compare expressions across languages (except of course in historical-comparative reconstruction). In contrast, more abstract characteristics are necessary to establish the cross-linguistic similarity between expressions. Examples of more abstract characteristics are the order of elements, the length of expressions, or the degree of fusion between elements (e.g. isolation, concatenation, or non-linear morphology). This is an important differentiation, as made implicitly in the semantic map literature. The first similarity leads to a LANGUAGE-SPECIFIC EXPRESSION METRIC (“constructions”) and the second to a CROSS-LINGUISTIC EXPRESSION METRIC (“strategies”). Most of the comparisons in the field of linguistic typology are based on comparing cross-linguistic strategies (cf. Croft 2003:31ff.). However, semantic maps are purely based on language-specific constructions. Given a language-specific metric, a LANGUAGE-SPECIFIC CONSTRUCTION (in the sense of Croft 2001; Goldberg 2006) is a set of language-specific expressions that are highly similar from the perspective of the metric. What exactly “highly similar” means is of course less obvious, but any disputable similarity-boundary will likely be reflected by an equally vague notion of what defines the construction involved. Though different operationalizations of similarity can be used (and see Section 7 for a few possibilities), I am strongly in favor of a gradient notion of language-specific constructions (i.e. individual expressions in a language are more or less similar on a continuous scale). I think it is misguided to look for any strict definition of constructions that discretely classifies all expressions of a language into separate constructions. Being the counterpart to constructions, a TYPOLOGICAL STRATEGY is a set of expressions that are highly similar from the perspective of a cross-linguistic metric (the term “strategy”, now commonly found in the typological literature, was probably first used in this sense by Keenan & Comrie 1977:64). Just as constructions are abstractions of language-specific metrics, strategies are abstractions of cross-linguistic metrics. For example, consider the causative/inchoative alternation, to be discussed extensively in Section 7. The English inchoative expression the vessel is destroyed has a causative counterpart the torpedo destroyed the vessel . Now, the language-specific construction to derive the anticausative from the causative in English for the verb destroy is to use an expression with the verb to be. From a cross-linguistic perspective, this alternation is an example of an “anticausative” typological strategy, using the terminology of Haspelmath (1993:91), because the inchoative is transparently derived from the causative. The main claim of the semantic map approach is that a metric on meaning (“semantic map”) can be established purely on the basis of many language-specific expression metrics (“constructions”), averaged over a diverse sample of languages. Cross-linguistic metrics (“strategies”) are not necessary for this goal.[6] 6. Coding and BehaviorThere are many different ways to establish a language-specific expression metric. In the next section, concrete examples of three different metrics on the same data will be discussed in detail. One somewhat atypical aspect of the following examples is that the metrics are based on pairs of expressions, not on single expressions as in traditional semantic maps (Haspelmath 2003). This approach—considering the relation between two expressions—is reminiscent of Keenan’s (1976:306-307) “transformational behavior”. Following Keenan, the terms “coding” and “behavior” have become widespread for the analysis of grammatical relations. Generalizing this distinction, I will use the term “coding properties” for properties of individual expressions, while “behavioral properties” are properties of the relation between expressions. The properties may be pragmatic, semantic, or syntactic. And of the syntactic ones, some concern properties internal to a single sentence [i.e. “coding”, MC] and others concern the relation between a b-sentence and some modification of it [i.e. “behavior”, MC]. (Keenan 1976:312) Under this definition, the opposition coding vs. behavior is independent from the opposition construction vs. strategy, as discussed in the previous section. There are thus four logically possible combinations that represent different approaches to characterizing and comparing expressions. First, a coding strategy is a cross-linguistic classification of the structure of a particular expression. This is the most prototypical kind of approach in linguistic typology. The classic example is the typology of relative clause structures distinguishing types like “relative pronoun strategy” or the “internally headed relative clauses” (Lehmann 1984; Comrie & Kuteva 2005). Second, a behavioral strategy is a cross-linguistic classification of the relation between various expressions (typically two, but possibly more). A classic example is the relation between a regular matrix sentence like John swept the floor and the corresponding action nominal construction John’s sweeping of the floor (cf. Keenan 1976:321). For this behavior, a cross-linguistic classification of possible strategies used by human languages has been developed by Koptjevskaya-Tamm (1993, 2005). Third, constructional coding is a characterization of the language-specific form of a expression. This is the typical information that is used in traditional semantic maps. The more similar two expressions are in terms of their constructional coding, the closer their meaning (when averaged over a large number of languages). Finally, constructional behavior is the fourth possibility. This method of characterizing expressions is not very widely acknowledged in the typological literature, but it will be the approach that I will use in the case study in the next section. The basic idea is to compare the combined language-specific forms of all alternative expressions that are relevant for the behavior. 7. Case Study7.1 Causative/inchoative alternationsAs an example of the approach presented here, I will reanalyze the data from Haspelmath (1993) on the causative/inchoative alternation. In his paper Haspelmath addresses the question as to how languages mark the predicate in the alternation between an inchoative expression like the water boiled and a causative expression like the man boiled the water . In the case of the English predicate boil there is no difference in the marking, but for other alternations, like die/kill or be destroyed/destroy, the difference between the inchoative and the causative version is reflected in the lexical or morphological form of the predicate. The approach of Haspelmath’s study is to investigate cross-linguistic strategies of expressing the relation between inchoative and causative meanings, but that aspect of his study will not be the main focus of this paper (some preliminary hints on the relation between strategies and meaning will be given at the end of Section 7.2). Instead, I will investigate the relations between the meanings of the predicates by investigating the language-specific marking that is used to express the inchoative/causative alternation. Haspelmath investigated the inchoative/causative alternation for 31 analytical primitives (“lexical meanings”) in 21 languages. The 31 meanings investigated are repeated here in Table 2 (adapted from Table 2 in Haspelmath 1993:97).[7] The translations of these meanings in all 21 languages are added as an appendix to Haspelmath’s paper, allowing for the current reanalysis of the data.[8]
Table 2: Inchoative/causative pairs investigated in Haspelmath (1993)
I will use the language-specific marking of the inchoative/causative alternation of the meanings listed in Table 2 as a proxy to the measurement of the similarity between the meanings. For example, the English expression of meaning 1, wake up/wake up, does not use any marking to differentiate inchoative from causative. This means that meaning 1 is somewhat alike to meaning 2, in English expressed as break/break, which likewise does not differentiate inchoative from causative. A similar situation is found in French. The French expressions of meanings 1 and 2 also use the same construction (viz. a reflexive pronoun with the inchoative: se réveiller/réveiller and se briser/briser, respectively). This is again an indication that these two meanings are somewhat alike. In German, though, meanings 1 and 2 do not use the same process (viz. an ablaut-like alternation in aufwachen/aufwecken vs. no differentiation in zerbrechen/zerbrechen, respectively), which is an indication that the meanings 1 and 2 are also somewhat different. The marking of the inchoative/causative alternation on the predicate is just one of very many possible approaches to investigating similarity between meanings, or, to paraphrase a claim made in Section 3, any notion of similarity is a question of perspective and is not in any sense pre-established by the nature of the expressions investigated. The rather abstract nature of the notion of similarity as used here (i.e. the formation of the inchoative/causative alternation) is appealing because it allows for the comparison of otherwise difficult-to-compare meanings, like “wake up” and “break”.[9] In the following section, I will discuss three different ways to operationalize this language-specific notion of similarity between expressions. 7.2 Metric A: Language-specific constructionsThe first example of a language-specific similarity between expressions will be based on establishing language-specific constructions. I will here define a construction as a regular morphosyntactic relation between an inchoative and a causative verb form. Such relations are purely language-specific (see the appendix for a complete survey of all constructions distinguished for this paper). For example, in English, the 31 meanings shown in Table 2 can be classified as belonging to seven language-specific constructions. There is one large class consisting of verbs that do not show any difference in morphology between inchoative and causative usage (viz. wake up, break, burn, open, etc.). The remaining six classes each consist only of one meaning, using different inchoative/causative alternations in each case (viz. die/kill, learn/teach, be destroyed/destroy, get lost/lose, go out/put out , and rise/raise). As an example, just the first three meanings are shown in Table 3, all three being marked as belonging to the same class (called “E-1”, where the “E” indicates that this is a language-specific class for English only). For other languages, these classifications will look different. For example, in French there are five different classes. First, there is one large class in which the inchoative form is marked with a reflexive pronoun (e.g. 1: se réveiller/réveiller and 2: se briser/briser ). Second, there is another large class in which there is no difference between inchoative and causative verb forms (e.g. 3: brûler/brûler). Then, there is a small class where the causative is formed by adding the verb faire (among the current 31 meanings this is found only for 13: fondre/faire fondre and 18: bouillir/faire bouillir). Finally, there are two French expressions that do not have any parallel among the current 31 meanings, so they make up their own class (viz. 4: mourir/tuer and 14: être détruit/détruir ).
Table 3: Excerpt of language-specific classes for inchoative/causative alternations
Once established for all languages in the sample, these language-specific classes (“constructions”) can now be used to calculate the (dis)similarity between the primitives (“lexical meanings”). Basically, every pair of meanings is considered separately for all 21 languages, and the number of languages is counted for which the two meanings belong to different constructions. The higher this number, the more languages put the meanings in different constructions, indicating that the meanings are different. For example, considering meanings 1 and 2 in the excerpt of the data shown in Table 3, these two meanings belong to the same class in English and in French, but to different constructions in just one language, namely German. So, the distance between meaning 1 and 2 is “1”. Likewise, the distance between 1 and 3 is “2” because two of these languages treat them differently, and between 2 and 3 the distance is “1” because only French treats them differently. The establishment of the language-specific constructions and the counting of differences together are a metric on meanings, and the result is a list of distances between all pairs of meanings. A different way of performing exactly the same calculation is obtained by a reformulation of the language-specific constructions into language-specific distance matrices. This reformulation might seem somewhat cumbersome at first, but it will allow for a much wider array of possible analyses—a few of which will be discussed in the next sections. The basic idea is to consider a language-specific construction to be a very simple notion of dissimilarity. As defined earlier, a construction can be considered to be a language-specific metric on expressions (cf. Table 1 and the discussion in Section 5). Such a metric only allows for the options “identical” (i.e. a dissimilarity/distance of “0”) or “different” (i.e. a dissimilarity/distance of “1”). From the perspective of English, the meanings 1, 2, and 3 are all identical (i.e. they belong to the same construction), which translates to a distance of zero between all pairs of these meanings. Of course, also the distance between each meaning and itself is zero (they necessarily belong to the same construction), so the result of reformulating the first three English meanings into a language-specific distance matrix is a matrix with all zeros (cf. the leftmost matrix in Figure 1—for convenience of presentation all matrices are shown completely, although distance matrices redundantly duplicate each entry in the upper and lower triangle). The same procedure can also be used for French and German, which will result in some distances of “1” because not all three meanings belong to the same class in these languages. Given these language-specific distance matrices, the cross-linguistic distance matrix on the meanings can now easily be computed by summing up these three matrices (cf. the rightmost matrix in Figure 1).[10]
Figure 1: Language-specific constructions as distance matrices. Adding them together results in a cross-linguistic distance matrix on the meanings
Doing these calculations for all 31 meanings in all 21 languages results in a 31×31 cross-linguistic distance matrix giving the dissimilarity for all pairs of meanings—an excerpt of which is shown in Table 4. The minimal value in this table is zero (i.e. the meanings belong to the same construction in all 21 languages), and the maximum is 21 (i.e. the meanings belong to different constructions in all 21 languages). These values can be normalized to the [0,1] interval by dividing them by 21 (shown in parentheses in the table). Just to give some perspective on these numbers, it appears that the pairs “close”–“open”, “open”–“break”, and “close”–“break” are relatively similar (they belong to the same construction in about half of the languages investigated). In contrast, “die/kill” is highly dissimilar from all others, as might have been expected, because the inchoative/causative alternation for this meaning is suppletive in most languages and thus different from all other alternations in the same language.
Table 4: Excerpt of the cross-linguistic dissimilarity matrix on meaning as established by summing up over all 21 language-specific classifications
A complete analysis of the full 31×31 distance matrix will not be pursued here, but one quick example will be given to indicate possible routes of analysis (see Cysouw 2008 for a more elaborate discussion). When multidimensional scaling is applied to the cross-linguistic distance matrix, then the first dimension (i.e. the dimension that explains most of the variation) appears to be related to the “scale of likelihood of spontaneous occurrence” (Haspelmath 1993:105).[11] On one side of this scale predicates are found that prototypically do not need an agentive instigator, like “boil”, “freeze”, and “burn” (and in the multidimensional scaling “die/kill” is also found to belong to this side). The other side of the scale holds such events that normally have a human agent, like “gather”, “connect”, or “change”. This scale was originally proposed by Haspelmath to explain the preference of certain meanings for particular behavioral strategies. Specifically, he argued that those meanings that are typically in need of a human instigator cross-linguistically have a preference for an anticausative coding strategy (i.e. the inchoative is derived from the causative), while the meanings on the other side of the scale have a preference for a causative strategy (i.e. the causative is derived from the inchoative). Now, instead of deriving the scale of likelihood of spontaneous occurrence from behavioral strategies, as Haspelmath did, in this paper the scale is purely based on the analysis of language-specific constructions. The semantic scale of likelihood of spontaneous occurrence (here defined as the first dimension of the MDS of the metric on meaning) can then be correlated empirically with the proportion of languages that use an anticausative strategy (see Figure 2).[13] The correlation is almost perfect ( r=.83, p<10 -8). This example indicates that a linguistic scale can be conceived of as a (significant) correlation between meaning-similarity and form-similarity. Figure 2: Correlation between preference for anticausative coding strategy and the first dimension of the MDS of the metric of meaning.
7.3 Metric B: Algorithmically approximating constructionsThe reformulation of constructions as language-specific metrics on expressions, as discussed in relation to Figure 1 above, allows for a wide variety of other approaches to establishing a semantic map. The basic idea of this reformulation is that for each language a language-specific distance matrix is calculated describing how similar the expressions of the meanings are from the perspective of each language individually. The cross-linguistic distances then are the result of simply summing up over all these language-specific distances. Using constructions, as done in the previous section, the language-specific matrices will only consist of “0” (indicating “same construction”) and “1” (indicating “different constructions”). However, all values in between “0” and “1” can also be used to indicate that two constructions are neither completely different nor completely similar. For example, one might argue that the German alternations aufwachen/aufwecken and versinken/versenken are different constructions, but also somewhat alike. They both involve a kind of ablaut, though the details are different. Neither considering them to be completely different nor completely identical will do justice to the empirical situation. To deal with such a situation, a gradient language-specific distance can be used. For example, one could set the language-specific distance between the two alternations above as 0.75 (see Table 5). The specification of gradient dissimilarities can be performed on the basis of a detailed analysis of each language individually. However, it is also possible to use a general method for measuring language-internal similarity. One such approach will be discussed in this section, and a simpler but also less satisfying method will be discussed in the next section.
Table 5: Different language-specific distances of some German inchoative/causative alternations
One method of comparing inchoative/causative alternations within the structure of a single language is to analyze each alternation as a collection of changes of letters needed to get from the inchoative to the causative string of letters. Changes are either a deletion of an existing letter or an insertion of a new letter. To match linguistic intuitions about what makes a similar change, the method distinguishes between making a change at the start of a word, at the end of a word, or in the middle of a word. For every inchoative/causative pair, this leads to a list of changes on how to get from the inchoative to the causative form. So, for example, to get from rise to raise only one change is needed, namely an <a> has to be inserted in the middle of the word. To compare two alternations, the number of shared letter changes is counted and then normalized by the maximum number of changes attested. The distance between two alternations will then be the complement of this value (i.e. 1−shared/maximum). For example, to get from the German inchoative aufwachen to causative aufwecken the following four changes are needed: 1) deletion of <a> inside the word (“ aufwchen”) 2) deletion of <h> inside the word (“ aufwcen”) 3) insertion of <e> inside the word (“ aufwecen”) 4) insertion of <k> inside the word (“ aufwecken”) To get from German inchoative versinken to causative versenken the following two changes are needed: 1) deletion of <i> inside the word (“ versnken”) 2) insertion of <e> inside the word (“ versenken”) These two sets of changes have one change in common (“insertion of <e> inside the word”), and the maximum number of changes needed is “4” (for the aufwachen/aufwecken alternation), so the distance between the two alternations is 1−1/4=.75 (cf. Table 5). This algorithm could be improved in various ways.[14] However, the main point is that it is relatively easy to get a rough estimate of the language-internal dissimilarity between two inchoative/causative alternations.[15] To get from language-specific dissimilarities to a cross-linguistic distance matrix, all individual matrices are added together. An excerpt of the resulting matrix is shown in Table 6, which can be compared with the same selection shown in Table 4. Although the two tables are not completely identical, the values are astonishingly close. The complete correlation between the results of this algorithmic notion of dissimilarity and the dissimilarity based on the manually established language-specific constructions is shown in Figure 3 ( r=.91). Shown on the x-axis in this figure are the dissimilarities (“distances”) from the metric discussion in the previous Section 7.2. On the y-axis, the distances from the algorithmic approach as discussed in this section are shown. The close match between these two methods suggests that automatic approaches can be very useful in the establishment of cross-linguistic metrics on meaning. In general, it appears that the errors introduced by the linguistically naive algorithm are easily corrected by summing up over many languages.
Table 6: Excerpt of the cross-linguistic distance matrix as established by the algorithmic approach
Figure 3: Correlation between cross-linguistic distances as established by language-specific classes and by the algorithmic approach
7.4 Metric C: Simplistic string-based similarityThe good results of the algorithmic approach to establishing language-specific similarities prompted me to try out an even simpler, even more linguistically naive algorithmic approach. It is based on the longest COMMON SUBSTRING measure of similarity between two strings of letters. This similarity consists of the length of the longest consecutive stretch of letters shared between two expressions. So, for example, house and mouse share 4 letters in a row. To use this measure of similarity for inchoative/causative alternations, I pasted the inchoative and the causative forms together into one string without spaces (e.g. French seréveillerréveiller or sebriserbriser) and established the longest common substring (in the French example this would be “2” for the string “se”). This approach of course finds all kinds of small random similarities (e.g. wakeupwakeup and breakbreak also have a longest common substring of “2” for the string “ ak”), and in general it only works well with concatenative morphology or morphologically independent markers (like the reflexive se in the French example above). Figure 4 shows the relation between the distances from this very simplistic approach (shown on the y-axis) to the distances from the linguistically sophisticated approach using language-specific classes, as discussed in Section 7.2. The match between this extremely simple measurement of language-specific similarity to the linguistically sophisticated similarity using language-specific classes is not as good as for the more elaborate algorithmic approach from the previous section ( r=.61, cf. Figure 4 with the previous Figure 3), though the correlation is still highly significant (Mantel test p<.00001), indicating that even with similarity measures which are linguistically very naive relatively good overall results are possible. Figure 4: Correlation between cross-linguistic distances as established by language-specific classes and by the longest common substring.
8. ConclusionBy using the world’s linguistic diversity, the study of meaning can be transformed from an introspective inquiry into a subject of empirical investigation. For this to be possible, the notion of meaning has to be operationalized by defining the meaning of an expression as the collection of all contexts in which the expression can be used. Under this definition, meaning can be empirically investigated by sampling contexts. A semantic map is a technique to show the relations between such sampled contexts. Or, formulated more technically, a semantic map is a visualization of a metric on contexts sampled to represent a domain of meaning. Or, put more succinctly, a semantic map is a metric on meaning. The relation between different contexts/meanings can be investigated by looking at their expressions in many languages. The more similar these expressions when averaged over all languages studied, the more similar the contexts. So, to investigate the similarity between contexts, only judgments about the local similarity between expressions within the structure of individual languages are needed. In general, this similarity between language-specific expressions is a special—language-specific—metric between contexts. A metric on meaning, then, is the cross-linguistic average of many language-specific expression metrics. A language-specific expression metric can be very fine-grained, and to a large extent automatically retrieved, opening up the possibility of speeding up the empirical study of meaning. It is important to realize, however, that for any resulting semi-automatically retrieved metric on meaning, the interpretation (“the meaning of the metric”) is of course still in the eye of the beholder, namely, the human investigator. AcknowledgmentsI thank Martin Haspelmath and Caterina Mauri for helpful comments on how to improve the presentation of the somewhat tedious subject of this paper. Further, many of the concepts used in this paper arose in discussion with Bernhard Wälchli and should often just as well be considered his ideas (cf. Wälchli & Cysouw 2010). I of course take complete responsibility for any remaining inconsistency or lack of clarity. ReferencesComrie, Bernard and Tania Kuteva. 2005. Relativization strategies. World Atlas of Language Structures, ed. by Martin Haspelmath, Matthew S. Dryer, David Gil and Bernard Comrie, 398-405. Oxford: Oxford University Press. Croft, William. 2001. Radical Construction Grammar: Syntactic theory in typological perspective. Oxford: Oxford University Press. -----. 2003. Typology and universals, 2nd edition. Cambridge: Cambridge University Press. (Cambridge Textbooks in Linguistics). -----. 2007. Exemplar semantics. Unpublished manuscript, available online at http://www.unm.edu/~wcroft/WACpubs.html. Croft, William and Keith T. Poole. 2008. Inferring universals from grammatical variation: Multidimensional scaling for typological analysis. Theoretical Linguistics 34/1.1-37. doi:10.1515/thli.2008.001 Cysouw, Michael. 2007. Building semantic maps: The case of person marking. New Challenges in Typology, ed. by Bernhard Wälchli and Matti Miestamo, 225-248. Berlin: Mouton de Gruyter. (Trends in Linguistics: Studies and Monographs 189). -----. 2008. Generalizing scales. Scales, ed. by Marc Richards & Andrej Malchukov, 379-396. Leipzig: Institut für Linguistik, Universität Leipzig. (Linguistische Arbeits-Berichte 86). Dahl, Östen. 1985. Tense and Aspect systems. Oxford: Blackwell. Goldberg, Adele E. 2006. Constructions at work: The nature of generalization in language. Oxford: Oxford University Press. Haiman, John. 1985. Natural syntax. Cambridge: Cambridge University Press. Haspelmath, Martin. 1993. More on the typology of inchoative/causative verb alternations. Causatives and transitivity, ed. by Bernard Comrie and Maria Polinsky, 87-120. Amsterdam: Benjamins. (Studies in Language Companion Series). -----. 1997. Indefinite pronouns. Oxford: Clarendon. (Oxford Studies in Typology and Linguistic Theory). -----. 2003. The geometry of grammatical meaning: Semantic maps and cross-linguistic comparison. The new psychology of language: Cognitive and functional approaches to language structure, ed. by Michael Tomasello, vol. 2, 211-242. Mahwah, NJ: Erlbaum. -----. 2010. Comparative concepts and descriptive categories in cross-linguistic studies. Language 86. doi:10.1353/lan.2010.0021 Keenan, Edward L. 1976. Towards a universal definition of ‘subject’. Subject and topic, ed. by Charles N. Li, 303-333. New York, NY: Academic Press. Keenan, Edward L. and Bernard Comrie. 1977. Noun phrase accessibility and universal grammar, Linguistic Inquiry 8/1.63-99. Koptjevskaja-Tamm, Maria. 1993. Nominalizations. London: Routledge. -----. 2005. Action nominal constructions. World Atlas of Language Structures, ed. by Martin Haspelmath, Matthew S. Dryer, David Gil and Bernard Comrie, 254-257. Oxford: Oxford University Press. Lehmann, Christian. 1984. Der Relativsatz: Typologie seiner Strukturen, Theorie seiner Funktionen, Kompendium seiner Grammatik. Tübingen: Narr. Levinson, Stephen C. 2003. Space in language and cognition: Explorations in cognitive diversity. Cambridge: Cambridge University Press. (Language, Culture & Cognition 5). Levinson, Stephen C. and Sérgio Meira. 2003. 'Natural concepts' in the spatial topological domain – Adpositional meanings in crosslinguistic perspective: An exercise in semantic typology. Language 79/3.485-516. doi:10.1353/lan.2003.0174 Majid, Asifa, Melissa Bowerman, Miriam van Staden and James S. Boster. 2007. The semantic categories of cutting and breaking events: A crosslinguistic perspective. Cognitive Linguistics 18/2.133-152. doi:10.1515/cog.2007.005 R Development Core Team. 2007. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Wälchli, Bernhard. 2005. Co-compounds and natural coordination. Oxford: Oxford University Press. Wälchli, Bernhard and Michael Cysouw. 2010. Lexical typology through similarity semantics: Toward a semantic map of motion verbs. Linguistics. doi:10.1515/ling-2012-0021 Wierzbicka, Anna. 1996. Semantics: Primes and universals. Oxford: Oxford University Press.
Appendix: Language-Specific Classes of Causative/Inchoative Alternations
[1] It might be worthwhile to consider more precise definitions of such chunks of meaning as used in typology, for example using Natural Semantic Metalanguage (Wierzbicka 1996). [2] The terms “comparative concept” as used by Haspelmath (2010) and “etic grid” as used by Levinson & Meira (2003: 487) are highly similar, if not identical, concepts to what I call “analytical primitive”. [3] For some first attempts at comparing the meaning of language-specific expressions, see Cysouw (2007) and Wälchli & Cysouw (2010). [4] It is an open question whether different approaches to measuring meaning converge. If something like “the” meaning exists, then this should be the case. Given the framework for investigating meaning as sketched in this paper, this question becomes an empirical problem. [5] This approach assumes that every meaning is expressible in all human languages. The expression of a meaning might be easier in some languages and take more effort in others, but it is possible everywhere. However, there are various obvious complications with this assumption; see for example Levinson (2003) for a challenge to this assumption regarding the expression of spatial concepts. Further, I will ignore the complications arising from the fact that most languages will have many different ways to express a particular meaning. This is not problematic for the goal of computing meaning similarities, but the mathematical details will become a bit more involved. [6] One auspicious prospect is that an association between a cross-linguistic metric (“strategy”) and a language-specific metric (“construction”) represents a generalization of what is known in linguistics as a “hierarchy” or a “scale”. Establishing such a correlation is not trivial because language-specific metrics cannot be compared directly across languages (see the example at the end of Section 7.2 for a first glimpse of this prospect and see Cysouw 2008 for a more elaborate discussion). [7] The primitives used in this paper represent a somewhat special kind of lexical meaning because they are neutral with respect to the causative/inchoative alternation. For example, the English pair kill/die is considered to be a single primitive here, notwithstanding the lexical suppletion. It is important to realize that not all languages have suppletion for the same primitives, so cross-linguistically the pair kill/die has to be treated as equivalent to a non-suppletive pair like destroy/be destroyed. [8] To simplify the calculations, I have maximally included one expression for each meaning in each language. In some cases, Haspelmath lists more than one possible expression, and in those cases I have semi-randomly chosen one of the options. If possible, I have discarded idiosyncratic alternations showing inchoative/causative morphology that was not found in any other sampled expressions of the same language. Only when all alternatives used constructions which are also found elsewhere did I randomly select one of them. This was only necessary in a handful of cases. [9] Most theories of meaning will not have much to say about the relation between “wake up” and “break” other than coincidental points such as the observation that in English the metaphor break of day is used for the morning, which is also the prototypical time to wake up. [10] This reformulation opens up the possibility of comparing the structure of lexicalization between languages. This can be done by correlating the language-specific distance matrices from Figure 1. In effect, each distance matrix represents the language-specific perspective on the relation between the meanings. The similarity between two such matrices can be interpreted as a measure of how similarly languages deal with the coding of meanings. The details and implications of this approach to language comparison have to be left for another paper though. [11]12 For this calculation, classic multidimensional scaling was used through the implementation “cmdscale” in the statistical environment R (R Development Core Team 2007). All other calculations and graphs in this paper were also produced by using R. [13] Haspelmath, following up on earlier work by Nedjalkov, uses the fraction of anticausative by causative (A/C) strategies as an index for the cross linguistic preference for either of these strategies. The usage of this particular fraction is unfortunate because the resulting values are very unevenly distributed (they range between zero and infinite). I have used A/(A+C) here instead. Another possibility would be to use log(A/C). [14] There are various questionable decisions being made in this algorithm. First, it operates on letters, where ideally it would work on sounds. Second, there is no reason to restrict the algorithm to only insertions and deletions—also exchanges could be used, or other operations. Further, every insertion and deletion is equally weighted, though some might be more significant than others. And instead of dividing by the maximum number of changes one could also use another normalization like dividing by the average number of changes. [15] I thank Hagen Jung for assistance with the implementation of this algorithm. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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