1. Introduction

1What is the relationship between language universals and linguistic variation? A passage from Geertz, serving as the tagline of an email I received from a colleague, presents an answer:

…the notion that the essence of what it means to be human is most clearly revealed in those features of human culture that are universal rather than in those that are distinctive to this people or that is a prejudice that we are not obliged to share…It may be in the cultural particularities of people — in their oddities — that some of the most instructive revelations of what it is to be generically human are to be found… (Geertz 1973:43)

2This quotation might be taken to assume that there are two positions on universals of human culture, including universals of human language. The first is a position that Geertz calls ‘uniformitarianism’, and we will call extreme universalism: the view that all cultures, including all languages, possess certain specific traits in common, and these represent our common humanity. In linguistics, these are called unrestricted universals, and form the basis of what is called Universal Grammar in Chomskyan linguistic theory. Revisiting the Geertz paper, it is clear that he does not believe such universals to be substantive or insightful into human nature. The diversity of cultural practices stands as an empirical refutation of extreme universalism. Likewise, the diversity of human languages, as revealed in language documentation and in typology, stands as an empirical refutation of extreme universalism in linguistic theory.

3But what is the alternative? The second position is one that could be called extreme relativism: each culture is unique (its ‘particularities’) and even incommensurable with other cultures; our common humanity is to be found perhaps only in our creativity and cultural uniqueness. That position is widespread in contemporary anthropology. But it is not the only position, nor is it the position that Geertz advocated:

Once one abandons uniformitarianism,…relativism is a genuine danger; but it can be warded off only by facing directly and fully the diversities of human culture…and embracing them within the body of one’s conception of man, not by gliding past them with vague tautologies and forceless banalities (Geertz 1973:41)

4It is difficult to imagine what insights into human nature might look like if human nature is not a matter of unrestricted universals. A forthcoming paper by Evans and Levinson is titled ‘The myth of language universals’; but it turns out that language universals are meant in a very narrow sense, namely unrestricted, exceptionless properties of human languages. Indeed, the insight of Greenbergian typology is that there are language universals but they are not manifested as properties common to all languages, as in the Chomskyan approach to universals. The third position can be called typological universalism: cultures, or at least languages, vary in innumerable ways; but there are patterns of variation that reflect universal properties that we might call the nature of language, as Geertz describes the nature of man:

The notion that unless a cultural phenomenon is empirically universal it cannot reflect anything about the nature of man is about as logical as the notion that because sickle-cell anemia is, fortunately, not universal, it cannot tell us anything about human genetic processes. It is not whether phenomena are empirically common that is critical in science…but whether they can be made to reveal the enduring natural processes that underlie them (Geertz 1973:44)

5This is the essence of the typological approach to language: by examining diversity, one can use techniques to uncover the enduring processes that underlie language and reveal its nature.

6The early, classic technique was the implicational universal, introduced by Greenberg in his seminal paper on language universals over forty years ago. A Greenbergian language universal such as ‘When the descriptive adjective precedes the noun, the demonstrative and the numeral, with overwhelmingly more than chance frequency, do likewise (Universal 18, Greenberg 1966/1990:69) allows for language variation — adjectives may precede or follow the noun — but constrains it — demonstratives and numerals are overwhelmingly likely to precede the noun as well, if the adjective precedes. (The fact that ‘language universals’ is still taken to mean unrestricted universals of the form ‘All languages have X’, as in Evans and Levinson’s paper, is a reflection of how difficult typological universals are to grasp, or the dominance of Chomskyan linguistics, or both.) Evans and Levinson acknowledge such universals, but focus on the fact that they have exceptions. Yet this is a fact that Greenberg already observed in his paper, and anyway, this is not the underlying process that Greenberg is seeking. He proposes a competing motivation model, with a principle of dominance (a preference of one order over another) competing with a principle of harmony (two orders being harmonic, such as two modifiers either preceding or following the noun). These competing motivations must be interpreted probabilistically, as any realistic quantitative model of empirical phenomena, not least human behavior, must be. What matters is not that there are exceptions to the implicational universal but that the implicational universal itself is just an approximation to a richer empirical reality that is nevertheless governed by common principles.

7In this paper, I will describe the recent use of some quantitative techniques to infer language universals from the structural diversity of human languages. The fact is that human languages are structurally more diverse than even many typologists are willing to admit. First, there are no universals of formal grammatical and lexical categories, which are generally taken to be the building blocks of syntactic theories (formal syntactic theories, at least). This is coming to be widely accepted by typologists with regard to the category of ‘subject’, but is still resisted for basic parts of speech such as ‘noun’ and ‘verb’ (Croft 2001). Nevertheless, as argued in the works cited, there is ample empirical reason to reject all formal categories as universals.

8Second, there are no universals of conceptual categories underlying formal linguistic categories either. That is, there do not exist broad categories such as ‘object’ or ‘process’ or ‘containment’ that directly underlie formal linguistic categories. This is an alternative that is sometimes proposed for the analysis of formal linguistic categories, but it too falls in the face of linguistic diversity: linguistic categories are diverse not just in their formal linguistic behavior, but in their conceptual structure as well.

9Nevertheless, languages are not completely unconstrained in the structure of their grammatical and lexical categories. The diversity that has been uncovered in large scale typological studies, or even more clearly in finer-grained typological and even individual language studies, can be analyzed using quantitative techniques. These techniques reveal that what forms the basis of human conceptualization in language are not broad conceptual categories but particular situation types, holistically conceived: that is, their complex Gestalt of semantic properties are apprehended by speakers holistically. Numerous examples of these will be given in §§2-3. Particular situation types are related to each other, and the conceptual relationships between situation types are also universal. These universals are only revealed through the incredible diversity of language structures.

2. Variation and universals across languages

10One important aspect of language in which both extreme universalist and extreme relativist claims have been made is in categorization. Categorization is of course a fundamental property of the linguistic system. Words define categories because (apart from proper names), they are used to denote a range of entities. The same is true of grammatical morphemes and constructions; in fact, the range of uses of grammatical morphemes and constructions is even greater than most words.

11Virtually all linguists assume that there is some semantic coherence in the applicability of a single word or morpheme to multiple entities in the world. The notion of ‘semantic coherence’ can be made more precise as the following principlegoverning the form-meaning relation in language: if two meanings are expressed by the same form, then they have been judged as similar by at least some speakers.

12The basic fact of linguistic diversity now asserts itself: a word in one language refers to a different set of entities than a word in another language. For example, English put on and put in divide up placement actions much differently than the Korean counterparts: in English, one puts a cassette in a case and an apple in a bowl, but puts a top on a pen; whereas Korean uses the verb kkita is used for the first and last of those actions, but nehta for the middle action (and this is only a subset of the variation found in this domain; Bowerman and Choi 2001:480-84). The diversity of the form-meaning mapping and the differences in categorization that it implies comes out especially clearly when one examines a large number of situation types in a single semantic domain where multiple words or constructions are used. For example, Bowerman and Choi’s comparison of English and Korean placement actions in their paper uses thirteen placement actions which are all slightly but significantly different from one another.

13This fact poses a serious problem for the extreme universalist position. On the face of it, the concepts denoted by words cannot be the same across languages if the words have different denotations (and this is the norm rather than the exception). An extreme universalist could argue in defense that the differences in linguistic categorization across languages are relatively minor and uninteresting compared to the similarities in the conceptual categories defined by linguistic forms.

14An extreme relativist would have much less difficulty with this fact of diversity of linguistic categories:if two meanings are expressed by the same form in one language and by different forms in another language, then speakers of the two languages conceptualize the two meanings in different ways. There is at least one problem with the relativistic analysis: it assumes that linguistic forms are monosemous, that is, there is a single general meaning that provides a set of individually necessary and jointly sufficient conditions covering all and only the uses of a linguistic form. An alternative analysis is polysemy: a word has multiple uses that are semantically related but the set of uses cannot be defined by a set of necessary and sufficient conditions. Cruse (1992) and Croft (2001:112-19) provide several arguments questioning the plausibility of monosemy analysis. For instance, different uses of a linguistic form often have different grammatical behavior, suggesting that the uses do not form a single coherent linguistic category. Also, most attempts to provide monosemy analyses of linguistic categories provide only necessary, but not sufficient, conditions. The polysemy account implies that speakers conceptualize individual meanings/uses in basically the same ways, but that one language will manifest some similarity relations among meanings by linguistic categorization but another language will manifest other similarity relations. The results of research such as Kay and Kempton (1984) and Choi and Bowerman (1991), who show that linguistic category boundaries influence attention to distinguishing features across concepts, is compatible with the polysemy approach as well as the monosemy approach.

15There is actually an empirical typological way to investigate this question. One can compare the linguistic categorization of meanings across a number of languages for a set of meanings or uses in a particular semantic domain, and examine the semantic coherence and consistency of the resulting classification of the meanings with a large number of languages. The results of this type of crosslinguistic analysis in typology disconfirms both the extreme universalist position and the extreme relativist position, and supports a typological universalist position.

16The type of analysis described in the preceding paragraph is called the semantic map model in typology (Croft 2003, Haspelmath 2003). The approach is essentially distributional analysis, but done across meanings and across languages. For example, Haspelmath’s semantic map analysis of indefinite pronouns looks at nine different meanings that are expressed by indefinite pronoun forms across 40 languages. The semantic, crosslinguistic distributional data for two languages in Haspelmath’s sample, Romanian and Kazakh, are given in Table 1:

Table 1. Romanian indefinite pronouns (data from Haspelmath 1997:264-65)

	Rumanian				Kazakh
	va-	vre- -un	ori-	ni-	älde-	bir	bolsa da	eš
Specific known	Y	N	N	N	Y	Y	N	N
Specific unknown	Y	N	N	N	Y	Y	N	N
Irrealis nonspecific	Y	N	N	N	N	Y	N	N
Question	Y	Y	N	N	N	Y	Y	N
Conditional	Y	Y	N	N	N	Y	Y	N
Comparative	N	N	Y	N	N	N	Y	N
Free choice	N	N	Y	N	N	N	Y	N
Indirect negation	N	Y	N	Y	N	Y	N	N
Direct negation	N	N	N	Y	N	N	N	Y

17Semantic, crosslinguistic distributional analysis—the essence of the typological method (Croft 2003) often yields coherent results, that is, the crosslinguistic data form a regular pattern. In this particlar case, and others like it, the regular pattern can be represented as a conceptual space. The conceptual space for indefinite pronouns that is proposed by Haspelmath is given in Figure 1:

18The conceptual space is an arrangement of the meanings into a graph (network) structure such that any language-specific form, such as the indefinite pronouns of Romanian and Kazakh, can be mapped onto a single, connected subgraph of the total graph (the Semantic Map Connectivity Hypothesis; Croft 2001:96). The subgraph representing the denotation of the language-specific form is that form’s semantic map. The semantic maps for the Romanian and Kazakh pronouns are given in Figure 2, using a bounded shape to pick out the relevant subgraph (Haspelmath 1997:264, 288):

19The semantic map model offers a novel way to separate the language-specific from the language-universal. The categories defined by linguistic forms—the semantic maps in Figure 2—are language-specific (particular). The structure of the conceptual space—the meanings and the relationships between them represented by the graph structure in Figure 1—is universal: it is the foundation on which speakers of any language form their linguistic categories. The foundation provides the constraint that any language-specific category must denote a connected subgraph of the conceptual space. As far as the semantic map model is concerned, the formal linguistic categories can vary indefinitely otherwise. (There is evidence of constraints here as well, but they cannot easily be represented in the semantic map model, and have not been explored in detail; so we will not discuss them in this paper.)

20 Before investigating the implications of the existence of a universal conceptual space for extreme universalist and extreme relativistic theories, I will describe a technical improvement on the semantic map model, namely, the use of multidimensional scaling to construct the conceptual space, as applied to another example, the semantics of spatial adpositions.

21While the theory and method behind the semantic map model is valid, the practical use of it is limited. There is no measure of goodness of fit for a semantic map model. Instead, typologists generally allow for no exceptions: if any language in the sample subsumes two meanings under one form, then those meanings must be linked in such a way that the network satisfies the Semantic Map Connectivity Hypothesis for all languages in the sample. Also, there is no interpretation of the spatial dimensions of the model. The spatial arrangement in Figure 1 is just a matter of visual convenience; all that matters are the links between meanings (the lines in Figure 1). A semantic map is usually constructed by hand, and therefore is constructible for only a small number of meanings, such as the nine in Figure 1; if the data is less clean, then even that is impossible. Finally, there is no mathematically well understood and computationally tractable technique to construct a conceptual space automatically.

22Multidimensional scaling (MDS) allows one to construct conceptual spaces automatically, without the problems in the semantic map model (Croft and Poole 2008). MDS constructs a spatial model, so that similarity, more precisely dissimilarity, is modeled as distance in a low-dimensional space. The spatial dimensions are therefore semantically interpretable. For example, in Croft and Poole (2008:26), a two-dimensional spatial model of tense-aspect data from Dahl (1985) clearly has a tense dimension and an aspect (perfective-imperfective) dimension. Lower-dimensional spatial models are superior because they constrain the analysis further; the more dimensions are added, the easier it is to make every point close to every other point with which it shares a linguistic form. Hence there is a tradeoff between minimizing spatial dimensions and maximizing goodness of fit. Measures of goodness of fit (Croft & Poole 2008:12-13) allow one to analyze noisy data and indicate how many spatial dimensions are suitable for analysis. Semantic maps are modeled as linear bisections of the conceptual space (called ‘cutting lines’ when the space is two-dimensional, as in the examples in Croft & Poole [2008] and below). MDS is mathematically well-understood and computationally tractable, so the data analysis can be easily run on a personal computer. Finally, Poole has developed a nonparametric unfolding algorithm, Optimal Classification (Poole 2000, 2005), which maximizes correct classification of the data (i.e. accuracy of the cutting lines/semantic maps), and can directly analyze distributional data of the sort that is presented in Table 1.

23The utility of MDS in general and Optimal Classification in particular can be illustrated by a reanalysis of the spatial adposition data presented in Levinson et al. (2003; I am grateful to Keith Poole for performing the MDS analysis, and to Sergio Meira for providing the raw data and the statistics for their analysis). Levinson et al. use a very fine-grained set of meanings for their analysis of spatial relations, namely a set of 71 pictures designed originally by Melissa Bowerman and Eric Pederson for elicitation (the pictures are published in Levinson and Wilkins 2006:570-75). Levinson et al. collected and analyzed the linguistic forms used for the picture set in nine languages: Tiriyó, Trumai, Yukatek, Basque, Dutch, Lao, Ewe, Lavukaleve and Yélîdnye.

24Levinson et al. encountered the practical problems cited above in trying to apply the semantic map model to the data, and turned to an MDS algorithm in standard statistical package (ALSCAL in SPSS 7.5). This algorithm, like most MDS algorithms, uses a dissimilarity matrix. A dissimilarity matrix does not use the original distributional data directly. A sample of the original distributional data is given in Table 2:

Table 2. Original data format for the first eight Tiriyó adpositions in the Levinson et al. data for pictures 11-16

	tao	awë	hkao	juuwë	po	rehtë	epoe	epinë
11	0	0	1	1	0	0	0	0
12	0	0	0	0	0	0	0	0
13	0	0	0	0	0	0	1	0
14	1	1	0	0	0	0	0	0
15	0	0	0	0	0	0	0	0
16	0	0	0	0	0	0	0	1

25A dissimilarity algorithm computes the dissimilarity of every pair of pictures according to how frequently the pictures were or were not described with the same adposition in the nine languages. For example, in the matrix, pictures 11 and 12 would be given a score depending on how many adpositions in the nine languages include both picture 11 and picture 12. A sample of the result is given in Table 3:

Table 3. Upper left corner of Levinson et al.’s dissimilarity matrix (0 = identity, 10 = complete dissimilarity)

Pictures	1	2	3	4	5	6	7
1	0.000	8.890	8.610	9.000	8.590	8.890	8.740
2	8.890	0.000	8.680	8.860	8.750	8.810	8.750
3	8.610	8.680	0.000	8.720	8.680	8.810	8.540
4	9.000	8.860	8.720	0.000	8.860	8.920	8.720
5	8.590	8.750	8.680	8.860	0.000	8.710	8.600
6	8.890	8.810	8.810	8.920	8.710	0.000	8.740
7	8.740	8.750	8.540	8.720	8.600	8.740	0.000

26The result of Levinson et al.’s MDS analysis using the dissimilarity matrix is presented in Figure 3 (this is a replotting of Levinson et al. 2003:904, Figure 10, rotated 90 degrees counterclockwise):

27The ALSCAL goodness of fit statistics are an S-STRESS of .286 in two dimensions, and a Pearson r² between the actual dissimilarities and the reproduced dissimilarities of .755. These represent a good though not excellent fit. However, the relationship between semantic structure and the spatial model is not that strong. Figure 3 labels the “clusters” of pictures created by the MDS analysis according to a rough semantic label. However, there are many points scattered in the space that are not part of any of the clusters; examination of the pictures that those points represent show that many of them involve attachment, while some of them involve containment (IN).

28The reason for the partial semantic incoherence of Figure 3 can be found in Table 3. Most of the dissimilarity scores are crammed into a small part of the 10 point scale (from 8.5 to 9.0 in the section displayed in Table 3). This is because the data is very lopsided: many of the adpositions are used either for most of the pictures, or for only a few pictures. The lopsidedness of the data compresses the dissimilarity measure and therefore limits the ability of the algorithm to make fine-grained discriminations of degrees of (dis)similarity.

29Poole’s Optimal Classification algorithm constructs the spatial model directly from the original data. In other words, the distances are not compressed as with a dissimilarity algorithm. Poole (2000, 2005) describes mathematically how this is done; broadly, this is by successive approximations from an initial spatial model to maximize correct classification. For this reason, this type of algorithm can better handle very lopsided data. The fitness measures in (1) imply that a two-dimensional model is best, as it was for Levinson et al.’s analysis. (The first fitness measure, Correct Classification, is percent of pictures correctly classified according to each adposition. The algorithm maximizes this value. This measure is extremely high and indicates a better fit to the data than given by the dissimilarity algorithm. The second fitness measure, Aggregate Proportional Reduction of Error, basically describes how much the spatial model improves on a null model where all pictures are classified alike. The APRE values are low here because of the lopsidedness of the data.)

(1)	Dimensions	Classification	APRE
	1	94.1	.300
	2	95.8	.501
	3	97.1	.661

30The spatial model of the Levinson et al. data by Optimal Classification is given in Figure 4:

31The spatial configuration in Figure 4 is broadly the same as the spatial configuration in Figure 3. The crucial difference is the near-absence of scattered points. (The most isolated points, pictures 53 and 64, represent ‘gum under table’ and ‘person behind chair’, both spatial configurations quite different from those found in the other pictures in the set.) The pictures that involved attachment whose points are scattered in Figure 3 are now part of the ATTACHMENT cluster in Figure 4, and the pictures that involved containment whose points are scattered in Figure 3 are now part of the IN cluster in Figure 4. In addition, the ON-TOP and ON/OVER clusters in Figure 3 are now a single cluster in Figure 4. This groups together all of the superadjacency spatial relations, which makes semantic sense.

32Moreover, the pictures that are strung out between clusters are mostly semantically coherent. The pictures whose points are strung out between IN and ATTACH are pictures 18, 30, 39, 51, and 62. All but 51 involve a Figure ‘through’ a round opening in the Ground. In other words, the intermediate pictures between the containment and attachment clusters involve partial containment and partial attachment. Likewise, the pictures whose points are strung out between ATTACH and ON/OVER/ON-TOP are pictures 3, 7, 11, and 23. All but 11 are some type of surface attachment—in other words, they involve both surface contact/support and attachment.

33Thus, the spatial model that is produced by the unfolding algorithm is semantically highly coherent: pictures representing similar spatial relations are close to each other, and a spatial distribution of pictures represents differences in the spatial relations described by those pictures. Moreover, the curvilinear structure going from the superadjacency cluster to the attachment cluster to the containment cluster (see Croft and Poole 2008:17-18) represents a more fine-grained version of the hierarchical scale of six situation types (a subset of the 71 pictures) proposed by Bowerman and Choi (2001:484-86).

34What does the semantic map model, and its MDS implementation, suggest about universals and relativity? Based on the MDS analysis presented here, the analyses presented in Croft and Poole (2008), and unpublished analyses performed by Croft and Poole, both the extreme universalist and extreme relativist positions are disconfirmed (Croft and Poole 2008:31-32).

35The extreme universalist position predicts that the relationships among functions will emerge with just one language, or a few languages; if anything, the model will deteriorate with more languages, because more noise would be introduced into the data. But regularity in the spatial model appears only with the inclusion of many languages with variation in categories. In an unpublished MDS analysis of the data from Croft (1990) on how events are categorized by causative, inchoative and stative constructions in English, French, Korean and Japanese, the spatial model was not very informative. The reason was that only four languages were used, and in addition Korean is similar to Japanese in this part of their grammars, as are English and French. Studies based on more languages and more diverse languages lead to more regularity, despite their nonuniformity.

36The extreme relativist position implies that the spatial models positioning the functions would be radically different for each language, but the spatial model for each language would be semantically coherent, representing the semantic organization of that language. As other languages are added, the fitness of the spatial model produced by MDS for a given number of dimensions of the model would deteriorate because the other languages would have different semantic systems that are incompatible with the first language’s system. (This effect is a consequence of the fact that in MDS, unlike factor analysis or principal components analysis, the data is reduced to a fixed and generally small number of dimensions.) In fact, as just noted, the opposite happens: the addition of more languages and more variation leads to better spatial models at the same low dimensionality.

37What positive conclusions can be drawn from the analysis? Levinson et al. argue that their MDS analysis (despite its flaws), supports the following hypothesis (Levinson et al. 2003:502, 508): ‘the domain of topological relations defines a coherent semantic space with a number of strong attractors, that is, categories that languages statistically tend to recognize even if some choose to ignore them’. Levinson et al. are correct that a coherent, in fact universal, conceptual (semantic) space is confirmed by the data. However, their description of its structure is incorrect—too strong in some ways and too weak in others.

38The description of categories as ‘attractors’ is rather unclear: it appears to be a description of the semantically coherent clusters in their MDS analysis (which are even more coherent in the unfolding analysis in Figure 4); but Levinson et al. also seem to treat them as ‘foci’ (as in the research on universals of color terms; 513), and express uncertainty as to which of these analyses are correct (511-512).

39There are two major problems with Levinson et al.’s interpretation of the MDS analysis, and of the typological universals that underlie these patterns. First, the data that is used to construct the MDS spatial model of semantic relations between the spatial situations represented by the pictures is not data about category prototypes: it is data about category boundaries. Category boundaries cannot be predicted from category prototypes (Croft and Cruse 2004, chapter 4; Croft and Poole 2008:33-34). But category boundaries give similarity judgements, which can be used to reveal the structure of the conceptual space, instead of constructing it a priori, e.g. by arbitrarily positing certain semantic features as defining spatial relations in language. So, it is not accurate to describe the result of the analysis as providing something like a category prototype. I am not denying that crosslinguistic category prototypes exist (see Croft 2003, chapter 6 for several examples). But they are not omnipresent, and they do not appear to exist here.

40The second problem is the greater one. Levinson et al. formulate their discussion of the linguistic categorization patterns in terms of the clusters in their MDS analysis, representing conceptual categories like containment, attachment, superadjacency, etc. The clusters do indeed reveal something about conceptual features that are linguistically relevant. But the clusters do not act as conceptual categories which ‘languages statistically tend to recognize even if some choose to ignore them’. Figure 5 gives the cutting lines (semantic maps) for all of the language-specific adposition categories in Levinson et al.’s sample:

41The points represent the spatial relations for each picture, as in Figure 4. The cutting lines represent every language-specific adposition category in the data. The arrows at the end of each cutting line indicate which side of the cutting line represents the situation types expressed by the adposition. One can immediately see that the clusters are not infrequently cut up by language-specific categories. In some cases, albeit not often, cutting lines cut through two clusters, grouping together part of one cluster with part of another cluster. It is incorrect for those languages to posit the clusters as linguistically relevant conceptual features.

42Levinson et al. propose that some languages (i.e., some speakers) ‘ignore’ the conceptual categories underlying the clusters. The problem here is that they assume that the cluster conceptual categories are the only candidates for semantic universals in the spatial model, and since they are invalid for some language-form categories, they are not universals—in the narrow sense of extreme univeralism. That is an incorrect analysis. The correct interpretation of the spatial models is that the clusters are epiphenomenal—they are properties of conceptual space, but not of linguistic semantic space per se. What is universal is a far more specific semantic construct, namely the situation type represented by each picture, and its relationship to every other situation type in the domain, represented by its position in conceptual space relative to the positions of all the other situation types in the conceptual space.

43For example, consider the spatial model of the conceptual space for the IN cluster in Figure 4, depicted in Figure 6 with the pictures corresponding to the situation types (the spatial model of the IN cluster in Levinson et al. 2003: 508, Figure 14 is less semantically coherent):

44Pictures 47 and 60 at the far right represent an enclosure relationship between a three-dimensional figure and a low barrier functioning as the ground. They are separated considerably from the remainder, which represent a more complete containment of the figure. Picture 32 at the bottom left is distinctive because the figure is immersed in a liquid which is in turn held by a container. The grouping in the upper right can also be more finely broken down. Pictures 54 and 14 represent figures in a boxy container with one full side open. Figures 67 and more distantly 71 represent animate figures in a hollow object with a small opening on one side (the shape of the ground objects differs quite a bit, possibly justifying the conceptual distance). Finally, Pictures 2 and 19 both involve an apple in a more open, roundish ground (albeit quite different). On the whole, the spatial model represents a gradient, roughly from lower right to upper left, of increasing envelopment of the figure by the ground (except for the anomalous picture 19, whose inclusion relation suggests a positioning in the upper left). These fine-grained semantic differences and gradients are more important than the overall IN relationship, since some linguistic adposition categories cut through the IN conceptual cluster (see Figure 5).

45I agree with Levinson et al. that there are no universal formal linguistic categories, although their denotations are constrained by the structure of the conceptual space, and probably other factors. In fact—and this is the more radical analysis, but the only one supported by the data—there are no universal conceptual categories either, at least of relevance to language. The labeling of the clusters in Figure 4 is a simplistic representation of the structure of the conceptual space. What is universal is the holistic conceptualization of the situation types themselves, and the conceptual relationships between the holistic situation types represented as points in the conceptual space, as depicted in Figure 6. Speakers have basically the same conceptualization of highly specific, holistically represented situation types; and they have basically the same judgement of similarity, including degrees and dimensions of similarity, among these situation types. But they may linguistically group similar situation types in any way (possibly also subject to as yet undiscovered other constraints), as long as similarity is respected. Hence linguistic categories are semantically coherent in terms of similarity (modeled as spatial distance and direction in an N-dimensional space), as predicted by the polysemy model. But there appear to be no “big” conceptual categories that constrain linguistic categorization, just degrees of similarity in different dimensions.

3. Variation and universals in a single language

46When one designs an elicitation task such as the spatial pictures used by Levinson et al., and asks more than one speaker to verbalize the situation in the stimulus, different speakers will produce different utterances, with different words and constructions to describe the same stimulus. Intuitively, this is not surprising. Levinson et al. idealized away from this within-language variation (Levinson et al. 2003:503) for their crosslinguistic MDS analysis (as we also did since we used their data). But one need not do so. What does this within-language variation tell us about universals and relativity? In particular, does it support the model of what is universal and what is language-specific (or speaker-specific or even utterance-specific) that was inferred from typological data in the preceding section? The answer is ‘yes’.

47In order to investigate within-language variation in the verbalization of situations, one must control for the verbalization process as much as possible. One can do this by designing similar situations and elicit verbalizations of those situations from multiple speakers in a single language, not just across languages. Examples of this are the Pear film (Chafe 1980), the Bowerman-Pederson spatial pictures discussed above, and the cutting/breaking videos (Majid et al. 2004, Majid and Bowerman 2007). The same depicted situations are shown to different speakers in near-identical circumstances, and verbalizations elicited from speakers in near-identical circumstances, to maximize comparability.

48The data that will be used here to address the universals-relativity issue are from a study of twenty English Pear Stories narratives from Chafe (1980; Croft 2010). The verbalizations were divided into scenes, using the subchunking (Chafe 1977a,b) of the movie sequence that emerged from comparison of the stories. The utterances for every speaker who verbalized the scene were compared.

49The general result is that there is variability in the verbalization of every scene, at least when there were a large number of verbalizations of the scene. The utterances as a whole varied, but so did the occurrences of individual verbs and constructions: while some speakers used the same verbs or constructions for the same scene, for almost every scene there was some variation in the verbs or constructions used.

50There is a “relativistic” interpretation of this within-language variation: each speaker has her own construal of each scene. The different words and constructions of a language offer different construals of experience, and a speaker’s choice is guided by the construal imposed by the words and constructions she chooses. This position is essentially a solipsistic one—relativity restricted to individuals rather than cultures.

51However, there are social cognitive problems with the relativistic/solipsistic interpretation (Croft 2009:413-15). The use of language is a social act, of communication. The words and constructions chosen by the speaker are intended to frame the communicated experience in a certain way. But the hearer cannot read the speaker’s mind. Moreover, the experience being communicated has many alternative construals (this being the reason for different verbalizations of the experience). So the hearer must rely on his knowledge of the construal imposed by the words and constructions chosen by the speaker. Yet the speaker’s and hearer’s interpretation of the construal provided by the words and constructions is determined by their previous use of and exposure to those words and constructions; and those histories of use are different for speaker and hearer. Finally, each experience being communicated is unique and different, so the interlocutors must rely on their shared experience (common ground; Clark 1996) at the current moment for understanding. Hence, there is a high degree of indeterminacy in the communication process. It is this indeterminacy—not just alternative construals of a scene, but indeterminacy in the language used to describe a particular construal—that causes the variation in verbalization.

52But given this indeterminacy, the variation is structured. And the structure indicates that speakers are sensitive to semantic differences and relationships among slightly different scenes, but in a probabilistic way. The same verbs/constructions were used for multiple scenes in the Pear film, but in different proportions. And in some cases, the differences in the proportions of verbs/constructions used correspond to differences between otherwise similar scenes.

53For example, events involving a human participant involved in the event but with an unintended outcome were coded using three different argument structure constructions: the subject encoded the human participant as an experiencer or undergoer as in (2); the subject encoded another participant as in (3)-(4); or an existential construction was used without a subject in the usual sense as in (5):

(2)	2,67	and then he . . crashes into a rock.
(3)	11,68	[1.2 [.25] and [.65]] his bike hits into a rock,
(4)	7,53	[.25] and the pears all [.45] spill on the ground,
(5)	3,21	a--nd . . there's a stone in the way,
	3,22	so his bicycle falls over,

54The distribution of construction types across unintended human events in the Pear film is given in Table 4:

Table 4. The verbalization of unintended human events (Croft 2010, Table 11)

	Exp/Und-Sbj	Other-Sbj	Exist	Other	Total
D8. The cyclist falls/bike falls	15	2	–	2	19
D7. The cyclist hits a rock/bike hits rock	14	5	3	–	22
A4. Drop pears/pears drop	1	2	–	–	3
D5. The cyclist loses hat/hat flies off	2	11	–	–	13
G4. He is missing a basket/the basket is missing	2	12	5	–	19
D9. He spills pears/The pears spill	2	17	–	1	20

55Each scene was verbalized by more than one argument structure construction, but in different proportions. The proportions indicate sensitivity to subtle semantic differences in the scenes. The events involving the cyclist and his bicycle have a higher proportion of experiencer/undergoer subjects (D7, D8), because the cyclist is more likely to be assumed to have control over the bicycle. Events involving a person and his possessions (hat, basket, pears) have a lower proportion of experiencer/undergoer subjects (A4, D5, D9, G4), because these objects are more likely to be assumed to be out of the control of the human participant.

56A second example is the second mention of nonhuman participants in the Pear film. Here there is variation in the use of a possessive pronoun as in (6), or a definite article as in (7):

(6)	1,16	and he [.3] dumps all his pears into the basket,
(7)	6,10	and dumps the pears into a basket.

57Table 5 gives the summary distribution of definite articles and possessives in second mentions of nonhuman participants in the Pear film scenes:

Table 5. The verbalization of second mentions of nonhumans (adapted from Croft 2010, Table 6)

	Definite Article	Possessive Pronoun	Other	Total
tree (13 scenes)	44	1	–	45
goat (2 scenes)	9	1	1	11
ladder (5 scenes)	21	3	–	24
pears (6 scenes)	43	13	14	70
bicycle/bike (2 scenes)	8	20	–	28
hat (2 scenes)	12	23	2	37
apron (2 scenes)	–	4	–	4

58The fewest possessives are found with more alienable and more animate entities (the tree and the goat). The most possessives are found with entities that are more inalienable and less animate, such as articles of clothing (hat, apron). The two artifacts present a subtler semantic contrast: the ladder is less likely to be owned by the worker (the pearpicker), and is less often verbalized with a possessive, while the bicycle is more likely to be owned by the cyclist, and is more often verbalized with a possessive.

59Our final example is the use of the verb see in verbalizations of scenes in the Pear film. The verb see is used for four scenes in the Pear film by the speakers; the distribution of see and alternative verbs is given in Table 6:

Table 6. The verbalization of SEE scenes (adapted from Croft 2010, Table 4)

	See	Other Verb	Other verbs used
C3 (cyclist-pears)	4	2	look at
E4 (boys-cyclist)	7	–
F1 (boys-hat)	3	12	notice, find, come across, run across
G4 (proposition)	3	15	notice, discover, realize, look at

60The alternative verbs make clear differences among the scenes where other speakers used see. Scene G4 (the pearpicker sees that a basket is missing) is clearly a cognition event, not a perception event, since alternative verbs include cognition verbs (notice, discover, realize)—one need not even have the giveaway clausal complement to recognize this. Scenes C3 and E4 varies with look at (if anything). They are typical perception situations: the cyclist sees the pears in the basket, and three boys see the fallen cyclist. There is a historical semantic relationship between ‘see’ and ‘look at’ (Croft 2010): in Indo-European languages, ‘see’ historically comes from ‘look at’ (Buck 1949, §15.51). Scene F1 has a different distribution of verbs. It turns out that F1 is more like a finding scene: the boys see/find the hat that had blown off the cyclist’s head. And in fact in Indo-European, ‘find’ historically comes from ‘see’, ‘notice’, or ‘come/run across’ (Buck 1949, §11.32). Again, the variation in verbalization tells us about the fine-grained semantic differences among the scenes.

61What does this regularity tell us about universals and relativity in the relationship between form and meaning? The semantic differences among the scenes are indicated not by discrete choices of one verb/construction over another, but by different frequency distributions of all the relevant verbs/constructions. The frequency distributions are part of speaker’s mental representation of the form-meaning mapping, as in the usage-based model: the speaker is exposed to the frequency distribution of alternative verbalizations of similar experiences. Hence, a description of how meaning is encoded in language must be in terms of the frequency distribution of the constructions used for that meaning. (This is a different and more reliable frequency measure than token frequency of the different meanings/uses [situation types] expressed by a form, since we do not know what the token frequency of each meaning is. Nevertheless, the relative frequency of a meaning for its form may also influence its cognitive representation.) For example, the frequency distribution for the definite article-possessive pronoun contrast is given in Figure 7:

62The horizontal dimension is essentially a one-dimensional conceptual space and the referent types are arranged as discrete points in that space according to degree of possessibility. In other words, the representation of meaning required for the frequency distribution is identical to the representation of meaning for the crosslinguistic analysis in section 2: a conceptual space with semantically meaningful dimensions, in which are situated points that represent very specific situation types.

63Just as with the crosslinguistic universals, the “universal” (cross-speaker) patterns do not have to do with formal or conceptual categories. Instead, particular situations are represented by frequency distributions of certain forms. Those frequency distributions themselves indicate subtle differences in very particular situations, and the use of the same form(s) across those particular situations indicate conceptual relationships between particular situations—e.g., situations vary as to human intentionality or responsibility (Table 4), or human control/ownership (Table 5 and Figure 7). Thus, a specific choice of words may imply a specific construal of a particular scene, but probabilistically, it indicates a universal (cross-speaker, and possibly crosslinguistic) understanding of the fine-grained semantics of the particular situation type and its relationship to other fine-grained situation types.

4. Conclusions

64An examination of variation across languages and within languages suggests that there is a place for universals of human cognition and behavior, but not of the form that is usually considered in debates on the topic. Invariant (unrestricted) universals, the type posited by extreme universalists, do not exhaust what is common to human beings. Focusing on those unrestricted universals that do exist (if indeed any do) leaves out much of what is characteristic of human beings, at least with respect to language and the conceptualization of experience implicit in language structures.

65Instead, variation is an essential aspect of humanity; this is one of the insights described by Geertz (see §1), and also by Greenberg. Greenberg and his successors were able to identify underlying universals of language, typological universals that constrain variation. More recently, quantitative models allow typologists to analyze the high degree of variation in verbalization across speakers and across languages, and uncover the universals in variation, including variation in verbalization by speakers of the same language. The interpretation of these quantitative analyses is that what is universal are not linguistic formal (lexicogrammatical) categories, or even conceptual categories. What is universal is the holistic conception of highly particular situation types, and the conceptual relationships among those situation types. Conceptual categories are epiphenomenal, though probably interesting to study in their own right. Formal linguistic categories appear to vary indefinitely as long as they respect the universal conception of particular situation types and their conceptual relationships, though there are probably additional constraints on linguistic categories besides the distribution of situation types in conceptual space.

66Finally, it should be said that this is quite preliminary work. The models illustrated in this paper are relatively simple representations. It is very important for advances in linguistic theory to develop richer models that can capture more facets of semantic structure than those described in this paper.