R1.1. Kinship grammar as grammar

The present theory may have implications for the nature and scope of grammar. The distinction between grammar – the rule-governed, generative part of language – and the lexicon – the arbitrary, memorized part – is commonly equated with the distinction between syntax and words-plus-morphemes. (Leaf, for example, seems to equate these as a matter of definition.) But even if we somehow ignore phonological grammar, these two distinctions don't really line up very well. Many items in the lexicon are bigger than words, including idioms like “kick the bucket,” and syntactically anomalous constructions like “the ___ [comparative phrase], the ___ [comparative phrase]” (e.g., “the more, the merrier”; Jackendoff Reference Jackendoff2002, pp. 167–82).

Conversely, the evidence from kin terminology implies that, in some semantic fields, words behave like pieces of grammar. More precisely, kin terminologies (the way kin types are split and merged), rather than kin terms (the actual words used for kin), are grammatically structured. Like the inflections of frequently used regular verbs, kin term meanings may be memorized but are apparently also subject to an OT-style process of evaluation often enough to keep them grammatical. Hogeweg, Legendre, & Smolensky (Hogeweg et al.) present their own version of the distinction between kin terminology and kin terms. They also clarify the difference between (1) theories of how the contribution of words to meaning varies with context, and (2) the present theory of how the context-independent meanings of kin categories are structured.

The CS&G theory is just one example of the very wide range of application of OT. In his comment, Biró asks, “Will Optimality Theory colonize all of higher cognition?” The target article suggests an answer: OT-style grammar can colonize only “grammar-friendly” domains of language, domains that support a successful process of constraint discovery. In constraint discovery, language learners explore their motor, perceptual, and conceptual capacities to discover universal prototypical and distinctive features. Since others in the community are doing the same, learners can count on constraints being mutually known and can move on to using linguistic evidence to determine how constraints are ranked. Different linguistic environments may differ in how thoroughly they encourage learners to explore different regions of constraint space, but in any region they explore, learners are expected to discover (not copy) much the same constraints. For example, most languages don't encourage their learners to explore the constraint space for sign-language phonology, but in those that do, learners seem to end up finding the same constraints (Brentari Reference Brentari1998). Contra Bloch and Hudson, then, theories of constraint discovery have more substance than the banal observation that learning plays a role in constraint acquisition; they require that constraints be grounded in precultural universals.

Another take on these issues comes from Miers and Nevins. Miers outlines a version of Optimality Theory applied to kin terminology that departs substantially from the standard version in its treatment of faithfulness and markedness. This work might have a place within the framework outlined by Nevins, who discusses a range of theories in phonology that may deliver some of the same results as OT without using OT. Following the hypothesis of Cross-Modular Structural Parallelism, Nevins suggests that phonology and kin terminology may represent the same linguistic architecture operating on two different “alphabets.” If this proposal can be made to work, it may offer a new approach to delimiting the potential scope of grammar. Clearly this is a large topic that deserves more attention than I give it here.

R1.2. Kinship space and other conceptual spaces

Because different domains of conceptual structure represent very different sorts of content, we might expect them to be organized very differently. However, according to the target article, the conceptual structure of kinship borrows much of its organization from the conceptual structure of space. This result is consistent with other research finding parallel organization across semantic fields. Together with evidence regarding conceptual structure in nonhuman primates, this may have implications for the evolution of cognition; I discuss several relevant responses below.

Bennardo's work considerably advances our understanding of the extension of spatial thinking to more abstract domains (and counters the skepticism on this score of El Guindi and McConvell). He demonstrates a relationship between universals of spatial cognition and universals of kinship cognition. But he goes further, finding systematic covariation between cultures of space and kinship: A culture that prefers one frame of reference over another for representing space is likely to make a parallel choice in representing kinship. This work goes beyond the target article in demonstrating the integration of culture across cognitive domains.

Seyfarth & Cheney (see also Cheney & Seyfarth Reference Cheney and Seyfarth2007) review evidence that many nonhuman primates not only recognize their kin, but also have abstract representations of social categories that facilitate social inference. They note that some of these representations, and the vocalizations associated with them, may be categorical rather than metric, digital rather than analog. Their observations imply that the organizing principles of human kin terminology – sex, kinship distance and grade (rank), and group membership – are probably primitives of social cognition in nonhuman primates and other social mammals and birds. Thoughts about kinship and other social relationships may be the first abstract thoughts that any animal had.

What are the roots of social cognition? Cross-domain parallels in the organization of conceptual structure might reflect the human gift for metaphorical thinking, but the evidence for abstract thinking about social relationships in nonhuman primates suggests an evolutionary scenario. The mental organs adapted to representing space seem to have been exapted to represent more abstract relationships, starting with kinship and social organization. Modeling kin relationships as relationships in an abstract kinship space would have some immediate payoffs, allowing inferences like: “If A is above B and B is above C, then A is above C,” and so on. This scenario implies that homology as well as adaptation has played a role in the evolution of the mind. The conceptual structure of kinship may be adapted for doing genealogy and solving social problems on Pleistocene savannahs, but it may also owe some of its organization to a more ancient history.

R1.3. Kinship, from conceptual structure to social structure

Conceptual structure is likely used not only in communication, but in cognition and social interaction more generally. In the target article, the focus was on kin terminology, which gives a particularly clear view of the conceptual structure of kinship. However, as a number of commentators remark (or complain), there is more to human kinship than kin terms (Bloch, Gerkey & Cronk, Knight, Levinson). This section responds to these comments by briefly sketching the broader relevance of the CS&G theory to social coordination and social structure. The discussion covers some of the games people play involving their kin and how conceptual structure may influence the outcomes of these games. This may be part of a larger story, of how universal conceptual primitives facilitate convergence on shared moral norms in a number of social domains.

Marriage, in particular deciding who may marry whom, is one social arena in which human beings often find themselves playing coordination games. An accepted set of rules, even if partly arbitrary, that divide each person's relations into marriageable and unmarriageable on the basis of kinship can regulate sexual competition and foster suprafamilial alliances.

Another family of coordination games involving kin may involve what I have labeled group nepotism (Jones Reference Jones2000; Reference Jones2004). Altruism toward kin is a public good. Natural selection favors higher levels of kin altruism if people coordinate their assistance than if each acts separately. When two brothers, for example, must choose how much help to give a needy third brother, their effective coefficient of relatedness when they act independently is the standard Hamiltonian 1/2; when they act together it ranges up to 7/10. (The mathematics involved is covered in Jones [2000] as “The Brothers Karamazov Game.”) Especially in large groups of distant kin, the evolutionarily expected level of altruism toward the needy is much higher if groups can impose enforceable public commitments on their members. This may be relevant to the distribution of gains from collective action in large descent-based groups like the Lamalera whale hunting parties (Alvard Reference Alvard2003) cited by Gerkey & Cronk, and more generally to the establishment of norms of generalized (rather than balanced) reciprocity among kin.

The norms that govern marriage and socially imposed altruism toward kin have some of the same structure as the rules that govern kin terminology. Both terms and norms are sensitive to genealogical distance, but allow other principles to orient and reshape kinship space. Kin terminologies often treat parallel or unilineal relations as closer than cross or non-unilineal; marriage rules often use the same distinctions to divide kin into those too close to marry and those preferred or prescribed as spouses. Kin terminologies sometimes move affines into the consanguine category – for example, treating a sister-in-law as a kind of sister; marriage rules sometimes follow suit, extending incest taboos to affines (Héritier Reference Héritier2002). Kin terminologies may treat certain classes of sibling as equivalent – for example, equating a woman's son and her sister's son; norms of sharing may be built around the ideal (often evaded in practice, of course) of the unity of the sibling group. More generally, both terms and norms impose categorical distinctions on a continuously varying world. “[K]inship systems have a digital character” (Levinson) and “a formal kinship system is designed to minimize scope for disputation: It does this by eliminating shades of grey” (Knight).

The parallels between kin terminology and social organization are a familiar topic in social anthropology. They are commonly assumed to result from the influence of each culture's social structure on its terminology (see sect. R2.2). But I suggest there is something more going on: Norms and terms have some of the same structure because they draw on the same conceptual building blocks. Both of these causal pathways are discernible in Figure 1 in the target article. The first pathway starts from “local organization” and follows the arrows along the bottom row to “kin terminology.” The second starts from “primitives of conceptual structure” and follows the arrows either to “local organization” or to “kin terminology.”

The dependence of both moral codes and semantic grammar on universal conceptual primitives may be a general phenomenon, applying to more than kinship (Pinker Reference Pinker2007, pp. 228–33). For example, in making judgments about the morality of causing and avoiding harm, people normally do not rely on the maxim of the greatest good for the greatest number, but turn instead to intuitions deriving from the conceptual structure of causation and agency (Mikhail Reference Mikhail2007; see Wierzbicka for the corresponding conceptual primitives: because, do, and happen).

The hypothesis, then, is that the CS&G theory is relevant to the social organization of kinship because the ingredients of conceptual structure go into the making of social structure. The outcomes of coordination games depend not just on material factors, but on the mutual knowledge that players bring to the table, including knowledge deriving from precultural universals of cognition. This hypothesis, although rooted in an evolutionary perspective on human behavior, departs from theories in human behavioral ecology in which social organization is the unintended by-product of individual strategizing among inclusive-fitness-maximizers – monads with gonads. Representations of the social order – not just as it is, but as it should be – play a role in making society.

R2.1. Is the theory too complicated?

Behme, Hudson, and Wierzbicka argue that the CS&G theory is too complicated and unintuitive. Hudson starts off by proposing the “easier explanation” that the structure of kin terminologies is overtly represented in native speakers' terms. (See Coult Reference Coult1966 for an early version of this.) Hudson argues that, for example, the availability of the inclusive term parent in English allows the construction of further categories like aunt (parent's sister) and grandfather (parent's father). But then he takes it back. As he observes, the concept Sibling seems to be involved in defining cousin (Parent's Sibling's Child), even though the word sibling is used infrequently or not at all by many English speakers. (In my anthropology classes, students usually define cousin disjunctively, as something like aunt's or uncle's child.) Examples like this, rather than an unnatural love of complexity for its own sake, have led anthropologists to postulate extra levels of representation beyond what is overtly expressed. Thus the advocates of componential analysis propose distinctive features as an underlying level of representation of kin terms, while the practitioners of kinship algebra distinguish the abstract structure of kin categories from the actual terminology, with the latter derived from the former by adding sex distinctions and/or cross-sex equations.

Wierzbicka proposes that kin terms specific to one language can be defined based on a few core kin terms lexicalized more-or-less universally, “father,” “mother,” “husband,” and “wife.” This proposal is part of a larger program of assembling a collection of universal semantic primitives that can serve as building blocks for defining culture-specific words and concepts.

I have no quarrel with the specific primitives on Wierzbicka's carefully crafted list. However, the principle that we explain the natives' use of language using only translations of terms shared by the natives with everyone else runs into problems when we turn from the lexicon to grammar. For example, the difference in verb argument structure between “She rolled the ball” and “The ball rolled” turns on universally lexicalized concepts from Wierzbicka's list, such as because, do, and happen. But to explain in detail which micro-classes of verbs take what constructions, and how this varies across languages, it is necessary to look “under the hood” at the internal structure of these concepts. This level of representation is not so evident in the lexicon, nor so readily accessible to the consciousness of native speakers (Pinker Reference Pinker2007, pp. 65–73; see Legendre et al., Reference Legendre, Sorace, Smolensky, Smolensky and Legendre2006, for an OT treatment of verb micro-classes across languages.) The same applies to kin terms. We need to know something about the feature structure or other relational properties of kin types to explain why ”mother and father” is a natural class but ”mother and husband” is not.

In short, kin terminology is not simple. Like other areas of grammar, it involves nonovert representations. It's not clear what the metric for complexity is, but the CS&G theory is not notably more complex than any well-developed alternative. If anything, the theory has the advantage of borrowing some of its complexity from other domains of language and cognition. The machinery of Optimality Theory, and maybe even the local version of optimization supported here, is imported from outside the domain of kinship, while the conceptual structure of kinship takes some of its organization from the conceptual structure of space.

R2.2. Does kin terminology derive from social organization?

Variation in kin terminology is correlated with variation in social organization. For example, bifurcate merging aunt and uncle terms are more common in societies with matrilineal and/or patrilineal descent groups or other social categories (Murdock Reference Murdock1949, pp. 156, 164–166, 180–183; Whiting et al. Reference Whiting, Burton, Romney, Moore and White1988). (Bifurcate merging aunt terms means one word for Mother and Mother's Sister, another word for Father's Sister; bifurcate merging uncle terms means one word for Father and Father's Brother, another word for Mother's Brother.) The Seneca, with bifurcate merging terminology and matrilineal descent groups, fit this generalization.

Correlations between kin terminology and social organization and culture have led some anthropologists to argue that sociocultural explanations can supersede cognitive-linguistic ones in accounting for what is systematic in kin terminology. Hudson, Behme, Leaf, and perhaps Levinson support social structural explanations of kin terminology. El Guindi argues for understanding kinship as holistically “embedded in cultural knowledge,” effectively denying the content/structure distinction proposed in the target article. Jordan & Dunn argue that a historical approach to kin terminology “immediately reduces the amount of variation that needs to be accounted for by the OT framework.”

The real question is whether arguments of this kind can be cashed out in the form of hypotheses linking social categories and statuses to terminology in detail. The record of past attempts is not encouraging. A number of anthropologists have proposed explanations of kin terms along the lines of “‘K’ means ‘woman of my mother's patriclan,’” or “‘L’ means ‘resident male of my father's hamlet,’” but these typically have been shown not to predict the assignment of kin terms very accurately (Gould Reference Gould2000, pp. 371–78; Lounsbury Reference Lounsbury and Hammel1965). Seneca cousin terms provide a case in point: They are quite regular, but, as Kronenfeld, McConvell, and Salazar note, the division they establish between classificatory siblings and cross cousins doesn't map cleanly onto any social-structural divide. On present evidence, the effect of social organization on kin terminology is mostly loose and indirect, filtered through cognitive-linguistic principles.

Ideally, then, a theory of kin terminology should be consistent with two findings: first, kin terminology correlates with social organization; second, there is no one-to-one mapping between kin terms and social categories. The CS&G theory accounts for both findings by positing an indirect connection between social structure and kin terminology. Local social organization, acting probabilistically and with some time lag, influences the local ranking of universal kin term constraints. This ranking in turn generates kin terminologies through constraint interaction governed by principles of Optimality Theory. This is shown in Figure 1 in the target article, where a series of arrows runs along the bottom row from “local organization” to “kin terminology.”

The rest of this subsection reviews a specific case, the relationship between matrilineal descent and cousin terminology in Seneca, comparing several alternative approaches (Leaf, McConvell, Salazar) and taking a side trip through Chinese cousin terms (Liu et al.) to show the strength and flexibility of the present theory. The last two paragraphs summarize the argument.

According to Leaf, “Seneca terminology embodies Seneca social conceptions just as English terminology embodies English social conceptions.” He writes that Seneca cousin terms “form groups based on a specific contrast between own matrilineal clan as against all other clans. … Own brothers and sisters are grouped with mother's sister's children and contrasted with all other relations on one's own generation. Children of ha-nih (father and father's brother) who are also children of own mother are in own sibling group, children of other ha-nih are in the all others group.”

But Leaf's account of Seneca terminology is wrong. Morgan, whom Leaf cites, is quite clear that the Seneca contrast is not between mother's sister's children and all other cousins, but between cousins linked through same-sex parents and cousins linked through opposite-sex parents (Morgan Reference Morgan1997[1871], pp. 156–157, 160–161, 162, Plates VI, VIII) – not matrilineal versus nonmatrilineal cousins, in other words, but parallel versus cross. The belief that social organization is directly reflected in kin terminology seems to have led Leaf to misread the evidence.

McConvell and Salazar approach the same topic from the other end. Both note the ubiquity of parallel/cross distinctions in kin terminologies and propose that the relevant distinction is the sexually symmetrical one between links through same-sex and opposite-sex siblings. McConvell suggests this could be handled by a Distinguish Parallel /Cross constraint. Applied to the Seneca case, this would achieve descriptive adequacy at the cost of severing the connection between kin terminology and social organization. The two commentators take this course because, although sympathetic to the use of Optimality Theory, they are skeptical about one of the constraints in the target article, Distinguish Matrikin. This constraint requires that kin in Ego's matriline (stippled in Fig. 2) be distinguished from kin in the adjacent matrilines of Mother's Brother's Child (vertical stripes) and Father, Father's Sister, and Father's Sister's Child (horizontal stripes).

There are two issues at stake here. One involves the placement of the boundary between adjacent matrikin. It may be possible to redraw this boundary to make more room for the parallel/cross-sibling distinction McConvell and Salazar emphasize.Footnote ¹ But this revision, whatever its merits, is of little consequence in the present case. The more relevant issue is that McConvell and Salazar treat parallel versus cross as a single, sexually symmetrical distinction. But Distinguish Matrikin is asymmetric with respect to sex – it registers distinctions based on different maternal links, not different paternal links, consistent with Seneca matrilineality.

Clearly some discussion is needed of how a sexually asymmetric constraint can generate the sexually symmetric terminology of Seneca. The rest of this subsection supplies this discussion, showing how Distinguish Matrikin interacts with other constraints to generate a sexually symmetrical cousin terminology in the case of Seneca, while its patrilineal counterpart, Distinguish Patrikin, interacts with a differently ranked set of constraints to generate the sexually skewed Chinese cousin terminology. This discussion, rather than uncovering a fatal flaw in Distinguish Matrikin, as McConvell and Salazar suppose, ends up showcasing a major strength of Optimality Theory: one constraint can produce a variety of effects, depending on how it interacts with others.

To show how the present theory generates different cousin terminologies, we start with the following abbreviated version of the Seneca ranking, Distinguish Matrikin » Distinguish Sex » Minimize Parents' Siblings. (We ignore relative age here.) We can follow the process in slow motion if we stick to replacing just adjoining pairs of elements at each move. With the two parallel cousin types, Mother's Sister's Child and Father's Brother's Child, the first move is to replace Mother's Sister with Mother (same matriline, same sex), and Father's Brother with Father (same matriline, same sex), generating Mother's Child and Father's Child respectively. These replacements obey the injunction to Minimize Parents' Siblings – including embedded Parent's Sibling – and don't violate higher ranking constraints. These outputs become inputs on the next round. Because Father's Child does not belong to Father's matrikin and so is not adjacent to Mother's matrikin, it can be merged with Mother's Child, as some type of sibling.

On the other hand, the high-ranking Distinguish Matrikin bars mergers of the two cross cousin types, Mother's Brother's Child and Father's Sister's Child with Parent's Child.Footnote ² The best the lower-ranking Minimize Parents' Siblings can do is to insist that these two types be combined into a single cross cousin term. Thus Distinguish Matrikin, interacting with other constraints, can generate a standard parallel/cross distinction.

But in other contexts, Distinguish Matrikin and Distinguish Patrikin produce different effects. Chinese cousin terms, presented by Liu et al., offer a serendipitous opportunity to show that the present constraints work well across a wider range of terminologies, an important desideratum in OT. In Chinese terminology, a father's brother's children are separate both from siblings and from other cousins. Other cousins are lumped together, not distinguished as parallel or cross. In other words, Chinese terms skew patrilineally.

The patrilineally skewed constraint, Distinguish Patrikin, can generate the basic pattern of Chinese cousin terms as part of the ranking Distinguish Patrikin » Distinguish Distance » Minimize Parents' Sibling's ____ » Distinguish Sex. (We ignore sex and relative age of cousins here, and some obvious morphology.) There are two crucial differences here from the Seneca ranking. First, Chinese assigns high rank to a constraint attuned to patrilineal rather than matrilineal distinctions, reflecting the patrilineal character of traditional Chinese society. Second, the constraint Distinguish Distance ranks high, and prevents parents' siblings and embedded parents' siblings from being merged with parents and embedded parents. The distance constraint prevents Mother's Sister's Child from being equated with Mother's Child, thus blocking the parallel cousin/sibling equations seen in Seneca. In this context, Minimize Parents' Sibling's ____, in interaction with lower-ranking constraints, enforces a merger of nonpatrilineal cousins, rather than cross cousins.Footnote ³

In summary, the asymmetrical constraints Distinguish Matrikin and Distinguish Patrikin can generate either symmetrical parallel/cross distinctions like those in Seneca, or asymmetrical distinctions like those in Chinese, depending on how they interact with other constraints. At least for now, it seems that the two skewed constraints are necessary, but an additional unskewed parallel/cross constraint is superfluous.

In the end, the criticisms of Leaf and of McConvell and Salazar complement each other. Leaf presumes a direct connection between Seneca matrilineality and Seneca terminology, and gets the facts about the latter wrong. McConvell and Salazar argue that the parallel/cross distinctions observed in Seneca and other terminologies reflect the operation of one or more underlying parallel/cross principles, and leave Seneca terminology divorced from Seneca social organization. In spite of their different conclusions, these commentators share the assumption that the principles governing kin terminologies should be visible on the surface. By contrast, the present theory, which distinguishes between underlying constraints and the surface distinctions generated by constraint interaction, has more room to accommodate systematic but indirect connections between social structure and kin terminology.

R2.3. Componential analysis

Componential analysis treats kin terms as bundles of distinctive features; the theory lacks separate machinery for handling markedness and kin term extensions. Kay defends “li'l ol' componential analysis” as an alternative to the CS&G theory, which he claims cannot handle Seneca descending generation terms or extended cousin terms. This subsection corrects several mistakes in Kay's comment, shows how the CS&G theory deals with some special characteristics of Seneca kin terms, and compares componential analysis and other approaches to distant kin terms.

Kay claims that the proposed constraint Distinguish Matrikin can't handle Seneca terminology for children and siblings' children. These include sex-of-Ego distinctions with female and male speakers using different terms for their kin. The pattern to be explained goes as follows: the Seneca term for ‘daughter' is also used for Woman's Sister's Daughter and Man's Brother's Daughter. The term for ‘son' is also used for Woman's Sister's Son and Man's Brother's Son. Four additional terms cover Woman's Brother's Daughter, Woman's Brother's Son, Man's Sister's Daughter and Man's Sister's Son. According to Kay, “Here the OT analysis fails. Ego's sister's child is a member of Ego's matriline regardless of Ego's sex.” However, the second sentence is true, but irrelevant to the issue at hand. What matters is Ego's children's matriline (not Ego's matriline, as Kay has it), because some of Ego's sibling's children, and not others, are classified with Ego's children (not with Ego) as ‘daughter' and ‘son.' Whether Ego's children belong to Ego's sister's matriline depends on the sex of Ego: “yes” if Ego is female, “no” if Ego is male. Distinguish Matrikin gets this right.

The machinery for handling a terminology of this sort was discussed in Jones (Reference Jones2003b). It can be used to account for markedness relationships involving sex-of-Ego distinctions. We begin with a notation for inverse kin terms: if X is K to Y, then Y is K⁻¹ to X. If John is uncle to Dylan, then Dylan is uncle⁻¹ (i.e., Man's Sibling's Child) to John (ignoring uncles by marriage; see also Gould Reference Gould2000, p. 28). In this notation, the six Seneca terms above are female and male versions of Child, (Father's Sister)⁻¹, and (Mother's Brother)⁻¹. This notation shows that Seneca does not distinguish nieces and nephews from aunts and uncles as clearly as English does. This is evident not only in the distribution of terms but in their morphology. The Seneca term for my mother's brother is roughly ‘he-uncle-me,' while the terms for the inverse, my sister's daughter/son (man speaking), are built from the same root and are roughly ‘I-uncle-her/him’ (Kay Reference Kay1975). The inverseness of Seneca descending generation terms is there in plain sight.

The target article presented a Distinguish Grade constraint. The constraint keeps ascending and descending generations separate, and older and younger kin within a generation. In doing so, it prevents a kin type from being equated with its inverse. But Seneca presents an in-between case, in which some descending generation terms are neither completely distinct nor completely separate from the corresponding ascending generation terms. We can handle this by breaking Distinguish Grade into two constraints, one of which is more lax about enforcing hierarchical distinctions. Consider the following constraint ranking:

This repeats the constraint ranking for Seneca from the target article, with several changes: (1) Distinguish Grade comes in a lax version, which allows partial equations of inverses, and a strict one, which doesn't, (2) two markedness constraints have been added for the first descending generation, and (3) Distinguish Generations has been tweaked to allow mergers in equidistant generations (see Note 2 in target article).

The new constraint ranking handles the special features of Seneca terms for descending generations (and younger siblings) without much extra machinery. Changing the ranking can generate distinctions found in other languages. For example, moving Minimize Children up one place would produce a terminology with distinctions between Father⁻¹ (Man's Child) and Mother⁻¹ (Woman's Child). And the same trick of breaking up faithfulness constraints into graded lax and strict versions can handle other sorts of morphological variation, like whether Seneca sex distinctions are carried by roots or affixes, or how English -in-law, grand-, and great- affixes work (a topic raised by Leaf).

Kay also rejects the proposed analysis of Seneca cousin term extension by one-adjoining-pair-at-a-time replacement. “[N]o such set of local rules can account for the Seneca cross/parallel facts.” This is wrong. Take the kin type that he gives, the fourth cousin “father's mother's father's mother's brother's daughter's son's son's child.” Note that in many cultures, nobody starts with such an elaborate formula when reckoning kin terms; they would begin with “My father's ‘cross cousin’ is father to that person” (Levinson, Read). In other words, Kay's formula is to kin terminology what one of Proust's long sentences is to syntax: a possible case that one would be unlikely to encounter in everyday life. Nonetheless, a set of one-adjoining-pair-at-a-time replacement rules following the constraint ranking in section 3.1 in the target article gives the right answer, with no need to “imagine rewrite rules that look…at nonadjacent nodes.”Footnote ⁴

Kay claims that “componential analysis, gets the whole job done … with less machinery.” This is not quite right. Componential analysis gets the job done in fewer steps (in a highly artificial example), but at the cost of more machinery, in the form of a special Iroquois-cross distinctive feature. This is problematic, regardless of whether we use componential analysis or Optimality Theory. There are a variety of ways of extending terms to more distant kin (Godelier et al. Reference Godelier, Trautmann, Tjon and Fat1998): Does each of these call for a new distinctive feature or a new constraint?

Perhaps rules for distant kin term extensions are open-ended and transmitted through explicit instruction, more like rules for games or poetic forms than rules of grammar. In this case, there would be no theoretical problem with multiplying distinctions indefinitely. Or perhaps humans have specialized adaptations for classifying kin all the way out to second cousins. This is Miers' position, if I have understood him correctly.

But there is a more parsimonious possibility: Distinctions may emerge through the interaction of a limited set of constraints according to rules of local optimization. To explore this further, let us return to the second-cousin formula Mother's Mother's Brother's Son's Son. In Seneca, the categorization of this relative as a cross cousin rather than some kind of sibling depends only on the sexes of the two linking relatives in the parental generation. The sex of the two linking relatives in the grandparental generation is irrelevant. In other terminologies, the opposite is true: A cross-sex connection in the grandparental generation determines the classification regardless of the sexes in the parental generation. And in so-called Dravidian terminologies, sexes in both parental and grandparental generations make a difference to the outcome. This looks like a markedness/faithfulness trade-off between neutralizing linking-sex distinctions in one generation or the other, and accounting carefully for both generations, in the course of local optimization. In other words, it looks like a good fit for the machinery developed in the target article. At this stage, we cannot be sure this is the right approach, but it seems worth exploring.Footnote ⁵

One final note on distinctive features: while componential analysis probably doesn't work as a complete theory, it can generate some common patterns on its own. For example, we can get from bifurcate merging aunts (Father's Sister≠Mother's Sister=Mother) to bifurcate collateral (Father's Sister≠Mother's Sister≠Mother) by activating a distance (or lineal/collateral) distinction. Musgrave & Dowe, however, think this has to do with differential markedness: that in the first case, but not the second, cross-kin are marked relative to parallel. On the standard definition of markedness (Jones Reference Jones2004) this is wrong. The reason the distance distinction doesn't split Father's Sister in the second case is that there's no distance inside Father's Sister to split, not because the type is marked. For an example that does involve differential markedness, see the relative age distinctions among Chinese uncles in Liu et al.'s comment, which are activated for the unmarked but not the marked type.

R2.4. Kinship algebra

Read lays out the basics of kinship algebra, an alternative approach to kin terminology. He argues for a strict separation between (1) kin terminologies as formal systems to be studied in the framework of abstract algebra, without reference to genealogy, and (2) rules mapping kin terminologies onto genealogy. Lyon also cautions that “kinship terminologies can be produced without reference to any notion or instance of genealogical relatedness.” I respond with a parable.

Once upon a time, Professor P developed a formal theory of the shape of pants, called pants geometry. Pants geometry borrowed from topology and other branches of mathematics, taking into account, for example, that pants are highly symmetrical from right to left, but not from top to bottom. With a modest set of parameters, the theory claimed to account for the shapes of everything from bell-bottoms to lederhosen to skorts. With this theory in hand, Professor P announced that pants could be defined in purely geometric terms without reference to the human form. He also reminded his readers that many pants, including most of those given as birthday presents, are never worn. He declared that the old anthropomorphic definition of pants as a garment worn on the lower body and covering the legs separately had at last been overturned, and deplored the sloppy habit of referring to pants “legs.”

Of course Professor P's victory over anthropomorphism in the field of pants studies was illusory. It's not just a coincidence that pants and people have legs and seats, that men's pants generally have flies and men have …, etc. Similarly, it is not a necessary truth, but an empirical finding in need of theoretical explanation, that every society has a system of terms systematically related to one another in such a way that they can be mapped onto genealogical positions, and that the natives themselves can do this mapping – even if those terms are used for nongenealogical purposes as well.

I suggest that a contrast proposed by Sperber (Reference Sperber1996, pp. 134–46) is useful here, between the evolved (or proper) domain of an adaptation, and its cultural domain (see also Sperber & Hirschfeld Reference Sperber and Hirschfeld2004). For example, humans in all likelihood have evolved machinery for assessing the mental states of others (the evolved domain of “theory of mind”), but they also employ this machinery in culturally specific ways in attributing mental states to ghosts, oracles, storms, and agents of disease (the cultural domain of theory of mind). Perhaps the way to break out of the seemingly endless argument about what kinship terms “really” mean is to ask instead about the evolved and cultural domains of kin categorization. From this perspective, Read's achievement is an exceptionally rigorous characterization of the machinery for tracking genealogy (and maybe for doing other things; see sect. R1.3).

There are more down-to-earth differences between kinship algebra and the current approach. Part of what characterizes kin terminologies, according to kinship algebra, are structural equations. Some of these are universal, defining the very domain of kinship (e.g., Sibling of Sibling=Sibling), others are found in some terminologies but not others (e.g., the English rule Spouse of Sibling=Sibling of Spouse). These equations have consequences that ramify through kinship systems and give them much of their structure. But there is the same problem with structural equations as with replacement rules: it's not clear within the theory what limits there are on allowed equations.

R2.5. Comparing theories

By way of a summary, let's return to Kronenfeld's question: What does the present theory buy us that we don't get from other approaches? Some of the alternative theories imply that kin terminology is psychologically simple, perhaps because its complexities derive from the social system rather than the mind. But these theories seem to have trouble accounting for kin terminology in detail. The other alternatives, which allow for autonomous cognitive-linguistic processes, have different strengths and weaknesses. Componential analysis has identified a set of distinctive features, comparable to those in phonology, that help to define the natural classes into which kin types are organized. Yet markedness effects are generally left out, and descriptive adequacy achieved only at the cost of multiplying contrived, undermotivated features. Derivational approaches, including reduction rules and kinship algebra, are successful in showing how rules for extending kinship terms out from a small core can account for patterns of variation in particular cases, but leave unanswered questions about what replacement rules or structural equations are allowed. As Levinson writes, “[p]revious approaches, such as componential analysis and reduction rule analysis…have each captured part of the phenomenon but somehow have failed to give us an exhaustive way to think about the typology of kinship systems.”

Ideally we would like to get the best of each of these approaches in one package. In a package deal, for example, we might find that the range of possible replacement rules is somehow constrained by the need to respect distinctive features. This deal, I claim, is what the present theory offers, by including distinctive features and markedness effects in a unified framework, and handling derivations by stepwise optimization. That the deal also includes a new take on the relationship between social structure and kin terminology, and on the conceptual structure of kinship, makes it even more of a bargain.