2.1. English and Seneca

This section and following ones turn to two kin terminologies, American English (henceforth English) and Seneca, to illustrate basic principles. English kin terms are probably familiar to most readers (Goodenough Reference Goodenough1965). The rules governing English kin terms are similar to those in most modern Western European languages and Japanese. Seneca is another matter. The Seneca Indians are one of the original five (later six) nations in the Iroquois League of modern upstate New York. The comparison of English and Iroquois provided one of the earliest demonstrations that kin terms in different languages may be organized on very different lines (Morgan Reference Morgan1954/1851; Reference Morgan1997/1871; Trautmann Reference Trautmann1987).

Portions of the two terminologies are shown in Figure 2. The figure gives terms in both languages for types of siblings, parents, aunts, uncles, and cousins relative to an anchor called Ego. Terms for distant generations (grandparents, etc.), descending generations (niece, grandson, etc.) and affines (wife, brother-in-law, etc.) are omitted. There is a strong consensus on terms among speakers of each language. Spelling of Seneca terms follows Morgan, sacrificing accuracy for accessibility.

Figure 2. Some English and Seneca kin terms, in relation to Ego (center of chart). Circles are females, triangles males, squares either sex. Relative age (older or younger than Ego) is shown for siblings and some cousins. Shading indicates different lines of descent through females (matrilines).

We may note several things about Figure 2. Not only do English and Seneca of course have different words for kin, they also have different kin terminologies – two kin types called by different terms in English may be called by a single term in Seneca, and vice versa. Both terminologies are regular: In neither case are terms scattered randomly around the diagram. For example, English systematically labels every Parent's Sibling's Child a cousin. Seneca is just as systematic in its own way. Cousins related through parents of opposite sex (‘cross cousins’ in anthropological jargon) are ahgareseh, while cousins related through parents of the same sex (‘parallel cousins’) are equated with appropriate sibling types. (In this article, capitals indicate kin types, italics indicate native-language kin terms, and single quotation marks indicate glosses of kin terms.)

Some distinctions are quite important in both languages: Kin in different generations are terminologically separate for all kin types shown. Other distinctions are moderately important: In both languages a sex distinction holds for parents' siblings and siblings, but not for cousins (except where cousins are equated with siblings in Seneca). Some distinctions are more important in one language than the other: English cares more about the distinction between near and distant kin than Seneca, while Seneca, but not English, distinguishes some kin by whether they are parallel or cross, and by relative age.

Some aspects of Seneca kin terminology are probably related to Seneca social organization. The Seneca were matrilineal, organized in kin groups based on descent through the female line (Morgan Reference Morgan1954/1851; Palmer Reference Palmer1934). Small-scale descent groups, or lineages, were associated with residence in longhouses. The core of each lineage was a group of related women. A man left his family and went to live with his wife's kin when he married; a woman continued to live with her mother and sisters and their dependent children and husbands. Inheritance and succession to office were matrilineal as well: not from father to son, but from a woman to her daughters, sisters, and sisters' daughters, and from a man to his brothers and sisters' sons. On a larger scale, each lineage belonged to one of eight named clans, with multiple lineages in each clan. Clans were exogamous (out-marrying), so that a woman and her husband came from different clans. As a result, Ego belonged to the same clan as his or her Mother, Mother's Sister, and all their children, while Ego's Father along with Father's Sister and her children belonged to another clan, as did the children of Mother's Brother.

2.2. Applying OT

Social factors like those above probably influence English and Seneca kin terminologies, but the terminologies are also governed by cognitive/linguistic principles. Here, I treat these in the framework of Optimality Theory. We begin with two lists of the constraints governing a portion of kin terminology in English and Seneca. The same constraints appear in both lists, but in different order.

The constraints are of two kinds. One kind, taking the generic form Distinguish Feature, requires that kin terms be multiplied as necessary to preserve information about distinctions such as generation, genealogical distance, sex, and so on. The other kind, of the generic form Minimize Kin Type, requires that speakers use as few terms as possible for kin types such as Cousin, Parent's Sibling, and so on. Clearly these requirements for maximizing information and minimizing terms cannot be satisfied simultaneously. Instead each language makes a conventionalized trade-off between constraints by ranking them, with each constraint taking strict precedence over lower-ranking constraints. The constraint ranking defines the grammar of each language, establishing a shared code among speakers and listeners.

Consider how the left-hand ranking governs the categorization of, say, an Older Mother's Brother's Son (i.e., older than Ego). In English, this relative is merged with other parent's sibling's children, as cousin. But there are other possibilities. The kin type could be merged with Parent's Brother or with Older Brother. It could receive its own separate expression, or be categorized as ‘older cousin,’ sex unspecified. In OT, all these possibilities – all possible distinctions and equations involving a given kin type – are evaluated, in parallel, by the first constraint. Only those candidates that incur the fewest violations of the constraint survive; the rest are eliminated. The survivors are then filtered through the second constraint, and so on, until just one optimal categorization survives.

The first constraint in the English ranking, Distinguish Generations, demands that different generations of kin be kept terminologically distinct. This eliminates any terminology that puts cousins in the same category as uncles. The second constraint, Distinguish Distance, demands that near and distant kin be distinguished. This eliminates any terminology equating cousins and siblings. The third constraint, Minimize Cousins, would be perfectly satisfied if English had no cousin terms. But the two preceding constraints have eliminated this possibility. Instead Minimize Cousins is partially satisfied: it selects as the winning candidate a single ‘cousin’ term, with no distinctions by sex or age. The effacement of sex and age distinctions violates two other constraints, Distinguish Sex and Distinguish Grade. (The latter enforces distinctions related to seniority and social rank, including relative age.) But these rank lower than Minimize Cousins, so the violations are moot. With the constraints acting in the order given, ‘cousin’ – equivalent to ‘parent's sibling's child’ – is the optimal output.

Next, consider parents' siblings in English. Since Distinguish Distance and Distinguish Sex outrank Minimize Parents' Siblings, these relatives are distinguished, from parents, and by sex, as aunt and uncle. English sibling terms are similar. Distinguish Sex ranks higher than Minimize Siblings, which ranks higher than Distinguish Grade, so English has two sibling terms, brother and sister, distinguished by sex but not relative age.

Seneca cousin and sibling terms follow a different logic. The high rank of the Distinguish Generations constraint means that Seneca, like English, avoids cross-generation equations. But the next constraint on the list, Distinguish Matrikin, does something else. This constraint dictates that relatives in cross or adjacent matrilines be distinguished, so that cross cousins (stripes in Fig. 2) are distinguished from parallel cousins and siblings (stippled or white). But the constraint allows kin in the same matriline, or nonadjacent matrilines, to be merged. (See next section for more discussion.) In combination with Minimize Cousins this results in the Seneca combination of one term for “cross cousin,” and the equation of parallel cousins with siblings.

Parents' siblings in Seneca follow a similar pattern. Father's Sister and Mother's Brother get separate terms from other aunts and uncles, distinguished by sex, reflecting the high rank of Distinguish Matrikin and Distinguish Sex. Mother's Sister and Father's Brother are equated with the parents in their respective matrilines, Mother and Father, because Minimize Parents' Siblings trumps Distinguish Distance, the constraint that keeps parents' siblings and parents apart in English. Finally, the ranks of Distinguish Sex, Distinguish Grade, and Minimize Siblings, result in siblings (and parallel cousins equated with siblings) being distinguished both by sex and relative age.Footnote ¹

2.3. Generating variation

There are many other ways of classifying cousins and other kin. For example, French makes a sex distinction among cousins that English and Seneca don't. Consider the French movie title Cousin, Cousine: A close translation, following anthropological convention, would be Parent's Sibling's Son, Parent's Sibling's Daughter. But the English language remake of the movie was instead entitled Cousins, losing the racy cross-sex pairing of the original.

Suppose, in the English constraint ranking above, we move Distinguish Sex up one place. With this constraint now outranking Minimize Cousins, the new ranking generates a kin terminology with a sex distinction among cousins as well as siblings. This is how Optimality Theory handles variation in kin terminology. The same constraints, in two different rankings, generate English and Seneca terminologies. A small change in the English ranking generates another terminology, and further permutations generate many more. With the right constraint rankings, separate cousin terms disappear completely, and Cousin merges with other kin types, in the same or different generations. With other rankings, all siblings are covered by one generic term, or they are distinguished by relative age but not by sex. Each of these possibilities is found, fairly frequently, among the world's languages (Murdock Reference Murdock1970; Nerlove & Romney Reference Nerlove and Romney1967).

Kin terminology is prodigiously variable. Introductory treatments of the topic often limit themselves to listing a few major typological variants of, say, cousin terminology: Thus English and French have “Eskimo”-style cousin terms, while Seneca is “Iroquois” (Fox Reference Fox1967; Stone Reference Stone2000). But no list of manageable size can really accommodate the complex permutations and interdependencies involved: For example, English resembles Seneca, not French, in ignoring sex distinctions among cousins. Yet kin terminology is also highly constrained. Languages around the world have independently hit on similar patterns, while largely steering clear of other imaginable possibilities. Kin terminologies are not perfectly regular, but overwhelmingly so (D'Andrade Reference D'Andrade and Kay1971; Nerlove & Romney Reference Nerlove and Romney1967).

OT offers an account of variation and universals in kin terminology, as the outcome of variable rankings among universal constraints. OT is a generative theory, going beyond surface generalizations and one-culture-at-a-time formal analysis to show how interaction between principles generates terminologies, without overgenerating and producing rare or nonexistent terminologies.

In kin terminology, as in phonology, research in the framework of OT builds on and synthesizes previous work. The theory I present here very much depends on previous theories of kin terminology, each of which, I suggest, elaborates on a different aspect of kin terminology to offer a partial view of the subject. The organization of terminology around distinctive features is the starting point for componential analysis (Goodenough Reference Goodenough1965; Reference Goodenough1967). Markedness and prototype effects receive particular attention in structural linguistic analysis (Greenberg Reference Greenberg1966; Reference Greenberg1975; Reference Greenberg, Denning and Kemmer1990; Hage Reference Hage2001). The extension of kin terms to genealogically distant kin is the basis of reduction rules (Lounsbury Reference Lounsbury and Hunt1964a; Reference Lounsbury and Goodenough1964b; Scheffler Reference Scheffler1968). And the abstract algebra of kin categories, including identity elements, reciprocals, relative products, and abstract symmetries, is where kinship algebra begins (Read Reference Read1984; Reference Read2001a). Each of these receives some attention in the rest of this paper: distinctive features in section 3.1, markedness in 3.2, genealogical extension in 4.1, and formal relations between categories, and their relation to genealogy, in 5.2.

Yet each of these alternative approaches, I would argue, has its limitations. Componential analysis is particularly successful in discovering semantic contrasts among kin terms, less successful in accounting for where contrasts are active and inactive, and how contrasts are extended to more distant relations. Markedness theory is a set of observations, not a generative theory. Reduction rules and kinship algebra handle terms for more distant relatives in a more natural, less post hoc way than componential analysis, but don't offer much explanation of why particular reduction rules or structural equations operate, and not others. The rest of this article will suggest how these limitations can be overcome in the framework of Optimality Theory.

3.1. Seven faithfulness constraints

Kin terms typically fall into natural classes, defined by the presence or absence of distinctive features (Goodenough Reference Goodenough1965; Reference Goodenough1967). This property of kin terminologies is accommodated in OT by faithfulness constraints, which forbid terminological mergers of kin types differing with respect to some feature. Here I introduce a set of faithfulness constraints, and briefly contrast them with some traditional distinctive features.

1. 1. Distinguish Sex. A kin type's sex is not a relationship, but an absolute category. You are a parent or a younger sibling in relation to someone, but a female or a male on your own. All kin terminologies make some absolute sex distinctions, which can be handled by a Distinguish Sex constraint.

2. 2. Distinguish Distance. A distance function for consanguineal kin types can be defined as follows: Let a consanguineal chain consist of (1) any number of parent types, followed by (2) at most one sibling type, followed by (3) any number of child types. Formulas fitting this format include Younger Brother, Father's Daughter, Mother's Sister, and Older Mother's Mother's Brother's Son's Son. Count as one link each of the following: Parent, Sibling, and Child, except that Parent's Child, if present, counts as one link not two. Then Older Brother and Father's Daughter are one link from Ego, Mother's Sister two links, and Older Mother's Mother's Brother's Son's Son five links. Distinguish Distance is violated when kin at different consanguineal distances are equated with one another.

3. 3. Distinguish Grade. Some kin types are fully reciprocal: if A is grandparent to B, then B is always grandchild to A, and the converse. Some kin types are partially reciprocal: if A is aunt to B, then B is sometimes niece to A, and the converse, depending on their sex. Full and partial reciprocals are equidistant from Ego, so the previous constraint, Distinguish Distance, does nothing to distinguish them. Instead another constraint, Distinguish Grade, rules out any equation of reciprocals.

   But Distinguish Grade does more than this. It is concerned more generally with differences in grade or rank, distinguishing kin who outrank Ego from those outranked by Ego. The directed axes along which kin may rank higher or lower than Ego include:

   

   Any of these axes can be used to assign grades or ranks to kin types (not to be confused with constraint rankings!), so that, for example, Older Sibling ranks higher than Ego, and Younger Sibling lower. Along any axis, Distinguish Grade is violated whenever kin outranking Ego are equated with kin outranked by Ego, as long as ranks are not reversed on another axis.

   Rank distinctions in terminology commonly have some basis in social hierarchy. The first two axes above are based on the hierarchy of senior and junior kin. The last two may come into play where “wife-givers” outrank “wife-takers,” or vice versa (Needham Reference Needham1958; Parkin Reference Parkin1997).

   The two preceding constraints are concerned with where a kin type is positioned relative to Ego in the web of kinship. The next four constraints are concerned instead with where a kin type is positioned relative to a group or category to which Ego belongs. Since (barring close inbreeding) the open, bilateral network of kin connections among individuals has no natural borders, groups in kinship space must be constructed by treating some kinds of kinship links as defining within-group bonds, and others as defining between-group boundaries.

4. 4. Distinguish Matrikin. This constraint treats a mother-child link as a bond, and a father-child link as a boundary. It allows terminological mergers among the maternally linked kin around Ego, including Sibling, Mother, Mother's Sibling, and Mother's Sister's Child, but is violated by mergers between Ego's matrikin and those across a paternal boundary, like Father and his matrikin (Father's Sibling and Father's Sister's Child) or Mother's Brother's Child. The constraint also allows members of these out-groups to merge with one another. Applied throughout the genealogy, this principle divides kin into maternally linked groups bounded by paternal links.

   With some kin types, it isn't clear which side of the boundary they fall on. Father's Brother's Child – two paternal links away from Ego's matrikin and one paternal link from Father's matrikin – doesn't obviously belong to either insider or outsider matrikin. The simplest assumption consistent with the cross-cultural evidence is that this ambiguous kin type can be equated with either a cross cousin, a parallel cousin, or a sibling without violating Distinguish Matrikin. Its fate must be settled by other constraints. In the Seneca case, the classification of Father's Brother's Child is settled by the next constraint in the ranking, Minimize Cousins, which bars the kin type from being equated with any variety of cousin; it ends up instead being classified as some type of sibling.

5. 5. Distinguish Patrikin. This constraint is the sex-reversed version of Distinguish Matrikin, treating a father-child link as a bond, and a mother-child link as a boundary. In some cases, this and the preceding constraint act interchangeably on aunt, uncle, and cousin terms, consistent with the fact that many societies with patrilineal descent groups, and presumed high rank for Distinguish Patrikin, have more-or-less the same kin terminology as the matrilineal Seneca. Two separate constraints are necessary, however, because in other cases Distinguish Matrikin and Distinguish Patrikin have differing effects, producing matrilineal or patrilineal skewing. (For the role of these constraints in skewed Crow and Omaha cousin terminologies see Jones Reference Jones2003b. For effects on sex-of-speaker distinctions among siblings, see Jones Reference Jones, Jones and Milicic2010)

6. 6. Distinguish Generations. If we go through a genealogy and snip the connections between parents and children, but keep siblings together, and their spouses and cousins, we divide the network of kin into discrete, nonoverlapping generations. The corresponding constraint requires that kin in separate generations be distinguished from one another. Generational distinctions are found in every kin terminology. In some cases, generational and sex distinctions are almost the only ones active.Footnote ²

7. 7. Distinguish Affines. Let a kinship formula consist of any number of consanguineal chains (see above), each separated (and maybe preceded and/or followed) by a spouse term. Then Distinguish Affines treats any of the links between consanguines (kin by birth) as a bond and the links between affines (kin by marriage) as a boundary. It is violated when affines are equated with consanguines, or affine's affines with either. A low rank for Distinguish Affines results either in affines merging with consanguines (e.g., Brother-in-law=Brother) or consanguines with affines (e.g., Mother's Brother=Wife's Father), depending on the rank of different markedness constraints. Sometimes Distinguish Affines works with other constraints to divide kin into marriageable and nonmarriageable classes. In these cases, the machinery for categorizing kin is enlisted to regulate not just kin terminology, but also the moral grammar of marriage rights and obligations (Lévi-Strauss Reference Lévi-Strauss1969) – a vast topic about which I will say no more here.

By way of conclusion, it's worth noting how these faithfulness constraints differ from the traditional distinctive features found in other work on kin terminology. Specifically, the constraints listed above omit the familiar lineal/collateral and parallel/cross distinctions. The results here suggest that these distinctions are not part of the generative machinery in their own right, but derive from the interaction of more elementary constraints. For example, the distinction in English between lineal (or direct) mother and collateral aunt (Romney & D'Andrade Reference Romney and D'Andrade1964; Wallace & Atkins Reference Wallace and Atkins1960) results here from the interaction of Distinguish Distance with markedness constraints. No extra constraint is needed specifically to enforce the lineal/collateral distinction.

The parallel/cross distinction, too, may be derivative. In the present analysis, Seneca Father's Brother's Child is grouped with Mother's Sister's Child as a kind of sibling, not because the two have “parallelness” in common, but by default, because the interaction of Distinguish Matrikin with other constraints selects an unmarked expression for the ambiguously positioned Father's Brother's Child. Two faithfulness constraints privileging maternal and paternal links – Distinguish Matrikin and Distinguish Patrikin – seem to obviate a third specifically devoted to distinguishing parallel and cross.

3.2. Three markedness scales

There is more to the grammar of kinship than turning distinctive features on or off. This is why, after some initial successes, early attempts to define kin categories purely in terms of necessary and sufficient conditions ran into trouble. “Whole category definitions have the problem of becoming extremely complex and hard to follow (and thus cognitively unreasonable…) and fly in the face of much ethnographic usage information regarding focality and the special status of focal referents” (Kronenfeld Reference Kronenfeld2006, p. 210). This other side of kin terminology can be handled in OT through markedness constraints and markedness scales.

Consider this neat sequence, from English terms for affines:

The list shows a series of linguistic phenomena falling under the heading of markedness. Markedness is the linguistic flip side of cognitive prototypicality: The less prototypical a concept, the more marked the corresponding expression (Greenberg Reference Greenberg1966; Reference Greenberg1975; Reference Greenberg, Denning and Kemmer1990; Hage Reference Hage2001). Markedness sensu stricto involves converting a prototypical expression into a less prototypical one by adding a mark (like -in-law, grand-, or step-). Markedness can also take other forms, as shown above.

The varieties of markedness above fall along a scale. As genealogical distance from Ego increases, less and less effort is made to tailor distinctive terms for kin types. Wife gets a term to herself. Brother's Wife wears a term borrowed from another relative (sister), but altered to fit her (with the added suffix -in-law). Uncle's Wife wears a term borrowed from another relative (Parent's Sister), and not altered to fit her. And Cousin's Wife gets no generally accepted term of her own at all.

This sequence illustrates a general rule: More terminological resources are allocated to closer kin. This can be phrased as an implicational, or if-then, rule about cross-linguistic variation: If two kin terms differ in markedness, then the more distant is generally the more marked, other things being equal. In OT, this can be handled by a markedness scale: not a constraint per se, the scale limits allowed permutations of constraint rankings. In the case of genealogical distance, the scale stipulates that markedness constraints minimizing distant terms shouldn't rank lower than constraints minimizing close kin terms. For example, Minimize Cousins should rank at least as high as Minimize Siblings, implying that if Distinguish Sex outranks Minimize Cousins, it outranks Minimize Siblings too. This implies in turn that if a language makes a sex distinction among cousins, it makes a sex distinction among siblings, but not conversely. Similar reasoning applies to the relative age distinction. English, Seneca (both compounds and roots), and French all conform to these rules.

Not just genealogical distance, but other distinctive features and faithfulness constraints in Figure 3 have preferred, unmarked directions associated with them. There is good cross-cultural evidence for the following three markedness scales (Hage Reference Hage2001):

• A. Minimize Far Kin≥Minimize Near Kin (associated with Distinguish Distance and Distinguish affinity). Cousins are marked relative to siblings, grandparents relative to parents, children's spouses relative to children, siblings' spouses' siblings relative to siblings' spouses. More generally, given a compound kin type XY at a greater consanguineal or affinal distance than either of its component types, X and Y, we expect markedness scales of the form Minimize XY≥Minimize X and Minimize XY≥Minimize Y. Note that there is no implication about the markedness of XY relative to some other kin type Z. For example, Parent's Parent is marked relative to Parent, but not necessarily relative to Child.

• B. Minimize Junior Kin≥Minimize Senior Kin (associated with Distinguish Grade). Younger siblings are marked relative to older siblings. Nieces and nephews are marked relative to aunts and uncles. Grandchildren are marked relative to grandparents. More generally, other things being equal, if X is senior to Ego and Y is junior, we expect a markedness scale of the form Minimize Y≥Minimize X.

  Directional distinctions other than senior/junior distinctions don't have consistent associated markedness scales. Take brothers-in-law. Cultures vary in whether they assign a higher rank – and more terminological distinction – to the wife-giver who relinquishes a sister, the wife-taker who marries her, or neither. There is no universal scale of Wife's Brother relative to Sister's Husband.

• C. Minimize Cross Kin≥Minimize Parallel Kin This scale is a summary of two scales. One of these, associated with Distinguish Matrikin, makes Father's Sister and her children marked relative to Mother's Sister and her children. The other, associated with Distinguish Patrikin makes Mother's Brother and his children marked relative to Father's Brother and his children. More generally, cross kin, linked through opposite-sex relatives, are marked relative to parallel kin, linked through same-sex relatives.Footnote ³

Languages mostly follow the markedness scales above, but otherwise they freely invent markedness constraints of the form Minimize Kin Type as they see fit. For example, both English and Seneca treat aunts and uncles symmetrically, implying they have a single constraint, Minimize Parents' Siblings, regulating these terms. But other languages observe fewer (or more) distinctions among aunt terms than uncle terms, implying that they split Minimize Parents' Siblings into two constraints, Minimize Aunts and Minimize Uncles, with the former ranking higher (or lower) than the latter.

4.1. Further cousins

As we have seen, Seneca classifies first cousins as cross cousins or siblings, depending on the sex of connecting parents. But what about a second cousin, an Older Mother's Mother's Brother's Son's Son, say? One might imagine that the machinery of kin classification would choke on such a super-sized input, as English does on Cousin's Wife. But in Seneca the relative in question as ahgareseh – ‘cross cousin.’ Other second-cousin types are likewise classified as cross cousins or siblings, with siblings further distinguished by sex and relative age (Lounsbury Reference Lounsbury and Hunt1964a).

In some cultures, kin term extensions are socially important – dividing distant kin into marriageable and unmarriageable categories, for example. This doesn't apply among the Seneca, but the extension of the parallel/cross distinction to more distant cousins is highly systematic all the same. Anthropologists have developed several approaches to account for kin term extensions in Seneca and other languages, including reduction rules (Buchler & Selby Reference Buchler and Selby1968; Gould Reference Gould2000; Kronenfeld Reference Kronenfeld2009; Lounsbury Reference Lounsbury and Goodenough1964b; Scheffler Reference Scheffler1968) and kinship algebra (Read Reference Read1984; Reference Read2001a). There are important differences between these approaches (more on this in the next section), but here we are interested in what they have in common. Both offer what linguists call a derivational account of kin terms, in which arriving at appropriate terms for distant kin takes many small steps rather than one giant leap.

This is very different in spirit from standard Optimality Theory. Given an input, standard OT says, “Find the output, whatever it may be, that best satisfies constraints 1, 2, 3, and so on.” A derivational theory says, “Apply rule 1 to transform the input. Apply rule 2 (or maybe rule 1 again) to transform the result. And so on.” These approaches to kin terminology can be reconciled, but this requires a revised version of OT. The revised version says, “Find the output, whatever it may be, in the immediate neighborhood of the input, that best satisfies constraints 1, 2, 3, and so on. Repeat, using this output as the new input. Keep repeating until a steady state is achieved.” The journey from input to output, however long, will proceed in small steps.

Below I consider how one widely used derivational approach, the method of reduction rules, may be incorporated into OT. First, the sequence below shows how reduction rules work on a second cousin input in Seneca (following Lounsbury Reference Lounsbury and Hunt1964a). On the left are kin formulas, on the right, rules that transform one formula into the next. It is convenient (but maybe not absolutely necessary) to assume that, with each move, at most one pair of adjoining elementary kin types changes.

The last part of the sequence, from Older Mother's Brother's Son to ‘cross cousin,’ restates a familiar result for first cousins. In Seneca, Mother's Brother's Child cannot be subsumed under a sibling term: this would violate Distinguish Matrikin, the constraint keeping adjacent matrilines apart. Further constraints dictate that cross cousins are not distinguished by sex or relative age.

But something else is going on at the beginning. Here, the formula Mother's Brother is embedded on both sides in a larger formula. And this doubly embedded Mother's Brother is treated differently. According to the rule on the right, a Relative's Mother's Brother's Relative (written “___ Mother's Brother's ___”) should be replaced with that Relative's Father's Relative (written “___ Father's ___”). This is unexpected, because Mother's Brother and Father belong to adjacent matrikin, and in the case of first cousins, aunts, and uncles, Seneca is meticulous about keeping adjacent matrikin separate. But apparently when Mother's Brother is buried deeply enough inside a larger expression, the contrast between adjacent matrikin is neutralized. This is a markedness effect: A distinction observed with one kin type is ignored when that kin type is part of a larger formula.

OT is good at managing trade-offs between distinctive features and markedness. One might imagine that a constraint ranking like the following would handle Seneca cousin extensions:

• Minimize 2nd, etc., Cousins

• Distinguish Matrikin

• Minimize Cousins

• Distinguish Sex

• Distinguish Grade

• Minimize Siblings

This is a portion of the ranking previously given for Seneca, with the addition at the top of one constraint, Minimize 2nd, etc., Cousins, which decrees that second and further cousin terms must be eliminated even at the expense of merging adjacent matrilines.

But it takes more than just adding markedness constraints to manage kin term extensions. The ranking above gives the wrong results if we follow standard practice and allow moves of any size. In the present case, one potential move goes directly from the second cousin input to a sibling type like ‘older brother.’ This move obeys the Minimize Cousins constraint, and the next two as well, so ‘older brother’ should be the optimal output. More generally, all second and further cousins should be classified as siblings. Standard OT effectively short-circuits the piece-by-piece replacement given by the reduction rules above, giving results contrary to those in Seneca and many other languages.

We could get around this by declaring, by fiat, that Distinguish Matrikin extends cross and parallel distinctions out indefinitely in the appropriate fashion (Woolford Reference Woolford1984). But there are several problems with this. First, the proposed redefinition is ad hoc, with no motivation or grounding in markedness theory or otherwise. Furthermore, across cultures there are several different ways of extending the parallel/cross distinction, so we would be forced to introduce additional versions of Distinguish Matrikin to accommodate this variation. Finally, it is psychologically and ethnographically implausible that a formula like Older Mother's Mother's Brother's Son's Son is processed in one gulp.

A better solution is to incorporate the iterated processes featured in derivational theories into a revised version of OT. This means accepting a restriction on the size of moves, but allowing the output to be fed back into the input repeatedly. It means that on any one move, a constraint like Reduce 2nd, etc., Cousins will accept “partial payment” – a small move away from second or further cousin terms, such as replacing an embedded Mother's Brother with an embedded Father. Given this revision, we can generate the full array of Seneca cousin terms out to indefinite distances. (In practice, the Seneca usually gave up after third cousins.) Thus, by switching from one-shot, global optimization to multistep, local optimization, OT can capture the advantages of derivational approaches, with the added advantage that derivational rules aren't just stipulated, but derive systematically from constraint rankings.Footnote ⁴

4.2. Local optimality and minimal moves

The case for a more derivational, local version of Optimality Theory would be stronger if it applied to more than just kin terminology. Encouragingly, both phonology and syntax have been moving in this direction lately.

In phonology, standard OT, in spite of its successes, has trouble accounting for some phenomena. For example, in American English (McCarthy Reference McCarthy2007, pp. 1–2), it apparently takes two steps to get to the standard pronunciation of planted, the past tense of plant. On the first step, /plænt/ and /-d/ are combined, but an extra [ə] is added – thus [plænt.əd]. This avoids the articulatory challenge of pronouncing two dental stops in immediate succession. But unless speakers are being hypercorrect, there is normally a further change in pronunciation. The [t] is dropped, yielding [plæn.əd]. The [ə], introduced to solve the problem of a now-absent [t], is opaque – not motivated on the surface. For a derivational account this is not a problem: [ə] is added at one step, [t] is dropped at the next. But it is a problem for standard OT. What markedness or faithfulness constraints could possibly account for an added [ə] that makes the output both more marked and less faithful to the input?

Probably the most promising approach to phonological opacity within OT involves moving from global to local optimization. The argument is set forth at length in McCarthy (Reference McCarthy2007). In McCarthy's revised version of OT, candidate chain OT, only minimal moves in the immediate neighborhood of the input are allowed. The optimal output is selected in this neighborhood, the output is returned as input, and the process is repeated until no more locally optimal changes can be made. Optimization takes place according to strictly ranked constraints, as in standard OT.

All of this is very similar to the integration of OT and reduction rules proposed above for kin terms. For example, in candidate chain OT, some constraints may be written so that they are activated only after other constraints have been brought in to play. Similarly, with Seneca cousin terms, the parallel/cross distinction is effectual only after a formula has been boiled down to a first cousin expression.

In syntax as well, linguists have begun to explore localized versions of OT. These involve building up phrase structure trees one small step at a time, with each step governed by OT (Heck & Müller Reference Heck, Müller, Bainbridge and Agbayani2006; Müller Reference Müller2003). This research has the potential, if preliminary results hold up, of reconciling optimality and derivational approaches to syntax, which have grown far apart in recent decades.

In short, there is reason to suppose that kin terminology, phonology, and maybe syntax have a common architecture reflecting the principles of OT. But in each case, there are problems with the standard, global version of OT. It is liable to “short circuits,” getting wrong answers by taking big jumps from marked input to unmarked output. It also gets computationally implausible as combinatorial possibilities multiply. The alternative, local optimization, moving from input to final output in small steps, may be a general design feature of grammar.

5.1. Conceptual structure 1: Constraints and the space of kinship

Kinship is normally conceptualized in spatial terms.

Here I take this observation a step further by comparing the conceptual structure of physical space, as revealed by previous analyses of closed-class linguistic forms, with the conceptual structure of kinship space, as revealed by constraints on kin terms.

Consider the following scene: There is a focal object or figure. This object stands at some distance and in some direction and orientation in relation to a background object, or ground. The ground is at least as spatially extensive as the figure. Information about figure and ground is limited, but includes such distinctions as whether they are simplex (a single object) or multiplex (a group of objects treated as one thing). Information about the relationship between figure and ground is also limited. It is, roughly speaking, topological rather than metric, and digital rather than analog. It may include relationships like near and far, above and below, or inside and beside, but not actual measurements of distance or position.

This description could be a representation of material objects in physical space. It doesn't fit the rich representation of objects and space in conscious perception, but corresponds to a more pared-down conceptual representation in which most information about shape, texture, color and kind of objects, and about spatial metrics, has been stripped away. This mode of representation is manifest in English spatial prepositions, and across a wide range of languages in a variety of closed-class forms concerned with space (Levinson & Wilkins Reference Levinson, Wilkins, Levinson and Wilkins2006). But (I will argue) this description also fits the conceptual structure of kinship. The parallels are evident in Figure 3, where constraints on kin terms are divided horizontally into those concerned with (1) absolute qualities of the figure (the referent of the kin term), (2) the relationship – distance and direction – between figure and ground, and (3) the nature of the ground (the anchoring individual or group to whom the figure is related).

Taking these in turn: In the grammar of physical space, the bare, existential thing-hood of the figure is typically indicated by assigning it a noun. In kinship space, likewise, even though kinship is a relationship, kin types are mostly treated as abstract “things” by assigning nouns to kin terms. (Dahl & Koptjevskaja-Tamm Reference Dahl, Koptjevskaja-Tamm, Baron, Herslund and Sørenson2001; for scattered exceptions where kinship is indicated by verbs, see Evans Reference Evans, Vogel and Comrie1999.) And in kinship space, as in physical space, only a very limited subset of potentially relevant information about the figure actually registers grammatically. Usually the only nonrelational information about kin types that makes it into kin terms is their sex.

The second class of constraints, those concerned with kinship distance and rank, also shows obvious parallels with spatial grammar. For example, in both kinship space and physical space, the grammatical system mainly trades in quasitopological or qualitative, rather than metric, information. Thus age distinctions in sibling terms normally encode whether the sibling type in question is older or younger than Ego (as in Seneca), or, less often, the sibling's birth order: first, second, third, and so on. They don't normally encode age differences in years, or absolute ages. Nor do affinal distinctions register how long a couple has been married.

Finally, to understand what the third class of constraints on kin terms is up to, we turn once again to parallels with the conceptual structure of physical space. In closed-class forms relating to physical space, a commonly registered distinction is that between simplex objects (a bird, an island, a star) and bounded collections of objects (a flock, an archipelago, a constellation) (Jackendoff Reference Jackendoff1991; Talmy Reference Talmy and Talmy2000b). The same distinction is at work in kin terminologies: Kin terms can register the relationships of individuals to other individuals (near or far, higher or lower), but they may also register the relationships of individuals to more extensive background groups or categories (inside or across the group boundary). In the analysis here, three constraints – those distinguishing matrikin, patrikin, and generations – are sensitive not to the relationship between a kin type and an individual Ego, but to the relationship between a kin type and a bounded group to which Ego belongs.

Thus the findings here extend one of the major discoveries in the study of conceptual structure: kin terminology, like other abstract semantic domains, such as time, change of state, and possession, borrows much of its organization from the conceptual structure of space. What is new here is not the idea that we can talk about kinship space and kinship distance, but the tracing of close parallels in conceptual structure in both cases. Optimality Theory is an important part of the analysis, because the distinctive features uncovered using OT manifest the parallels with spatial cognition especially clearly.

5.2. Conceptual structure 2: Genealogy and the nature of the input

The conceptual structure of kinship has something in common with other domains of conceptual structure, but it has its own logic as well, deriving neither from conceptual structure in general, nor from Optimality Theory. For example, consanguineal distance is measured in a special way, starting from neighboring elements and counting links up and then down. This is more like pedigree distance, as measured by geneticists or genealogists, than physical distance as measured by surveyors. This subsection considers what's special about the structure of kin terminology, with a focus on what the present theory has to say about one of the most contentious issues in anthropology, the relationship between kinship and genealogy.

Anthropologists distinguish between genealogical definitions of kin terms – how genealogical positions map onto terms – and categorical definitions – how terms are related to one another. Up to this point, our application of OT to kin terminology has been straightforwardly genealogical. The input to the machinery of kin classification was stipulated to be a kin type – a genealogical formula – like Mother's Older Sister. The assumption, never explicitly defended, was that however much kin terms vary, they are built up from elementary types shared across cultures. An implication is that kin terms are intertranslatable: terms from one language can be defined using terms from another language (sometimes with the addition of extra distinctions, like Older or Younger). For example, in explaining Seneca aunt terms to an English speaker, one could say that in Seneca, mother's sister but not father's sister is equated with mother. Conversely, one could explain English aunt terms to a Seneca speaker by saying that English equates both the ahje (‘older sister’) and the kaga (‘younger sister’) of noyeh (‘mother’) with ahgahuc (‘father's sister’) rather than with noyeh.

But there are problems with a strictly genealogical approach to kin terms. It is commonly observed that people can, and often do, apply kin terms without knowing all the genealogical connections involved (Keesing Reference Keesing1975; Levinson Reference Levinson2006a; Read Reference Read, Feinberg and Ottenheimer2001b). To see how this is possible, note that a Seneca speaker can figure out that the ahje of a noyeh is a noyeh without actually knowing whether the kin involved are genealogical or classificatory older sister and mother. Another common observation is that in some societies even an individual known to be unrelated by birth or marriage – a resident anthropologist, perhaps – may be assigned a place as someone's daughter or brother, and then enfolded systematically into the whole network of kin.

Nongenealogical kinship is not fatal to the OT approach to kin terms; it can be accommodated by expanding the range of allowed inputs. Specifically, OT can handle nongenealogical inputs as long as these are amenable to evaluation by the kin term constraints, which are concerned with questions like “Is the input female or male?” and “Does the input belong to the same generation as Mother?”

Suppose, given a Seneca constraint ranking, we try the input ‘mother's’ ‘older sister,’ where the terms in single quotes are understood, not as genealogical formulas – what an English speaker might call “real” mother or older sister – but as glosses on Seneca categories. This input is well-formed, because even without knowing the exact genealogy, we can say that equating the input with ‘sister’ violates Distinguish Generations, equating it with ‘father's sister’ violates Distinguish Matrikin, and so on. Applying constraints as before we get the correct optimal output: ‘mother's older sister’ merges with ‘mother.’Footnote ⁵ Thus pluralism about allowed inputs in OT makes room for both genealogy and category. Allowing nongenealogical input is consistent with evidence that people can figure out appropriate kin terms using either explicit genealogical reckoning, or terminological shortcuts, or both, depending on the context.

So what does the formal analysis of the language of kinship tell us about the relationship between kinship and genealogy? Many anthropologists argue that, because kin terms are often applied where genealogies are unknown or nonexistent, a genealogical definition of kinship is unworkable (Read Reference Read2001a; Reference Read, Feinberg and Ottenheimer2001b). Some go even further and argue that definitions of kin terms, and theories about how people become kin and what kin share, are so widely variable as to call into question whether kinship even exists as a proper subject for cross-cultural study (Schneider Reference Schneider1984). According to some skeptics, anthropologists should abandon the study of kinship for the study of folk ideas of “relatedness,” an open-ended polythetic domain which might not overlap much with Western notions of parenthood and consanguinity (Carsten Reference Carsten1997).

But simply dismissing the connection between kinship and genealogy in this way means ignoring one of anthropology's great empirical findings: Pretty much every society has a system of kin terms. These are recognizable as kin terms by the way genealogy maps onto them. “It is clear that our informants quite generally ‘know’ which genealogical relatives go in which kin categories” (Lehman Reference Lehman and Hlaing1993, p. 99). Figure 2 shows a portion of this mapping for English and Seneca, and similar figures can be found in hundreds of articles and books on kinship. Somehow, the distinctive features that kin terminologies care about are systematically related to genealogical distinctions. According to the present theory, this follows from the restriction that inputs, whether genealogical or categorical, must be well-formed – amenable to evaluation by the kin term constraints. The result is a systematic correspondence between genealogical and kin term distinctions, mediated by the workings of OT, so that, for example, a faithfulness constraint concerned with consanguineal distance helps to generate a kin terminology with a lineal/collateral distinction (sect. 3.1).

There is a paradox here. Kin terms (according to many anthropologists) don't have genealogical definitions, but (according to considerable evidence) are genealogically structured. The present theory offers one possible resolution to this paradox: recognizing two levels of mental representation for kinship, corresponding to the content and conceptual structure of kin terms. (For content/structure distinctions in other semantic domains, see Grimshaw Reference Grimshaw2005; Pinker Reference Pinker1989; Reference Pinker2007). While the content of individual kin terms may vary widely and idiosyncratically across cultures and be deeply entangled with local theories of procreation and shared substances, the conceptual structure of kinship manifest in the grammar of kin terms is more universal – and shows every sign of being adapted for tracking genealogical connections.

5.3. The grammar faculty

Talking about kin – more specifically, using terms for different kin types – is a different problem than thinking about them. Thinking about kin involves fitting one's thoughts to local facts about kinship. Mastering a kin terminology involves, additionally, fitting one's words to local communicational conventions. Talking about kin is one example of a coordination game, in which the goal is to choose, not the one right answer, but the same answer as everyone else. Playing coordination games is something of a human specialty – maybe even the key human behavioral specialization (Levinson Reference Levinson, Enfield and Levinson2006b; Tomasello et. al. Reference Tomasello, Carpenter, Call, Behne and Moll2005). One approach to the grammar of kinship, then, and to grammar in general, is to consider its place among games of coordination and communication (Blutner et al. Reference Blutner, Hoop and Hendriks2006).

One way to play a coordination game involves a kind of mind reading, in which signaler and recipient cooperate by carrying out on-the-spot simulations of one another's inferential and performative dispositions (Sperber & Wilson Reference Sperber and Wilson1995/1986). If you and I both know that we are trying to coordinate our behavior, we may be able to arrive at a shared understanding through one-off signals we mutually recognize as intentional signs obeying maxims of cooperative communication. This kind of mind reading allows human beings to cooperate even without a shared language, as in situations of first contact between cultures.

Some communicative acts go beyond one-off exchanges by reproducing conventional signs. The learning of conventional signs is governed by further cooperative maxims (Bloom Reference Bloom2000). The learner not only connects a sign with a meaning, but also assumes that other members of the community will make the same connection when they interpret or produce the sign. She assumes that novel signs have novel meanings, rather than being synonyms of familiar signs (Diesendruck & Markson Reference Diesendruck and Markson2001).

Finally, conventionalization may go one step further. The precedents set by communicative acts may be generalized to produce systematic rules for encoding information. Human communication thus runs along a spectrum, from less to more conventionalized, from pragmatic to grammatical.

The contrast between pragmatic-inferential and grammatical-encoded communication is a commonplace in linguistics. But for many authors, grammar is just a synonym for syntax or morphosyntax (Sperber & Wilson 1995/1986). This article takes a more inclusive approach. Phonology is grammatical, and, according to the argument above, so is kin terminology. Grammatical principles may govern other semantic fields – including body parts, colors (Jones Reference Jones, Jones and Milicic2010; Kay & Maffi Reference Kay and Maffi1999), and spatial relationships (Levinson & Wilkins Reference Levinson, Wilkins, Levinson and Wilkins2006) – as well as the interface between semantics and morphosyntax – including pronouns and subject choice (Aissen Reference Aissen1999) and verb argument structure (Legendre et al. Reference Legendre, Sorace, Smolensky, Smolensky and Legendre2006) – and morphology and syntax more generally (Legendre et al. Reference Legendre, Grimshaw and Vikner2001).

Taken as a whole, this work implies that there is more to grammar than semantics, phonology, morphology or syntax in isolation. The rest of this article advances a strong hypothesis about this extra something, arguing that part of the uniquely human suite of adaptations for playing coordination games is a grammar faculty, adapted to facilitate the construction of locally shared codes of communication and interaction. This faculty interacts with, but is distinct from, domain-specific adaptations in conceptual structure, phonology, and syntax. In each domain, the grammar faculty solves several problems: (1) using ranked constraints to generate grammatical outputs, (2) matching the learner's constraint rankings with community rankings, and, more tentatively, (3) discovering constraints. I consider these in turn.

1. 1. How ranked constraints generate grammatical output is well-trodden ground in Optimality Theory. Not so well understood is why OT works the way it does – why, particularly, it resorts to ranking rather than quantitative maximization to handle constraint trade-offs. The grammar faculty hypothesis implies one answer (suggested independently by other researchers: Smolensky & Legendre Reference Smolensky, Legendre, Smolensky and Legendre2006), that constraint ranking is adapted to the demands of communication and other coordination games.

   By way of illustration, consider the functional demands of two tasks, allocating assistance to kin, and communicating about them. At its simplest, the first task is a matter of household economics, of distributing scarce resources among oneself and one's relatives. According to a well-known result in evolutionary theory, this can be treated as a maximization problem (subject to some restrictions: Frank Reference Frank1998). The evolutionarily optimal solution maximizes a quantity called inclusive fitness. The second problem is different. Given the problem of what to call different kin, there is an enormous array of possibilities for separating, marking, merging, and omitting terms. As members of a language community make trade-offs between supplying information and avoiding effort, the crucial consideration is that they make the same trade-offs. OT solves this coordination problem readily, asking of speakers and hearers only that they share a constraint ranking. With a shared constraint ranking, the Seneca, for example, can settle on Mother's Sister being called ‘mother,’ with further implications for other relatives (every Mother's Sister's Child is some type of sibling), without having to precisely equate quantitative feature weights or encyclopedic knowledge. Just as particulate inheritance in genetics improves the fidelity of replication between generations, the strict ranking of discrete constraints makes it easier for language communities to reproduce standardized codes. Although more theoretical work needs to be done, it is plausible that OT grammars flourish where they do because of their advantages for communication.

2. 2. Since constraint rankings vary across cultures, they have to be learned. This process is fairly well understood, at least in outline. Given a shared constraint set, language learners can solve the induction problem of generalizing from limited input to rules of language by using a procedure called constraint demotion to match their constraint rankings with those in the local speech community (Tesar & Smolensky Reference Tesar and Smolensky2000). Briefly, this works as follows: The learner begins with some constraint ranking – generally one in which markedness constraints outrank faithfulness constraints. When she hears others speaking in a way inconsistent with her current ranking, she identifies the constraints responsible for the inconsistency, and moves them far enough down in her constraint ranking to remove the inconsistency – but no farther – repeating as often as necessary. This procedure converges fairly quickly on the correct constraint ranking: With n constraints, the number of possible constraint rankings, ignoring scales, is n!, but the number of informative examples needed for the constraint demotion algorithm to work is a manageable n · (n-1).

   Applied to kin terms, constraint demotion implies that when a child learns that Mother's Sister is equated with Mother she is not just learning a single word. She is also learning a precedent that will affect other kin terms she learns. More specifically, she is learning that Minimize Parents' Siblings outranks Distinguish Distance, which blocks the inclination to learn distinct terms for certain more distant kin, like Mother's Sister's Child (given the scale Minimize Far Kin≥Minimize Near Kin). But not conversely: If she hears a Cousin called Sibling, this will not block her learning that his mother is called something other than Mother (D'Andrade Reference D'Andrade and Kay1971). The grammar faculty hypothesis thus has still-untested implications for how kin terms are learned.

3. 3. The grammar faculty faces one further problem. According to OT, constraints or constraint schemas are universal. But where do universals come from? This area of OT is not well-understood, but we can at least compare two possible kinds of answer.

   Constraints could be innate. In each of the domains in which grammar operates, language learners might face a fixed menu of constraints ready to be ranked. For each domain there would be a separate evolutionary story about where constraints come from. Applied to kin terms, this would imply that not just the conceptual structure of kinship, but actual constraints on kin terms – or maybe more abstract constraint schemas for space-like conceptual structure – are built into humans by natural selection.

   This simple solution is not very plausible for kin terms, or in general. In phonology, where the topic has received most attention, a recent review concludes that “the innateness hypothesis faces two obstacles: it fails to provide credible accounts of either the epigenesis or phylogenesis of [constraints]” (Bermúdez-Otero & Börjars Reference Bermúdez-Otero and Börjars2006). The alternative is that constraints are neither innate nor culturally acquired, but discovered. Theories of constraint discovery are not as well-developed as other areas of OT, but in general terms, constraint discovery involves a learner's grammar machinery monitoring her psychological operations – perceptual, conceptual, and motor – on the lookout for salient prototypical and distinctive features likely to be mutually relevant to speakers and hearers. (Bermúdez-Otero & Börjars, Reference Bermúdez-Otero and Börjars2006, review several proposals for phonology.) Constraint discovery is a coordination game, with each player trying to zero in on a set of constraints likely be chosen by everyone else. On this view, grammar would have a well-defined function, but its scope would be open-ended. Grammars could grow opportunistically, colonizing any “grammar-friendly” cognitive or perceptual domain in which universals of psychology provide common ground for developing shared codes.

Thus, the study of kin terms does not lead to the discovery of one special-purpose module: there is no Kin Term Acquisition Device. Instead, there is a conceptual structure of kinship, partly homologous with conceptual structure in other domains, partly of specialized design. And there is a grammar of kinship, bridging the gap between thoughts and words with communicational principles of more general application. The study of kin terms, in other words, leads beyond kin terms, to “fundamental structures of the human mind” (Lévi-Strauss Reference Lévi-Strauss1969, pp. 75, 84).

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