A hypothesis of the target article is that grammar – as conceived in Optimality Theory (Prince & Smolensky Reference Prince and Smolensky2004) – is a general cognitive capacity underlying cognitive universals in a range of cognitive domains 𝔻; the test case is 𝔻=kinship terminology. Because we find the target article unclear or ambiguous on a number of key points, and because OT's route to defining a 𝔻-theory – call it 𝕋 – is abstract and unfamiliar, we reformulate the hypothesis, through a concrete metaphor involving three machines.

To determine the name of Mother's Sister in Seneca, we begin with machine 𝒞, which displays the genealogical tree of Figure 2 of the target article (omitting shading and labeling). We select the Mother's Sister node of the tree; the machine produces an indigo card I containing a bit-string of n 0s and 1s. Next, on the machine 𝒢, we insert indigo card I after setting a dial to “Seneca”; 𝒢 produces an orange card O, also containing a string of n bits. Finally, on machine 𝒱 we insert orange card O after setting a dial to “Seneca”; 𝒱 responds with a word through its loudspeaker (noyeh).

𝒞 is conceptual structure, which is universal (= not language-particular): 𝒞 has no dial. Theory 𝕋 provides 𝒞's genealogical graph, the types of nodes, and so forth. 𝒞 produces an indigo card I in a universal alphabet. Each symbol on I corresponds to the +(1) or –(0) value of a feature ƒ _k (e.g., ±female). 𝕋 specifies the universal mapping from the tree on 𝒞's screen to the bit-string of feature values on card I – defining the universal feature-set {ƒ _k }.

𝒢 is an OT grammar, which receives indigo-card-input I and produces orange-card-output O. The bit-string on O depends on 𝒢's dial setting, a language L=Seneca. The elements of L are all the different orange cards' bit-strings that machine 𝒢 can produce. All points of 𝒞 that yield the same orange card can be thought of as constituting one of L's 𝔻-categories; for example, Mother's Sister and Mother are in the same Seneca kinship category.

𝒱 is the vocabulary; it receives 𝒢's output, the orange card O representing a category, and, depending on the setting of its language dial, produces a distinct name for that bit-string/category. This name can then be used to refer any relation in that category; it is ambiguous in the same sense that a category name is ambiguous about which category member is being referred to.

𝕋 specifies the workings of 𝒢. Conceptually (not computationally), each possible output bit-string is evaluated by a set of universal constraints provided by 𝕋. Markedness constraint M _k (“minimize[+ƒ _k ]”) states that value+for feature ƒ _k is dispreferred or “marked”. Faithfulness constraint F _k (“distinguish-ƒ _k ”) demands that ƒ _k 's value on orange O match ƒ _k 's value on indigo I. Constraint conflicts are resolved by ranking: Possible output A is preferred to possible output B if the highest-ranked constraint that has a preference between them prefers A. If no bit-string A is preferred to B, then B is optimal; B is the grammar's output O. Crucially, ranking is language-particular – determined by the 𝒢's dial.

Thus the hypothesis is that a theory 𝕋 of a domain 𝔻 can provide all these specifications: Crucially, the universal constraints in the grammar 𝒢 which, via OT computation, explain crosscultural patterns in the conceptual distinctions conveyed by different languages' 𝔻-vocabularies.

At first sight, the outcome of optimization in kinship seems to result in polysemous terms (one word=several meanings) for different kin types. Previous OT work on polysemy has focused on the optimization of communication by means of polysemous terms (e.g., Fong Reference Fong, Verkuyl, De Swart and van Hout2005; Hogeweg Reference Hogeweg2009; Zeevat Reference Zeevat, van Deemter and Kibble2002; Zwarts Reference Zwarts, Meier and Weisgerber2004; Reference Zwarts, Asbury, Dotlačil, Gehrke and Nouwen2008;). A word is assumed to correspond to a fixed set of semantic features. In production (which means word choice in this domain), the input is the meaning a speaker wants to express and the candidates are the bundles of features conflated by the lexicon of her language. Similarly, when a hearer interprets a word, the input is the bundle of features that are stored for this word and the candidates are any combination of semantic features. The optimal interpretation for a word will consist of all features in the input that are not in conflict with the (linguistic) context. In contrast, in the target article, an input is an elementary kin type from a set shared across cultures (e.g., Mother's Sister) and the output is a kin type with fewer (or the same) marked feature values (e.g., Mother), entailing that the complex and simple type share a term: noyeh in Seneca. It appears that noyeh is not polysemous – it simply refers to Mother, but can be used to refer to Sister's Mother because this latter type has first been “reduced” to the first type. From the perspective of the hearer this view would be problematic when the intended meaning was the more complex type: It is not clear by what process a hearer could arrive at the interpretation Sister's Mother upon hearing noyeh.

However, according to the reformulated hypothesis above, the output of the interpretation is an abstract category subsuming both Mother and Sister's Mother and the analysis concerns the structuring of conceptual categories rather than the use of words. In other words, where the optimization in the above-mentioned works takes place in machine 𝒱, optimization in the target article takes place in machine 𝒢. As such, optimization in kinship is simply neutralization of featural differences and, surprisingly, has more in common with previous OT analyses in the domain of phonology than with OT analysis in the domain of polysemy.