According to Evans & Levinson (E&L), the search for semantic universals is misguided because “many languages make semantic distinctions we … would never think of” (sect. 2.2.5, para. 3): no theory of universals can capture local linguistic exceptionality. This commentary shows that the exact opposite is true: apparent exceptionality provides highly robust evidence for Universal Grammar (UG). Here I summarize E&L's semantic argument, expose its fundamental flaw, then empirically refute their claim: two primitives are proposed that explain not only their primary example of “semantic distinctions we … would never think of,” but derive two Universals and two further semantic Surprises.

Consider E&L's argument from semantics. For limited counting, languages may use noun/verb marking instead of numerals: for example, English king~king-s; Sanskrit rājan~rājan-au~rājan-as “one~two~many kings.” Faced with singular~plural versus singular~dual~plural, accounting for number variation hardly appears challenging. However, Kiowa, say E&L (mis-citing Mithun), possesses “a marker that means roughly ‘of unexpected number’: on … ‘man’ it means ‘two or more,’ on … ‘leg’ … ‘one or more than two, … on ‘stone’ … ‘just two’” (sect. 2.2.5, para. 3). Thus, number systems present semantic distinctions too diverse for any universals to subsume. So, number variation refutes UG.

To reveal the flaw, consider chemistry. Common oxygen-carbon compounds (CO, CO₂) are odorless, colorless gases; but C₃O₂ is a colorless, odorous gas and C₁₂O₉, a white solid. Does such diversity mean these are not all constructed from the same two basic building blocks? No. Chemists simply recognize that atoms combined in surprising ways yield surprising properties. Analogously, linguists seek universal primitives and aim to explain cross-linguistic differences through the different ways these may combine. For Kiowa to refute UG, one must (a) look beyond surface appearances, (b) discover, by analysis, the building blocks it uses, and (c) show that these are irreconcilable with any universal (non-Kiowa-specific) set of primitives. E&L do none of these: Like early chemists, their interest lies only in listing differences between substances, not in discovering how their components explain those properties.

Such criticism is more than methodological. It empirically undermines E&L's position. To explain Kiowa requires just two primitives (rooted in Thomas Reference Thomas1955), and these same primitives derive two robust Universals (U_1/2) and two semantic Surprises (S_1/2) from unrelated languages. Thus, local linguistic exceptionality, properly analyzed, argues strongly for UG.

UG number theory is basic set theory, so the two primitives concern sets. The first asserts ([+atomic]) or denies ([−atomic]) that a set is a singleton. The second asserts ([+augmented]) or denies ([−augmented]) that some given property of the whole set also holds of a subset.Footnote ¹ English uses just [±atomic]: king is [+atomic], kings [−atomic]. Sanskrit uses both (momentarily ignore typefaces):

• singular = [+atomic−augmented]— singletons without singleton subsets

• dual = [−atomic−augmented]— nonsingletons without nonsingleton subsets

• plural = [−atomic+augmented]— nonsingletons with nonsingleton subsets

For example, {Henry, Richard} is [−atomic] (nonsingleton) and [−augmented] (lacking [−atomic] subsets).

UG aims to explain constraints on cross-linguistic variation. The primitives just cited do precisely this, deriving robust two universals concerning the expression of number in natural languages. In broad outline:

(U₁) Three is the highest number expressible grammatically in any language, without specialized numeral vocabulary (contra quadrals, see Corbett Reference Corbett2000). Derivation: three kings (e.g., {Alfred, Henry, Richard}) is a collection (hence [−atomic]); it has nonatomic subsets ({Alfred, Henry}) (hence [−atomic +augmented]); but no such subset itself has nonatomic subsets (hence [−atomic +augmented −augmented]). Therefore, [−augmented +augmented −atomic]=3. Moreover, by basic set theory, addition of extra primitives is either contradictory or redundant.Footnote ² So, trial (3) is the highest the number primitives of UG can reach.

(U₂) Languages with dual invariably have singular/plural (Corbett Reference Corbett2000), because the primitives required for dual ([±atomic], [±augmented]) also generate singular/plural (see Sanskrit above).Footnote ³ Likewise, languages with trial invariably have singular/dual/plural because the resources for trial ([±atomic], [±augmented], opposing +/− specifications) include [±atomic]/[±augmented], which generate dual, and so on.Footnote ⁴ (Harbour, in press, derives further analogous results.)

Important as such Universals are, the true test of these primitives, and UG, is whether they capture systems “we … would never think of.” In fact, these capture two semantic surprises E&L do not discuss, in addition to Kiowa.

(S₁) Although 2≠1+3, languages may create dual from singular+plural. Consider Hopi “this (one) ran/these (ones) ran” (Hale Reference Hale1997). Plural puma, “these,” and singular wari, “ran,” combine to create dual puma wari, “these two ran,” as follows:

• singular = pam wari

• Dual = puma wari

• Plural = puma yùutu

The semantic surprise that 1+3=2 follows from the primitives. The boldfacing in both tables is identical: dual/plural share [−atomic]/puma; singular/dual share [−augmented]/wari.

(S₂) Although “we” is plural, some languages treat the meaning {me, you} as singular. Winnebago -wĩ pluralizes both sh-'ũ, “you do,” and hĩ-'ũ, “you and I do,” giving sh-'ũ- wĩ, “you and other(s) do,” and hĩ-'ũ- wĩ, “you, I and other(s) do” (Lipkind Reference Lipkind1945). Anomalously, singular “we” arises because Winnebago uses only [±augmented] (Noyer Reference Noyer1992). Consequently, “we”={me, you, other(s)} is [+augmented] relative to “contains me, you”: it and its subset {me, you} both contain me, you. However, “we”={me, you} is [−augmented]: it contains me, you but has no proper subset that does. Thus, [±augmented] explains the semantically surprising singularity of some senses of “we.”

Finally, Kiowa. First, correcting E&L's errors, unsuffixed, “man”/”leg” mean “one or two”; “stick,” “more than one”; “hair,” “just two”; “stone,” “any number.” Suffixation yields “more than two men/legs,” “one stick,” “one, or three or more, hair(s)” (e.g., aa, “sticks,” aa- dau, “one stick”; aul, “two hairs,” au- dau, “one, or three or more, hair[s]”).

Nobody thinks groups of men odd, but pairs of hairs and solo legs normal. So, -dau does not mean “unexpected number of.” Actually, Kiowa is like French, with two minor differences. Both languages organize their nouns into classes, but, where French uses a property of animates [±feminine], Kiowa uses number primitives: for example, the “gender” of stick is [−atomic]. This cleverly avoids the French problem of giving sticks anatomical gender. However, it encounters a different difficulty: talking about “one stick” (where “one” is [+atomic] but “stick” is [−atomic]). All -dau does is register when such +/− conflicts occur (French faces similar mismatches – when [+feminine] la sentinelle references a [−feminine] guard – but lacks an analogous suffix). Nothing more exotic need be said (see Harbour Reference Harbour2006 for Jemez and full details in Harbour Reference Harbour2007).

E&L claim that there are no Universals and that semantic Surprises vitiate attempts to discover UG. Both claims have been refuted here: two primitives suffice to derive two Universals, E&L's prime example of something “we … would never think of,” and two further Surprises besides. Linguists, like chemists, must look beyond surface appearances to discover universal building blocks and their properties. E&L's critique of this program succeeds only in highlighting some of its compelling results.