Within chemistry, VALENCY refers to the capacity of an atom or group of atoms to combine in specific proportions with other atoms or groups of atoms. 1 The French linguist Lucien Tesnière is generally credited with introducing this term to linguistics, where it is used metaphorically for the capacity of a verb to combine with distinct arguments or valents (Crystal 1985). A verb like rain, which has no referential noun phrases associated with it, is said to be ZERO-PLACE or AVALENT; a verb like disappear, which takes only a subject argument, is said to be ONE-PLACE or MONOVALENT; verbs like devour and give are said to be TWO-PLACE (BIVALENT) and THREE-PLACE (TRIVALENT), respectively. This chemical metaphor has had a pervasive influence in linguistics: causative and applicative morphemes are now described as 'adding arguments,' while passives and middles are described as 'suppressing' or 'deleting' arguments, respectively. Entire sections of grammars are devoted to 'valency-changing,' 'valency-increasing,' or 'valency-reducing' processes, suggesting that the primary function of these grammatical processes is to regulate the number of arguments in clauses. The chemical metaphor contrasts with an older tradition that distinguishes just two classes of predicates—TRANSITIVE and INTRANSITIVE—and a category of VOICE. Passive voice and middle voice are seen within this tradition as altering the 'point of view' or 'centre of interest' (Jesperson 1924:167) within a clause rather than applying mathematical operations to it, and causatives and applicatives are sometimes included and sometimes excluded from the traditional range of voice-related phenomena. There are important issues here that need to be researched and clarified. One point distinguishing the theories of voice and valency, for example, is the issue of the degree to which grammars have the ability to COUNT. As an analogy, one commonly reads descriptions of stress systems in which accent is said to be placed on the third or fourth syllable from an edge, but these have generally been replaced by more restrictive theories in which rhythm operates in prosodic units of different sizes. In discovering this, we learn an important fact about language, that while counting may be a basic human cognitive process, it plays virtually no role in grammar. To an extent, then, voice and valency are competing theories of clause structure: (a) The theory of valency claims that there are at least four distinct grammatical classes of predicates (zero-, one-, two-, and three-place). The capacity of a predicate to occur with different numbers of noun phrases can itself be taken as a grammatical 1 The title of this paper extends a chain begun by Barber (1975) and continued by Croft (1994). The phonemic transcription used here for Creek is based on Mary R. Haas's work. The phonemes are /p t c k f s ł h m n w l y i i· a a· o o·/. /c/ is a voiceless palatal affricate; /ł/ is a voiceless lateral fricative. As a diphthong, /ay/ is pronounced and written /ey/; V· is a long vowel. Primary stress (realized as the last high pitch syllable in a word) is written with an acute accent an indicate falling tone and rising tone, respectively; n indicates nasalization indicates a stressed word-initial syllable (usually resulting from aphaeresis). I am grateful to Margaret McKane Mauldin and George Bunny for help with the Creek data cited in this paper, to Bob Dixon and Sasha Aikhenvald for organizing the workshop at which these ideas were developed, and to Ann Reed and two anonymous reviewers for comments. All mistakes are mine.