=+=

__N-ary opposition__In critical theory, an n-ary opposition (also n-ary system) is a set of n related terms or concepts which are spread over a 'spectrum' of meaning. The term, introduced by the columnist Anand Manikutty, is also used to refer to the opposition that exists among the n concepts. Binary and ternary oppositions are common types of n-ary oppositions. A binary opposition is a set of two related terms or concepts which are opposite in meaning. A ternary opposition is a set of three related terms or concepts. A ternary opposition may be a set of three related terms of concepts out of which two are opposite in meaning and the third is a null concept. Ternary opposition, also a term introduced by Anand Manikutty, is the system by which, in language and thought, three theoretical opposites are strictly defined and set off agsinst one another. It is the contrast between three mutually exclusive terms, such as positive, negative and zero. Another example : up, down and "middle" (although various other terms may be used in place of "middle" such as zero position). A third example is left, right and "middle". Again, various other terms may be used in place of "middle".

N-ary opposition is proposed as an important concept within structuralism which sees such distinctions as fundamental to all language and thought. In this extension of structuralism, a n-ary opposition is seen as a fundamental organizer of human philosophy, culture and language.

N-ary opposition was originated by the columnist Anand Manikutty as a response to Saussurean structrualist theory and the idea of binary oppositions. According to Ferdinand de Saussure, the binary opposition is the meanas by which the units of language have value or meaning. As Wikipedia puts its, "each unit is defined in reciprocal determination with another term, as in binary code. It is not a contradictory relation but, a structural, complementary one. Saussure demonstrated that a sign's meaning is derived from its context (syntagmatic dimension) and the group (paradigm) to which it belongs. An example of this is that one cannot conceive of 'good' if we do not understand 'evil'. In post-structuralism, it is seen as one of several influential characteristics or tendencies of Western and Western-derived thought, and that typically, one of the two opposites assumes a role of dominance over the other. The categorization of binary oppositions is "often value-laden and ethnocentric", with an illusory order and superficial meaning." However, as can be easily confirmed by anyone with an Internet connection, there are not only binary oppositions but also ternary oppositions, quarternary oppositions and so forth. This has been generalized to the idea of n-ary oppositions.

A short proof of the existence of n-ary oppositions follows. Note that n can take any integer value including potentially 1 and 0. Negative values are not currently supported.

**N-ary oppositions exist.**

__Theorem :__

__Proof.__N-ary oppositions exist if binary oppositions exists since a binary opposition is nothing but an n-ary opposition for N = 2. Even if binary oppositions don't exist, every concept in human language and thought has only a fixed number of meanings. So a crude upper bound for the number N for any language may be obtained by setting N to be the number of words in the language. Note that this number is finite for any language.

=+=