Dichotomy

An example of a dichotomy is the partition of a scene into figure and ground – the letters are foreground or figure; the rest is the background.

A dichotomy is any splitting of a whole into exactly two non-overlapping parts, meaning it is a procedure in which a whole is divided into two parts. It is a partition of a whole (or a set) into two parts (subsets) that are:

• jointly exhaustive: everything must belong to one part or the other, and
• mutually exclusive: nothing can belong simultaneously to both parts.

The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other.

Etymology

The term comes from the Greek dichotomia (Greek: "διχοτομία") (divided): dich- (form of dícha, in two, asunder); tomia- a combining form meaning cutting, incision, excision of an object.

Usage

• The above applies directly when the term is used in mathematics, philosophy, literature, or linguistics. For example, if there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice-versa, and they are jointly exhaustive, since they cover all of A, and together again give A.
• A false dichotomy is a logical fallacy consisting of a supposed dichotomy which fails one or both of the conditions: it is not jointly exhaustive nor mutually exclusive. In its most common form, two entities are presented as if they are exhaustive, when in fact other alternatives are possible. In some cases, they may be presented as if they are mutually exclusive although there is a broad middle ground (see also undistributed middle).
• Perceived Dichotomies are common in Western thought. C. P. Snow believes that Western society has become an argument culture (The Two Cultures). In The Argument Culture (1998), Deborah Tannen suggests that the dialogue of Western culture is characterized by a warlike atmosphere in which the winning side has truth (like a trophy). In such a dialogue, the middle alternatives are virtually ignored.
• In statistics, dichotomy may be the distinction of measurements into two groups in an ordinal scale, e.g. a "good" and a "bad" group.
• In economics, the classical dichotomy is the division between the real side of the economy and the monetary side. According to the classical dichotomy, changes in monetary variables do not affect real values as output, employment, and the real interest rate. Money is therefore neutral in the sense that it cannot affect these real variables.
• In set theory, a dichotomous relation R is such that either aRb, bRa or both.
• In biology, a dichotomy is a division of organisms into two groups, typically based on a characteristic present in one group and absent in the other. Such dichotomies are used as part of the process of identifying species, as part of a dichotomous key, which asks a series of questions, each of which narrows down the set of organisms. A well known dichotomy is the question "does it have a backbone?" used to divide species into vertebrates and invertebrates.
• In botany, a dichotomy is a mode of branching by repeated bifurcation. Thus a focus on branching rather than division.
• In computer science, more specifically programming language engineering, the term dichotomy is used to denote fundamental dualities in a language's design. For instance, C++ has a dichotomy in its memory model (heap versus stack), whereas Java has a dichotomy in its type system (references versus primitive data types).
• In the anthropological field of theology and in philosophy, dichotomy is the belief that humans consist of a soul and a body. (See Mind-body dichotomy) This stands in contrast to trichotomy.
• Dichotomy is also a method of execution wherein the victim is cut in two.^{[citation needed]}
• Divine Dichotomy as mentioned in the Conversations With God series of books by religious author Neale Donald Walsch.
• In Astronomy it is the phase of the moon or an inferior planet in which half its disk appears illuminated
• In sociology and semiotics, dichotomies (also sometimes called 'binaries' and/or 'binarisms') are the subject of attention because they may form the basis to divisions and inequality. For example, the Domestic-public dichotomy divides men's and women's roles in a society; the East-West dichotomy contrasts the Orient and the Occident. Some social scientists attempt to deconstruct dichotomies in order to address the divisions and inequalities they create: for instance Judith Butler's deconstruction of the gender-dichotomy and Val Plumwood's deconstruction of the human-environment dichotomy.
• The I Ching and taijitu represent the yin yang theories of traditional Chinese culture. However, these do not represent a true dichotomy as the symbol incorporates a portion of each in the other, representing a dialectic.
• In the classification of mental disorders in psychiatry or clinical psychology, dichotomous classification or categorization refers to the use of cut-offs intended to separate disorder from non-disorder at some level of abnormality, severity or disability.
• In Dialectical Behavioral Therapy, a treatment shown to have some success in treating some clients with Borderline Personality Disorder, an essential tool used is based on the idea of dichotomy. Dichotomy, in this case, is a self-defeating behavior using "all-or-nothing" or "black-and-white" thinking. The therapy teaches the patient how to change the dichotomy to a more "dialectical" (or "seeing the middle ground") way of thinking.

See also

• Binary opposition
• Bipartite (disambiguation)
• Borderline Personality Disorder
• Class (set theory)
• Dialectical Behavioral Therapy
• Dichotomy paradox
• Dualism
• Polychotomy
• Trichotomy
• Yin and Yang