Dichotomy

A dichotomy is the division of a proposition into two parts which are both mutually exclusive – i.e. both cannot be simultaneously true – and jointly exhaustive – i.e. they cover the full range of possible outcomes. They are often contrasting and spoken of as "opposites". The term comes from dichotomos (divided): dich- ( two) temnein (to cut).

Related Topics:
Proposition - Mutually exclusive - Jointly exhaustive

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• The above applies directly when the term is used in mathematics, philosophy 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 A is contained in 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 or not 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).
• Dichotomies are common in Western thought. C.P. Snow believes that Western society has become an argument culture. 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 monetary economics, a special branch of economics dealing with money and the financial system of a country, the classical dichotomy is the division between real money, which is measured in physical terms and is usually supposed to be a better indicator of money value due to its stability, and nominal money, which is measured in terms of a currency and hence is susceptible to inflation. According to Milton Friedman, who is commonly referred to as the father of monetary economics, different forces influence real and nominal variables (money value here) and changes in the money supply affect nominal variables but not real variables. This irrelevance of monetary changes for real variables is called monetary neutrality.
• 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 (classes versus primitive data types).
 
Dichotomy: Examples ►