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==Origin==
[[Greek]] ''dichotomia'' ("διχοτομία") , from ''dichotomos'' - ''dikho''-‘in [[two]], apart’, -''tomia'' - ‘cutting,’ from temnein ‘to cut, incision, excision of an object
*[http://en.wikipedia.org/wiki/17th_century 1610]
==Definitions==
*1: a division into [[two]] especially mutually exclusive or [[contradictory]] groups or [[entities]] <the dichotomy between [[theory]] and [[practice]]>; also : the [[process]] or practice of making such a division <dichotomy of the population into two opposed classes>
*2: the [[phase]] of the [[moon]] or an inferior planet in which half its disk appears [[illuminated]]
*3a : bifurcation; especially : repeated bifurcation (as of a [[plant]]'s stem)
:b : a system of branching in which the main [[axis]] forks repeatedly into two branches
:c : branching of an [[ancestral]] line into two equal diverging branches
*4: something with seemingly [[contradictory]] qualities <it's a dichotomy, this opulent Ritz-style [[luxury]] in a place that fronts on a boat harbor — Jean T. Barrett>
==Description==
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.
Such a partition is also frequently called a [http://en.wikipedia.org/wiki/Bipartition bipartition].
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.
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 and/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).
''Perceived Dichotomies'' are common in Western thought. [http://en.wikipedia.org/wiki/C._P._Snow C. P. Snow] believes that Western society has become an [[argument]] [[culture]] ([http://en.wikipedia.org/wiki/The_Two_Cultures ''The Two Cultures'']). In ''The Argument Culture'' (1998), [http://en.wikipedia.org/wiki/Deborah_Tannen 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.[http://en.wikipedia.org/wiki/Dichotomy]
[[Category: Logic]]
==Origin==
[[Greek]] ''dichotomia'' ("διχοτομία") , from ''dichotomos'' - ''dikho''-‘in [[two]], apart’, -''tomia'' - ‘cutting,’ from temnein ‘to cut, incision, excision of an object
*[http://en.wikipedia.org/wiki/17th_century 1610]
==Definitions==
*1: a division into [[two]] especially mutually exclusive or [[contradictory]] groups or [[entities]] <the dichotomy between [[theory]] and [[practice]]>; also : the [[process]] or practice of making such a division <dichotomy of the population into two opposed classes>
*2: the [[phase]] of the [[moon]] or an inferior planet in which half its disk appears [[illuminated]]
*3a : bifurcation; especially : repeated bifurcation (as of a [[plant]]'s stem)
:b : a system of branching in which the main [[axis]] forks repeatedly into two branches
:c : branching of an [[ancestral]] line into two equal diverging branches
*4: something with seemingly [[contradictory]] qualities <it's a dichotomy, this opulent Ritz-style [[luxury]] in a place that fronts on a boat harbor — Jean T. Barrett>
==Description==
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.
Such a partition is also frequently called a [http://en.wikipedia.org/wiki/Bipartition bipartition].
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.
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 and/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).
''Perceived Dichotomies'' are common in Western thought. [http://en.wikipedia.org/wiki/C._P._Snow C. P. Snow] believes that Western society has become an [[argument]] [[culture]] ([http://en.wikipedia.org/wiki/The_Two_Cultures ''The Two Cultures'']). In ''The Argument Culture'' (1998), [http://en.wikipedia.org/wiki/Deborah_Tannen 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.[http://en.wikipedia.org/wiki/Dichotomy]
[[Category: Logic]]
