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Dichotomy
 
 
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A dichotomy is any splitting of a whole into exactly two non-overlapping parts.

In other words, it is a partition
Partition of a set

In mathematics, a partition of a Set X is a division of X into non-overlapping "parts" or "blocks" or "cells" that cover all of X....
 of a whole (or a set) into two parts (subsets) that are:






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A dichotomy is any splitting of a whole into exactly two non-overlapping parts.

In other words, it is a partition
Partition of a set

In mathematics, a partition of a Set X is a division of X into non-overlapping "parts" or "blocks" or "cells" that cover all of X....
 of a whole (or a set) into two parts (subsets) that are:
  • mutually exclusive
    Mutually exclusive

    In simple terms, two events are mutually exclusive if they cannot occur at the same time ....
     : nothing can belong simultaneously to both parts, and
  • jointly exhaustive : everything must belong to one part or the other.


The two parts thus formed are complement
Complement (set theory)

In discrete mathematics and predominantly in set theory, a complement is a concept used in comparisons of sets to refer to the unique values of one set in relation to another....
s. In logic
Logic

Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical Trivium . The word derives from Greek language ?????? , fem....
, the partitions are opposites
Dual (category theory)

In category theory, a branch of mathematics, duality is a correspondence between properties of a category C and so-called dual properties of the opposite category Cop....
 if their exists a proposition
Proposition

This article is about the term proposition in logic and philosophy; for other uses see PropositionIn logic and philosophy, proposition refers to either the "content" or Meaning of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence....
 such that it holds over one and not the other.

Etymology


The term comes from the Greek dichotomia (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
    Mathematics

    Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
    , philosophy
    Philosophy

    Philosophy is the study of general problems concerning matters such as existence, knowledge, truth, beauty, justice, validity, mind, and language....
     or linguistics
    Linguistics

    Linguistics is the science study of natural language. Linguistics encompasses a number of sub-fields. An important topical division is between the study of language structure and the study of Meaning ....
    . 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 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. C.P. Snow believes that Western society has become an argument culture (The Two Cultures
    The Two Cultures

    The Two Cultures is the title of an influential 1959 Rede Lecture by United Kingdom scientist and novelist C. P. Snow. Its thesis was that the breakdown of communication between the "two cultures" of modern society — the sciences and the humanities — was a major hindrance to solving the world's problems....
    ). In The Argument Culture (1998), Deborah Tannen
    Deborah Tannen

    Deborah Frances Tannen is an United States professor of linguistics at Georgetown University, Washington, D.C., U.S.A.Although she has lectured worldwide in her field, and written or edited numerous academic publications on linguistics and interpersonal communication, she is best known for her general-audience books on interpersonal commu...
     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 economics, the classical dichotomy
    Classical dichotomy

    In macroeconomics, the classical dichotomy refers to an idea attributed to classical economics and pre-Keynesian economics that Real versus nominal value can be analyzed separately....
     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
    Set theory

    Set theory is the branch of mathematics that studies Set , which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics....
    , a dichotomous relation R is such that either aRb, bRa or both.
  • In biology
    Biology

    Biology is a branch of the natural sciences concerned with the study of living organisms and their interaction with each other and their environment ....
    , 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 vertebrate
    Vertebrate

    Vertebrates are members of the subphylum Vertebrata, chordates with Vertebras or Vertebral columns. The grouping sometimes includes the hagfish, which have no vertebrae, but are genetically quite closely related to lampreys, which do have vertebrae....
    s and invertebrate
    Invertebrate

    An invertebrate is an animal lacking a vertebral column. The group includes 98% of all animal species ? all animals except those in the Chordate subphylum vertebrate ....
    s.
  • In botany
    Botany

    Botany, plant science, phytology, or plant biology is a branch of biology and is the Scientific method of plant life and development....
    , a dichotomy is a mode of branching by repeated bifurcation
    Bifurcation

    Bifurcation means the splitting of a main body into two parts.Bifurcation or Bifurcated may refer to:*Bifurcation , the division of issues in a trial for example the division of a page into two parts....
    . Thus a focus on branching rather than division.
  • In computer science
    Computer science

    Computer science is the study of the theoretical foundations of information and computation, and of practical techniques for their implementation and application in computer systems....
    , 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
    Theology

    Theology is the study of the existence or attributes of a deity or gods, or more generally the study of religion or spirituality. It is sometimes contrasted with religious studies: theology is understood as the study of religion from an internal perspective , and religious studies as the study of religion from an external perspective....
     and in philosophy
    Philosophy

    Philosophy is the study of general problems concerning matters such as existence, knowledge, truth, beauty, justice, validity, mind, and language....
    , dichotomy is the belief that humans consist of a soul and a body. (See Mind-body dichotomy
    Mind-body dichotomy

    The mind-body dichotomy is the view that "mind" phenomena are, in some respects, "non-Matter" . In a religious sense, it refers to the separation of body and soul....
    ) This stands in contrast to trichotomy
    Trichotomy

    Generally, a trichotomy is a splitting into three disjoint parts. In mathematics, the law of trichotomy is most commonly the statement that for any numbers x and y, exactly one of the following relations holds:...
    .
  • Dichotomy is also a method of execution wherein the victim is cut in two.
  • Divine Dichotomy as mentioned in the Conversations With God
    Conversations with God

    Conversations with God is a sequence of nine books written by Neale Donald Walsch, written as a dialogue in which Walsch asks questions and God answers....
     series of books by religious author Neale Donald Walsch
    Neale Donald Walsch

    'Neale Donald Walsch' is an United States author of the series Conversations with God. The books so far in the series are Conversations With God , Friendship with God, Communion with God, The New Revelations, Tomorrow's God, What God Wants, Home with God: In a Life That Never Ends, and his newest book, Happi...
    .
  • In it is the phase of the moon or an inferior planet in which half its disk appears illuminated
  • In sociology
    Sociology

    Sociology is a branch of the social sciences that uses systematic methods of Empiricism and critical theory to develop and refine a body of knowledge about human social structure and activity, sometimes with the goal of applying such knowledge to the pursuit of social welfare....
     dichotomies are the subject of attention because they may form the basis to divisions and inequality. For example, the Domestic-public dichotomy
    Domestic-public dichotomy

    Domestic-public dichotomy refers to the divisions between men's roles and women's roles in life. Although these divisions are not being strictly utilized across the world today, they used to be shared across most prehistoric cultures....
     divides men's and women's roles in a society, which may cause inequalities between the two. Some social scientists attempt to deconstruct dichotomies in order to address the divisions and inequalities they create: for instance Judith Butler
    Judith Butler

    Judith Butler is an United States post-structuralist philosopher, who has contributed to the fields of feminism, queer theory, political philosophy, and ethics....
    's deconstruction of the gender
    Gender

    Gender comprises a range of differences between man and woman, extending from the biological to the social. Biologically, the male gender is defined by the presence of a Y-chromosome, and its absence in the female gender....
    -dichotomy and Val Plumwood
    Val Plumwood

    Val Plumwood , formerly Val Routley, was an Australian ecofeminism intellectual and activist, who was prominent in the development of radical ecosophy from the early 1970s through the remainder of the 20th century....
    's deconstruction of the human-environment
    Social environment

    The social environment ,also known as the milieu, is the identical or similar social positions and social roles as a whole that influence the individuals of a group....
     dichotomy.
  • The I Ching
    I Ching

    The I Ching , or ?Y? Jing? ; also called Classic of Changes or Book of Changes is one of the oldest of the Chinese classic texts....
     and taijitu
    Taijitu

    File:Yin and Yang.svgTaijitu is one term which refers to a set of geometric patterns used throughout history by various cultures. The most recognized form is composed of two semi-circular teardrop-shaped curves of different colors, or a circle separated by an S-shaped line, where each half is marked with a dot in the opposite color....
     represent the yin yang theories of traditional Chinese culture.


See also

  • Binary opposition
    Binary opposition

    In critical theory, a binary opposition is a pair of theoretical opposites. In structuralism, it is seen as a fundamental organizer of human philosophy, culture, and language....
  • Bipartite
    Bipartite

    Bipartite means having two parts, or an agreement between two parties. More specifically, it may refer to any of the following:* 2 In mathematics:...
     (disambiguation)
  • Dualism
    Dualism

    Dualism denotes a state of two parts. The word's origin is the Latin duo, "two" . The term 'dualism' was originally coined to denote co-eternal binary opposition, a meaning that is preserved in metaphysical and philosophical duality discourse but has been diluted in general usage....
  • Dichotomy paradox
  • Polychotomy
  • Trichotomy
    Trichotomy

    Generally, a trichotomy is a splitting into three disjoint parts. In mathematics, the law of trichotomy is most commonly the statement that for any numbers x and y, exactly one of the following relations holds:...
  • Class (set theory)
    Class (set theory)

    In set theory and its applications throughout mathematics, a class is a collection of Set which can be unambiguously defined by a property that all its members share....


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