Dichotomy
Overview

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
Partition of a set
In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X...

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
Mutually exclusive
In layman's terms, two events are mutually exclusive if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both....

: nothing can belong simultaneously to both parts.

The two parts thus formed are complements
Complement (set theory)
In set theory, a complement of a set A refers to things not in , A. The relative complement of A with respect to a set B, is the set of elements in B but not in A...

.
Discussions
Encyclopedia
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
Partition of a set
In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X...

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
Mutually exclusive
In layman's terms, two events are mutually exclusive if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both....

: nothing can belong simultaneously to both parts.

The two parts thus formed are complements
Complement (set theory)
In set theory, a complement of a set A refers to things not in , A. The relative complement of A with respect to a set B, is the set of elements in B but not in A...

. In logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

, 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 there exists a proposition
Proposition
In logic and philosophy, the term 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
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

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
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

, literature
Literature
Literature is the art of written works, and is not bound to published sources...

, or linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....

. 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
C. P. Snow
Charles Percy Snow, Baron Snow of the City of Leicester CBE was an English physicist and novelist who also served in several important positions with the UK government...

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 British scientist and novelist C. P. Snow. Its thesis was that "the intellectual life of the whole of western society" was split into the titular two cultures—namely the sciences and the humanities—and that this was a major...

). 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
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, 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
Classical dichotomy
In macroeconomics, the classical dichotomy refers to an idea attributed to classical and pre-Keynesian economics that real and nominal variables 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 sets, 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 natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, 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 animals that are members of the subphylum Vertebrata . Vertebrates are the largest group of chordates, with currently about 58,000 species described. Vertebrates include the jawless fishes, bony fishes, sharks and rays, amphibians, reptiles, mammals, and birds...

s and invertebrate
Invertebrate
An invertebrate is an animal without a backbone. The group includes 97% of all animal species – all animals except those in the chordate subphylum Vertebrata .Invertebrates form a paraphyletic group...

s.
• In botany
Botany
Botany, plant science, or plant biology is a branch of biology that involves the scientific study of plant life. Traditionally, botany also included the study of fungi, algae and viruses...

, a dichotomy is a mode of branching by repeated bifurcation. Thus a focus on branching rather than division.
• In computer science
Computer science
Computer science or computing 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 systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...

and in philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

, dichotomy is the belief that humans consist of a soul and a body. (See Mind-body dichotomy
Mind-body dichotomy
The mind-body problem is a philosophical problem arising in the fields of metaphysics and philosophy of mind. The problem arises because mental phenomena appear to be qualitatively and substantially different from the physical bodies on which they appear to depend. There are a few major theories on...

) This stands in contrast to trichotomy
Trichotomy
In mathematics, the Law of Trichotomy states that every real number is either positive, negative, or zero. More generally, trichotomy is the property of an order relation...

.
• 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 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 American author of the series Conversations with God. The nine books in the complete series are Conversations With God , Friendship with God, Communion with God, Conversations With God for Teens, The New Revelations, Tomorrow's God, and Home with God: In a Life That Never...

.
• In Astronomy it is the phase of the moon or an inferior planet in which half its disk appears illuminated
• In sociology
Sociology
Sociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...

and semiotics
Semiotics
Semiotics, also called semiotic studies or semiology, is the study of signs and sign processes , indication, designation, likeness, analogy, metaphor, symbolism, signification, and communication...

, 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
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; the East-West dichotomy
East-West dichotomy
The East-West dichotomy is a sociological concept used to describe perceived differences between Western cultures and the Eastern world. Cultural rather than geographical in division, the boundaries of East and West are not fixed, but vary according to the criteria adopted by individuals using the...

contrasts the Orient
Orient
The Orient means "the East." It is a traditional designation for anything that belongs to the Eastern world or the Far East, in relation to Europe. In English it is a metonym that means various parts of Asia.- Derivation :...

and the Occident. 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 American post-structuralist philosopher, who has contributed to the fields of feminism, queer theory, political philosophy, and ethics. She is a professor in the Rhetoric and Comparative Literature departments at the University of California, Berkeley.Butler received her Ph.D...

's deconstruction of the gender
Gender
Gender is a range of characteristics used to distinguish between males and females, particularly in the cases of men and women and the masculine and feminine attributes assigned to them. Depending on the context, the discriminating characteristics vary from sex to social role to gender identity...

-dichotomy and Val Plumwood
Val Plumwood
Val Plumwood , formerly Val Routley, was an Australian ecofeminist 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 of an individual, also called social context or milieu, is the culture that s/he was educated or lives in, and the people and institutions with whom the person interacts....

dichotomy.
• The I Ching
I Ching
The I Ching or "Yì Jīng" , also known as the Classic of Changes, Book of Changes and Zhouyi, is one of the oldest of the Chinese classic texts...

and taijitu
Taijitu
Taijitu is a term which refers to a Chinese symbol for the concept of yin and yang...

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
Classification of mental disorders
The classification of mental disorders, also known as psychiatric nosology or taxonomy, is a key aspect of psychiatry and other mental health professions and an important issue for consumers and providers of mental health services...

in psychiatry
Psychiatry
Psychiatry is the medical specialty devoted to the study and treatment of mental disorders. These mental disorders include various affective, behavioural, cognitive and perceptual abnormalities...

or clinical psychology
Clinical psychology
Clinical psychology is an integration of science, theory and clinical knowledge for the purpose of understanding, preventing, and relieving psychologically-based distress or dysfunction and to promote subjective well-being and personal development...

, dichotomous classification or categorization
Categorization
Categorization is the process in which ideas and objects are recognized, differentiated and understood. Categorization implies that objects are grouped into categories, usually for some specific purpose. Ideally, a category illuminates a relationship between the subjects and objects of knowledge...

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
Dialectical behavioral therapy
Dialectical behavior therapy is a system of therapy originally developed by Marsha M. Linehan, a psychology researcher at the University of Washington, to treat people with borderline personality disorder...

, a treatment shown to have some success in treating some clients with Borderline Personality Disorder
Borderline personality disorder
Borderline personality disorder is a personality disorder described as a prolonged disturbance of personality function in a person , characterized by depth and variability of moods.The disorder typically involves unusual levels of instability in mood; black and white thinking, or splitting; the...

, 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.

• Binary opposition
Binary opposition
In critical theory, a binary opposition is a pair of related terms or concepts that are opposite in meaning. Binary opposition is the system by which, in language and thought, two theoretical opposites are strictly defined and set off against one another. It is the contrast between two mutually...

• Bipartite
Bipartite
Bipartite means having two parts, or an agreement between two parties. More specifically, it may refer to any of the following:-Mathematics:* 2 * bipartite graph* bipartite cubic, a type of cubic function-Medicine:...

(disambiguation)
• Borderline Personality Disorder
Borderline personality disorder
Borderline personality disorder is a personality disorder described as a prolonged disturbance of personality function in a person , characterized by depth and variability of moods.The disorder typically involves unusual levels of instability in mood; black and white thinking, or splitting; the...

• Class (set theory)
Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets which can be unambiguously defined by a property that all its members share. The precise definition of "class" depends on foundational context...

• Dialectical Behavioral Therapy
Dialectical behavioral therapy
Dialectical behavior therapy is a system of therapy originally developed by Marsha M. Linehan, a psychology researcher at the University of Washington, to treat people with borderline personality disorder...

• Dualism
Dualism
Dualism denotes a state of two parts. 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 or common usages. Dualism can refer to moral dualism, Dualism (from...

• Polychotomy
Polychotomy
Polychotomy is a division or separation into many parts or classes which are static and not temporally dependent due to evolution. Polychotomy can be thought of as a generalization of dichotomy, which is a polychotomy of exactly two parts.-Examples of Usage:*****...

• Trichotomy
Trichotomy
In mathematics, the Law of Trichotomy states that every real number is either positive, negative, or zero. More generally, trichotomy is the property of an order relation...

• Yin and Yang
Yin and yang
In Asian philosophy, the concept of yin yang , which is often referred to in the West as "yin and yang", is used to describe how polar opposites or seemingly contrary forces are interconnected and interdependent in the natural world, and how they give rise to each other in turn. Opposites thus only...