A Carroll diagram, Lewis Carroll's square, biliteral diagram or a ''two-way table'' is a
diagram
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three ...
used for grouping things in a yes/no fashion. Numbers or objects are either categorised as 'x' (having an
attribute x) or 'not x' (not having an attribute 'x'). They are named after
Lewis Carroll
Charles Lutwidge Dodgson (; 27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet and mathematician. His most notable works are '' Alice's Adventures in Wonderland'' (1865) and its sequ ...
, the
pseudonym
A pseudonym (; ) or alias () is a fictitious name that a person or group assumes for a particular purpose, which differs from their original or true name ( orthonym). This also differs from a new name that entirely or legally replaces an individu ...
of
polymath
A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...
Charles Lutwidge Dodgson
Charles Lutwidge Dodgson (; 27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet and mathematician. His most notable works are ''Alice's Adventures in Wonderland'' (1865) and its sequel ...
.
Usage
Although Carroll diagrams can be as simple as the first one above, the most well known types are those similar to the second one, where two attributes are shown. The
'universe
' of a Carroll diagram is contained within the boxes in the diagram, as any
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual number ...
or
object
Object may refer to:
General meanings
* Object (philosophy), a thing, being, or concept
** Object (abstract), an object which does not exist at any particular time or place
** Physical object, an identifiable collection of matter
* Goal, an ...
has to either have an attribute or not have it.
Carroll diagrams are often learnt by
schoolchildren
A student is a person enrolled in a school or other educational institution.
In the United Kingdom and most commonwealth countries, a "student" attends a secondary school or higher (e.g., college or university); those in primary or element ...
, but they can also be used outside the field of
education
Education is a purposeful activity directed at achieving certain aims, such as transmitting knowledge or fostering skills and character traits. These aims may include the development of understanding, rationality, kindness, and honesty ...
, since they are a tidy way of categorising and displaying information.
See also
*
Diagram
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three ...
*
Karnaugh map
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a rediscovery of Allan Marquand's 1881 ''logi ...
*
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...
*
Venn diagram
A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationship ...
*
The Game of Logic
References
Further reading
*
*
External links
*
* {{cite web , title=Carroll Diagram (and Game of Logic) Interactive Demonstrator at lewiscarrollresources.net , url=http://lewiscarrollresources.net/gameoflogic
Lewis Carroll: Logic ''
Internet Encyclopedia of Philosophy
The ''Internet Encyclopedia of Philosophy'' (''IEP'') is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers. The IEP combines open access publication with peer reviewed publication of original p ...
''
Graphical concepts in set theory
Diagrams
Grouping