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Concept that is not defined in terms of previously defined concepts
In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously defined concepts. It
Primitive_notion
2001 studio album by New Order
Way" (featuring Billy Corgan) 5:05 4. "Vicious Streak" 5:40 5. "Primitive Notion" 5:43 6. "Slow Jam" 4:53 7. "Rock the Shack" (featuring Bobby Gillespie)
Get_Ready_(New_Order_album)
Expression which is not assigned an interpretation
{\displaystyle f(x)} . In some mathematical contexts, undefined can refer to a primitive notion which is not defined in terms of simpler concepts. For example, in
Undefined_(mathematics)
Joining of strings in a programming language
concatenation theory, also called string theory, string concatenation is a primitive notion. To concatenate is to join two or more sequential objects together
Concatenation
Collection of mathematical objects
other sets. Sets cannot be mathematically defined, since they form a primitive notion. Instead, they are characterized by basic properties (axioms) that
Set_(mathematics)
Topics referred to by the same term
Primitive notion, axiomatic systems Primitive polynomial (disambiguation), one of two concepts Primitive function or antiderivative, F′ = f Primitive
Primitive
Fundamental object of geometry
Euclidean geometry, a point is a primitive notion, defined as "that which has no part". Points and other primitive notions are not defined in terms of
Point_(geometry)
Result of multiplying types in type theory
the category of types. Most functional programming languages have a primitive notion of product type. For instance, the product T 1 × T 2 × . . . × T n
Product_type
Mathematical approach
theory, is an approach to topology where lattices of open sets are the primitive notion, and are not required to consist of subsets of points. In this approach
Pointless_topology
Standard system of axiomatic set theory
Informally, Zermelo–Fraenkel set theory is intended to formalize a single primitive notion, that of a hereditary well-founded set, so that all entities in the
Zermelo–Fraenkel_set_theory
Symbol representing a property or relation in logic
{\displaystyle a} and b {\displaystyle b} . Predicates are considered a primitive notion of first-order and higher-order logic, and are therefore not defined
Predicate_(logic)
Basic notion of sameness in mathematics
not equal are said to be distinct. Equality is often considered a primitive notion, meaning it is not formally defined, but rather informally said to
Equality_(mathematics)
3-volume treatise on mathematics, 1910–1913
"falsity" in the notion "primitive proposition". A raw (pure) formalist theory would not provide the meaning of the symbols that form a "primitive proposition"—the
Principia_Mathematica
Straight figure with zero width and depth
the text. In modern geometry, a line is usually either taken as a primitive notion with properties given by axioms, or else defined as a set of points
Line_(geometry)
Logical incompatibility between two or more propositions
consistency proofs would seem to necessitate the primitive notion of contradiction. Moreover, it seems as if this notion would simultaneously have to be "outside"
Contradiction
Mode of production
Primitive communism is a way of describing the gift economies of hunter-gatherers throughout history, where resources and property hunted or gathered
Primitive_communism
Number used for counting
their fixed order[page needed] and establish this order using the primitive notion of a successor. Every natural number has a successor, which is another
Natural_number
Symbol representing a mathematical concept
defined over the whole domain of discourse. Function symbols are a primitive notion, and are therefore not defined in terms of other, more basic concepts
Function_symbol
Axiom(s) of Set Theory
named cardinal. The simplest way to introduce cardinals is to add a primitive notion, Card(), and an axiom of cardinality to ZF set theory (without axiom
Set-theoretic definition of natural numbers
Set-theoretic_definition_of_natural_numbers
Indefinite integral
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable
Antiderivative
Law of thermodynamics establishing the conservation of energy
primitive notion, defined by calorimetry. It was presupposed as logically prior to the theoretical development of thermodynamics. Jointly primitive with
First_law_of_thermodynamics
1963 British horror film by Robert Wise
was happening all along, perhaps because of nervous impatience or a primitive notion that the real things are physical.". Later on, however, in her 1982
The_Haunting_(1963_film)
Proof assistant program
on a formulation of type theory with equality as the only primitive notion. The primitive rules of inference are the following: This formulation of type
HOL_Light
League" New Order Non-album single B-side to "Here to Stay" 2002 "Primitive Notion" New Order Get Ready 2001 "Procession" New Order Non-album single 1981
List of songs recorded by New Order
List_of_songs_recorded_by_New_Order
Italian mathematician and logician (1868–1937)
deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic
Alessandro_Padoa
Relation used in geometry
Geometry of 1868. Wilson based his definition of parallel lines on the primitive notion of direction. According to Wilhelm Killing the idea may be traced back
Parallel_(geometry)
Epistemologically probative proposition
Axiom Contradiction Foundationalism Introspection Law of identity Primitive notion Self-reference Self-refuting idea infinite regress Maddy, Penelope
Self-evidence
Philosophical problem about what constitutes knowledge
justification, evidence, certainty, etc. should be analyzed in terms of a primitive notion of knowledge, rather than vice versa. Knowledge is understood as factive
Gettier_problem
Expression in propositional calculus
106): "...it has become necessary to take propositional function as a primitive notion. Later Russell examined the problem of whether propositional functions
Propositional_function
Study of geometries as axiomatic systems
play a role is in deciding what the primitive notions and axioms should be. Thus, for Pasch, point is a primitive notion but line (straight line) is not,
Foundations_of_geometry
Subjective attitude that something is true
for example, every belief above 0.9 is a full belief. Defenders of a primitive notion of full belief, on the other hand, have tried to explain partial beliefs
Belief
Axiom set used in first-order logic
has the fewest variables and atomic sentences; C requires but one primitive notion, betweenness. This variant is the usual one given in the literature
Tarski's_axioms
Pair of mathematical objects
ordered pairs in mathematics. Hence the ordered pair can be taken as a primitive notion, whose associated axiom is the characteristic property. This was the
Ordered_pair
Polish–American mathematician (1901–1983)
a second-order theory whose individuals are spheres (a primitive notion), a single primitive binary relation "is contained in", and two axioms that,
Alfred_Tarski
American mathematician (1862–1932)
axioms for geometry so that points were the only primitive notion, thus turning David Hilbert's primitive lines and planes into defined notions. In 1902
E._H._Moore
concatenation theory, also called string theory, string concatenation is a primitive notion. Concurrency The ability of different parts or units of a program,
Glossary_of_computer_science
Minor planet found within the inner Solar System
life, and supporting the notion of an RNA world prior to a DNA-based origin of life on Earth, and possibly, as well, the notion of panspermia. Asteroids
Asteroid
American philosopher (1883–1964)
{\displaystyle \square } , meaning "necessity", which is stating a primitive notion, while the diamond notation, ◊ {\displaystyle \Diamond } , is left
C._I._Lewis
Computer science and recursion theory
the notion of recursive functions by use of the IF-THEN-ELSE construction common to computer science, together with four of the operators of primitive recursive
McCarthy_Formalism
Fundamental color in color mixing
yellow, red, and blue, plus black to add shades and contrast. Le Blon used primitive in 1725 to describe red, yellow, and blue in a very similar sense as Boyle
Primary_color
the initial functions. The notion of a set function being primitive recursive in ω has the same definition as that of primitive recursion, except with ω
Primitive recursive set function
Primitive_recursive_set_function
Concept in axiomatic set theory
predicativity. The subset relation ⊆ {\displaystyle \subseteq } is not a primitive notion in formal set theory and is not used in the formal language of the
Axiom_of_power_set
State of thermodynamic systems where no net flow of matter or energy occurs
mechanical pressures, on its surface. Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should
Thermodynamic_equilibrium
Set of all limit points of a set
entirely in terms of derived sets, derived sets have been used as the primitive notion in topology. A set of points X {\displaystyle X} can be equipped with
Derived_set_(mathematics)
1967 book by Arthur Koestler
triune brain has evolved, it has retained and built upon earlier, more primitive brain structures. The head portion of the "ghost in the machine" has,
The_Ghost_in_the_Machine
Study of parts and the wholes they form
contrasts with more usual axiomatizations of ZFC, which use only the primitive notion of membership. Lewis's work is named after his thesis that a class's
Mereology
Hungarian folk tale
original form of the tale", since it harks back to the ancient and primitive notion that humans and animals could freely interact in a mythical shared
Fehérlófia_(folk_tale)
Notion that species can revert to primitive forms
evolution (not to be confused with dysgenics) is the notion that species can revert to supposedly more primitive forms over time. The concept relates to the idea
Devolution_(biology)
yidn. Vol. IX. Brandeis University and CYCO Publishing House. "The Primitive Notion of Yahweh" [in Yiddish]. YIVO-Bleter 13 (1938): 477-504. "Biblical
Michael_Astour
Version of modal realism
There is a difference between reality and existence. Reality is a primitive notion: either something is real or it is not. Existence, on the other hand
Extended_modal_realism
1928 book by Margaret Mead
Coming of Age in Samoa: A Psychological Study of Primitive Youth for Western Civilisation is a 1928 book by American anthropologist Margaret Mead based
Coming_of_Age_in_Samoa
Axiomatic set theory devised by W.V.O. Quine
an alternative approach, Holmes takes the ordered pair (a, b) as a primitive notion, as well as its left and right projections π 1 {\displaystyle \pi _{1}}
New_Foundations
Non-scientific term for a transitional fossil
theory of the Great Chain of Being and the now-outdated notion that simple organisms are more primitive than complex organisms (orthogenesis). The term "missing
Missing link (human evolution)
Missing_link_(human_evolution)
Aspect of cryptography
and applies cryptographic methods, often as sequences of cryptographic primitives. A protocol describes how the algorithms should be used and includes details
Cryptographic_protocol
Character in Jean de l'Ours
original form of the tale", since it harks back to the ancient and primitive notion that humans and animals could freely interact in a mythical shared
Jean_de_l'Ours
Statement that is taken to be true
to fall into vagueness and a never-ending series of "primitive notions", either a precise notion of what we mean by x = x {\displaystyle x=x} (or, for
Axiom
Divine marriage
in a symbolic ritual where human participants represent the deities. The notion of hieros gamos does not always presuppose literal sexual intercourse in
Hieros_gamos
Concept of rebirth or re-creation
advanced individual organism mirrors the development of entire, more primitive species. In political theory, it is a central component of Roger Griffin's
Palingenesis
Stock character
in the American Southwest, LeBlanc further documents the mythical notion of primitive non-violence against foreign tribal peoples, internal strife and
Noble_savage
Proposed constructs pertaining to the vagus nerve
to serve different evolutionary stress responses in mammals: the more primitive branch is said to elicit immobilization behaviors (e.g., feigning death)
Polyvagal_theory
Human social group
are often vague and subject to change over time. In his 1975 study, The Notion of the Tribe, Fried provided numerous examples of tribes that encompassed
Tribe
Theorem that arithmetical truth cannot be defined in arithmetic
power exceeding that of the object language. The metalanguage includes primitive notions, axioms, and rules of inference absent from the object language
Tarski's undefinability theorem
Tarski's_undefinability_theorem
theory of conservation of energy 1677 – Baruch Spinoza puts forward a primitive notion of Newton's first law 1687 – Isaac Newton publishes his Philosophiæ
Timeline of classical mechanics
Timeline_of_classical_mechanics
Ethnic group indigenous to the Ryukyu Islands
forest and mountainous terrain (in which isolation was an advantage), with primitive farming and fishing. The central Chūzan polity was the most advantaged
Ryukyuans
Structured system of communication
of primitive language-like systems (proto-language) as early as Homo habilis (2.3 million years ago) while others place the development of primitive symbolic
Language
Leader of a tribal society or chiefdom
chiefs (geographically defined) or clan chiefs (an essentially genealogical notion). The descriptive "tribal" requires an ethno-cultural identity (racial,
Tribal_chief
Greatest common divisor of polynomials
the polynomial GCD has specific properties that make it a fundamental notion in various areas of algebra. Typically, the roots of the GCD of two polynomials
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Work by John Rawls
inclusion of 'decent hierarchical peoples' is demanded by the notion of toleration, a notion Rawls sees as integral to liberalism. In part, the Law of Peoples
The_Law_of_Peoples
Sexual behavior
advantageous because it allowed men to father more children.[citation needed] Primitive promiscuity or original promiscuity was the 19th-century hypothesis that
Promiscuity
Programming language concept
a primitive type within an object so that the value can be used as a reference. Unboxing is the reverse transformation of extracting the primitive value
Boxing_(computer_programming)
Cryptographic scheme
A commitment scheme is a cryptographic primitive that allows one to commit to a chosen value (or chosen statement) while keeping it hidden to others,
Commitment_scheme
Culture of mocking embarrassing content
Other celebrities have made public speeches fighting against the perceived notion that "tryharding" is cringe. In his 31st Screen Actors Guild Awards acceptance
Cringe_culture
Triangulation method
his work on it from 1934. If the points all lie on a straight line, the notion of triangulation becomes degenerate and there is no Delaunay triangulation
Delaunay_triangulation
Form of early Buddhism
called early Buddhism, the earliest Buddhism, original Buddhism, and primitive Buddhism, is Buddhism as theorised to have existed before the various
Pre-sectarian_Buddhism
Term from medieval scholastic philosophy
person). In modern philosophy of physics, it is sometimes referred to as primitive thisness. The term haecceity derives from the Latin word haecceitas, which
Haecceity
Mathematical set containing no elements
empty set is referred to as the "null set". However, null set is a distinct notion within the context of measure theory, in which it describes a set of measure
Empty_set
Property of points all lying on a single line
However, in most geometries (including Euclidean) a line is typically a primitive (undefined) object type, so such visualizations will not necessarily be
Collinearity
Cryptographic primitive
Non-interactive zero-knowledge proofs are cryptographic primitives, where information between a prover and a verifier can be authenticated by the prover
Non-interactive zero-knowledge proof
Non-interactive_zero-knowledge_proof
Mathematical model for deduction or proof systems
question) Usually only the syntax of a formal language is considered via the notion of a formal grammar. The two main categories of formal grammar are that
Formal_system
Swiss psychiatrist and psychotherapist (1875–1961)
that we have to make allowances for these primitive layers in our psyche." Jung also developed the notion of different evolutionary layers in the psyche
Carl_Jung
Field extension generated by a one element
However, in the case of finite fields, the term primitive element is usually reserved for a stronger notion, an element γ that generates L × = L − { 0 }
Simple_extension
Formatted data in computer science
table and an array mapped trie. It is a refined version of the more general notion of a hash tree. A HAMT is an array mapped trie where the keys are first
Hash_array_mapped_trie
1945 book by Maurice Merleau-Ponty
that in it he had taken "subject-object dualism as phenomenologically primitive" and "made use of a comparatively superficial psychologistic vocabulary"
Phenomenology_of_Perception
French mathematician (1875–1941)
l'intégration et la recherche des fonctions primitives. The problem of integration regarded as the search for a primitive function is the keynote of the book
Henri_Lebesgue
Japanese swordsman, strategist, writer, artist, and rōnin (c. 1584–1645)
While there are differing opinions on how it happened, the prevailing notion is that Musashi challenged Kojiro, requesting Hosokawa Tadaoki to organise
Miyamoto_Musashi
Type of energy transfer
notions of heat, work, and hotness as primitive elements, ... That heat is an appropriate and natural primitive for thermodynamics was already accepted
Heat
Computer science concept
type but also have primitive types that are not objects. Java provides wrapper object types that exist together with the primitive types so developers
Type_system
Artifacts purported to challenge historical chronology
religious descriptions of prehistory, ancient astronaut theories, and the notion of vanished civilizations that possessed knowledge or technology more advanced
Out-of-place_artifact
Fundamental unit of cognition
the direction of modification. Complex concepts contrast with simple or primitive ones, which are not composed of other concepts. Simple concepts are closely
Concept
Equatorial region thought uninhabitable
impenetrable to sailors or explorers. That notion became a deterrent for European explorers until the 15th century and the notion that the torrid zone was uninhabitable
Torrid_zone
Set of elements common to all of some sets
elements of B {\displaystyle B} that also belong to A . {\displaystyle A.} The notion of intersection as an algebraic operation with sets as operands has been
Intersection_(set_theory)
Austrian philosopher and logician (1889–1951)
29 November that year, a four-minute talk defining philosophy as "all those primitive propositions which are assumed as true without proof by the various sciences"
Ludwig_Wittgenstein
Subtribe of carnivores
to the relationships among South American canids, most frequent was the notion of there being three genera and subgenera after Langguth 1969 and 1970:
Cerdocyonina
Language family native to Eurasia
Asian and European languages and theorized that they were derived from a primitive common language that he called Scythian. He included in his hypothesis
Indo-European_languages
Additional mathematical object
metric: there is a notion of distance between points. A geometry: it is equipped with a metric and is flat. A topology: there is a notion of open sets. There
Mathematical_structure
Period from 1800 CE until the present
be, or to have been, the primitive form of society everywhere from India to Ireland. The Inner organization of this primitive Communistic society was laid
Late_modern_period
1979 short film directed by Sam Raimi
Monkey Pignut Swindle. While those films were described as "goofy" and primitive by members of the cast and crew, Raimi eventually produced the short film
Within_the_Woods
1985 novel by Kurt Vonnegut
the themes and characters in Galápagos. Devolution – Notion that species can revert to primitive forms Dysgenics – Decrease in genetic traits deemed desirable
Galápagos_(novel)
Mathematical set with some added structure
topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself.[better source needed] A space consists of selected mathematical
Space_(mathematics)
Branch of mathematical logic
related to the notion of normal form in term rewriting. More exotic proof calculi such as Jean-Yves Girard's proof nets also support a notion of analytic
Proof_theory
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