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• Primitive_notion abstract "In mathematics, logic, and formal systems, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory or other formal system, the role of a primitive notion is analogous to that of axiom. In axiomatic theories, the primitive notions are sometimes said to be "defined" by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress.Alfred Tarski explained the role of primitive notions as follows:When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be immediately understandable; the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings. At the same time we adopt the principle: not to employ any of the other expressions of the discipline under consideration, unless its meaning has first been determined with the help of primitive terms and of such expressions of the discipline whose meanings have been explained previously. The sentence which determines the meaning of a term in this way is called a DEFINITION,...In axiomatic set theory the fundamental concept of set is an example of a primitive notion. As Mary Tiles wrote:[The] 'definition' of 'set' is less a definition than an attempt at explication of something which is being given the status of a primitive, undefined, term.As evidence, she quotes Felix Hausdorff: "A set is formed by the grouping together of single objects into a whole. A set is a plurality thought of as a unit."When an axiomatic system begins with its axioms, the primitive notions may not be explicitly stated. Susan Haack (1978) wrote, "A set of axioms is sometimes said to give an implicit definition of its primitive terms."An inevitable regress to primitive notions in the theory of knowledge was explained by Gilbert de B. Robinson:To a non-mathematician it often comes as a surprise that it is impossible to define explicitly all the terms which are used. This is not a superficial problem but lies at the root of all knowledge; it is necessary to begin somewhere, and to make progress one must clearly state those elements and relations which are undefined and those properties which are taken for granted.↑ ↑ ↑ ↑".
• Primitive_notion wikiPageID "23706".
• Primitive_notion wikiPageLength "4812".
• Primitive_notion wikiPageOutDegree "43".
• Primitive_notion wikiPageRevisionID "672012078".
• Primitive_notion wikiPageWikiLink 0_(number).
• Primitive_notion wikiPageWikiLink Alessandro_Padoa.
• Primitive_notion wikiPageWikiLink Alfred_Tarski.
• Primitive_notion wikiPageWikiLink Axiom.
• Primitive_notion wikiPageWikiLink Axiomatic_set_theory.
• Primitive_notion wikiPageWikiLink Axiomatic_system.
• Primitive_notion wikiPageWikiLink Axiomatic_theory.
• Primitive_notion wikiPageWikiLink Bertrand_Russell.
• Primitive_notion wikiPageWikiLink Category:Concepts_in_logic.
• Primitive_notion wikiPageWikiLink Category:Philosophy_of_logic.
• Primitive_notion wikiPageWikiLink Category:Set_theory.
• Primitive_notion wikiPageWikiLink Empty_set.
• Primitive_notion wikiPageWikiLink Epistemology.
• Primitive_notion wikiPageWikiLink Euclidean_geometry.
• Primitive_notion wikiPageWikiLink Felix_Hausdorff.
• Primitive_notion wikiPageWikiLink Formal_system.
• Primitive_notion wikiPageWikiLink Foundations_of_geometry.
• Primitive_notion wikiPageWikiLink Foundations_of_mathematics.
• Primitive_notion wikiPageWikiLink Gilbert_de_B._Robinson.
• Primitive_notion wikiPageWikiLink Gilbert_de_Beauregard_Robinson.
• Primitive_notion wikiPageWikiLink Hilberts_axiom_system.
• Primitive_notion wikiPageWikiLink Hilberts_axioms.
• Primitive_notion wikiPageWikiLink Infinite_regress.
• Primitive_notion wikiPageWikiLink International_Congress_of_Philosophy.
• Primitive_notion wikiPageWikiLink Intuition.
• Primitive_notion wikiPageWikiLink Intuition_(knowledge).
• Primitive_notion wikiPageWikiLink Logic.
• Primitive_notion wikiPageWikiLink Logicism.
• Primitive_notion wikiPageWikiLink Mary_Tiles.
• Primitive_notion wikiPageWikiLink Mathematical_logic.
• Primitive_notion wikiPageWikiLink Mathematics.
• Primitive_notion wikiPageWikiLink Naive_set_theory.
• Primitive_notion wikiPageWikiLink Natural_semantic_metalanguage.
• Primitive_notion wikiPageWikiLink Notion_(philosophy).
• Primitive_notion wikiPageWikiLink Object_theory.
• Primitive_notion wikiPageWikiLink Peano_arithmetic.
• Primitive_notion wikiPageWikiLink Peano_axioms.
• Primitive_notion wikiPageWikiLink Philosophy_of_mathematics.
• Primitive_notion wikiPageWikiLink Set_theory.
• Primitive_notion wikiPageWikiLink Successor_function.
• Primitive_notion wikiPageWikiLink The_Principles_of_Mathematics.
• Primitive_notion wikiPageWikiLink Theory_of_knowledge.
• Primitive_notion wikiPageWikiLink World_Congress_of_Philosophy.
• Primitive_notion wikiPageWikiLink Zero.
• Primitive_notion wikiPageWikiLinkText "Primitive notion".
• Primitive_notion wikiPageWikiLinkText "Primitives".
• Primitive_notion wikiPageWikiLinkText "primitive (undefined) object type".
• Primitive_notion wikiPageWikiLinkText "primitive notion".
• Primitive_notion wikiPageWikiLinkText "primitive signs".
• Primitive_notion wikiPageWikiLinkText "primitive terms".
• Primitive_notion wikiPageWikiLinkText "primitive".
• Primitive_notion wikiPageWikiLinkText "primitives".
• Primitive_notion wikiPageWikiLinkText "undefined terms".
• Primitive_notion hasPhotoCollection Primitive_notion.
• Primitive_notion wikiPageUsesTemplate Template:Reflist.
• Primitive_notion subject Category:Concepts_in_logic.
• Primitive_notion subject Category:Philosophy_of_logic.
• Primitive_notion subject Category:Set_theory.
• Primitive_notion hypernym Concept.
• Primitive_notion type Concept.
• Primitive_notion comment "In mathematics, logic, and formal systems, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory or other formal system, the role of a primitive notion is analogous to that of axiom.".
• Primitive_notion label "Primitive notion".
• Primitive_notion sameAs 무정의_용어.
• Primitive_notion sameAs m.05xh_.
• Primitive_notion sameAs Неопределяемое_понятие.
• Primitive_notion sameAs อนิยาม.
• Primitive_notion sameAs Q6453739.
• Primitive_notion sameAs Q6453739.
• Primitive_notion wasDerivedFrom Primitive_notion?oldid=672012078.
• Primitive_notion isPrimaryTopicOf Primitive_notion.