Primitive notion: Difference between revisions

Revision as of 01:24, 24 February 2025

Latest revision as of 13:16, 9 August 2025

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{{short description|Concept that is not defined in terms of previously defined concepts}}

In [[mathematics]], [[logic]], [[philosophy]], and [[formal system]]s, a '''primitive notion''' is a concept that is not defined in terms of previously- defined concepts. It is often motivated informally, usually by an appeal to [[Intuition (knowledge)|intuition]] or taken to be [[self-evident]]. In an [[axiomatic theory]], relations between primitive notions are restricted by [[axiom]]s.<ref>More generally, in a formal system, rules restrict the use of primitive notions. See e.g. [[MU puzzle]] for a non-logical formal system.</ref> Some authors refer to the latter as "defining" primitive notions by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of [[infinite regress]] (per the [[regress problem]]).

For example, in contemporary geometry, ''[[point (geometry)|point]]'', ''line'', and ''contains'' are some primitive notions.