In [[mathematics]], [[logic]], and [[formal system]]s, a '''primitive notion''' is aan 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. For example in [[naive set theory]], the notion ofIn an [[empty set]] is primitive. (That it exists is an implicit [[axiom]].) For a more formal discussion of the foundations of mathematics see the [[axiomatic set theory]] article.or In an axiomatic theory orother [[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 theone or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of [[infinite regress]].
'''Examples'''. In:
* [[Naive set theory]], the [[empty set]] is a primitive notion. (To assert that it exists would be an implicit [[axiom]].)
* [[Peano arithmetic]], the [[successor function]] and the number [[zero]] are primitive notions.
