Primitive notion: Difference between revisions

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Revision as of 14:05, 12 July 2014

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* [[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.

* [[Axiomatic system]]s, the primitive notions will depend upon the set of axioms chosen for the system. This was discussed by [[Alessandro Padoa]] at the [[International Congress of Mathematicians]] in Paris in 1900.{{cn}}

* [[Euclidean geometry]], under [[David Hilbert|Hilbert]]'s axiom system]] the primitive notions are ''point, line, plane, congruence, betweeness'' and ''incidence''.

* [[Euclidean geometry]], under [[GiuseppeFoundations of geometry#Pasch and Peano|Peano]]'s axiom system]] the primitive notions are ''point, segment'' and ''motion''.

* [[Philosophy of mathematics]], [[Bertrand Russell]] considered the "indefinables of mathematics" to build the case for [[logicism]] in his book [[The Principles of Mathematics]] (1903).