In his book on [[philosophy of mathematics]], ''[[The Principles of Mathematics]]'' [[Bertrand Russell]] used thesethe following notions: For thefor class-calculus ([[set theory]]), he used [[relation (mathematics)|relation]]s, taking [[set membership]] as a primitive notion. To establish sets, he also requiresestablishes [[propositional function]]s as primitive, as well as the phrase "such that" as used in [[set builder notation]]. (pp 18,9) Regarding relations, Russell takes as primitive notions the [[converse relation]] and [[complementary relation]] of a given ''xRy''. Furthermore, logical products of relations and [[relative product]]s of relations are primitive. (p 25) As for denotation of objects by description, Russell acknowledges that a primitive notion is involved. (p 27) The thesis of Russell’s book is "Pure mathematics uses only a few notions, and these are logical constants." (p xxi)
