Content deleted Content added
m Added link Tags: Mobile edit Mobile app edit iOS app edit App section source |
m →Examples: Typo. |
||
Line 18:
* Arithmetic of [[real number]]s: Typically, primitive notions are: real number, two [[binary operation]]s: [[addition]] and [[multiplication]], numbers 0 and 1, ordering <.
* [[Axiomatic system]]s: The primitive notions will depend upon the set of axioms chosen for the system. [[Alessandro Padoa]] discussed this selection at the [[International Congress of Philosophy]] in Paris in 1900.<ref>[[Alessandro Padoa]] (1900) "Logical introduction to any deductive theory" in [[Jean van Heijenoort]] (1967) ''A Source Book in Mathematical Logic, 1879–1931'', [[Harvard University Press]] 118–23</ref> The notions themselves may not necessarily need to be stated; Susan Haack (1978) writes, "A set of axioms is sometimes said to give an implicit definition of its primitive terms."<ref>{{citation|first=Susan|last=Haack|year=1978|title=Philosophy of Logics|page=245|publisher=[[Cambridge University Press]]|isbn=9780521293297}}</ref>
* [[Euclidean geometry]]: Under [[Hilbert's axiom system]] the primitive notions are ''point, line, plane, congruence,
* [[Euclidean geometry]]: Under [[Foundations of geometry#Pasch and Peano|Peano's axiom system]] the primitive notions are ''point, segment'', and ''motion''.
| |||