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For example, in contemporary geometry, ''point'', ''line'', and ''contains'' are some primitive notions. Instead of attempting to define them,<ref>[[Euclid]] (300 B.C.) still gave definitions in his ''[[Euclid's Elements|Elements]]'', like "A line is breadthless length".</ref> their interplay is ruled (in [[Hilbert's axiom system]]) by axioms like "For every two points there exists a line that contains them both".<ref>This axiom can be formalized in [[predicate logic]] as "[[universal quantifier|∀]]''x''<sub>1</sub>,''x''<sub>2</sub>[[Set membership|∈]]''P''. [[existential quantifier|∃]]''y''∈''L''. ''C''(''y'',''x''<sub>1</sub>) [[logical conjunction|∧]] ''C''(''y'',''x''<sub>2</sub>)", where ''P'', ''L'', and ''C'' denotes the set of points, of lines, and the "contains" relation, respectively.</ref>
[[]]==Details==
[[Alfred Tarski]] explained the role of primitive notions as follows:<ref>[[Alfred Tarski]] (1946) ''Introduction to Logic and the Methodology of the Deductive Sciences'', p. 118, [[Oxford University Press]].</ref>
:When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be immediately understandable; the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings. At the same time we adopt the principle: not to employ any of the other expressions of the discipline under consideration, unless its meaning has first been determined with the help of primitive terms and of such expressions of the discipline whose meanings have been explained previously. The sentence which determines the meaning of a term in this way is called a DEFINITION,...
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