In a non-axiomatic or simplified axiomatic treatment of geometry, the concept of a primitive notion may be too abstract to be dealt with.
22.
It is more concise than Pieri's because Pieri had only two primitive notions while Tarski introduced three : point, betweenness, and congruence.
23.
ZFC is intended to formalize a single primitive notion, that of a models from containing urelements ( elements of sets that are not themselves sets ).
24.
Hence relations can be defined by set theory, thus the theory of relations does not require any axioms or primitive notions distinct from those of set theory.
25.
And, of course, they missed what was happening all along, perhaps because of nervous impatience or a primitive notion that the real things are physical ."
26.
These axiom systems describe the space via primitive notions ( such as " point ", " between ", " congruent " ) constrained by a number of axioms.
27.
The idea that there are certain sequences of sounds which if said will make everyone very unformfortable for reasons they can't quite explain is a very primitive notion.
28.
Then G�del [ 1940 ] further modified the theory : " his primitive notions are those of set, class and membership ( although membership alone is sufficient ) ".
29.
Stating definitions and propositions in a way such that each new term can be formally eliminated by the priorly introduced terms requires primitive notions ( axioms ) to avoid infinite regress.
30.
The metalanguage includes primitive notions, axioms, and rules absent from the object language, so that there are theorems provable in the metalanguage not provable in the object language.
