In the geometries where the concept of a line is a primitive notion, as may be the case in some synthetic geometries, other methods of determining collinearity are needed.
32.
:" [ Descartes'] claim that mind-body unity is a primitive notion on a par with the primitive notions of thinking and extended substance . . ."
33.
:" [ Descartes'] claim that mind-body unity is a primitive notion on a par with the primitive notions of thinking and extended substance . . ."
34.
Alessandro Padoa celebrated the reduction of primitive notions to merely " point " and " motion " in his report to the 1900 International Congress of Philosophy.
35.
Alessandro Padoa shared in this expression of Peano's logico-geometrical program that reduced the number of primitive notions from the " four " used by Moritz Pasch.
36.
Forder also gives, by combining axioms from different systems, his own treatment based on the two primitive notions of " point " and " order ".
37.
Given some " primitive formulas " such as PM's primitives S 1 V S 2 [ inclusive OR ], ~ S ( negation ) one is forced to define the axioms in terms of these primitive notions.
38.
Peano's work, largely a translation of Pasch's treatise into the notation of symbolic logic ( which Peano invented ), uses the primitive notions of " point " and " betweeness ".
39.
Cantor's definition turned out to be inadequate; instead, the notion of a " set " is taken as a primitive notion in axiomatic set theory, and the properties of sets are defined by a collection of axioms.
40.
This is can be confusing because current mathematical practice does not distinguish between predicative and non-predicative functions, and in any case PM never defines exactly what a " predicative function " actually is : this is taken as a primitive notion.
