(Stumpf, 1939 1940, p. 126) For Stumpf admits that the basic concepts of arithmetic (the concept of number) and geometry (the concept of space) have their origins in experience.
It is in this sense that the basic concepts of arithmetic and set theory are not topic-neutral, since they distinguish some objects (the empty set, the number 0) from others.
The grammatical formulae can then be seen as (or codified by) the numbers obtainable from the basic numbers after some finite series of applications of the operations, and thus their set is characterizable in terms of concepts of arithmetic and set theory (in fact arithmetic suffices, with the help of some tricks).
The concept of "responsible arithmetic" is wondrous.
A concept of quasi-arithmetic mean refers to convex combinations and strictly monotone continuous functions.
The method is based on the concept of bounding hyperplane arithmetic, which can be viewed as a generalization of interval arithmetic.
This chapter introduces the concept of fixed point arithmetic in VHSIC hardware description language (VHDL), where VHSIC stands for very high speed integrated circuit.
The leading idea of the arithmetizers was that the concepts and first principles of arithmetic and analysis are to be found in the concepts of the understanding (as a Kantian might put it), independently of one's geometric intuitions concerning any spatial or temporal continua.
October 6, 1831 Braunschweig, Germany February 12 , 1916Braunschweig, Germany Richard Dedekind, in full Julius Wilhelm Richard Dedekind (born October 6, 1831, Braunschweig, duchy of Braunschweig [Germany] died February 12 , 1916 Braunschweig) German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts.
But few of Frege's definitions of arithmetic concepts are nearly so simple (see Gottlob Frege, §2.5).
