...MATHEMATICS. 1. xPuRK Mathematics is the class of all propositions of the form "p implies q" where p and q are propositions containing one or more variables,...propositions which it considers, namely the notion of truth. 2. The above definition of pure mathematics is, no doubt, somewhat unusual. Its various parts, nevertheless,...

...modcrne " — a spirit, as he says, which is diametrically opposed to Kant's theory of mathematics. tion, and such further notions as may be involved in the...propositions which it considers, namely the notion of truth."1 " By the help of ten principles of deduction and ten other principles of a general logical...

...terms of the following: Implication, the relation of a term to a class of which it is a member (e), the notion of such that, the notion of relation, and...propositions which it considers, namely, the notion of truth. A proposition80 is de"Thus, if x is a real number (*•«£), and we write xtq implies, for any such...

...Implication, the relation of a term to a class of which it is a member the notion of surlt tlirit, the notion of relation, and such further notions as...the above form. In addition to these, Mathematics iifes a notion which is not a constituent of the propositions which.it considers — namely, the notion...

...84. 128. Pure Mathematics is the class of all propositions of the form "p implies q," where p and q are propositions containing one or more variables,...which it considers — namely, the notion of truth. RUSSELL, BERTHAND. Principles of Mathematics (Cambridge, 1903), pl 129. The object of pure Physic is...

...constants are all notions definable in terms of the following: Implication, the relation of a term to the class of which it is a member, the notion of such...which it considers, namely, the notion of truth." (Principia Mathematica, p. 3.) " The connection of mathematics with logic, according v the above account,...

...which it is a member, the notion of „such that", the notion of relation and such further notions, äs may be involved in the general notion of propositions of the above form." Kürzer faßt wieder M. B och er, der die Gesichtspunkte von Kempe und Russell zu vereinigen sucht,...

...notions definable in terms of a class of the following: Implication, the relation of a term to a class of relation, and such further notions as may be involved...which it considers — namely, the notion of truth. Principles of Mathematics (p. 1) The nineteenth century which prides itself upon the invention of steam...

...all propositions of the form 'p implies q', where p and q are propositions each containing at least one or more variables, the same in the two propositions,...propositions which it considers, namely the notion of truth. 2. The above definition of pure mathematics is, no doubt, somewhat unusual. Its various parts, nevertheless,...

...all propositions of the form 'p implies q', where p and q are propositions each containing at least one or more variables, the same in the two propositions,...propositions which it considers, namely the notion of truth. conditions be imposed on each occasion ('p' over propositions, 'x ' over real numbers, or whatever)....