...the rules. In this sense all mathematical reasoning is necessary, namely, it has followed the rules. Mathematical reasoning is deductive in the sense that...no external verification of definitions is required by mathematics as long as it is considered merely as mathematics. Mathematical definitions either possess...

...angeblichen Unwert der Mathematik, Jahresbericht der Deutschen Maihemaliker Vereinigung (1904), p. 357. 233. Mathematical reasoning is deductive in the sense that...is concerned (apart from any existential import), needs only the test of self-consistency. Thus no external verification of definitions is required in...

...was .indebted for his theorem of the binomial and the principle of Universal gravity. — Laplace. Mathematical reasoning is deductive in the sense that...is concerned (apart from any existential import), needs only the test of self-consistency. Thus no external verification of definitions is required in...

...the Inductive Sciences Volume I Part 1, Book 2, Chapter 1, section 2 (p. 83) Whitehead, Alfred North Mathematical reasoning is deductive in the sense that...reasoning is concerned (apart from any existential import) needs only the test of self-consistency. Thus no external verification of definitions is required in...

...the original phenomena for which they have been substituted, will only need the test of consistency. 'Thus no external verification of definitions is required...mathematics, as long as it is considered merely as mathematics.'1 Whitehead, as we shall see, goes beyond this limited sphere and tends to give these...