Quote: mathematical methods in philosophy can only build car-castles while philosophical methods in mathematics result in mere verbiage

Quotation

The evidence of mathematics rests upon definitions, axioms, and demonstrations. I shall be satisfied with showing that none of these forms can be employed or imitated in philosophy in the sense in which they are understood by mathematicians; and that the geometrician, if he employs his method in philosophy, will succeed only in building car-castles, while the employment of the philosophical method in mathematics can result in nothing but mere verbiage. ... [p. A729/B757] "Philosophical definitions are, therefore, merely expositions of given concepts, while mathematical definitions are constructions of concepts originally formed.   Google-1   Google-2

Published before 1923

Additional Titles

Quote: a definition in philosophy describes a concept while a definition in mathematics constructs a concept

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