“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, the same in the two propositions, and neither p nor q contains any constants except logical constants.”
Where human rationality is concerned, simple measures analogous to deductive correctness in mathematics don’t capture many important aspects that reflect aesthetic of purpose or quality of understanding. In mathematics, understanding of an argument is often more important than its deductive correctness, for a flawed presentation of a sound idea can be fixed, or given a rigorous foundation long after it’s first formulated.
[This distinction (and analogy that carries it over from the similar argument about mathematics) deserves a full-length article, but for now I’ll just point it out.]
Compare with what Russell said about mathematics:
Where human rationality is concerned, simple measures analogous to deductive correctness in mathematics don’t capture many important aspects that reflect aesthetic of purpose or quality of understanding. In mathematics, understanding of an argument is often more important than its deductive correctness, for a flawed presentation of a sound idea can be fixed, or given a rigorous foundation long after it’s first formulated.
[This distinction (and analogy that carries it over from the similar argument about mathematics) deserves a full-length article, but for now I’ll just point it out.]
+1