Mathematical vs. Verbal Reasoning

George Bernard Shaw (1856 — 1950) once said that as a boy he (1) let someone assume that a=b, (2) permitted several steps of algebra, and (3) found that he had accepted a proof that 1=2. This incident had a deep impact on Shaw’s thought process and forever after, he distrusted assumptions and algebra. The conclusions of a mathematical theory can be retranslated into words, but rarely can they be found by verbal reasoning.

George Bernard Shaw
George Bernard Shaw

In reply to Shaw’s criticism of the formal mathematical reasoning, the economist Philip H. Wicksteed (1844 — 1927) nicely puts:

“Mr Shaw arrived at the sapient conclusion that there “was a screw loose somewhere”– not in his own reasoning powers, but — “in the algebraic art”; and thenceforth renounced mathematical reasoning in favour of the literary method which enables a clever man to follow equally fallacious arguments to equally absurd conclusions without seeing that they are absurd. This is the exact difference between the mathematical and literary treatment of the pure theory of political economy.”

Philip H. Wicksteed
Philip H. Wicksteed

In other words, a mathematical idea, if correctly put and checked, is better than the one that is put in words, for words can never possibly explain in thousands what an equation can. That si where the importance of mathematical shows.


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