Quote of the day

The first intellectual operation in which I arrived at any proficiency, was dissecting a bad argument, and finding in what part the fallacy lay; and though whatever capacity of this sort I attained was due to the fact that it was an intellectual exercise in which I was most perseveringly drilled by my father, yet it is also true that the school logic, and the mental habits acquired in studying it, were among the principal instruments of this drilling. I am persuaded that nothing, in modern education, tends so much, when properly used, to form exact thinkers, who attach a precise meaning to words and propositions, and are not imposed on by vague, loose, or ambiguous terms. The boasted influence of mathematical studies is nothing to it; for in mathematical processes, none of the real difficulties of correct ratiocination occur.

-J.S. Mill, Autobiography

I believe “school logic” is a.k.a. scholastic logic and is something along the lines of “philosophical” logic and what Mill covered in his A System of Logic. Sometimes I found combinatorics problems to require careful thinking in order to avoid plausible-looking mistakes. At Art of Problem Solving, instructors suggest “counting in two ways”, i.e. using two different counting strategies and comparing the results.