14 A corroboration of this point of view seems to come from some of the so-called tests for logical thinking, which include questions such as What is the next number in the (!) sequence 1, 3, 6, 10 … ? and (in slightly simplified form) Which of the following four figures differs from the other three: a square; a cross; a circle; a triangle? Questions of this kind do indeed test a valuable ability, viz. the ability to guess what the man who formulated them had in mind, e.g. the circle, because it is the only figure that is round (although, of course, the square is the only one with four corners; the cross the only one with a ramification point; the triangle the only one with exactly three corners). What in this way certainly is not tested is logical thinking. Yet the marks youngsters make in such tests highly correlate with their achievements in elementary mathematics! Far from demonstrating that those test questions have more to do with logic than with guessing and empathy this correlation rather seems to indicate that the presentation of elementary mathematics has more to do with guessing and empathy than with logical thinking.

(Karl Menger, an eminent mathematician of the 20th Century, was the son of Carl Menger, one of the preceptors of the Marginal Revolution in economics, and founder of the Austrian School of economics.)