柏拉图格言和训练转移Plato's motto and the transfer of training

58° Plato's motto and the transfer of training.

PLATO

PLATO, “the most winged, most charming, and best loved of all the philosophers of the Western World,” was born in or near Athens in 427 B.C. He studied philosophy under Socrates there, and then set out upon his extensive wanderings for wisdom, studying mathematics under Theodorus of Cyrene on the African coast and becoming an intimate friend of the eminent Pythagorean Archytas. Upon his return to Athens around 387 B.C., he founded his famous Academy there, an institution for the systematic pursuit of philosophical and scientific inquiry. He presided over his Academy for the rest of his life, and died in Athens in 347 B.C. at the venerable age of eighty. Almost all the important mathematical work of the fourth century B.C. was done by friends or pupils of Plato, making his Academy the link between the mathematics of the earlier Pythagoreans and that of the long-lived school of mathematics at Alexandria. The Athenian school lasted some nine hundred years, until the Christians obtained from Emperor Justinian a decree that in 529 A.D. closed its doors forever.

Plato’s influence on mathematics was not due to any mathematical discoveries he made, but rather to his enthusiastic conviction that the study of mathematics furnished the finest training field for the mind, and hence was essential in the cultivation of philosophers and those who should govern his ideal state. This belief explains the renowned motto over the door of his Academy:

Let no one unversed in geometry enter here.

Thus, because of its logical element and the pure attitude of mind that he felt its study creates, mathematics seemed of utmost importance to Plato, and for this reason it occupied a valued place in the curriculum of the Academy.

In recent decades there has been vigorous controversy over the question of mental discipline and transfer of training, with contentions ranging from one extreme to the other. Thus there are those who, like Plato, claim that the study of mathematics develops the pupil’s respect for truth and therefore results in honesty, that it develops neatness, power of concentration, and especially the power to think clearly. But the advent of a mechanistic psychology cast grave doubt upon the validity of such claims, and it was quite conclusively shown that transfer of training is not complete, automatic, and inevitable. There are many examples of dishonesty, lack of neatness, and failure to think clearly in nonmathematical situations on the part of students of mathematics, and many uncritical people have interpreted this to mean that transfer of training is nonexistent. Competent psychologists today seem agreed that the truth lies between the two extreme positions; transfer of training can take place if the subject is taught with this specific purpose in view.