588 Dr WHEWELL, ON PLATO'S SURVEY OF THE SCIENCES. 



and the anticipations of Plato on this head were more true than he himself could have con- 

 ceived. 



When the above view of the nature of true astronomy has been proposed, Glaucon says : 



" That would be a task much more laborious than the astronomy now cultivated.'''' Socrates 

 replies : " I believe so : and such tasks must be undertaken, if our researches are to be good 

 for anything." 



After Astronomy, there comes under review another Science, which is treated in the same 

 manner. It is presented as one of the Sciences which deal with real abstract truth ; and 

 which are therefore suited to that developement of the philosophic insight into the highest 

 truth, which is here Plato's main object. This Science is Harmonics, the doctrine of the 

 mathematical relations of musical sounds. Perhaps it may be more difficult to explain to 

 a general audience, Plato's views on this than on the previous subjects : for though Harmonics 

 is still acknowledged as a Science including the mathematical truths to which Plato here refers, 

 these truths are less generally known than those of geometry or astronomy. Pythagoras is 

 reported to have been the discoverer of the cardinal proposition in this Mathematics of Music : 

 — namely, that the musical notes which the ear recognizes as having that definite and harmonious 

 relation which we call an octave, & fifth, a fourth, a third, have also, in some way or other, the 

 numerical relation of 2 to 1, 3 to 2, 4 to 3, 5 to 4. I say "some way or other," because the 

 statements of ancient writers on this subject are physically inexact, but are right in the essen- 

 tial point, that those simple numerical ratios are characteristic of the most marked harmonic 

 relations. The numerical ratios really represent the rate of vibration of the air when those 

 harmonics are produced. This perhaps Plato did not know : but he knew or assumed that 

 those numerical ratios were cardinal truths in harmony : and he conceived that the exactness of 

 the ratios rested on grounds deeper and more intellectual than any testimony which the ear 

 could give. This is the main point in his mode of applying the subject, which will be best 

 understood by translating (with some abridgement) what he says. Socrates proceeds : 



($11 near the end.) "Motion appears in many aspects. It would take a very wise 

 man to enumerate them all : but there are two obvious kinds. One which appears in astro- 

 nomy, (the revolutions of the heavenly bodies,) and another which is the echo of that*. As the 

 eyes are made for Astronomy, so are the ears made for the motion which produces Harmonyf: 

 and thus we have two sister sciences, as the Pythagoreans teach, and we assent. 



((? 12.) " To avoid unnecessary labour, let us first learn what they can tell us, and see 

 whether anything is to be added to it; retaining our own view on such subjects: namely 

 this : — that those whose education we are to superintend — real philosophers — are never to 

 learn any imperfect truths : — anything which does not tend to that point (exact and permanent 

 truth) to which all our knowledge ought to tend, as we said concerning astronomy. Now 

 those who cultivate music take a very different course from this. You may see them taking 

 immense pains in measuring musical notes and intervals by the ear, as the astronomers measure 

 the heavenly motions by the eye. 



" Yes, says Glaucon, they apply their ears close to the instrument, as if they could catch the 

 note by getting near to it, and talk of some kind of recurrences \. Some say they can distinguish 



• duritTTpCHpov avrou. + irpos kvapixoviov (popdv wxa irayijvai. t •jriiKUai/iaTa otto. 



