500 ADDITIONS. 



propositions are represented as Realities more real than the Phenom- 

 ena ; as a Natural Philosophy of a higher kind than the study oi 

 Nature itself can teach. This is no doubt an erroneous assumption : 

 yet even in this there is a germ of truth ; namely, that the mathemat- 

 ical laws, which prevail in the universe, involve mathematical truths ; 

 which being demonstrative, are of a higher and more cogent kind than 

 mere experimental truths. 



Notions, such as these of Plato, respecting a truth at which science 

 is to aim, which is of an exact and demonstrative kind, and is imper- 

 fectly manifested in the phenomena of nature, may help or may mis- 

 lead inquirers ; they may be the impulse and the occasion to great dis- 

 coveries ; or they may lead to the assertion of false and the loss of true 

 doctrines. Plato considers the phenomena which nature offers to the 

 senses as mere suggestions and rude sketches of the objects which the 

 philosophic mind is to contemplate. The heavenly bodies and all .the 

 splendors of the sky, though the most beautiful of visible objects, be- 

 ing only visible objects, are far inferior to the true objects of which 

 they are the representatives. They are merely diagrams which may 

 assist in the study of the higher truth ; as we might study geometry 

 by the aid of diagrams constructed by some consummate artist. Even 

 then, the true object about which we reason is the conception which 

 we have in the mind. 



We have, I conceive, an instance of the error as well as of the truth, 

 to which such views may lead, in the speculations of Plato concerning 

 Harmony, contained in that part of his writings (the seventh Book of 

 the Republic), in which these views are especially urged. He there, 

 by way of illustrating the superiority of philosophical truth over such 

 exactness as the senses can attest, speaks slightingly of those who take 

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

 the astronomers measure the heavenly motions by the eye. " They 

 screw their pegs and pinch their strings, and dispute whether two notes 

 are the same or not." Now, in truth, the ear is the final and supreme 

 judge whether two notes are the same or not. But there is a case 

 in which notes which are nominally the same, are different really 

 and to the ear ; and it is probably to disputes on this subject, which 

 we know did prevail among the Greek musicians, that Plato here re- 

 fers. We may ascend from a note A { to a note C 3 by two octaves and 

 a third. We "may also ascend from the same note A! to C 3 by fifths 

 four times repeated. But the two notes C 3 thus arrived at are not the 

 same : they differ by a small interval, which the Greeks called a Com- 



