306 PHYSICAL SCIENCE IN THE MIDDLE AGES. 



due attention, become perfectly distinct, and capa- 

 ble of being positively applied and verified. The 

 subject which is thus dealt with, in the doctrines 

 of which we now speak, is Number; a notion 

 which tempts men into these visionary specula- 

 tions more naturally than any other. For num- 

 ber is really applicable to moral notions, to 

 emotions and feelings, and to their objects, as 

 well as to the things of the material world. More- 

 over, by the discovery of the principle of musical 

 concords, it had been found, probably most unex- 

 pectedly, that numerical relations were closely 

 connected with sounds which could hardly be dis- 

 tinguished from the expression of thought and 

 feeling; and a suspicion might easily arise, that 

 the universe, both of matter and of thought, might 

 contain many general and abstract truths of some 

 analogous kind. The relations of number have so 

 wide a bearing, that the ramifications of such a sus- 

 picion could not easily be exhausted, supposing men 

 willing to follow them into darkness and vague- 

 ness; which it is precisely the mystical tendency 

 to do. Accordingly, this kind of speculation ap- 

 peared very early, and showed itself first among 

 the Pythagoreans, as we might have expected, from 

 the attention which they gave to the theory of har- 

 mony : and this, as well as some other of the doc- 

 trines of the Pythagorean philosophy, was adopted 

 by the later Platonists, and, indeed, by Plato him- 

 self, whose speculations concerning number have 





