HISTORY OF PHILOSOPHY. 565 



numbers were transferred to the objects themselves. The formulae 

 of mathematics were converted into arbitrary laws. 



Nor did the mischief end here. Mathematical reasoning cannot 

 from its precise nature be applied to the elucidation of ethics. But 

 the Pythagoreans, regardless of distinctions, broke down this barrier, 

 and physical phenomena and ethical abstractions were alike sub- 

 jected to the laws of number and magnitude. 



The monad or unity with them occupied the highest place. 

 Every thing they said was derived from it, for all numbers are 

 formed by the repetition of it ; it is simple in itself, for it is the re- 

 sult of no combination; it reproduces itself only by successive multi- 

 plication, as it is its own mathematical exponent ; it is then the 

 essential element, the active principle, the universal cause, and 

 therefore eminently perfect. 



The duad or two is on the contrary imperfect; it is produced 

 by composition ; it is the passive principle, chaos or matter. 



There are two species of number, even and odd ; the first are im- 

 perfect, the second perfect. For the first are formed from the second 

 by multiplication or addition, which is not the case in the converse. 



The next two numbers also had their mystic properties, three as 

 being the sum of the first and second ; four as the first square number ; 

 ten, the sum of the four first numbers, constituted the decad, a 

 symbol which played an important part among the Pythagoreans. 

 They applied it to every branch of knowledge, and reduced all 

 fundamental nomenclatures to it. We will now turn from the con- 

 sideration of these strange fancies, to that which is really worthy of 

 praise in their doctrines. They perceived that independently of the 

 primitive element in the formation of all bodies, there was a species 

 of collective unity, under which objects and effects of the same nature 

 were to be arranged. They then applied this extended view to 

 nature : " Existent beings are bound together by a chain of affinities 

 similar to that which unites numbers ; all these affinities tend to 

 one centre ; the world thus forms a symmetrical whole, in which no 

 one portion is perfectly independent of another." Nothing can be 

 more sublime or majestic than this picture of the harmony which 

 exists in the universe. Having approached thus nearly to the idea 

 of the divine First Cause, it is a matter of astonishment that they did 

 not actually arrive at it. But their fantastic ideas on the powers 

 and properties of number excluded them from feeling the want of 

 any further cause. The immutable and eternal character which, as 

 they conceived, attached itself to this unity, was sufficient to explain 

 all that was requisite ; they did not attempt to separate the idea of 

 the divinity from a material object, but identified it with fire or 

 light ; they admired the antique tradition of the world's soul, and 

 conceived the universe to be an animated being. They adopted a 

 pantheism (which Virgil and Ovid afterwards adorned with the most 

 brilliant poetical images), that bears a striking analogy to the system 

 of emanations before mentioned, and perhaps was borrowed from it. 

 Pythagoras and his disciples admitted hierarchies of genii and in- 

 ferior deities scattered over space. They attached much importance 

 to dreams and predictions, and Pythagoras himself pretended to the 



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