XLiii.] CLASSIFICATION OF THE SCIENCES. 203 



co-exist with the same thing co-exist with each other,^ — 

 these have not been discovered by logicians : — logicians 

 have not taught lis these truths, but have only made us 

 aware that we know them, and have always known them. 

 Logic is exclusively occupied with determining the founda- 

 tions of knowledge, and leaves the other sciences to build 

 the superstructure ; or, to use a difterent metaphor, logic 

 works backward to the fiindamental principles and as- 

 sumptions of knowledge, and leaves the other sciences to 

 work forward to inferences.^ 



It is for this reason — namely, because logic is not an Logical 

 organon of knowledge — that no looical notation can be of '^°^'^*''^" '^ 



° o o 2iot an 111- 



any use except for the purpose of illustrating the truths strument 

 of logic itself. The notations of arithmetic and algebra jug'^'^^"'^' 

 are instruments of vast utility and power, but no notation 

 of logic can be of the slightest use as an instrument of 

 reasoning ; though it may be — and, I think, in Professor 

 Boole's hands ^ has been — of great use in showing the 

 laws of reasoning.* 



Logic is, on every ground, to be regarded as the first of 

 the sciences. I do not mean the first in the sense of the 



1 Tlie first of these three axioms is that which is called, in the language 

 of technical logic, the principle of identity and contradiction ; the second 

 is the dictum de omni et nulla, on which the syllogism is based ; the third 

 is that which Mr. Mill places at the foundation of his logic. 



2 Questions however arise in many, perhaps in all sciences, which, 

 like those of logic, have to do, not with extending knowledge, but with 

 settling its basis. No one will question the great service done to science 

 by Euclid in stating the postulates and axioms as he has done ; and yet 

 this work did not extend our knowledge : but it is always desirable, not 

 only to extend knowledge as much as possible, but to settle its founda- 

 tions ; — not only to infer as much as possible, but to infer it from the 

 smallest possible number of primary principles. 



^ See Boole's Laws of Thought. 



* In the chapter on Mental Intelligence (Chap. XXXIX.), and in the 

 present, I have throughout spoken of the laws of logic as being laws of the 

 universe, and being laws of thought only because they are laws of the 

 universe. Consequently, I altogether difler with those who would class 

 logic as a branch of psychology ; I think it would be as rational to call 

 mathematics a branch of psychology because space and time are forms of 

 thought, as to call logic a branch thereof because the laws of logic are laws 

 of thought. 



