CHAP. I.] NATURE AND DESIGN OF THIS WORK. 5 



their mutual place and relation. All sciences consist of general 

 truths, but of those truths some only are primary and fundamen- 

 tal, others are secondary and derived. The laws of elliptic mo- 

 tion, discovered by Kepler, are general truths in astronomy, but 

 they are not its fundamental truths. And it is so also in the 

 purely mathematical sciences. An almost boundless diversity of 

 theorems, which are known, and an infinite possibility of others, 

 as yet unknown, rest together upon the foundation of a few sim- 

 ple axioms ; and yet these are all general truths. It may be 

 added, that they are truths which to an intelligence sufficiently 

 refined would shine forth in their own unborrowed light, with- 

 out the need of those connecting links of thought, those steps 

 of wearisome and often painful deduction, by which the know- 

 ledge of them is actually acquired. Let us define as fundamental 

 those laws and principles from which all other general truths of 

 science may be deduced, and into which they may all be again 

 resolved. Shall we then err in regarding that as the true science 

 of Logic which, laying down certain elementary laws, confirmed 

 by the very testimony of the mind x permits us thence to deduce, 

 by uniform processes, the entire chain of its secondary conse- 

 quences, and furnishes, for its practical applications, methods of 

 perfect generality ? Let it be considered whether in any science, 

 viewed either as a system of truth or as the foundation of a prac- 

 tical art, there can properly be any other test of the completeness 

 and the fundamental character of its laws, than the completeness 

 of its system of derived truths, and the generality of the methods 

 which it serves to establish. Other questions may indeed pre- 

 sent themselves. Convenience, prescription, individual prefe- 

 rence, may urge their claims and deserve attention. But as 

 respects the question of what constitutes science in its abstract 

 integrity, I apprehend that no other considerations than the 

 above are properly of any value. 



6. It is designed, in the next place, to give expression in this 

 treatise to the fundamental laws of reasoning in the symbolical 

 language of a Calculus. Upon this head it will suffice to say, that 

 those laws are such as to suggest this mode of expression, and 

 to give to it a peculiar and exclusive fitness for the ends in view. 



