CHAP. I.] NATURE AND DESIGN OF THIS WORK. 1 1 



If we may judge from the mathematical sciences, which are the 

 most perfect examples of method known, this directive function 

 of Method constitutes its chief office and distinction. The fun- 

 damental processes of arithmetic, for instance, are in themselves 

 but the elements of a possible science. To assign their nature is 

 the first business of its method, but to arrange their succession 

 is its subsequent and higher function. In the more complex 

 examples of logical deduction, and especially in those which form 

 a basis for the solution of difficult questions in the theory of 

 Probabilities, the aid of a directive method, such as a Calculus 

 alone can supply, is indispensable. 



10. Whence it is that the ultimate laws of Logic are mathe- 

 matical in their form ; why they are, except in a single point, 

 identical with the general laws of Number ; and why in that par- 

 ticular point they differ ; are questions upon which it might not 

 be very remote from presumption to endeavour to pronounce a 

 positive judgment. Probably they lie beyond the reach of our 

 limited faculties. It may, perhaps, be permitted to the mind to 

 attain a knowledge of the laws to which it is itself subject, with- 

 out its being also given to it to understand their ground and 

 origin, or even, except in a very limited degree, to comprehend 

 their fitness for their end, as compared with other and conceivable 

 systems of law. Such knowledge is, indeed, unnecessary for the 

 ends of science, which properly concerns itself with what is, and 

 seeks not for grounds of preference or reasons of appointment. 

 These considerations furnish a sufficient answer to all protests 

 against the exhibition of Logic in the form of a Calculus. It is 

 not because we choose to assign to it such a mode of manifes- 

 tation, but because the ultimate laws of thought render that mode 

 possible, and prescribe its character, and forbid, as it would 

 seem, the perfect manifestation of the science in any other form, 

 that such a mode demands adoption. It is to be remembered 

 that it is the business of science not to create laws, but to discover 

 them. We do not originate the constitution of our own minds, 

 greatly as it may be in our power to modify their character. 

 And as the laws of the human intellect do not depend upon our 

 will, so the forms of the science, of which they constitute the ba- 

 sis, are in all essential regards independent of individual choice. 



