CHAP. I.] NATURE AND DESIGN OF THIS WORK. 7 



conversant, and those which present themselves in the particular 

 science of Number, the law in question is deserving of more 

 than a passing notice. It may be said that it lies at the very 

 foundation of general reasoning, that it governs those intellec- 

 tual acts of conception or of imagination which are preliminary to 

 the processes of logical deduction, and that it gives to the pro- 

 cesses themselves much of their actual form and expression. It 

 may hence be affirmed that this law constitutes the germ or semi- 

 nal principle, of which every approximation to a general method 

 in Logic is the more or less perfect development. 



7. The principle has already been laid down (5) that the 

 sufficiency and truly fundamental character of any assumed sys- 

 tem of laws in the science of Logic must partly be seen in the 

 perfection of the methods to which they conduct us. It remains, 

 then, to consider what the requirements of a general method in 

 Logic are, and how far they are fulfilled in the system of the pre- 

 sent work. - 



Logic is conversant with two kinds of relations, relations 

 among things, and relations among facts. But as facts are ex- 

 pressed by propositions, the latter species of relation may, at 

 least for the purposes of Logic, be resolved into a relation among 

 propositions. The assertion that the fact or event A is an inva- 

 riable consequent of the fact or event B may, to this extent at 

 least, be regarded as equivalent to the assertion, that the truth 

 of the proposition affirming the occurrence of the event B always 

 implies the truth of the proposition affirming the occurrence of 

 the event A. Instead, then, of saying that Logic is conversant 

 with relations among things and relations among facts, we are 

 permitted to say that it is concerned with relations among things 

 and relations among propositions. Of the former kind of relations 

 we have an example in the proposition "All men are mortal;" 

 of the latter kind in the proposition " If the sun is totally 

 eclipsed, the stars will become visible." The one expresses a re- 

 lation between " men" and " mortal beings," the other between 

 the elementary propositions " The sun is totally eclipsed ;" 

 " The stars will become visible." Among such relations I sup- 

 pose to be included those which affirm or deny existence with 

 respect to things, and those which affirm or deny truth with re- 



