178 KANSAS CITY REVIEW OF SCIENct:.. 



The case is different with natural law. For instance, the law of gravitation 

 would vanish with matter but need not reappear with it. 



Propositions which are independent of existence, in the sense just illustrated, 

 are therefore emblems of necessity, and our knowledge of necessity must result 

 from the determination of the truth or falsity, or what is the same thing, the possi- 

 bility or impossibility of them. Now these propositions are of two kinds : know- 

 able and unknowable. It will, therefore, be necessary to distinguish them. 



No one can conceive of an impossible thing, and whosoever thinks he can 

 will find by reflection that his conception is of something which is not, in his 

 opinion, Hkely to happen. For instance we can conceive of the Gorgon's head, 

 the winged horse and the golden fleece and such things are possible, but by 

 no means probable. Still, possibility is not limited by conception. 



Take the proposition "space is limited." We cannot conceive of a limit to 

 space without conceiving of space beyond that limit. We cannot conceive of 

 space as boundless, for we cannot conceive of infinity. Yet we know that space 

 is either limited or it is not. The proposition is unknowable, and so is any propo- 

 sition neither extreme of which is conceivable. Again, these propositions, being 

 either true or false, there cannot be one of which both extremes are conceivable 

 because one must be impossible. The only propositions, therefore, which are 

 knowable are those of which one extreme is conceivable, the other not. 



(This is substantially the Principle of the Conditioned as enunciated by Sir 

 WiUiam Hamilton.) 



Knowable propositions are of two kinds, self-evident and demonstrable, or 

 to be less general, axioms and theorems. Axioms are called self-evident be- 

 cause the mind comes by the knowledge of them apparently without effort. 



Now since these propositions, as well as the human mind, may be regarded 

 as independent of phenomenal existence, it was thought necessary by many phi- 

 losophers to account for the knowledge of necessity as it obtains with us, just as 

 they would, did there exist nothing but mind and truth. This view, of course, 

 necessitated a relation between mind and truth which would be independent of 

 fact, and as it was impossible to see how the mind could be affected by abstract 

 truth except through the medium of fact, many philosophers got rid of the diffi- 

 culty by assuming the ideas of axioms to be innate. But it would do just as well 

 to assume that these propositions in some unknown way affected the mind and 

 it would be more philosophical. 



Still, in either case, more would be assumed than could ever be proven. To 

 deal with this question it must be treated just as it is presented to us, and in this 

 aspect we will endeavor to find the conditions of the possibility of necessary knowl. 

 edge. It cannot be denied that we could gain the knowledge of axioms just as 

 we do the knowledge of law. Nor can it be denied that we get the knowledge 

 theorems by reasoning from axioms in precisely the same manner that we get the 

 knowledge of law by reasoning from fact. 



Moreover, the notion of causality is as necessary to the knowledge of theo. 

 rems as it is to the knowledge of law. So that if we for convenience deprive 



