236 THE PRINCIPLES OF SCIENCE. [CHAP. 



with certainty. In the first place, whatever feeling is 

 actually present to the mind is certainly known to that 

 mind. If I see blue sky, I may be quite sure that I 

 do experience the sensation of blueness. Whatever I do 

 feel, I do feel beyond all doubt. We are indeed very 

 likely to confuse what we really feel with what we are 

 inclined to associate with it, or infer inductively from 

 it; but the whole of our consciousness, as far as it is 

 the result of pure intuition and free from inference, is 

 certain knowledge beyond all doubt. 



In the second place, we may have certainty of inference ; 

 the fundamental laws of thought, and the rule of substitution 

 (p. 9), are certainly true ; and if my senses could inform me 

 that A was indistinguishable in colour from B, and B from 

 C, then I should be equally certain that A was indistinguish- 

 able from C. In short, whatever truth there is in the 

 premises, I can certainly embody in their correct logical 

 result. But the certainty generally assumes a hypothetical 

 character. I never can be quite sure that two colours 

 are exactly alike, that two magnitudes are exactly equal, 

 or that two bodies whatsoever are identical even in their 

 apparent qualities. Almost all our judgments involve 

 quantitative relations, and, as will be shown in succeeding 

 chapters, we can never attain exactness and certainty 

 where continuous quantity enters. Judgments concerning 

 discontinuous quantity or numbers, however, allow of cer- 

 tainty ; I may establish beyond doubt, for instance, that 

 the difference of the squares of 1 7 and 1 3 is the product 

 of 17 + 13 and 17 13, and is therefore 30 X 4, or 120. 



Inferences which we draw concerning natural objects 

 are never certain except in a hypothetical point of 

 view. It might seem to be certain that iron is magnetic, 

 or that gold is incapable of solution in nitric acid ; but, 

 if we carefully investigate the meanings of these state- 

 ments, they will be found to involve no certainty but 

 that of consciousness and that of hypothetical inference. 

 For what do I mean by iron or gold? If I choose a 

 remarkable piece of yellow substance, call it gold, and 

 then immerse it in a liquid which I call nitric acid, and 

 find that there is no change called solution, then conscious- 

 ness has certainly informed me that, with my meaning of 

 the terms, " Gold is insoluble in nitric acid." I may further 



