272 THE PRINCIPLES OF SCIENCE. 



discontinuous quantity or numbers, however, allow of cer- 

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

 the difference of the squares of 17 and 13 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, indeed, 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 statements, they will be found to involve no cer- 

 tainty 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 consciousness has certainly informed me that with 

 my meaning of the terms, ' Gold is insoluble in nitric 

 acid.' I may further be certain of something else ; for if 

 this gold and nitric acid remain what they were, I may be 

 sure there will be no solution on again trying the experi- 

 ment. If I take other portions of gold and nitric acid, 

 and am sure that they really are identical in properties 

 with the former portions, I can be certain that there will 

 be no solution. But at this point my knowledge becomes 

 purely hypothetical ; for how can I be sure without trial 

 that the gold and acid are really identical in nature with 

 what I formerly called gold and nitric acid. How do 

 I know gold when I see it ? If I judge by the appa- 

 rent qualities colour, ductility, specific gravity, &c., I 

 may be misled, because there may always exist a sub- 

 stance which to the colour, ductility, specific gravity, and 

 other specified qualities, joins others which we do not 

 expect. Similarly, if iron is magnetic, as shown by an 

 experiment with objects answering to those names, then 

 all iron is magnetic, meaning all pieces of matter identical 



