XLV.] REMAKKS ON THE LOGIC OF THE SCIENCES. 231 



of unconscious intelligence. It is also true that self- 

 contradiction is a proof of error : but tliis test also needs 

 caution in its application ; for it is always necessary, and 

 often difficult, to determine whether a contradiction is real 

 or only verbal. 



4. Lastly, the fallacy that precision is the criterion of that pre- 

 certainty. I have insisted above at some length on the is^i^e 

 important truth that certainty without precision or definite- criterion of 

 ness is characteristic of the facts of life. It is important 

 clearly to conceive this distinction between certainty and 

 precision, because a vague notion appears to be very com- 

 mon, that precision is the criterion of certainty, and that 

 no truth can be perfectly certain unless it is capable of 

 being stated with numerical accuracy ; and consequently 

 that the certainty which is attainable in the moral and 

 political sciences is inferior in degree to that which is 

 attainable in the mathematical and the physical ones. 

 This notion is never, I think, stated as a formula ; indeed, 

 it would refute itself if it were ; for were it true that no 

 numerically indefinite proposition can be quite certain, it 

 would follow that because no man knows how long he has 

 to live, it is therefore not quite certain whether he is to 

 die at all : a conclusion which it would be impossible to 

 accept. But the notion of some necessary connexion be- 

 tween certainty and precision is, I think, implied in such 

 expressions as " mathematical certainty " and " mathe- 

 matical precision;" and in the belief, which is often 

 avowed and oftener implied, that no general truths are 

 attainable concerning the social relations of man ; that 

 historical and political science are consequently impossible, 

 and that history is, and ever must be, a mass of mere facts, 

 and politics a chaos of mere opinions. The prevalent un- 

 belief in the possibility of historical and political science, 

 however, though it allies itself with the lingering notion 

 that determinations cannot he certain unless they are also 

 precise, is chiefly due to the fact that the political group 

 of sciences is still in a very immature state. But, as I 

 have remarked in the introduction to this work,^ the time 



1 Vol. I. p. 6. 



