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



229 



■within moderate limits no doubt, but without any ascer- 

 tainable law. Thus, in that branch of biology which is 

 most nearly connected with chemistry, it is impossible to 

 state the effect of medicines, or of poisons, with the same 

 kind of accuracy to which we are accustomed in chemistry. 

 We know that laudanum will produce sleep, and that 

 strychnine will kUl ; but, even if the constitution of the 

 patient is known, it is impossible to say how much 

 laudanum will be sufficient to cause sleep, or how much 

 strychnine will be sufficient to kill, with the same kind of 

 precision with which we can say how much of an acid is 

 required in order to saturate a given quantity of alkali. 

 But the determinations of biological science, though thus This does 

 inferior in precision to those of the inorganic sciences, are any"m- ^ 

 in no sense, and in no degree, inferior to them in certainty, certainty. 

 The same is true, and even more eminently so, in the 

 higher branches of biology. Thus, the law that all actions 

 tend to become habitual, is as well established as it is 

 possible for such a law to be ; but it is impossible, in any 

 case whatever, to say how many times an action must be 

 repeated in order to make it habitual, or, again, for how 

 long it must be discontinued in order to destroy the habit 

 by disuse. In the sciences of society also, in morals and The same 

 in politics, there are laws of general tendencies, but no ^oy^g" 

 quantitative laws ; consequently there is certainty without 

 precision. It is, for instance, as certain as anything can Certainty 

 be, that the tendency of falsehood is injurious to human precision, 

 happiness ; but it is never possible to tell how much injury 

 any particular falsehood will do, or has done. The ethical 

 bearing of this truth is very important, but it does not 

 belong to the subject of this work. 



We may enumerate four fallacies on the subject of the Four 

 relation of mathematics and of logic to the other sciences. anrUhdr 

 They all, I believe, have their origin in the fact that origin : 

 mathematics and logic were the earliest sciences in the 

 field; and they are relics of the time when those were 

 almost the only sciences, and when Pascal wrote of " the 

 geometrical spirit," meaning the scientific spirit. These 

 four fallacies are as follow : — 



