ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 607 



This last class of difficulties can only be entirely overcome by 

 making the idea of probability perfectly clear in our minds in the 

 way set forth in our last paper. 



III. 



To get a clear idea of what we mean by probability, we have to 

 consider what real and sensible difference there is between one degree 

 of probability and another. 



The character of probability belongs primarily, without doubt, to 

 certain inferences. Locke explains it as follows : After remarking 

 that the mathematician positively knows that the sum of the three 

 angles of a triangle is equal to two right angles because he appre- 

 hends the geometrical proof, he thus continues: "But another man 

 who never took the pains to observe the demonstration, hearing a 

 mathematician, a man of credit, affirm the three angles of a triangle 

 to be equal to two right ones, assents to it ; i. e., receives it for true. 

 In which case the foundation of his assent is the probability of the 

 thing, the proof being such as, for the most part, carries truth with 

 it ; the man on whose testimony he receives it not being wont to 

 affirm anything contrary to, or besides his knowledge, especially in 

 matters of this kind." The celebrated " Essay concerning Humane 

 Understanding" contains many passages which, like this one, make 

 the first steps in profound analyses which are not further developed. 

 It was shown in the first of these papers that the validity of an 

 inference does not depend on any tendency of the mind to accept it, 

 however strong such tendency may be ; but consists in the real fact 

 that, when premises like those of the argument in question are true, 

 conclusions related to them like that of this argument are also true. 

 It was remarked that in a logical mind an argument is always con- 

 ceived as a member of a genus of arguments all constructed in the 

 same way, and such that, when their premises are real facts, their 

 conclusions are so also. If the argument is demonstrative, then this 

 is always so ; if it is only probable, then it is for the most part so. 

 As Locke says, the probable argument is "such as for the most part 

 carries truth with it." 



According to this, that real and sensible difference between one de- 

 gree of probability and another, in which the meaning of the distinc- 

 tion lies, is that in the frequent employment of two different modes 

 of inference, one will carry truth with it oftener than the other. It 

 is evident that this is the only difference there is in the existing fact. 

 Having certain premises, a man draws a certain conclusion, and as far 

 as this inference alone is concerned the only possible practical ques- 

 tion is whether that conclusion is true or not, and between existence 

 and non-existence there is no middle term. " Being only is and noth- 

 ing is altogether not," said Parmenides ; and this is in strict accord- 

 ance with the analysis of the conception of reality given in the last 



