ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 709 



dence, in this sense, that two arguments which are entirely indepen- 

 dent, neither weakening nor strengthening each other, ought, when 

 they concur, to produce a belief equal to the sum of the intensities of 

 belief which either would produce separately. Now, we have seen 

 that the chances of independent concurrent arguments are to be mul- 

 tiplied together to get the chance of their combination, and therefore 

 the quantities which best express the intensities of belief should be 

 such that they are to be added when the chances are multiplied in order 

 to produce the quantity which corresponds to the combined chance. 

 Now, the logarithm is the only quantity which fulfills this condi- 

 tion. There is a general law of sensibility, called Fechner's psycho- 

 physical law. It is that the intensity of any sensation is proportional 

 to the logarithm of the external force which produces it. It is en- 

 tirely in harmony with this law that the feeling of belief should be as 

 the logarithm of the chance, this latter being the expression of the 

 state of facts which produces the belief. 



The rule for the combination of independent concurrent arguments 

 takes a very simple form when expressed in terms of the intensity of 

 belief, measured in the proposed way. It is this : Take the sum of 

 all the feelings of belief which would be produced separately by all 

 the arguments pro, subtract from that the similar sum for arguments 

 con, and the remainder is the feeling of belief which we ought to have 

 on the whole. This is a proceeding which men often resort to, under 

 the name of balancing: reasons. 



These considerations constitute an argument in favor of the con- 

 ceptualistic view. The kernel of it is that the conjoint probability of 

 all the arguments in our possession, with reference to any fact, must 

 be intimately connected with the jus.t degree of our belief in that 

 fact ; and this point is supplemented by various others showing the 

 consistency of the theory with itself and with the rest of our knowl- 

 edge. 



But probability, to have any value at all, must express a fact. It 

 is, therefore, a thing to be inferred upon evidence. Let us, then, con- 

 sider for a moment the formation of a belief of probability. Suppose 

 we have a large bag of beans from which one has been secretly taken 

 at random and hidden under a thimble. We are now to form a prob- 

 able judgment of the color of that bean, by drawing others singly 

 from the bag and looking at them, each one to be thrown back, and 

 the whole well mixed up after each drawing. Suppose the first draw- 

 ing is white and the next black. "We conclude that there is not an 

 immense preponderance of either color, and that there is something 

 like an even chance that the bean under the thimble is black. But 

 this judgment may be altered by the next few drawings. When we 

 have drawn ten times, if 4, 5, or 6, are white, we have more confidence 

 that the chance is even. When we have drawn a thousand times, if 

 about half have been white, we have great confidence in this result. 



