118 PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



admit that a given authority, producing a universal proposition, has his weight in no material 

 degree lowered by the very great antecedent improbability of his statement. Their admission 

 is quite correct, but, so far as I know, not yet explained by the theory. 



On looking at this theory, we find it appear that almost every sound process of mathe- 

 matical application has results counterpart to its own among the results of the operations of 

 unassisted thought. I should wonder at no one who suspected that a manifestation of the 

 secrets of the brain would exhibit something more like a calculating machine for the apprecia- 

 tion of probabilities than any one, as matters stand, could venture to mention without ridicule, 

 or to maintain without deserving it. Kant has gone so far as to call our mental organization, 

 in this respect, a weighing machine with unstamped weights. 



The verifications of theory above mentioned will lead all who feel their force to have confi- 

 dence in the converse, namely, in the theory ultimately confirming every widely observed 

 result. 



Now we have before us the following phenomena, gathered from observation : — 



1. That an authority, or a witness, of whose value we have a previously acquired notion, 

 produces an effect upon us by his testimony which partly depends upon the preconceived pro- 

 bability of his statement : so that, whatever his general credit may be (short of imputed infalli- 

 bility), his particular credit with regard to any one statement is a function of the proba- 

 bility of that statement, as well as of his previous character. 



2. That the universal proposition is, a priori, very much less probable than the contrary 

 particular : that, X and Y being terms on the connexion of which evidence has never been 

 offered, it is very much (not to say infinitely) more probable that some Xs are not Ys than 

 that every X is Y. 



3. That an authority, stating a proposition on the connexion of the terms of which we 

 have no previous opinion, does not produce any very marked difference in our disposition to 

 trust him, by stating the particular rather than the universal. We receive his statement, one 

 of us with another, with much the same reliance, whether it be ' every X is Y,' or • some Xs 

 are not Ps. 1 



The difficulty derived from the apparent incompatibility of the third phasnomenon with 

 the first two, and the necessity of admitting that the universal and its contrary particular are 

 each made to be of an even chance a priori, was with me long antecedent to the explanation. 

 This admission I imagined to have been made by the logicians : nor was I singular here. I 

 have heard more than one person versed both in mathematics and in technical logic, express 

 himself for the superior antecedent probability of the particular proposition, in terms which 

 implied that he thought himself in opposition to general opinion. . 



An observation which contains the spirit of the true answer would be triumphantly met by 

 many from the common maxims of the theory. Suppose a person in whose accuracy (accuracy of 

 statement, a compound function of veracity and judgment) we have ordinary confidence, to draw 

 a card from the pack and to announce that it is the seven of spades. We cannot conceal from 

 ourselves that we believe he has made a correct statement as much as we believed that he was 



