124 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
In like manner 
4 = the probability that any single prediction will be fulfilled 
in some manner. 
: = = the general probability of unpredicted occurrence; which, 
in case of prediction, becomes probability of fortuitous ful- 
fillment. 
> ; - = the probability that any single prediction will be 
fulfilled by reason of a logical connection. 
Since the skillful predictions are mingled indistinguishably with 
all the unskillful ones, and are vitiated accordingly, the value of 
the vitiated probability of the skillful prediction of any single 
occurrence may be represented by the product 
: c ¢ o—e (cs — op)? 
re (<- s— ;) x een, ™ op(s — 0)(s — p)’ 
as before. 
Prof. C. 8. Peirce (in Science, 1884, Nov. 14, Vol. IV, page 453) 
deduces the first of these factors as the unqualified value of 2, 
making no allowance for the vitiation, and tacitly assuming that 
an assortment of predictions is the logical equivalent of a jumble 
of the same predictions. He obtains his result by the aid of the 
supposition that part of the predictions are made by an infallible 
prophet, and the others by a man ignorant of the future. If Prof. 
Peirce had called on omnipotence instead of omniscience, and sup- 
posed the predictions to have been obtained from a Djinn careful to 
fulfill a portion of them corresponding to the data, the remainder 
of the occurrences being produced by an unknown Djinn at ran- 
dom, he would have obtained by parallel reasoning the second 
factor, i — se These Djinns represent, respectively, the 
known and unknown forces of nature, and gauge the prophet’s 
knowledge with principal reference to the proportion of predictions 
fulfilled. Prof. Peirce’s test refers principally to the proportion of 
occurrences predicted. THis test eliminates sins of omission; the 
other, sins of commission; and both are necessary to a proper 
estimate of the prophet’s comparative rectitude. 
