[bowman] fundamental PROCESSES IN HISTORICAL SCIENCE 553 



statement in the record is correct. These probabiHties of 199,990/- 

 200,000 in a mathematical table, and 49/50 in a trustworthy record, 

 and all similar averages produced by accredited operation of correct 

 processes, may be called for convenient identification "formal probabil- 

 ity," because they constitute a form of probability which differs funda- 

 mentally from pure probability. Pure probability is the result of 

 favorable chances acting against unfavorable, but in formal proba- 

 bility only the second half of this condition is fulfilled. The inciden- 

 tal error is due to unfavorable chance, but the force acting against this 

 unfavorable chance, and producing the essential correctness in the 

 results as a whole, is not, as it should be in a case of pure probability, 

 merely favorable chance or chances, but a conscious, intelligent and 

 competent operator applying correct processes in a set effort to pro- 

 duce correct results. For this reason, in scientific and other activity, 

 formal probability even of comparatively low degree, if only it reaches 

 the average of essential correctness required by the exactness of the 

 branch of science or activity involved, imparts to its conclusions in- 

 dividually a value which pure probability does not. This difference 

 in values can be established as a fact in actual experience. In actual 

 experience a civil engineer, even when planning a structure, the safety 

 of which involves the lives of men, will use without further test any 

 one of the 200,000 numerical quantities in such a work as Chambers' 

 Tables. If the number of unlocated errors in these 200,000 quantities 

 be taken as 25, the probability on which this confident action of the 

 engineer" rests will be approximately 200,000:25 = 8,000:1; if the num- 

 ber oLerrors be taken as 10, the approximate probability will be 200,- 

 000:10 = 20,000:1; and even if the total number of errors be placed at 

 the unreasonably low estimate of 1, the approximate probability will 

 be only 200,000:1. But, in actual experience, it is also found that 

 the heart which lies ordinarily with its lower point turned to the left 

 in the human body is turned in some instances toward the right, and 

 in these exceptional cases the other organs, and their respective posi- 

 tions to left and right in the human trunk, are similary reversed. By 

 members of the medical profession, these instances of reversed organs, 

 which are very rare, are estimated as occurring approximately in the 

 proportion of one out of a million. If, then, a surgeon, having to 

 release a gathering in this part of the body, should assume that the 

 respective organs are in the usual position, and, on this assumption, 

 should insert his needle without further test, i.e., without locating 

 the actual position of the heart by the sound or impulse of its lower 

 point against the left or right walls of the chest respectively, he would 

 take this action in the strength of an approximate probability of 

 1,000,000:1 that the position of the organs is normal. And yet, if 



