136 THE ANATOMY OF SCIENCE 



each as possessing a certain estimated degree of 

 probability ; and the result of a generalized syl- 

 logism will be a numerical fraction representing 

 in its turn a probability/ Let us suppose that a 

 certain statement has but one chance in a mil- 

 lion of proving false.^ Suppose now that we 

 have a million such statements, what is the like- 

 lihood that all of these statements Tsdll together 

 prove to be true when tested? It is less than an 

 even chance. 



A chemist who needs to know the density of 

 mercury at its boiling point finds in the litera- 

 ture records of half a dozen determinations. 

 Sometimes he is satisfied to take their average, 

 but ordinarily he scrutinizes the methods which 

 have been emplo3^ed and estimates the reliabil- 

 ity of each investigator. He thus gives a differ- 

 ent weight to each determination on the basis of 

 its relative value, and in assigning these several 

 weights he is not using mathematics but com- 

 mon sense. It is only after this part of his task 



1 See Charles S. Peirce, Popular Science Monthly, 1878. 



2 This is a very high degree of probability ; we feel sure 

 that the sun will rise to-morrow, but during the whole of 

 written history the sun has risen and set less than a million 

 times. Of course, owing to our knowledge of astronomy, we 

 have other reasons for believing that the sun will rise, in 

 addition to the fact that it has always done so. 



