Why Do We Believe What Science Says? 27 



measurement is "correct." The second is the more com- 

 plicated matter of determining whether a relationship we 

 have observed is a "real" relationship or only the result 

 of "chance." 



We shall discuss these two cases separately. It may come 

 as a shock to many people, but it has been well known 

 to scientists for a long time that it is impossible to measure 

 anything absolutely accurately. There is always a margin 

 of error. The errors may be of several different sorts but 

 some possibiHty of error is always there. What the scientist 

 does, therefore, is to make several measurements, average 

 them up, and give a figure for the probabiUty that anyone 

 who makes the same measurements will get the same 

 average result. (Actually the procedure is somewhat more 

 complicated than this and there are several ways of stating 

 the probability of error, but the point is that the scientist 

 recognizes the probability that he is wrong and makes this 

 numerically clear to everybody else.) 



The second use of probability theory is much more 

 important and interesting, for it bears directly on the prob- 

 lem of how we know that what we have observed about 

 the past has anything to do with the future. So long as 

 science was concerned with things that seemed to happen 

 every time something else happened, as in the motion of 

 bilUard balls, Hume's worries about the theory of knowl- 

 edge were of interest to theorists and philosophers, but 

 they didn't bother practical men. Nowadays, however, 

 science is increasingly interested in relationships which 

 are much more complicated and involve so many variables 

 that it is difficult to arrange things so that the same result 

 occurs every time. The following example may help to 

 make clear how such situations are handled. 



A given form of pneumonia is known to have a case 

 fataUty rate which varies between 5 and 20 percent. We 



