Arguments Applying Statistics

§4.2

Consider the following argument, and let’s assume that the premises are certain:

Map 40a:

If P1 said that all Frenchmen were Catholic the argument would be a valid deduction, but, as it stands, the argument is invalid. Does it, though, give us any reason to believe its conclusion? Does it make the conclusion even epistemically possible? For all that P1 says, there may be only two Catholics among the tens of millions of Frenchmen. So, if these premises were the only support we had for the conclusion, the conclusion would be unfounded. But suppose we changed the argument as follows:

Map 40b:

This is clearly an improvement. If most Frenchmen are Catholic, then isn’t the conclusion that Pierre is probable? After all, given that he’s French, isn’t he more likely to be Catholic than not? And if we change P1 again to be more specific as to how many Frenchmen are Catholic, can’t we then say more precisely how probable it is that Pierre is Catholic?

Map 40c:

We have here an extremely simple example of statistical reasoning. Statistics is the science that deals with the interpretation and analysis of quantitative data about the prevalence of traits within groups, and it is sometimes used to draw conclusions about how certain we can be that an individual has a certain trait.