The Language of Argument

1 9 1

S t a t i s t i c a l A p p l i c a t i o n s

Only about 3 percent of the small ellipse is left of the line to represent the

premise that 3 percent of Obama’s relatives voted for Romney. The area that

lies within both ellipses represents the people who are both Republicans

from California and also relatives of Obama. About 42 percent of that area is

left of the line to represent the premise that 42 percent of Republicans from

California who were relatives of Obama voted for Romney. The whole dia-

gram now shows how all of these premises can be true, even though they

lead to conflicting conclusions.

This series of arguments illustrates in a clear way what we earlier called

the defeasibility of inductive inferences: A strong inductive argument can

be made weak by adding further information to the premises. Given that

Marvin is a Republican from California, we seemed to have good reason to

think that he voted for Romney. But when we added to this the additional

piece of information that he was a relative of Obama, the original argument

lost most of its force. And new information could produce another reversal.

Suppose we discover that Marvin, though a relative of Obama, actively

campaigned for Romney. Just about everyone who actively campaigns for

a candidate votes for that candidate, so it seems that we again have good

reason for thinking that Marvin voted for Romney.

It is clear, then, that the way we select our reference classes will affect the

strength of a statistical application. The general idea is that we should define

our reference classes in a way that brings all relevant evidence to bear on the

subject. But this raises difficulties. It is not always obvious which factors are

relevant and which are not. In our example, party affiliation is relevant to

how people voted in the 2012 election; shoe size presumably is not. Whether

gender is significant, and, if so, how significant, is a matter for further statis-

tical research.

These difficulties concerning the proper way to fix reference classes reflect

a feature of all inductive reasoning: To be successful, such reasoning must

take place within a broader framework that helps determine which features

are significant and which features are not. Without this framework, there

would be no reason not to consider shoe size when trying to decide how

someone will vote. This shows how statistical applications, like all of the

other inductive arguments that we will study, cannot work properly without

appropriate background assumptions.

Carry the story of Marvin two steps further, producing two more reversals

in the strength of the statistical application with the conclusion that Marvin

voted for Romney.

Exercise III

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