The Language of Argument

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C H A P T E R 8 ■ A r g u m e n t s T o a n d F r o m G e n e r a l i z a t i o n s

We now have a statistical application that gives us strong support for the

claim that Marvin did not vote for Romney. This is incompatible with our

first statistical application, which gave strong support to the claim that he

did. To overlook this conflict between arguments based on different refer-

ence classes would be a kind of fallacy. Which statistical application, if either,

should we trust? This will depend on which of the reference classes we take

to be more relevant. Which counts more, political affiliation or family ties?

That might be hard to say.

One way of dealing with competing statistical applications is to combine

the reference classes. We could ask, for example, what percentage of Repub-

licans from California who are relatives of Obama voted for Romney? The

result might come out this way:

Forty-two percent of Republicans from California who were relatives

of Obama voted for Romney.

Marvin is a Republican from California who is a relative of Obama.

[ Marvin voted for Romney.

This statistical application provides very weak support for its conclusion.

Indeed, it supplies some weak support for the denial of its conclusion—that

is, for the claim that Marvin did not vote for Romney.

This situation can be diagrammed with ellipses of varying sizes to repre-

sent the percentages of Californians and relatives of Obama who do or do

not vote for Romney. First, we draw an ellipse to represent Republicans from

California and place a vertical line so that it cuts off roughly (very roughly!)

97 percent of the area of that ellipse to represent the premise that 97 percent

of the Republicans from California voted for Romney:

Voted for Romney

Republicans from California

Did not Vote for Romney

Next, we add a second ellipse to represent Obama’s relatives:

Voted for Romney

Republicans from California

Obama’s

relatives

Did not Vote for Romney

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