The Language of Argument

1 7 1

V a l i d i t y f o r C a t e g o r i c a l A r g u m e n t s

It is evident that the information in the diagram for the conclusion is not

already contained in the diagram for the premises. The arrow shows differ-

ences in informational content. Thus, this form of syllogism is not valid.

Notice that the difference between these diagrams not only tells us that this

form of syllogism is invalid; it also tells us why it is invalid. In the diagram for

the premises, there is no shading in the upper left area, which includes peo-

ple who are doctors but are not pediatricians and do not like children. This

shows that the premises do not rule out the possibility that some people are

doctors without being pediatricians or liking children. But if anyone is a doc-

tor and not a person who likes children, then it is not true that all doctors like

children. Because this is the conclusion of the syllogism, the premises do not

rule out all of the ways in which the conclusion might be false. As a result,

this conclusion does not follow by virtue of categorical form.^3

Here is an example of an invalid syllogism with particular premises:

Some doctors are golfers.

Some fathers are doctors.

∴ Some fathers are golfers.

Doctors

Pediatricians

People who

like children

Doctors

Premises:

All pediatricians are doctors.

All pediatricians like children.

Conclusion:

All doctors like children.

People who

like children

Fathers Golfers

Fathers

Premises: Conclusion:

Golfers

Doctors

Examine this diagram closely. Notice that in diagramming “Some doc-

tors are golfers,” we had to put an asterisk on the boundary of the circle for

97364_ch07_ptg01_151-176.indd 171 15/11/13 10:29 AM

some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,

affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.