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Invalid Syllogism

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 dif- ferences 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 people 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 doctor and not a person who likes children, then it is not true that all doctors like chil- dren. 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 con- clusion does not follow by virtue of categorical form.3

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

Some doctors are golfers. Some fathers are doctors.

Some fathers are golfers.



People who like children


Premises: All pediatricians are doctors. All pediatricians like children.

Conclusion: All doctors like children.

People who like children

Fathers Golfers

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