The Language of Argument

1 7 0

C H A P T E R 7 ■ C a t e g o r i c a l L o g i c

We diagram the conclusion “No circles have sides” as follows:

Circles Things having sides

That information is clearly already contained in the Venn diagram for the

premises, so this syllogism is also valid.

Let’s try a syllogism with a particular premise:

All squares have equal sides.

Some squares are rectangles.

∴ Some rectangles have equal sides.

It is a good strategy to diagram a universal premise before diagramming a

particular premise. The diagram for the above argument then looks like this:

Rectangles

Squares

Things having

* equal sides

Here’s the diagram for the conclusion—that there is something that is a rec-

tangle that has equal sides:

Rectangles

Things having

* equal sides

The asterisk in the middle area of this diagram says that something is in

both circles, and that information already appears in the diagram for the

premises, so this argument is valid.

So far we have looked only at valid syllogisms. Let’s see how this method

applies to invalid syllogisms. Here is one:

All pediatricians are doctors.

All pediatricians like children.

∴ All doctors like children.

We can diagram the premises at the left and the conclusion at the right:

97364_ch07_ptg01_151-176.indd 170 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.