The Language of Argument

1 6 8

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

Venn Diagrams for syllogisms. In a previous section, we used Venn

diagrams to test the validity of immediate inferences. Immediate inferences

contain only two terms or classes, so the corresponding Venn diagrams need

only two overlapping circles. Categorical syllogisms contain three terms or

classes. To reflect this, we will use diagrams with three overlapping circles.

If we use a bar over a letter to indicate that things in the area are not in the

class (so that S indicates what is not in S), then our diagram looks like this:

In each of the last two syllogisms, what is the subject term? The predicate

term? The middle term? The major premise? The minor premise? The form

of the syllogism (using S, P, and M)? Is the syllogism valid? Why or why not?

Exercise VI

Given the restrictions in the definition of a categorical syllogism, there are

exactly 256 possible forms of categorical syllogism. Explain why.

Honors Exercise

S P

SPM

__

SPM

_

SPM

_

SPM

M

___

SPM

__

SPM

_ __

SPM SPM

This diagram has eight different areas, which can be listed in an order that

resembles a truth table:

S P M

S P M

S P M

S P M

S P M

S P M

S P M

S P M

Notice that, if something is neither an S nor a P nor an M, then it falls completely

outside the system of overlapping circles. In every other case, a thing is assigned

to one of the seven compartments within the system of overlapping circles.

97364_ch07_ptg01_151-176.indd 168 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.