The Language of Argument

1 6 6

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

Finally, we can see that A propositions also do not always validly convert.

From a proposition with the form “All S is P,” we may not always infer its

converse, which has the form “All P is S.”

S P P S

A: All S is P. Converse of A: All P is S.

Since the diagram is not symmetrical, the information changes when the di-

agram is flipped; the shading ends up in a different circle. That shows why

this form of argument is not always valid.

Traditionally, other immediate inferences have also been studied, but we will

not run through them all here. The single example of conversion is enough to

illustrate how Venn diagrams can be used to test some arguments for validity.

Use Venn diagrams to determine whether the following immediate inferences

are valid:

1. All dinosaurs are animals. Therefore, all animals are dinosaurs.


2. Some pterodactyls can fly. Therefore, some flying things are pterodactyls.


3. Some eryopses are not meat eaters. Therefore, some things that eat meat
   are not eryopses.


4. No tyrannosaurus is a king. Therefore, no king is a tyrannosaurus.


5. Some dinosaurs are reptiles. Therefore, all dinosaurs are reptiles.


6. Some dinosaurs are not alive today. Therefore, no dinosaurs are alive today.


7. All dimetrodons eat meat. Therefore, some dimetrodons eat meat.


8. No dinosaurs are warm-blooded. Therefore, some dinosaurs are not
   warm-blooded.

Exercise V

The Theory of the Syllogism

In an immediate inference, we draw a conclusion directly from a single A, E, I,

or O proposition. Moreover, when two categorical propositions are contradic-

tories, the falsity of one can be validly inferred from the truth of the other, and

the truth of one can be validly inferred from the falsity of the other. All these

forms of argument contain only one premise. The next step in understanding

categorical propositions is to consider arguments with two premises.

An important group of such arguments is called categorical syllogisms. The

basic idea behind these arguments is commonsensical. Suppose you wish to

prove that all squares have four sides. A proof should present some link or

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