Abstract: The technique of
successive applications of logical relations drawn from the square of opposition and
further immediate inferences is discussed and illustrated.
I. Before attempting successive immediate inferences, be able to write out from memory
all the logical relations from the Square of Opposition and the Further Immediate
Inferences. |
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A. The Square of Opposition
includes (1) contradiction, (2)
contrariety, (3) subcontrariety, and (4) subalternation. |
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B. Further Immediate Inferences include (5) conversion, (6)
obversion, and (7) contraposition. |
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C. These seven logical relations compose a kind of
"tool-kit" used to do inferences one after the other (hence the name
"successively"). |
| II. Successive immediate inferences are used to establish
whether two different statements about some state of affairs are logically related in some
way. |
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A. The object of the exercise is to try to establish a truth
value for a statement, if we know in advance the truth value of the other statement. |
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B. Often, this technique is used to interpret the meaning of
a statement which is initially difficult to understand. |
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1. For example, if a movie critic admits, |
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"Some violent movies are events which do not cause
aggressive behavior." |
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2. Does this admission indirectly imply that some violent
movies cause aggressive behavior? We can prove the first statement does not entail the
second statement as follows. |
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Statement |
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Reason |
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T.V. |
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1. Some violent movies are events which do
not cause aggressive behavior. |
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given |
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true |
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2. Some violent movies are not events which
cause aggressive behavior. |
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obversion |
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true |
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3. Some violent movies are events which
cause aggressive behavior. |
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subcontrariety |
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unknown |
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3. If the movie critic believes "Some violent movies are
events which cause aggressive behavior," then the critic would have to try to
establish its truth some other way. |
| III. Rules of Thumb for solving Successive Immediate
Inferences. |
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A. A good initial strategy to solve such problems is to try
the following approach. |
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1. Compare the subject and predicate classes
of both statements and note the differences. Begin by using inferences to match
exactly the subject and predicates of both statements. |
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a. If there is a two-complementary
class difference, contraposition is used in a step. |
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b. If there is a one-complementary
class difference, obversion is used in a step. |
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c. If the classes are
simply reversed
in order, conversion is used in a step. |
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2. Once the exact classes are matched, use
inferences from the Square of Opposition to match the statement form. |
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3. If the use of
step (1) match classes and
step (2) match statement fails to get a truth value, try reversing the order of steps. |
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B. Some inferences, of course will result in an undetermined
truth value because the two statements are not logically related. |
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1. Even so, you should try to maintain a truth value
(i.e.,
true or false ), if possible, for each step. |
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2. The shortest route is generally the best. Nevertheless, if
you get an undetermined truth value, go back through the problem and try reversing steps. |
Philosophy 103: Introduction to Logic
