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Immediate Inference

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Immediate Inference
Logic 513
Lansangan, Maricris A.Sicat, Mary Joy G.
10/1/2012
I. Title
–
Immediate Inference
II. Objectives:
To comprehend what the concept of immediate inference is.
To acquire better understanding of the relationships existing among the categorical propositions.
To clearly distinguish the three types of valid immediate inferences.
III. Introduction
The square of opposition expresses the relationships between the four standard forms of categorical propositions. These are relationships of compatibility or incompatibility.However, there are also relationships of logical equivalence among categorical propositions. If two propositions are related in such a way that the truth of one implies the truthof the other, they are equivalent from a logical standpoint.In the traditional analysis of categorical reasoning, three particular operations wereidentified. These operations were called
immediate inferences
. Let us examine each of these inturn.
IV. Topic
An
immediate inference
is aninferencewhich can be made from onlyonestatementor proposition.For instance, from the statement All toads are green. we can
make the immediate inference that No toads are not green. There are a number of immediateinferences which canvalidly be made using logical operations, the result of which is alogically
equivalentstatement form to the given statement. There are also invalid immediate inferenceswhich aresyllogistic fallacies. A.
Conversion
: interchanging the subject and predicate terms of a categorical proposition (it isvalid, or preserves the truth value) for the
E
and
I
propositions only).1. Notice that the truth value is preserved for those statements with symmetrical distributionstatus: the E and I.
2. If an A or O proposition is converted, an undetermined truth value results.3. The complete table for conversion is as follows. Note especially that we are not reversingthe subject and predicate positions. Only the terms in the subject and predicate areinterchanged. For this reason, it might be helpful to invent actual classes for S and P whenyou first study the relations.
If All S is P is given true, then All P is S is undetermined.
If All S is P is given false, then All P is S is undetermined.
If No S is P is given true, then No P is S is true.
If No S is P is given false, then No P is S is false.
If Some S is P is given true, then Some P is S is true.
If Some S is P is given false, then Some P is S is false.
If Some S is not P is given true, then Some P is not S is undetermined.
If Some S is not P is given false, then Some P is not S is undetermined.
4. Another way to remember that only the E and I statements preserve thetruth value in conversion is to note that flipping the E and I Venn Diagramsover results in the same logical geography being displayed. I.e., their diagrams are symmetrical respectively.B.
Obversion
: changing the quality and replacing the predicate term with its complementaryclass (valid, or preserves truth value for all propositions--the
A
,
E
,
I
, and
O
).1. The
complementary class
is the class of everything not in the srcinal class. E.g., thecomplementary class of light bulbs is non-light bulbs. Usually, one just tacks on non- to obtain a complementary class. But note that the complementary class of light bulbs isnot non light bulbs. 2. Often, in English, certain prefixes indicate complementary classes.For example, un-, in-, de-, im-, dis- and others are sometimes so used. However,English being what it is, relying on the prefixes is risky. Consider ravel and unravel or flammable and inflammable or imflammable. For this reason, it is usually safer to usethe prefix non- in a kind of logical pseudo-English.3. Often common sense requires thinking what the true complement of a class is to be. Thecomplementary class of objects to be admired cannot be non-objects to be admired. Sometimes, only the context of the argument yields a clue as to the complementary class. Becareful not to empty your classes--there are fundamental philosophical implications here.4. The complete table for obversion is as follows.
If All S is P is given true, then No S is non-P is true.
If All S is P is given false, then No S is non-P is false.
If No S is P is given true, then All S in non-P is true.
If No S is P is given false, then All S is non-P is false.
If Some S is P is given true, then Some S is not non-P is true.
If Some S is P is given false, then Some S is not non-P is false.
If Some S is not P is given true, then Some S is non-P is true.
If Some S is not P is given false, then Some S is non-P is false.
C.
Contraposition
: replacing the subject term by the complement of its predicate term andreplace the predicate term by the complement of its subject term (valid, or preserves truth valueonly for the
A
and
O
propositions).1. Notice that contraposition is the same thing as successive obversion, conversion, andobversion of a proposition. In effect, contraposition does these operations in one step.Compare the following two inferences.
Statement
Reason
Truth Value
1. All S are P. given true2. All non-P is non-S. contraposition true
Statement
Reason
Truth Value
1. All S are P. given true2. No S are non-P. obversion true3. No non-P is S. conversion true4. All non-P is non-S. obversion true2. It might be helpful to visualize this picture of the generaloperation of contraposition.3. Again for contraposition, as for obversion, one has to be carefulabout describing the class complement for exactness.4. The table for all the contrapositives is as follows.
If All S is P is given true, then All non-P is non-S is true.
If All S is P is given false, then All non-P is non-S is false.
If No S is P is given true, then No non-P is non-S is undetermined.
If No S is P is given false, then No non-P is non-S is undetermined.
If Some S is P is given true, then Some non-P is non-S is undetermined.
If Some S is P is given false, then Some non-P is non-S is undetermined.
If Some S is not P is given true, then Some non-P is not non-S is true.

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