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5.7 2. Standard-Form Sorites – Reducing Terms and Ordering Premises…
5.7
2. Standard-Form Sorites – Reducing Terms and Ordering Premises
You have seen that there are four criteria for standard-form sorites:
Criteria for a Standard-Form Sorites
1. Each component statement in the sorites must be a standard-form categorical proposition.
2. Each term in the sorites must occur twice.
3. The first premise of the sorites must contain the predicate term from the conclusion.
4. Each successive premise must have one term in common with the preceding one.
Criteria 3 and 4, in particular, often require that you rearrange the given order of a sorites’ premises. But criterion 2 also often requires that one or more of the premises undergo the operations for reducing the number of terms in an argument before you are able to put the argument into the form of a standard-form sorites.
Recall the following operations for reducing the number of terms in an argument. The operation of conversion involves switching the subject term and the predicate term in a categorical proposition. The operation of obversion involves changing the quality of a statement (from affirmative to negative, or vice versa) while leaving the quantity unchanged; it also involves replacing the predicate term with its term complement. And the operation of contraposition involves switching the subject term and the predicate term in a categorical proposition and then replacing each term with its term complement. Recall also that you sometimes need to apply two operations to a single line in order to obtain a properly reduced statement. For example, you may find that you first need to perform a conversion operation in order to situate terms in a way that then allows you to perform an obversion operation.
Consider the following sorites, Argument A, along with its reduced form. Determine which operations for reducing the number of terms were employed to arrive at the given reduced-argument form. Then, put the sorites into standard form by arranging its reduced premises in an order that conforms to the four criteria for standard-form sorites.
Argument A
P1: All J are D.
P2: Some L are not non-O.
P3: All L are non-D.
P4: All non-J are non-B.
C: Some non-B are not non-O.
Reduced Form for Argument A
P1: All J are D.
P2: Some L are O.
P3: No L are D.
P4: All B are J.
C: Some O are not B.
To arrive at the reduced form of Argument A, P1 was .
To arrive at the reduced form of Argument A, P2 was .
To arrive at the reduced form of Argument A, P3 was .
To arrive at the reduced form of Argument A, P4 was .
To arrive at the reduced form of Argument A, C was .
Now arrange the premises from the reduced form of Argument A so that the argument conforms to the criteria for standard-form sorites.
Standard-Form Version of Argument A
P1:
P2:
P3:
P4:
C: Some O are not B.
Consider the following sorites, Argument B, along with its reduced form. Determine which operations for reducing the number of terms were employed to arrive at the given reduced-argument form. Then, put the sorites into standard form by arranging its reduced premises in an order that conforms to the four criteria for standard-form sorites.
Argument B
P1: No U are non-A.
P2: Some T are not non-L.
P3: All A are J.
P4: All non-U are non-T.
P5: No non-P are J.
C: Some P are L.
Reduced Form for Argument B
P1: All U are A.
P2: Some T are L.
P3: All A are J.
P4: All T are U.
P5: All J are P.
C: Some P are L.
To arrive at the reduced form of Argument B, P1 was .
To arrive at the reduced form of Argument B, P2 was .
To arrive at the reduced form of Argument B, P3 was .
To arrive at the reduced form of Argument B, P4 was .
To arrive at the reduced form of Argument B, P5 was .
To arrive at the reduced form of Argument B, C was .
Now arrange the premises from the reduced form of Argument B so that the argument conforms to the criteria for standard-form sorites.
Standard-Form Version of Argument B
P1:
P2:
P3:
P4:
P5:
C: Some P are L.
