DISJUNCTIVE SYLLOGISM
A disjunctive syllogism is a syllogism whose major premise is a disjunctive preposition while its minor premise and conclusion are categorical proposition. EXAMPLE: The man is either honest honest or dishonest. But, he is honest. Therefore, he is not dishonest.
What is a disjunctive proposition?
Disjunctive proposition propo sition is one whose subject or predicate consist of parts which exclude each other. It is sometimes called “either -or” statements. Examples:
(1) A body is either in motion or at rest. (2) Jose is either writing or singing. What are the types of disjunctive propositions? (A) Proper or perfect disjunction is one whose parts are exclusive from one another.
Examples: (1) A body is either in motion or at rest. (2) It is either raining or not raining. (B) Improper or imperfect disjunction is one whose parts are not mutually exclusive.
Examples: (1) Jose is either writing or singing. (2) Either Pedro or Juana is dishonest.
TYPES OF DISJUNCTIVE SYLLOGISM 1. Proper Disjunctive Syllogism A) Ponendo Tollens Tollens (“ponendo” to accept, “tollens” to reject). Ponendo tollens is guided by the rule: if one part is accepted in the minor premise, the other part must be rejected in the conclusion. In order to be valid, the first part must be accepted in the minor premise and the other part is rejected in the conclusion. Examples: (1) The man is either honest or dishonest. But he is honest. Therefore, he is not dishonest.
(2) The sea is either not in low tide or high tide. It is not in low tide. Therefore, it is in high tide. B) Tollendo Ponens (“tollendo” to reject, “ponens” to accept). Tollendo ponens is guided by the rule: if one part is rejected in the minor premise, the other part must be accepted in the conclusion. In order to be valid, the first part is rejected in the minor premise while the second part must be accepted in the conclusion. Examples: (1) The man is either honest of dishonest. But, he is not honest. Therefore, he is dishonest. (2) The prisoner is either educated or uneducated. But he is not educated. Therefore, he is educated.
There is only one invalid mood for proper disjunctive syllogism. It is called Fallacy of Affirming the Disjunct ( Modus Ponens). This fallacy is committed when the alternant is accepted in both premise and conclusion. Examples: (1) Either the bulb is burnt or it is not receiving electricity. But, the bulb is burnt out. Therefore, it is not receiving electricity. (2) His statement is either true or false. But it is false. Therefore, it is true.
2. Improper Disjunctive Syllogism
There is only one valid mood for improper disjunctive syllogism, the Ponendo Tollens (Accept-Reject). It is guided by the rule: if one part is accepted in the minor premise, the other part must be rejected in the conclusion. In order to be valid, the first part must be accepted while the other part must be rejected. Examples: (1) Your cup of coffee is either hot or cold. But it is hot. Therefore, it is not cold.
(2) Jesus Christ was resurrected either on Sunday or Saturday. He resurrected on Saturday. Therefore, he did not resurrect on Sunday.
There is only one invalid mood for improper disjunctive syllogism, the Fallacy of Tollendo Ponens (Reject-Accept). This fallacy is committed by rejecting the alternant in the minor premise and then accepting the other in the conclusion. Examples: (1) Your cup of coffee is either hot or cold. But it is not hot. Therefore, it is cold. (2) Mary’s dress is either black or white. But, it is not white. Therefore, it is black.
TECHNIQUE IN DETERMINING A VALID OR AN INVALID DISJUNCTIVE SYLLOGISM 1. Identify the alternant. 2. Determine whether the alternant are proper or improper disjunct. 3. If proper, determine wheteher it is Ponendo Tollens or Tollendo Ponens. If improper, it is a Ponendo Tollens, since this is the only valid mood for the improper disjunctive syllogism. 4. Determine whether the syllogism is valid or invalid by applying the rule of disjunctive syllogism. **********
