Chapter 6 Hypothetical Syllogism
Hypothetical Syllogism
A hypothetical syllogism is a type of deductive argument which consists of the first
premise (analogically called major premise), the second premise (analogically the minor
premise), and the conclusion. The major premise is a hypothetical or sequential proposition,
while the minor premise and the conclusion are categorical propositions. A hypothetical
syllogism proceeds by stating two alternatives in the major premise, one of which is affirmed
or denied by the minor premise , while the other is affirmed or denied in the conclusion.
There are three types of a hypothetical syllogism, namely, the conditional, the
disjunctive, and the conjunctive.
The Conditional Syllogism
A conditional syllogism is one in which the major premise is a conditional proposition
and the minor premise and the conclusion are categorical propositions.
Rules for a Valid Conditional Syllogism
1. Modus Ponens: The truth of the antecedent logically follows from the truth
of the consequent. If we posit or accept the antecedent in the minor
premise, then we must also accept the consequent in the conclusion.
Example:
If Rene is a musician, then he is an artist.
But Rene is a musician.
Ergo, he is an artist.
In summary:
2. Modus Tollens: The falsity of the consequent logically implies the
falsity of the antecedent. If we sublate or reject the consequent in the minor
premise, then we must sublate or reject the antecedent in the conclusion.
Example:
If monkeys are thinkers, then they are rational beings.
But monkeys are not rational beings.
Ergo, they are not thinkers.
1. If A (antecedent), then C (consequent)
But A.
Ergo, C.
2. If A, then C.
But not C.
Ergo, not A.
Disjunctive Syllogism
A disjunctive syllogism is one in which the major premise is a disjunctive proposition,
while the minor premise and the conclusion are categorical propositions. A disjunctive
proposition consists of alternatives that exclude each other.
1. Complete Disjunction
A complete disjunction is one which consists of parts that are mutually
exclusive or contradictories. There are only two valid moods.
PonendoTollens: If we posit or accept one disjunct in the minor premise, then we
must sublate or reject the other disjunct in the conclusion.
Example:
Mr. Dawa is either educated or uneducated.
But Mr. Dawa is educated.
Ergo, he is not uneducated.
a.
b. Tollendo Ponens: If we sublate or reject one disjunct in the minor
premise, then we must posit or accept the other disjunct in the conclusion.
Example:
A servant is either obedient or disobedient.
But this servant is not disobedient.
Ergo, this servant is obedient.
2. Incomplete Disjunction
An incomplete disjunction is one in which the disjuncts are not mutually
exclusive or contraries. (Only 1 mood is valid)
PonendoTollens: If we posit or accept one disjunct in the minor premise, then we
must sublate or reject the other in the conclusion.
Example:
Mr. Lasala is either tall or short.
But Mr. Lasala is tall.
Ergo, he is not short.
Conjunctive Syllogism
a.
A conjunctive syllogism is one in which the major premise is a conjunctive
proposition while the minor premise and conclusion are categorical propositions. A
conjunctive proposition is one which denies that contrary predicates cannot be attributed to
the same subject as the same time and in the same sense. There is only one valid mood.
a.
PonendoTollens: If we posit or accept one conjunct in the minor premise, then we
must sublate or reject the other in the conclusion.
Example:
Hillary could not have been in Oslob and New York at the same time.
But Hillary was in Oslob.
Ergo, she was not in New York.