The two rules of a syllogism are as follows:
1. Rule One: There must be three terms – the major premise, the minor premise, and the conclusion – no more, no less. A syllogism is a logical argument consisting of three propositions, where two premises lead to a logical conclusion. Each of these three terms plays a specific role in the syllogism. The major premise is the general statement or principle, the minor premise is the specific statement or example, and the conclusion is the logical inference drawn from the premises.
To illustrate this rule, let’s consider an example:
Major premise: All mammals are animals.
Minor premise: Dogs are mammals.
Conclusion: Therefore, dogs are animals.
In this example, the major premise states a general truth about mammals and animals. The minor premise provides a specific instance by mentioning dogs as mammals. From these two premises, we can logically conclude that dogs are also animals. This syllogism adheres to Rule One as it includes the three required terms.
2. Rule Two: The minor premise must be distributed in at least one other premise. In logic, a term is said to be distributed when it refers to all members of a particular class or category. To ensure a valid syllogism, the term used in the minor premise must also be distributed in either the major premise or the conclusion.
Continuing with our previous example:
Major premise: All mammals are animals.
Minor premise: Dogs are mammals.
Conclusion: Therefore, dogs are animals.
Here, the term “mammals” in the minor premise is distributed because it refers to all members of the class “mammals.” It is also distributed in the major premise as it refers to all mammals being animals. This adherence to Rule Two ensures that the syllogism is valid.
However, if we were to modify the example:
Major premise: All mammals are animals.
Minor premise: Some dogs are mammals.
Conclusion: Therefore, dogs are animals.
In this modified example, the term “mammals” in the minor premise is not distributed because it only refers to some dogs, not all dogs. This violation of Rule Two makes the syllogism invalid.
The two rules of a syllogism are crucial for constructing valid logical arguments. Rule One ensures the presence of the three necessary terms: major premise, minor premise, and conclusion. Rule Two ensures that the minor premise, which contains the specific example, is distributed in at least one other premise. Adhering to these rules enhances the validity and effectiveness of syllogistic reasoning.