(i) Fallacy of Four Terms:
The fallacy of four terms occurs in a syllogism when there are four terms instead of the required three terms. In a valid syllogism, there must be exactly three terms: the major term, the minor term, and the middle term. If an argument contains four terms, it becomes invalid because it violates the structure of a syllogism.
Example of Fallacy of Four Terms:
Premise 1: All dogs are animals.
Premise 2: Some animals are pets.
Conclusion: Some pets are dogs.
In this argument, the terms are: "dogs," "animals," "some animals," and "pets." There are four terms, which makes the syllogism invalid.
(ii) Fallacy of Exclusive Premises:
The fallacy of exclusive premises occurs when both premises in a syllogism are negative (E or O forms). This is a logical error because two negative premises cannot lead to a valid conclusion in a categorical syllogism. The structure of a valid syllogism requires at least one affirmative premise to allow the conclusion to follow logically.
Example of Fallacy of Exclusive Premises:
Premise 1: No dogs are cats.
Premise 2: No cats are animals.
Conclusion: No dogs are animals.
Here, both premises are negative, and no valid conclusion can be drawn. This is a fallacy of exclusive premises.
Conclusion: The fallacy of four terms occurs when a syllogism contains more than three terms, and the fallacy of exclusive premises arises when both premises are negative. Both lead to invalid reasoning.