Illicit major is a logical fallacy committed in a categorical syllogism that is invalid

Validity

In logic, argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form is valid if and only if every argument of that logical form is valid....

 because its major term

Major term

The major term is the predicate term of the conclusion of a categorical syllogism. It appears in the major premise along with the middle term and not the minor term. It is an end term .Example:...

 is undistributed in the major premise but distributed in the conclusion.

This fallacy has the following argument form:

1. All A are B
2. No C are A
3. Therefore, no C are B

Example:

1. All cats are mammals
2. No dogs are cats
3. Therefore, no dogs are mammals

In this argument, the major term is "mammals". This is distributed in the conclusion (the last statement) because we are making a claim about a property of all mammals: that they are not cats. However, it is not distributed in the major premise (the first statement) where we are only talking about a property of some mammals: Only some mammals are dogs.

The error is in assuming that the converse of the first statement (that all mammals are dogs) is also true.

However, an argument in the following form differs from the above, and is valid:

1. All A are B
2. No B are C
3. Therefore, no C are A

External links

• Illicit Major The Fallacy Files