Illicit major

Short description: Formal fallacy

Illicit major is a formal fallacy committed in a categorical syllogism that is invalid because its major term 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 dogs are mammals
2. No cats are dogs
3. Therefore, no cats 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 (Camestres):

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

## See also

* Illicit minor
* Syllogistic fallacy

## External links

* Illicit Major The Fallacy Files

* v
* t
* e

Formal fallacies

* Masked man
* Mathematical fallacy

In propositional logic|

* Affirming a disjunct
* Affirming the consequent
* Denying the antecedent
* Argument from fallacy

In quantificational logic|

* Existential
* Illicit conversion
* Proof by example
* Quantifier shift

Syllogistic fallacy|

* Affirmative conclusion from a negative premise
* Exclusive premises
* Existential
* Necessity
* Four terms
* Illicit major
* Illicit minor
* Negative conclusion from affirmative premises
* Undistributed middle

* Other types of formal fallacy
* List of fallacies

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