Definition

The middle term in the premises of a standard form categorical syllogism never refers to all of the members of the category it describes:

• All a's are b's.
• All c's are b's.
• Therefore, all a's are c's (or all c's are a's).

Explanation

A standard categorical syllogism is made of three propositions (two premises and a conclusion) and uses three terms (minor, major and middle). For example:

• Premise₁: Plato (minor term) is a man (middle term).
• Premise₂: Men (middle term) are mortal (major term).
• Conclusion: Therefore, Plato (minor term) is mortal (major term).

Examples

All Russians were revolutionists, and all anarchists were revolutionist, therefore, all anarchists were Russians.
The middle term is 'revolutionist'. While both Russians and anarchists share the common property of being revolutionist, they may be separate groups of revolutionists, and so we cannot conclude that anarchists are otherwise the same as Russians in any way.

All trespassers are shot, and someone was shot, therefore, someone was a trespasser.
The middle term is 'shot'. While 'someone' and 'trespassers' may share the property of being shot, it doesn't follow that the someone in question was a trespasser; he may have been the victim of a mugging.

Counter-examples

None.

Advices

Show how each of the two categories identified in the conclusion could be separate groups even though they share a common property.