The problem here is that the last term is the in fact the middle term (that connects the first two statements) is assumed to refer to the same thing -- typically all of the members in its category, yet this is seldom true. Thus, in the first example above, neither all Californians nor all women cover all of the beautiful people in the world (some British men are beautiful).

In effect, the 'reasonable' assumption is that the first two statements are of the form A=B and C=B, from which the mathematically sound conclusion is that C=A. Unfortunately, syllogisms deal with sets, not mathematical variables, so your wrong, I'm not a fool.


You live on Sunny Street. You have a gun. Nobody else on Sunny Street has a gun. There was a murder on Sunny Street last night. You were involved.

You live on Sunny Street. You have a gun. The person was knifed. You were not involved.