Syllogistic Errors
The fallacies in this section are all cases of invalid categorical syllogisms. A categorical syllogism is an argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice. For example, the classic: (1) All men are mortal. (2) Socrates is a man. Therefore, (3) Socrates is mortal.
The fallacy is committed when a standard form categorical syllogism contains four terms.
The middle term in the premises of a standard form categorical syllogism never refers to all of the members of the category it describes.
The predicate term of the conclusion refers to all members of that category, but the same term in the premises refers only to some members of that category.
A standard form categorical syllogism has two negative premises (a negative premise is any premise of the form 'No S are P' or 'Some S is not P').
The conclusion of a standard form categorical syllogism is affirmative, but at least one of the premises is negative.
A standard form categorical syllogism with two universal premises has a particular conclusion. The idea is that some universal properties need not be instantiated. It may be true that 'all trespassers will be shot' even if there are no trespassers. It may be true that 'all brakeless trains are dangerous' even though there are no brakeless trains. That is the point of this fallacy.