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.
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.