Formal fallacies are therefore invalid arguments arguments where the concluding statement does not necessarily follow from the statements preceding it. The concluding statement may actually be objectively true, but it's truth does not depend on or follow from the other statements. A change in the actual terms used in an argument may affect the actual truth value of the argument, but a change in terms will not affect the validity or invalidity of the argument. But if only some men were green, then Socrates would not necessarily be green. Because the terms themselves do not affect validity, we can substitute symbols for the terms.
All men are mortal.
Therefore Socrates is mortal. Therefore c is b. No matter what terms you may put in the place of a, b, and c, if all a are members of the class called b, and c is a member of the class called a, the c must necessarily be a member of the class called b. Because there are only a small number of possible relationships between the terms, these relationships can also be represented by symbols. When this is done, the whole form of an argument can be written in symbols.