There are a number of reasons why it may not be legitimate to generalize from what has been shown for a given term. The argument may rest on assumptions that special to this term. The predicate we would like to assert generally may contain the term. The term, while not itself appearing in an assumption or the result of the generalization, may share vocabulary with one or the other, and the argument may depend on this connection. These possibilities can all be avoided by requiring that the term we generalize on be an unanalyzed term and not appear outside the scope line whose goal we generalize. These requirements are more stringent than necessary on logical grounds, but they are simple to state and cost us little since they can be met simply by introducing a new unanalyzed term in any general argument.

While the chance of illegitimate generalization could be avoided in many cases also by using a special set of terms in general arguments, this would not handle cases of multiply general conclusions, where we need to have general arguments in the scope of other general arguments. In this case, the requirements insure that independent terms are independent of one another and represent multiple independent dimensions of generality.