A deduced proposition should be stated strictly in terms of concepts and relations in the theory of grammar. A prediction, on the other hand, should be stated in terms of notions/concepts that express linguistic intuitions. And it is important to distinguish them clearly; otherwise, it can become difficult to tell what statement in the theory is meant to capture what linguistic intuitions, making it difficult, and in fact impossible, strictly speaking, to test the predictions of one's hypotheses.

There is a third type of statement, which makes reference to both types of concepts noted above. Without this type of statement, we cannot make predictions on the basis of propositions deduced from the hypotheses. The third type of propositions/statements is what expresses how theoretical concepts and relations are connected to our linguistic intuitions. (19) in the JK handout, for example, is the third type of statement.

(19)BVA(X,Y) can obtain if {X_i, t_i} is a chain formed by A-movement, where X is a QP and Y is a dependent term.
　　　　... X_i [... Y ... t_i ... ] ...

Except for a few places, the distinctions among the three types of statements are made clearly.

A typical way in which the first two types of concepts are mixed in a statement in actual practice in the field is something like the following:

"In such and such sentence, we have a clear intuition that A and B cannot be coindexed, thus confirming our prediction."

Coindexation is a theoretical concept and we do not have judgments about whether two expressions can or cannot be coindexed with each other.