Doubt and doubtful may be followed by a subordinate clause beginning with that, whether, or if: I doubt that (or whether or if ) the story is true. It is doubtful that (or whether or if ) the story is true. There is some doubt that (or whether or if ) the story is true. In negative or interrogative sentences, that almost always introduces the subordinate clause: I do not doubt that the story is true. Is it doubtful that the story is true? Is there any doubt that the story is true?
The expressions doubt but and doubt but that occur in all varieties of standard speech and writing: I don't doubt but she is sincere. There is no doubt but that the charges will affect his career. Doubt but what occurs mainly in informal speech and writing: There is no doubt but what the rainy weather will hurt the crops.

Did you mean induct?