The paper discusses major issues concerning the A104-10 transcendental-object theory. For that theory, our de re knowledge becomes related to its object just because our understanding (using the concept of a transcendental object) thinks a certain object to stand related to the intuition via which we know. Employing an apparatus of intensional logic, I argue that this thought of an object is to be understood as a certain sort of intuition-related, de dicto thought. Then I explore how, via such a de dicto thought, we can nevertheless achieve de re knowledge. This question involves an important Kantian reduction of de re to de dicto outer-object thinking, which I consider. Finally, I investigate some further topics about the transcendental object. I endeavor to show, throughout, that Kant’s theory of that object is crucially related to matters of intensionality.