 We shall directly examine the intentional-object theorists approach in section 7. Before doing so, in section 3, we shall examine the way singular thoughts about concrete particulars in space and time can be and have been construed as paradigms of genuine intentional relations. On this relational construal, an individual’s ordinary singular thought about a concrete physical particular involves a genuine relation between the individual’s mind and the concrete physical particular. In sections 4–5, we shall examine two puzzles that further arise on the orthodox paradigm. First, we shall deal with the puzzle of how a rational person can believe of an object referred to by one singular term that it instantiates a property and simultaneously disbelieve of the same object referred to by a distinct singular term that it instantiates the same property. Section 4 is devoted to Frege’s solution to this puzzle. In section 5, we shall scrutinize Russell’s solution to the puzzle of true negative existential statements. In section 6, we shall see how the theory of direct reference emerged within the orthodox paradigm out of a critique of both Frege’s notion of sense and Russell’s assumption that most proper names in natural languages are disguised definite descriptions.