I use the work of Joseph Owens to clarify Klein’s account of the symbolic understanding of numbers and resulting mathematics of algebra. I show that the distinction between first and second intentions, widely used in the scholastic tradition and adapted by Klein, functions differently in the case of Descartes because his understanding of the relation of mind to world differs fundamentally from the “form-receptive realism” characteristic of the tradition. Through first intentions we cognize actual beings in the world, while through second intentions we reflect on our own thinking and produce concepts of concepts, such as genus and species. Second intentions, then, necessarily involve the mind’s ability to reflect on its own activities in knowing the world. I argue that Descartes’s account of this reflexivity differs from that of the scholastic tradition because Descartes separates mind and world in such a way that we know ideas rather than beings in the world, with the result that there are no first intentions for Descartes. Rather, the Cartesian mind “applies itself” to the corporeal imagination and abstracts intelligible contents, such as “mere multitudinousness,” which is indeterminate manyness, and then the intellect activates the imagination to symbolize this concept with a particular representation, for example, the letter x, in which the mind apprehends and symbolizes its own conceiving. This, according to Klein, is the concept-formation at work in the modern algebraic equation, which is the language of physics.