 The interpretive debate over how to understand Kant’s view of the role of intuition in mathematical reasoning has had the strongest influence on the shape of scholarship in Kant’s philosophy of mathematics; this debate is directly related to the question (described above) of the syntheticity of mathematical axioms, theorems and inferences. In his general discussion of mental representation, Kant implies that immediacy and singularity are both criteria of non-conceptual, intuitive representation, the species of representation that grounds synthetic judgment. In a series of papers, Charles Parsons (Parsons 1964, 1969, 1984) has argued that the syntheticity of mathematical judgments depends on mathematical intuitions being fundamentally immediate, and he explains the immediacy of such representations in a perceptual way, as a direct, phenomenological presence to the mind. Jaakko Hintikka (Hintikka 1965, 1967, 1969), developing an idea from E.W. Beth’s earlier work, counters that the syntheticity of mathematical judgments instead depends only on the singularity of their intuitive constituents. Hintikka assimilates mathematical intuitions to singular terms or particulars, and explains the use of intuition in a mathematical context by analogy to an application of the logical rule of existential instantiation. These two positions have come to be known as the “phenomenological” and “logical” interpretations, respectively.