In this paper I discuss four ways in which Schulting’s phenomenalist interpretation of Kant faces the challenge of accounting for the possibility of objective cognition. First, I ask whether objective cognition requires the understanding to be a faculty of absolute, not merely relative spontaneity. Second, is objectivity compatible with thinking of the transcendental ‘I’ as an indexical? Third, does objectivity require that the objects have being independently of the understanding? Finally, is it a threat to objectivity if objects can be given to me in sensibility without standing under the categories?