According to the “truthmaker maximalism”, every true contingent proposition is made true by something in the world, called its truthmaker. Although at first sight the maximalism seems to be a natural position, it has serious difficulties, especially concerning negative truths. In view of this, many truthmaker theorists adopt some non-maximalist position. It is not clear, however, whether these non-maximalists are justified, since existing reasons to justify the non-maximalism are not good enough. In this paper, then, I shall propose a new reason for the non-maximalism, which consists in the observation that the maximalism cannot acknowledge the widely accepted view that certain inferences involving logical constants are valid in the properly logical sense.