Argument is a foundational concept in argumentation theory. While many scholars have proposed perspectives on this topic, it remains controversial. Recently, Siegel published two papers addressing the concept of argument, distinguishing four senses of argument and asserting that the abstract propositional sense holds priority. Consequently, he argues that epistemic function of argument are also primary. Siegel’s understanding of the four senses of argument is insightful, and his argument in support of the priority claim is compelling. However, to justify a priority claim, we need to consider potential alternatives and make comparisons. If there are multiple plausible answers to the question of priority, then we should suspend judgment. In this paper, I present new counterarguments to Siegel’s priority claim. I clarify the meaning of conceptual priority, arguing that it has a close relationship with grounding in metaphysics. My counterarguments have two parts. First, I posit that argumentative precedents—instances of the fourth sense of argument in Siegel’s theory—are conceptually prior, meaning that the abstract propositional sense of argument is grounded in precedents. Siegel’s priority claim represents a specific form of conceptual grounding that concerns thin and thick modes, whereas my claim about priority involves the truth-maker mode and the objective basis mode. Second, I distinguish between the basic function, which is epistemic, and the oriented function, which reflects arguers’ goals. These two functions exist at the same conceptual level with abstract propositional sense of argument. Both Siegel’s argument and mine are plausible. Therefore, I contend that the problem of priority is inherently complex and underdetermined.