Solutions of disk-shaped molecules that self-assemble into linear aggregates pose an interesting question as to whether or not it might sometimes be appropriate to regard the solute as an amphiphile and, if so, how could the strength of this amphiphilic behavior be quantified or measured. This paper proposes an answer by mapping linear self-assembly onto the isodesmic chemical equilibria of an exactly solvable one-dimensional model. In particular, the concentration dependence of the aggregation number is seen to be dominated by one of two different regimes, depending on the presence and strength of a solvophobic solute core. The amphiphilic regime is associated with a large value of the Henry Law constant for solvating the two ends of a linear aggregate. Here, the aggregation is driven by solvent "pressure" and the aggregation number rises rapidly with increasing concentration to quickly saturate at its high concentration value. In the opposite regime, the linear self-assembly is driven by solute-solute attraction and the aggregation number displays the well-known square-root-concentration form. This analysis defines protocols for identifying and classifying discotic amphiphiles, from experimental data on any aspect of a linear aggregation distribution.