companionship problem

The "companionship problem" in philosophy, specifically within resemblance nominalism, arises when two distinct properties consistently occur together, a phenomenon known as "companion properties." This presents a challenge because if all red things are also round, resemblance nominalism might incorrectly identify only one natural class instead of two distinct properties (redness and roundness). This raises questions about whether the mere possibility of such coinciding properties is enough to undermine the theory, which posits that universals correspond to fundamental ways things resemble each other.1

The core issue is that if properties always appear as a pair, it becomes difficult to distinguish them as separate respects in which objects can be similar. This complicates the idea of identifying distinct "natural classes" based on resemblance, as the coincidence of properties could obscure the individuality of each property.1