Procedures for generating arbitrary matching‐to‐sample performances may generate only conditional discriminations. Rational grounds for this distinction are proposed, based on the properties that any equivalence relation must possess. Empirical tests are described for determining whether subjects trained on conditional discriminations are also engaged in true matching to sample. A series of studies then leads to the conclusion that proof of true matching to sample by monkeys, pigeons, or baboons is yet to be provided. Whether the absence of such proof reflects experiential factors or species‐defined limitations is not presently clear. 1982 Society for the Experimental Analysis of Behavior