Detectable polymorphism of host resistance and parasite host range is a poor guide to the specificity of a host--parasite interaction. I analyse a simple haploid model to support this claim. The model assumes that the true specificity is `matching-allele', in which each of n host alleles causes resistance to only one of n different parasite alleles. The detectable polymorphism in samples from a matching-allele system would lead one to infer the gene-for-gene specificity commonly observed in plant-pathogen interactions. Gene-for-gene and matching-allele specificity require very different fitness assumptions to explain observed patterns of polymorphism. Yet models for each type of specificity can easily be constructed that fit the available data. In addition, the currently favoured `elicitor-receptor' model for the biochemistry of plant-pathogen recognition agrees equally well with gene-for-gene or matching-allele specificity. I do not claim that the simple matching-allele specificity is the correct model for plant--pathogen genetics. My point is that one cannot reconstruct both specificity and population history from patterns of resistance among host--parasite pairs in a sample. I draw two conclusions: first, inferred specificity and polymorphism are only useful when compared with a family of theoretical models; and secondly, biochemical models of specificity must be tested by their population genetic consequences.