Further advances in research into the etiology of schizophrenia will depend on the identification of an unambiguous indicator of the genotype associated with the development of schizophrenia. Such an indicator would permit accurate assessment of the relatives of probands as 'affected', or not, so that the data generated in twin and family studies could be tested for the best fit to various genetic models that have been proposed. Schizoidia or schizoid personality has been considered by clinicians to be such an indicator, but it has been beset by semantic and logical difficulties. Most troublesome has been the extent to which the concept implies (merely) a phenotypic resemblance to schizophrenia, or a genotypic connection with it, or both. Four different but overlapping meanings for the concept of schizoidia are presented, in an effect to clarify the semantic and logic involved. Following Popper's notions about the testability and refutability of theories, the authors, identified with both monogenic and polygenic theories, apply the definitions to their first-hand observations of the cotwins in the Maudsley-Bethlem Schizophrenic Twin Study. Pushing the concept to its limits, 91% of 22 MZ pairs and 45% of 33 DZ pairs contained 'disordered' cotwins.