Schizophrenia is well-known among mental illnesses for the severity of the thought disorders disorders it involves, and for their widespread and spectacular manifestations ranging from deviant social behavior to delusion, not to mention affective and sensory distortions. The goal of this paper is twofold: (i) to discuss how the concepts of rationality and logicality may apply to conversational contexts in which one of the speakers is schizophrenic, and (ii) to present the initial steps of a scientific research project on one specific manifestation, namely disorders in conversational speech. The theoretical background of the paper relies both on psycholinguistics and on formal semantics !formal . The chapter provides two examples of analyses. I also offers a discussion of the philosophical and epistemological implications of the work.