Psychosis is a complex psychiatric disorder characterised by disturbances in cognition and language. Natural language processing (NLP) promises to resolve the long-standing debate between Bleuler and Kraepelin as to whether semantic changes are at the core of psychosis or whether they are merely downstream consequences of an essentially cognitive disorder. This cross-sectional study examines semantic fluency in people with psychosis compared with healthy controls, with the aim of elucidating the role of cognitive impairment and formal thought disorder (FTD). Participants (32 patients with non-organic psychosis and 32 healthy controls) completed three semantic fluency tasks (animals, clothes, food) and were assessed for cognitive variables and negative symptoms. FTD was assessed using the Scale for the Assessment of Thought, Language and Communication (TLC) and semantic coherence was measured using the Covington Vector Semantics Tool (CoVec). Results showed that patients produced fewer words in the fluency tasks, with correlations suggesting associations with psychomotor speed, working memory and negative symptoms. Measures of semantic coherence differed between the two groups, with patients showing higher semantic coherence, particularly in the fluency task based on clothes. However, the relationship between FTD and semantic coherence was inconclusive due to the limited variance in FTD scores. Our study highlights the complexity of semantic processing deficits in psychosis and calls for further research in computational linguistics for the early detection of psychosis.