Extinctions are important indicators of biodiversity status. When they are detected, they may trigger the redirection of conservation resources to save other species. Yet declaring extinctions is inherently uncertain. Relevant evidence for consideration includes information on threats, the time series of species records and the effort employed to search for remaining individuals. Quantitative tools have been developed to infer extinctions from data on the timing of records. In contrast, inference of extinction from threats relies on expert judgement and is susceptible to subjective influences. To use qualitative information on threats, we suggest experts should construct an argument map to identify reasons, evidence and sources in support of a claim that a species has gone extinct, as well as objections, evidence and sources as to why the claim may not be true. The reasons must explicitly address: i) whether identified threats are sufficiently severe and prolonged to cause local extinction; and ii) whether such threats are sufficiently extensive to eliminate all occurrences. Transparent mapping of reasons and objections enables experts to estimate subjective probabilities that each alternative claim is true, allowing an overall probability of extinction to be calculated. We provide examples illustrating how typical evidence may be evaluated. To deal with uncertainties, we suggest bounded estimates of subjective probabilities are obtained from multiple experts in a structured elicitation. The method requires no detailed mathematical analysis, but relies on structured reasoning. The subjective estimates of probabilities must be based on the severity and pervasiveness of threats alone, to allow comparison with estimates derived independently from other sources of information such as time series of records.