According to one of the most influential hypotheses in cognitive sciences, human thinking consists of symbolic reasoning in a Language of Thought (LoT). One of the main challenges in this approach is to identify what primitives are in the LoT. Literature has generally assumed this identification is possible, but the question has not been studied directly. We for the first time ask a more fundamental question: Can the primitives of the human LoT be even in principle recovered from behavioural data? We show for the important fragment of Boolean thinking that this depends in part on their complexity: simple LoTs are easier to recover than complex ones.