In the pursuit to clarify the concept of "BCI illiteracy", we investigated the possibilities of attaining basic binary (yes/no) communication via brain‑computer interface (BCI). We tested four BCI paradigms: steady‑state visual evoked potentials (SSVEP), tactile, visual, and auditory evoked potentials (P300). The proposed criterion for assessing for the possibility of communication are based on the number of correct choices obtained in a given BCI paradigm after a short calibration session, without prior training. In this study users answered 20 simple "yes/no" questions. Fourteen or more correct answers rejected the null hypothesis of random choices at P=0.05. All of the 30 healthy volunteers were able to attain above‑chance choices in at least one of the four paradigms. Additionally, we tested the system in clinical settings on a patient recovering from disorders of consciousness, achieving successful communication in 2 out of 3 paradigms. In light of these facts, after a review of the sparse literature, and in the interest of motivating further research, we propose a paraphrase of de Finetti's provocative statement: "BCI illiteracy does not exist".