Various dimensions of the cultivation of mindfulness in its early Buddhist historical setting can be better appreciated in the light of their doctrinal background. One aspect of this doctrinal background is the ancient Indian tetralemma, which differs from the Aristotelian logic that has informed much of Western thought. The tetralemma proposes that, in addition to affirmation and denial, at times a particular situation may be more appropriately captured by a combination of both (partly yes and partly no). Or else, another situation may call for neither affirmation nor negation. Although at first sight the resultant fourfold perspective can appear puzzling, closer inspection shows this model of thought to have a considerable potential for countering mental rigidity and enabling the transcendence of binary thought patterns, thereby being perhaps relevant to research on the relationship between mindfulness and cognitive flexibility.