In this paper I develop a cross‐cultural critique of contemporary critical thinking education in the United States, the United Kingdom, and those educational systems that adopt critical thinking education from the standard model used in the US and UK. The cross‐cultural critique rests on the idea that contemporary critical thinking textbooks completely ignore contributions from non‐western sources, such as those found in the African, Arabic, Buddhist, Jain, Mohist and Nyāya philosophical traditions. The exclusion of these traditions leads to the conclusion that critical thinking educators, by using standard textbooks are implicitly sending the message to their students that there are no important contributions to the study of logic and argumentation that derive from non‐western sources. As a case study I offer a sustained analysis of the so‐called Hindu Syllogism that derives from the Nyāya School of classical Indian philosophy. I close with a discussion of why contributions from non‐western sources, such as the Hindu Syllogism, belong in a Critical Thinking course as opposed to an area studies course, such as Asian Philosophy.