In education, the concept of 'thinking skills' has long been contentious. This article revisits the 2010 debate between Stephen Johnson and Harvey Siegel on whether thinking can be taught as a general skill. To weigh in on this ongoing dispute, it contributes a novel perspective by augmenting key insights from 4E cognition to avoid treating cognition as a purely brain-based computational perspective which treats the brain as separate from the rest of the body and its environment. I argue that given the elusiveness of the concept of 'thinking skills', scholars must first reach a sufficiently precise and pluralistic understanding of so-called 'thinking skills' to avoid talking past another. Such precision, I contend, is a necessary condition, an antecedent epistemic obligation, so to speak, prior to the design of curricula which prioritize the acquisition of the much-heralded, yet heavily disputed, '21st-century thinking skills' ((Varas et. al., 2023) assortment of the following: Critical thinking, Creativity, Collaboration, Communication, information, and media literacy, Computing and ICT literacy, Cross-cultural understanding and Career, and learning self-reliance (Trilling and Fadel, 2009). See (Dishon and Gilead, "British J Educ Stud" 69:393-413, 2021)) for a critical analysis of the unquestioned exaltation of said twenty-first century skills). To ground the discussion in policy, I revisit the influential UK "McGuinness Report," examining how it influenced higher education institutions' approaches to thinking skills and how it shaped their understanding of those skills, including critical thinking. One key finding of my analysis is that both domain-specific knowledge and contextually sensitive, generalizable thinking skills are vital for fostering a robust understanding of how to nurture and enhance thinking skills in educational settings. More importantly, such thinking skills are best viewed through the lens of 4E cognition rather than as decontextualized, disembodied cognitive outcomes. In short, this paper demonstrates that in an era focused on developing 21st-century skills, clarifying exactly what we mean by 'thinking skills'--particularly through the lens of novel 4E cognition frameworks--must inform the future design of effective thinking-skills curricula.