The current dominant approach on the assessment of critical thinking takes as a starting point a conception of criticality that does not commit to any substantive view or context of meaning concerning what issues are relevant to be critical about in society or in life. Nevertheless, as a detailed examination of the identification of assumptions shows, when going from the theory of critical thinking to the praxis of producing and evaluating arguments, the critical person will inevitably make such commitments from particular perspectives, using particular contexts of meaning. But then she may fail to take notice of relevant ones and may end up using her critical powers in a mercenary way. It is then proposed, in the context of assessment of critical thinking, to choose and use some privileged contexts of meaning, while making them available for critical scrutiny and allowing for the possibility that new ones be brought up by those being assessed.