Constructivist pedagogies cannot achieve their critical thinking ambitions. Constructivism, and constructivist epistemological presuppositions, actively thwarts the critical thinking process. Using Wittgenstein's private language argument, this paper argues that corrective mechanisms—the ability to correct a student's propositions and cognitions against the background of a shared, knowable world—are indispensible to critical thinking. This paper provides concrete examples of actual constructivist practice and shows how a particular constructivist classroom exercise can be modified to incorporate critical thinking elements as detailed by the American Philosophical Association. Finally, the paper states the significance of these arguments, particularly as they extend from the educational arena into the public and governmental domains.