This chapter describes the philosophical ambitions of political constructivism along with several criticisms. The philosophical ambitions are characterized in terms of protagorean objectivity, which refers to the claim that political principles are dependent on us by their very nature and yet are fully objective. Critics argue that political constructivism is vulnerable to a Euthyphro-type dilemma whenever it pursues this ambition. The chapter explains the Euthyphro-type dilemma in terms of four related challenges that critics have raised against constructivism.