Norms are ideals that serve as guiding beacon in many human activities. They are considered to transcend accepted social and cultural practices, and reflect some universal, moral principles. In this chapter, we will show that norms are cognitive constructs by considering several examples in the domains of language, art and aesthetics, law, science and mathematics. We will argue that, yes, norms are ideals that we posit, so in this respect they go beyond current social and cultural values. However, norms are posited using cognitive mechanisms and are based on our existing knowledge and wisdom. In this sense, norms are what we, as an individual or as a society, strive for, but they show the horizon effect in that they recede and transform as we progress towards them, and sometimes this transformation can be radical.