The Noble Lie proposed by Plato for the Just City in Republic III has been much misunderstood. Its agenda is twofold: to get the citizens of the City to see their society as a natural entity, with themselves as all ‘family' and akin; and to get the Guardians in particular to make class mobility, on which the justice of the City depends, a top priority. Since the second is taken to depend on the first, the Lie passage amounts to an argument (1) that the survival of a just community depends on the existence of social solidarity between elite and mass, which allows for full class mobility and genuine meritocracy; (2) that this solidarity in turn depends on an ideology of natural unity; and (3) that such ideologies are always false. So the Lie really is a lie, but a necessary one; as such it poses an awkward ethical problem for Plato and, if he is right, for our own societies as well.

So-called ‘Leibniz shifts’ (in which the position of the universe, or its velocity, is 'shifted' by some constant amount) have been at the center of the debate between proponents of the relationist and absolutist conceptions of space since Samuel Clarke introduced them in his correspondence with Leibniz in 1715–1716. Fast forward three hundred years, and Leibniz shifts are still prominent in debates about the ontology of spacetime, despite the vast difference in background physical theory between the 1700s and today. In this paper we use Leibniz shifts (and a close cousin introduced by Kant himself, orientation shifts) to explore the structure of Kantian space. The paper has three main tasks, along with a subsidiary one. First, we will show that Kant’s commitments entail that Leibniz shifts do not represent genuinely distinct possibilities. Second, we will elucidate what it is about the structure of Kantian space that explains this. Third, we will explain why shifts in orientation represent genuinely distinct possibilities, although Leibnizian static and dynamic shifts (of position and velocity, respectively) do not. Finally, we will explore the consequences of our argument for the mereological and modal structure of Kantian space.