According to Kant’s Critique of the Power of Judgement, in the end all estimation of magnitude is sensible, or ‘aesthetic’, and the absolutely great in aesthetic estimation is called ‘the mathematical sublime’. This article identifies the relevant sensible element with an inner sensation of a temporal tension: in aesthetic comprehension, the imagination encounters an inevitable tension between the successive reproduction of a magnitude’s individual parts and the simultaneous unification of these parts. The sensation of this tension varies in degree and facilitates aesthetic estimation in general. But in the special case where it comes to involve a sense of exceeding our imagination’s limit, we judge a magnitude to be mathematically sublime. Pace Kant, I argue that this limit is private and contingent rather than transcendental, such that the judgement of the mathematical sublime is neither universal a priori nor necessary.

Descartes believed the extended world did not terminate in a boundary: but why? After elucidating Descartes’s position in §1, suggesting his conception of the indefinite extension of the universe should be understood as actual but syncategorematic, we turn in §2 to his argument: any postulation of an outermost surface for the world will be self-defeating, because merely contemplating such a boundary will lead us to recognise the existence of further extension beyond it. In §3, we identify the fundamental assumption underlying this argument by comparing Descartes’s and Malebranche’s respective conceptions of the ontological status of modes of extension.

For a $ \mathbb{Z} $-cover $\widetilde {M} \rightarrow M$ of a translation surface, which is a lattice surface, and which admits infinite strips, we prove that almost every direction for the straightline flow is ergodic.

In “The Beauty of the Infinite,” David Hart offers a persuasive case for why the beauty of God's infinity is at the heart of the Christian evangel of peace, a peace funded by our analogical participation in God's Trinitarian life. At the heart of his argument is an appropriation of Gregory of Nyssa's concept of infinity, which presupposes a “non‐dialectical creation of out of nothing.” He then links this understanding of infinity with what he calls the “Christian evangel of peace”, which he contrasts with what he calls a “genealogy of violence” (identified with Hegel, Nietzsche, and Heidegger). His main contribution lies in his use of this understanding of God's infinity to rethink important issues in Trinitarian and Christological doctrine. Nonetheless, the question can be raised about whether his argument does justice to classically Christian understandings of the following: the presupposition, rooted in creation, of a shared human rationality, the importance of law, the centrality of the prophetic critique of idolatry and individual and corporate sin, and the place for lament in biblical depictions of Christ's death and the Christian life.

A group G is locally graded if every finitely generated nontrivial subgroup of G has a nontrivial finite image. Let N (2, k)* denote the class of groups in which every infinite subset contains a pair of elements that generate a nilpotent subgroup of class at most k. We show that if G is a finitely generated locally graded N (2, k)*-group, then there is a positive integer c depending only on k such that G/Zc (G) is finite.