Kant says that there is a close affinity between the sublime and moral feelings of respect. This suggests a relatively unexplored way that aesthetic experience could be morally improving. We could come to respect persons by experiencing them as sublime. Unfortunately, this is not at all our ordinary experience of people, and it’s not clear how one would come to it. In this paper I argue that this possibility is realized in the portraits of Thomas Eakins. Through a handful of (...) specific techniques, Eakins suggests an incomparable psychological depth to the subjects of his portraits, a suggestion that causes the viewer to experience that subject as sublime in a way not unlike their experience of a vast ocean or endless abyss. -/- . (shrink)

It is an essential part of Kant's conception of regulative principles and ideas that those principles and ideas are in a certain sense indeterminate. The relevant sense of indeterminacy is cashed out in a section in the Antinomies where Kant says that the regress of conditions of experience forms not a “regressus in infinitum” but a “regressus in indefinitum.” The mathematics that Kant appears to rely on in making this distinction turns out to be problematic, as Jonathan Bennett showed long (...) ago. But I suggest that despite this, there is another mathematically legitimate way to make Kant's point, one enunciated by, among others, Michael Dummett. This reading is corroborated, I suggest, by Kant's conception of reason as a radically open-ended endeavor. -/- . (shrink)

Many people find comparisons of the value of persons distasteful, even immoral. But what can be said in support of the claim that persons have incomparable worth? This chapter considers an argument purporting to show that the value of persons is incomparable because it is so great—because it is infinite. The argument rests on two claims: that the value of our capacity for valuing must equal or exceed the value of things valued and that our capacity for valuing is unbounded (...) in a very strong sense. After laying out this argument, I consider its implications for how we should regard each other. In particular, I suggest that it complicates efforts to understand morality as a system of principles. Instead, I propose that an aesthetic attitude, not unlike our experience of the sublime, is an apt response to humanity’s infinite value. -/- . (shrink)

ABSTRACT I suggest how a broadly Kantian critique of classical logic might spring from reflections on constructibility conditions. According to Kant, mathematics is concerned with objects that are given through ‘arbitrary synthesis,’ in the form of ‘constructions of concepts’ in the medium of ‘pure intuition.’ Logic, by contrast, is narrowly constrained – it has no objects of its own and is fixed by the very forms of thought. That is why there is not much room for developments within logic, as (...) compared to the progress in mathematics. Kant’s view of logic remains critical, though – through considerations that are effectively on the scope and limits of classical logic and which play a part in his transcendental idealism. The most important ones are to be found in his critique of the use of reductio ad absurdum proofs in metaphysics and his solutions to the ‘antinomies of pure reason.’ Arguably, these considerations carry over to mathematics as well – by way of ‘analogues’ to the antinomies – in particular in resolving infinity paradoxes. (shrink)

Kant's first antinomy uses a notion of infinity that is tied to the concept of (finitary) successive synthesis. It is commonly objected that (i) this notion is inadequate by modern mathematical standards, and that (ii) it is unable to establish the stark ontological assumption required for the thesis that an infinite series cannot exist. In this paper, I argue that Kant's notion of infinity is adequate for the set-up and the purpose of the antinomy. Regarding (i), I show that contrary (...) to appearance, the Critique can even accommodate a modern notion of infinity without consequences for the antinomy; and regarding (ii), that the ‘ontological’ consequence indeed follows once its covertly epistemic character is adequately understood. (shrink)

This work analyzes two perspectives, Atomism and Infinite Divisibility, in the light of modern mathematical knowledge and recent developments in computer graphics. A developmental perspective is taken which relates ideas leading to atomism and infinite divisibility. A detailed analysis of and a new resolution for Zeno's paradoxes are presented. Aristotle's arguments are analyzed. The arguments of some other philosophers are also presented and discussed. All arguments purporting to prove one position over the other are shown to be faulty, mostly by (...) question begging. Included is a sketch of the consistency of infinite divisibility and a development of the atomic perspective modeled on computer graphics screen displays. The Pythagorean theorem is shown to depend upon the assumption of infinite divisibility. The work concludes that Atomism and infinite divisibility are independantly consistent, though mutually incompatible, not unlike the wave/particle distinction in physics. (shrink)

In this article, I claim that the Antinomy of pure reason emerges as the result of synthetic activities that require succession. In this regard, I show that cosmological conflicts involve different kinds of representations: cosmological ideas, purely conceptual representations of the unconditioned and the product of non-temporal synthetic activities; and putative complete series of spatiotemporal conditions, which require temporal synthetic activities. As I show, purely conceptual representations cannot produce cosmological conflicts: The Antinomy requires the interaction of reason, understanding, and sensibility. (...) I also discuss the maxim and principle of pure reason, how they lead to the unconditioned, and how the cosmological syllogism produces the Antinomy. (shrink)

En este artículo examino el concepto de infinito en Pascal y Kant en el contexto del análisis contemporáneo de la secularización moderna, realizado por H. Blumenberg y H. Arendt. Los aspectos principales de mi análisis son: primero, el paso del sentido del término ‘infinito’ del ámbito trascendente al inmanente. Segundo, la comprensión de la modernidad secular como una mundanización desmundanizada. Tercero, la aplicación secular del concepto de infinito a la historia, en el ideal moderno del progreso. En mi opinión, estos (...) rasgos de la secularización moderna pueden observarse de manera especial en el concepto de infinito que aparece en Pascal y Kant. (shrink)