We prove that any subset of $\overline {\mathbb {Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountably many transcendental entire functions over $\mathbb {C}^m$ with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer-Verlag, Berlin, 1976)].

Karin de Boer has given the best account so far of the reform of Wolffian metaphysics that Kant promised. But does such a reform cohere with the revolutionary goal that Kant also affirmed? Standpoint is singled out as the central meta-concept of Kant’s revolutionary goal, and it is argued that, in the second and third critiques, Kant himself developed his revolutionary insight into the perspectival character of both concept and judgement in ways that he did not anticipate at the time of the first critique, when his promise to reform metaphysics was made. The question is raised what room Kant’s revolution leaves for doctrinal and not merely disciplinary judgements in both general and special metaphysics, and also whether the opening of new vistas may have drained metaphysical reform of its interest.

In this paper I offer a novel interpretation of Wittgenstein's claim that ‘ethics is transcendental’ (TLP 6.421). Initially, I set out to offer said interpretation by resorting to both Wittgenstein's understanding of ethics and his understanding of the transcendentality of logic—which entails taking Wittgenstein as endorsing a Kantian understanding of the notion ‘transcendental’. This leads to the claim that ethics is transcendental insofar as it is the condition of a certain ethical experience. Nevertheless, this interpretation involves some inadequacies due to certain incompatibilities between the Tractatus Logico-Philosophicus and the aforementioned Kantian understanding of the notion ‘transcendental’. I identify the peculiarities of Wittgenstein's understanding of the notion ‘transcendental’, and on this basis, I set forth a novel interpretation of 6.421. Specifically, I argue that ethics is transcendental insofar as it is internal to or constitutive of a certain mystical view: viewing the world sub specie aeterni as something valuable.

Our main result states that, under an exponential map whose Julia set is the whole complex plane, on each piecewise smooth Jordan curve there is a point whose orbit is dense. This has consequences for the boundaries of nice sets, used in induction methods to study ergodic and geometric properties of the dynamics.

A core thesis of Kitcher's is that thinking about objects requires awareness of necessary connections between one's object-directed representations ‘as such’ and that this is what Kant means by the transcendental unity of apperception. I argue that Kant's main point is the spontaneity or ‘self-made-ness’ of combination rather than the requirement of reflexive awareness of combination, that Kitcher provides no plausible account of how recognition of representations ‘as such’ should be constituted and that in fact Kant himself appears to lack the theoretical resources to clearly distinguish between (first-level) consciousness and self-consciousness or apperception properly so-called.

In the second edition Preface of Religion Within the Bounds of Bare Reason Kant responds to an anonymous review of the first edition. We present the first English translation of this obscure book review. Following our translation, we summarize the reviewer's main points and evaluate the adequacy of Kant's replies to five criticisms, including two replies that Kant provides in footnotes added in the second edition. A key issue is the reviewer's claim that Religion adopts an implied standpoint, described using transcendental terminology. Kant could have avoided much confusion surrounding Religion, had he taken this review more seriously. We therefore respond to three objections that Kant failed to address: how the Wille–Willkür distinction enables the propensity to evil to be viewed as coexisting with freedom of choice; how moral improvement is possible, even though the propensity to evil is necessary and universal; and how a ‘deed’ can be regarded as ‘noumenal’.

It is shown that any subset of can be the exceptional set of some transcendental entire function. Furthermore, we give a much more general version of this theorem and present a unified proof.