Recent mathematical results, obtained by the author, in collaboration with Alexander Stokolos, Olof Svensson, and Tomasz Weiss, in the study of harmonic functions, have prompted the following reflections, intertwined with views on some turning points in the history of mathematics and accompanied by an interpretive key that could perhaps shed some light on other aspects of (the development of) mathematics.

Kant's conception of autonomy presents the following problem. If, following Kant's explicit lead, we consider autonomy as the universal principle of morality and ground of the actions of rational beings (e.g. G 4:452), then self-legislation is best understood as a prescription by reason to itself. Applied to individual cases of willing, the term 'autonomy' describes the bringing of a set of practical attitudes under rational legislation. Agents may count as autonomous then, insofar as and only to the extent that they (...) are able to implement reason's prescription. This is the bare Kantian picture. The problem, as Schiller originally put it, is that this is also a picture of self-alienation, since parts of one's identity, feelings, emotions, and attachments, are kept at arm's length and treated with suspicion (e.g. AW XXb: 280). Schiller's point is that there must be something that makes autonomy different from mere rationomy. For Schiller this matters because he thinks that a rationalist prescriptive ethic is deeply unattractive and because, anticipating contemporary theories of personal autonomy, he wants to defend an integrative conception of autonomous agency. No such further commitments are needed, however, to see that the bare picture needs adding to it, to show how the principle of reason's self-legislation not only has a grip on individual agents, but also can express their autonomy. (shrink)

En este artículo se analizan los conceptos hegelianos de infinito malo e infinito verdadero al hilo de una revisión de la noción de infinitud en la tradición filosófica alemana con la que discute. Puntualmente, abordaremos las formulaciones sobre la relación finitud-infinitud en la obra de Kant, Fichte y Schlegel antes de exponer la interpretación que hace Hegel de la manera en la que la filosofía trascendental y el romanticismo alemán se aproximaron a este asunto. Finalmente, presentamos la verdadera forma en (...) la que, según Hegel, hay que entender lo infinito. (shrink)