FLORENSKY’S PHILOSOPHICAL IDEAS AND THE THEORY OF SETS OF CANTOR

The article considers the role of the idea of actual infinity in the works of Florensky. The introduction briefly traces the history of ideas about the actual infinity in European culture to the works of George Cantor. The reaction of European scientists and religious figures to the emergence of the “naïve” theory of Cantor sets is characterized. A detailed analysis of the connection between Florensky and George Cantor’s ideas is given. Many quotations from the 1904 work on the symbols of Infinity are given, which illustrate the influence of Cantor’s works on Florensky. The presentation of Florensky’s religious and philosophical ideas of Cantor about the actual infinity is given. Emphasized understanding Florensky transfinite numbers Cantor as symbols.

Kantian Perspectives on Private Law

This chapter articulates the Kantian approach to private law. It begins by explaining the aims and ambitions of Kantian legal philosophy more generally and, in particular, introducing the Kantian idea that a particular form of thought is appropriate to a particular domain of inquiry or conduct. The chapter situates the Kantian view within a broad natural law tradition. For the part of that tradition that Immanuel Kant develops, the moral structure of natural law is animated by a conception of personal interaction that is so familiar as to be almost invisible. Despite its centrality to both morality and law, in the absence of legal institutions, this natural law is inadequate to its own principles. It requires legal institutions to render it fully determinate in its application consistent with everyone’s independence. It also requires public institutions of adjudication. The chapter further looks at Kant’s “division” of private rights, distinguishing first between the innate right that everyone has simply in virtue of being human and acquired rights that require an affirmative act to establish them. It then goes through the Kantian division of the titles of private right, situating them in relation to the distinction between persons and things. Finally, the chapter articulates the Kantian account of what might be called the naïve theory of remedies—that is, that the remedy is an imperfect continuation of the right that was violated.

The Dawn of Language

Language is a quintessential human capacity. In this chapter, we ask whether the human capacity for language relies on innate knowledge. As a case study, we examine the rules of phonology. This, seems like a curious choice. Most people believe they know how phonology works, and in their naïve theory, phonology requires no knowledge at all. Phonological patterns, people believe, are simply governed by the constraints of their ears, lips, and tongues. But a careful analysis of the anatomy of a syllable suggests this theory might be misinformed. These conclusions receive further support from an unexpected source—the phonology of sign languages. All these results suggest that our capacity for language could well be due to innate knowledge of abstract rules.

The dual systems in temporal cognition: A spatial analogy

The model presented by the authors can explain an inherent contradiction in people's naïve theory of time. In this commentary I suggest a way in which another paradox of our phenomenal temporality may be addressed along these lines. In the final section, I also discuss some concerns that may arise about the clear-cut distinction between humans and non-human animals.

On believing that time does not flow, but thinking that it seems to

Hoerl & McCormack (H&M) posit two systems – the temporal updating system and the temporal reasoning system – and suggest that they explain an inherent contradiction in people's naïve theory of time. We suggest there is no contradiction. Something does, however, require explanation: the tension between certain sophisticated beliefs about time, and certain phenomenological states or beliefs about those phenomenological states. The temporal updating mechanism posited by H&M may contribute to this tension.