This is a discussion of sequences and first-order recurrence (or difference) equations and the behaviour of the solutions to such equations. It contains some economic applications.

I look at Wittgenstein’s statement, in his letter to Russell, of the “main contention” of his book. I consider also the relation between his main contention and what he describes in the book as his fundamental idea. I discuss also what he means when he says that what he calls his main contention, and his main point is the cardinal problem of philosophy.

There are still may supporters of laissez faire and of a market that is supposed to operate efficiently and smoothly if left alone. That free market is supposed to “lift all boats” and leave everyone better off and free. However, reality indicates otherwise. Abuses of the market are common, corruption exists, rent seeking is easily observed, and differences between rich and poor grow, leading to resentment and to populist policies. It would help if the market fundamentalists were more explicit about the role that they would expect the government to play. Socialists and leftists do not seem to have any doubts. Some role is obviously needed for the government, and that role cannot remain constant over time. It is not sufficient to keep repeating that the government should stay out of the market.

This chapter concluds the book and sketches some of the limits of what may be expected from international law

Part III is dedicated to the critique of pure reason, namely, the discipline contained in the Critique that is charged with accomplishing its task as the doctrine of method of metaphysics. I argue that the critique of pure reason has a positive and a negative task. Chapter 5 is dedicated to its negative task. The critique must show that metaphysics is capable of systematic coherence. I take a body of cognitions to be systematically coherent when: (a) the cognitions belonging to it are interconnected in a way that involves relations of either logical implication, explanatory support or both, and (b) it does not contain contradictions. Kant establishes that metaphysics is able of systematic coherence by setting limits to cognitions. I argue that Kant sets these limits by limiting the validity of the root concepts for the cognition of objects analysed by transcendental philosophy. I consider how and where these limits are established. I claim, first, that Kant does not follow a univocal strategy in establishing these limits and, second, that he presents arguments for establishing these limits in the Aesthetic, Analytic, and Dialectic. I focus on the arguments in the Aesthetic and the Dialectic in particular.

Chapter 6 is dedicated to reconstructing how Kant sets limits to the validity of the categories. In my reading, the argument that establishes these limits belongs to the negative part of the critique of pure reason. I first find confirmation that it is correct to distinguish between a positive and a negative argument concerning the validity of the categories, the former belonging to transcendental philosophy and the latter to the critique of pure reason, in three different texts by Kant: the transcendental deduction of the categories, the Metaphysical Foundations of Natural Science and On the Use of Teleological Principles in Philosophy. However, since these texts provide different pictures concerning how the two arguments are related to one another, I analyze in which sense the negative argument depends on the positive one by reconstructing relevant passages in the B-deduction.

An arbitration agreement expresses the consent of the parties to a legal relationship to submit the settlement of their disputes to an arbitral tribunal. As such, it is a unique type of contractual arrangement. While it has a contractual origin, it also confers the arbitral tribunal a jurisdictional power to settle legal disputes which would otherwise be submitted to State courts, hence bearing jurisdictional effects. This dual nature is further demonstrated by the variety of rules governing arbitration agreements, mainly contracts and procedural law, to such extent that it is a commonplace to assert nowadays that arbitration is dual or sui generis. These two aspects further need to be assessed by taking into account the unique legal framework enacted over the years to safeguard or limit the legal effects of arbitration agreements. This Chapter further dives into the sui generis nature of arbitration agreements and the dialectical tension between the contractual and jurisdictional aspects of arbitration as a dispute settlement mechanism. While the validity and applicability of arbitration agreements, mostly inspired by contracts law and the principle of party autonomy, determine the arbitrators’ jurisdiction, the legal mechanisms triggered by arbitration agreements are mainly focused on safeguarding the arbitral tribunal’s jurisdiction.

Provides fraction versions of Hardy inequalities.

Introduces fractional Sobolev spaces, gives their most important properties and explains their connection with interpolation theory.

This chapter addresses what Heidegger considers one of the basic problems of philosophy, that is, the alleged incompatibility between the notion of Being, our thinking, and logic. To begin with, it discusses how Heideggerians have dealt with this incompatibility by discussing what Casati calls an irrationalist and rationalist interpretation of Heidegger’s philosophy. Then, the chapter argues that both of these interpretations face exegetical and philosophical problems. To conclude, it defends an alternative way of addressing the incompatibility between our thinking, logic, and the notion of Being. In this connection Casati notes Heidegger’s suggestion, in some of his late works, that the real problem lies in the philosophical illusion that we can actually assess the limits of our thinking and, thereby, our logic. Heidegger’s philosophy aims, the chapter submits, at freeing us from such a philosophical illusion by delivering an experience that reminds us that we can never look at our thinking, as it were, from “on high,” i.e., from a standpoint that would enable us to grasp its limits or determine that it has no limits whatsoever.

In Chapter 2, we build on resilience theory to provide a framework of analysis to understand how the intensity of nature adversity generated by climate change affects and limits business adaptation. Adaptation responses can span a broad range of strategies beginning with unawareness to deliberately ignoring nature adversity conditions. Next, protective adaptation –seeking to preserve the status quo of core business features- including substitution of nature’s resources and services, buffering from negative conditions, government lobbying, and engaging in alliances or mergers and acquisitions. And then, at the highest levels of nature adversity: adopting diversification strategies (e.g., in terms of products/services, industry participation, and geographic location) or even abandoning businesses altogether.

The infra-low-frequency vibrations are most dangerous and harmful for humans. They affect a person as an operator or passenger of the vehicles and other vibrating machines, and his environment the rest of a day and night. These are longtime and thus devastating effects since human natural frequencies dramatically coincide with forced vibrations of the machines in the same spectra, resulting in permanent broadband resonances. The general and industrial standards regulate exposure time of vibration impacts to humans, since conventional vibration protection systems, to put it mildly, do not quite cope with the functions assigned to them. Moreover, they operate as vibration amplifiers rather than vibration systems just in these frequency spectra. Besides, new potentially hazard vibrations, for example, in the near-zero frequencies appear with advent of the machines of next generation under intensive development, such as high-speed railroad trains for long distances and multiple-purpose helicopters. Fundamentally other design methods and proper technology are required to provide the infra-low-frequency vibration protection of humans inside and outside operating transport vehicles, construction equipment, and other machines, especially since a gap increases between efficiency of the conventional systems and vibration limits required for health, activity, and comfort of humans

The chapter takes up the question of how and why Kant marks the limits of metaphysics, particularly in light of the skeptical challenges to reason’s use raised by Hume and Bayle. Here Kant’s distinction between our cognitive faculties – the heterogeneity thesis – plays a crucial role, since it allows Kant to set the boundaries of metaphysics at the cognizable, which requires sensible content that dogmatic metaphysics is unable to provide. Kant’s account of limits and boundaries bears a suggestive similarity to the claims Wittgenstein makes in the Tractatus, and the essay lays out some of the fruitful ways in which the latter work can help shed light on Kant’s argument in the Prolegomena.

This chapter concludes the book and sketches some of the limits of what may be expected from international law

A detailed phenomenological analysis of the various manifestations of corporeality can help to grasp and make sense of how the body is apprehended in different psychopathological conditions. I will argue that once distinguished the body-object (the representational, explicit and ultimately visible manifestation of one's corporeality) from the lived body (the proto-reflexive semi-experiential/semi-representational manifestation of one's corporeality), the latter should be distinguished from the living body. What I will call here the ‘living body’ is the immediately felt, pathic, purely impressive, pre-reflective, non-representational, experiential and invisible manifestation of one's corporeality. I will also propose that the living body possess two distinct profiles: self-affection or the primordial bodily chiasm enforcing one's feeling of belonging to oneself and to the world, and the sheer flesh or chaotic plurality of invisible bodily forces immediately felt without the intercession of a representation. A further manifestation of corporeality is the body-for-others; that is the experience of feeling one's corporeality when it is looked at by another person. I will match these different profiles of corporeality to specific anomalous psychopathological conditions, namely the appearance of the sheer, chaotic flesh to the borderline person's form of existence; the body as a corporealized, restricted, inhibited and rigid body to melancholia; the mechanic, robotic functioning object “out there” to schizophrenia; and finally the body apprehended through the gaze of the other to the existence of persons with eating disorders

The relations between embodiment and temporality reach from the micro-temporality of conscious experience to the enactment of human existence. First, the basic internal time consciousness is marked by the rhythmicity of vital processes (heartbeat, respiratory rhythm, daily periods, etc.). Moreover, the bodily drives, urges, and needs, which may be subsumed under the term conation, crucially determine the future-directed temporality of primary experience. On the other hand, the body forms an extract of sensorimotor and affective experience which are sedimented in implicit or body memory, thus shaping an individual's capacities and dispositions. Finally, existential temporality is essentially characterized by the vital processes of birth, growth, aging, and dying.

Body, time, and intersubjectivity are equally interconnected. First, interbodily resonance establishes the primary experience of the shared present, beginning in the child's early development. Thus, a basic contemporality emerges, which later continues in social synchronizations and temporal orders as the basis of social life. However, this temporal alignment is also subject to desynchronizations, for example, in backlogs of tasks, in guilt, remorse, or grief – situations that require processes of psychosocial resynchronization.

All these interconnections are subject to various kinds of disturbances which are also found in psychopathology and thus crucially determine the emergence and course of mental disorders.

In recent decades, empirical research has developed across many areas of intellectual property law. This chapter examines challenges that can arise in conducting, or drawing upon, empirical research in IP law. These include assessing a study’s value in terms of methodology, sample choice and size, execution and reporting, as well as the conclusions that might reasonably be drawn from the research. As IP scholars generate more empirically informed research, there can be value in asking whether the studies are robust and well executed, whether they reveal information or viewpoints previously not recognised, and whether they produce work from which legal or scholarly lessons can be drawn. Robust, well-conducted and analysed empirical studies may provide insights that develop IP scholarship in new ways and potentially improve policy and decision making. This underlines the importance of not being complacent about empirical analysis but being open to rigorous questioning, both individually and collectively, about our practices.