In Chapter 8, I deal with the threat that the present account strips arithmetical knowledge of all the important characteristics traditionally associated with it: apriority, objectivity, necessity and universality. I argue that apriority can be saved in the strong sense of arithmetical knowledge being contextually a priori in the context set by our cognitive and physical capacities. Objectivity can be saved in the sense of maximal inter-subjectivity, while necessity can be saved in the sense of arithmetical theorems being true in all possible worlds where cognitive agents with proto-arithmetical abilities have developed. Finally, universality of arithmetical truths is saved through arithmetic being universally applicable and shared by all members of cultures that develop arithmetic based on proto-arithmetical abilities.

Wittgenstein’s Tractatus deploys modal vocabulary, especially “possibility.” Some readers take this to signal commitment to substantive modal theories. For others, it is metaphysical nonsense to be thrown away. We steer a middle path. We uncover the central role of possibility in Wittgenstein’s philosophical development from criticism of Russell’s multiple-relation theory of judgment to the conception of propositions as pictures in the Tractatus. In this conception, modality is not the subject matter of theorizing but an ineluctable aspect of picturing of reality whose showing forth Wittgenstein aims to help us see by operationalizing the construction of propositions.

In this chapter, I interpret section 6.361 of Wittgenstein’s Tractatus – containing Wittgenstein’s second reference to Heinrich Hertz in the book – in the context of the nearby framing remarks concerning the ‘law of causality’. Attention to the relevant details of Hertz’s work sheds light on a number of Wittgenstein’s remarks about mechanics in the 6.3s and, in particular, explains Wittgenstein’s claim that ‘What can be described can happen too, and what the law of causality is meant to exclude cannot even be described’ (6.362). For Wittgenstein, to describe events in causal terms is to describe them via an appeal to temporal and spatial asymmetries. However, no alternative is available: a description that did not appeal to such asymmetries would not be a description of anything. According to the Tractatus, descriptions are recognized as causal when they are embedded in a unified theoretical framework, but causal powers, understood as relations of material necessity, do not exist.

This introductory chapter provides the rationale for the book, as well as its organization. As part of the linguistic landscape, public signage provides glimpses of a culture and its changes. The ability to read signs is a practical skill essential for daily survival in the target language environment. But there seems to have been a general neglect of signs in the typical Chinese language curriculum, even at advanced levels of instruction. This book aims to rectify the situation.

In this chapter, the semantical framework of Chapter 7 is fine-tuned in order to provide a semantics for Anderson and Belnap’s logic E of relevant entailment. It is shown how a form of logical necessity can be represented in the semantics, and this is used to motivate the postulates that are needed to characterize that logic. A labelled deduction system (introduced in Chapter 7) is also used to show how to derive the axioms of E easily.

This chapter considers the criteria for collective self-defence that are shared with individual self-defence. It is uncontentious to say that the same criteria that apply to individual self-defence – armed attack, necessity, proportionality, the reporting requirement, and the ‘until clause’ – also apply to collective self-defence. Indeed, this is an inevitable consequence of the way the concepts appear in Article 51 of the UN Charter. The nature and application of these criteria in the context of individual self-defence have been examined at great length in the existing literature. This chapter therefore does not provide in-depth analysis of all of their aspects. That said, it does provide a brief overview of these requirements to ensure that this book presents a comprehensive picture of the operation of collective self-defence today. The chapter’s main focus, though, is to examine how the operation of these criteria works specifically in the context of collective self-defence actions, which is something that has been largely overlooked in scholarship.

Chapter 6 provides an overview of the general aspects of the right of self-defence. It first examines the concept of an ‘armed attack’ as found in Article 51, with the aim of shedding some light on the difficult issues and questions raised by this prerequisite for the invocation of the right of self-defence. It then goes on to provide an examination of the twin customary principles of necessity and proportionality, including a specific look at the controversial concept of armed reprisals, before moving on to examining military action for the protection of nationals who are located abroad. The right of self-defence exists in both individual and collective forms, and the chapter takes a specific look at the right of collective self-defence. Finally, it examines the role of the UN Security Council in the invocation and implementation of the right of self-defence, an aspect of the right which is prominent throughout Article 51.

This chapter explores the Laudian critique of the (allegedly) puritan doctrine of absolute predestination, and particularly absolute reprobation. This critique imputed an absolute, fatal or stoic necessity to questions of salvation and damnation, which, the Laudians claimed, reduced the role of human free will and moral effort to nothing. In so doing it created desperately difficult pastoral dilemmas for ministers trying to rescue members of their flocks from the desperation such doctrines all too often induced. This was particularly the case for absolute reprobation. It was in the course of dealing with puritan error on this subject that the Laudians came to deal with the topic of predestination, and faute de mieux, to adumbrate their own position, asserting that saving grace was offered to all, that Christ died for the sins of the whole world, that God willed the salvation of every sinner, that human effort was required for salvation, that true faith could be totally and finally lost and that no one was simply doomed to damnation; contentions which they defended not as resolutions of the paradoxes at the heart of the debate about predestination, but rather as saving truths central to the nature of Christianity.

Machiavelli cannot accomplish conversion of the world by himself. He has to convince future philosophers to follow or obey him. This is his succession problem.

Drone programs in the counterterrorism context rest on the use of force in self-defense not against an (imminent) act, but against individuals in the light of their personal or behavioral characteristics. Because drone programs are motivated by the objective of permanently addressing future threats before they materialize, technology and legal rhetoric are used as instruments to authorize action against individuals who are not presently perpetrating terrorist acts, nor even clearly preparing, such acts. Some states active in the transnational war on terror have proposed a legal framework for the continuous anticipation of armed attacks against individuals who show signs of hostile intent. These changes in military strategy and legal discourse are not merely the result of how states decide to use force in the counterterrorism context, but also of what technology allows them to do. As such, drones facilitate and arguably intensify the phenomena of the individualization and dematerialization of the use of force. Although the interpretation of self-defense proposed by some states active in the war on terror is still highly contested on some points, the chapter shows that even if some limitations remain, concessions to the extensive interpretation of some limitations appear to have a direct cascade effect on the remaining checks because these limitations are interconnected.

Chapter 9 studies access to landlocked land and shows that most jurisdictions aptly use a mixture of ex ante and ex post viewpoints to design their doctrines. This chapter follows American parlance and divides the doctrine into “easements of necessity” and “statutory easements.” They have intuitive appeal: for statutory easements, owners of servient land should be compensated; easements should be necessary; and the location of the passage should cause the least damage to the servient land. As for easements of necessity, the landlocked owners can only gain access to land held by the grantor at the time of the conveyance. The prevalent scheme under statutory easement to solve this legal entanglement is neither the property rule nor the liability rule, but a “hybrid rule,” an unheralded mixture of the property rule and liability rule. Chapter 9 argues that the hybrid rule stipulates that the extent of statutory easements should be set at where the marginal social benefit of prescribed passage sharply declines, and passage locations should be determined following the least damage rule. As for easements of necessity, the limited access rule and the gratuity requirement make economic sense from an ex ante viewpoint.

In this chapter, I present Aristotle’s arguments in his books on Physics defending the claim that there is purposiveness in nature independent of thinking, foresight and deliberation. Hegel’s arguments for objective purposiveness are correctly understood only in light of those of Aristotle. In fact, I argue that the sense in which teleology is for Hegel the truth of mechanism (and, ultimately, of causality) is the sense in which, for Aristotle, final causes are the cause of ‘that which comes to be by nature’ and the cause of other kinds of causes (matter, efficient causes and even form) being where they are and having the effects that they eventually have. The chapter revises Aristotle’s understanding of this connection.

Hegel intends to prove two different claims about purposive connections in his Logic: (1) that teleology is the truth of mechanism and (2) that inner purposiveness is the truth of the external reference-to-an-end. I devote this chapter to the analysis of the first of these arguments. To this end, I introduce Hegel’s concept of ‘mechanism’, whose main ingredient is the idea that mechanisms are determined as causes merely from without. This feature disqualifies mechanisms as self-sufficient explainers. I compare Hegel’s understanding of this shortcoming with Hume’s and Kant’s misgivings about the cognition of causal relations. For Hegel, mechanical causes are in themselves apparent and the relations they maintain with other causes are in themselves contingent. It is this essential contingency of the ‘necessary’ that makes Hegel judge mechanical relations to be untrue. Mechanical objects with indeterminate causal powers appear essentially as means and, hence, hypothetically subordinated to self-determining causes.

In this chapter, the most common narratives relating to the function and purpose of investment treaties are analysed that emerged from our data. The overarching discursive framework of the narratives about IIAs’ purpose was marked by the faith in their important role in economic development of the studied countries (IIAs as articles of faith). This broader view was undergirded by the idea of a linear and progressive march of history, in which earlier state and economic formations are eventually transformed into the universally superior social order of capitalist legality, rule of law, and good governance (IIAs as progressive economic development). This broader progressive narrative about IIAs was translated in more specific narratives about IIAs in specific temporal and spatial contexts. International investment agreements were, thus, viewed either as a natural necessity, as a necessary (lesser) evil in the march towards economic progress, or simply as benign instruments that merely reflect the progress already undertaken. Finally, IIAs were also signed to express cultural affinity and played a symbolic role in showing political like-mindedness (IIAs as symbolic tokens of political affinity). In some cases, IIAs helped to project countries’ self-perception of their position in the stylised international relation hierarchy as ‘developed states’.

Some 66 billion years ago, a cataclysmic collision between the Earth and an asteroid ten to 15 kilometres in diameter caused the extinction of the non-avian dinosaurs. In 1908, an asteroid 50 to 70 metres in diameter levelled over 2,000 square kilometres of forest in Siberia, while in 2013 an asteroid 19 metres in diameter produced a shockwave over Chelyabinsk, Russia, sending over a thousand people to the hospital. The field of ‘planetary defence’ involves the detection, characterisation, risk assessment and, if necessary, deflection of asteroids and comets that have the potential to strike Earth. Yet there has been a lack of high-level diplomacy on this issue. In particular, the low probability of a major Earth impact happening in our lifetime makes planetary defence a low priority for political leaders, despite the existential consequences of impacts and their eventual certainty of occurring. There is also a shortage of widely agreed international law, including on the potential use of nuclear explosive devices for deflecting asteroids. Most importantly, there is a lack of agreement on who is responsible for vetting the science, assessing the risks and making decisions if Earth were faced with an actual impact threat. Is it the United Nations Security Council that decides? What if a Security Council decision is blocked by one of its veto-holding permanent members? Would a state that acted unilaterally be excused any illegality because of the necessity of its actions, according to the international law on ‘state responsibility’?

The chapter examines the ICJ’s contribution to the law on the use of force. The author considers the Court’s case law on the prohibition of the use of force and its potential exceptions, most notably the law on individual and collective self-defence. He identifies the main conceptualisations, inconsistencies, disagreements, and limitations of the Court’s opinions, arguing that although the Court initially had a significant influence, it has faded significantly over the years as a result of what appears to be a conscious or strategic decision of its judges.