The process of identifying and interpreting norms of customary international law, while appearing to be primarily based on an inductive analysis of state practice and opinio juris, is sometimes a deductive exercise based on logic and reason. Logic permeates every decision in international law. Logic manifests itself inherently throughout the process and can be identified in all steps of reasoning in identifying, interpreting and applying customary international law. Logic, however, can constitute the application of either an inductive or deductive inference. This chapter focuses on situations in which the International Court of Justice (ICJ) and the Permanent Court of International Justice (PCIJ) applied a deductive approach, identifying or interpreting norms of customary international law without seeming to consult state practice and opinio juris. Specifically, it considers whether norms that can be reasonably inferred or deduced from existing rules, or that are simply logical for the operation of the international legal system, can be identified as norms of customary international law under a complementary, supplementary or distinctive interpretive approach.

Satisfaction of the a priori principle(s) of the faculty of judgment by a representation is the means for achieving the faculty’s interest. In concept application and formation, this interest is the harmony of imagination and understanding. Since the application of available concepts is not accompanied by pleasure, such ‘unfree harmony’ must be distinguished from the ‘free harmony’ in concept formation and taste. The imagination apprehends a manifold and is here free because it is not guided by a concept; in concept formation, however, it is still bound to the empirically given manifold, while in taste it is ‘productively free’, it invents its own forms. When such freely invented forms agree with the given forms of conceptualized objects, we register this in the pleasure of taste. This revised view of the ‘free play’ of the faculties leads to a novel interpretation both of the ‘deduction of judgments of taste’, and of the relation of the two versions of the principle of judgment.

This chapter begins by differentiating qualitative and quantitative research. While some have argued that these approaches are incommensurable paradigms, this chapter argues that they are commensurable but suited to answering different research questions. It introduces a typology of research questions, with six types of question – three qualitative (describing phenomena, theoretical framing, and generating explanations) and three quantitative (measuring phenomena, testing theory, and exploring explanations). The chapter ends by reviewing heuristics to help researchers generate novel and productive research questions.

This chapter examines the first idea-complex of equality and obligation evident in WTO law by identifying each of its constituent elements and their inter-relationship as a coherent whole, that is, the way they align and thread together. The WTO Agreement’s focus on equality and distributive justice begets a primary emphasis in law on obligation, which in turn gives rise to a constitutive structure that is prospectively oriented and reasoned deductively.

This chapter details the practical, theoretical, and philosophical aspects of experimental science. It discusses how one chooses a project, performs experiments, interprets the resulting data, makes inferences, and develops and tests theories. It then asks the question, "are our theories accurate representations of the natural world, that is, do they reflect reality?" Surprisingly, this is not an easy question to answer. Scientists assume so, but are they warranted in this assumption? Realists say "yes," but anti-realists argue that realism is simply a mental representation of the world as we perceive it, that is, metaphysical in nature. Regardless of one's sense of reality, the fact remains that science has been and continues to be of tremendous practical value. It would have to be a miracle if our knowledge and manipulation of the nature were not real. Even if they were, how do we know they are true in an absolute sense, not just relative to our own experience? This is a thorny philosophical question, the answer to which depends on the context in which it is asked. The take-home message for the practicing scientist is "never assume your results are true."

The digitalization of business organizations and of society in general has opened up the possibility of researching behaviours using large volumes of digital traces and electronic texts that capture behaviours and attitudes in a broad range of natural settings. How is the availability of such data changing the nature of qualitative, specifically interpretive, research and are computational approaches becoming the essence of such research? This chapter briefly examines this issue by considering the potential impacts of digital data on key themes associated with research, those of induction, deduction and meaning. It highlights some of the ‘nascent myths’ associated with the digitalization of qualitative research. The chapter concludes that while the changes in the nature of data present exciting opportunities for qualitative, interpretive researchers to engage with computational approaches in the form of mixed-methods studies, it is not believed they will become the sine qua non of qualitative information systems research in the foreseeable future.

This chapter begins with an outline of logic and of the attempts to use it as a theory of human deduction. The fatal impediments to this approach led to the model theory in which models based on the meanings of premises yield deductive conclusions. And the chapter describes in detail the implementation of this theory’s account of deductions based on sentential connectives such as “if,” and how this simulation led to the discovery of systematic but compelling fallacies.The chapter outlines how algorithms based on models simulate deductions of the spatial relations among objects. And it points out the problems that need to be solved to extend accounts of elementary inferences from quantified assertions to deal with multiply-quantified relations. One alternative to the model theory is the idea that human deduction relies on probabilities. This approach concerns only which inferences people make, not the underlying mental processes by which they are made. The model theory fills the gap, because it applies to the deductions of probabilities, both those based on frequencies or proportions, and those based on evidence pertinent to unique events. The chapter ends with an account of why theories of human deduction need to be simulated in computer programs.

In this chapter, we discuss the fundamentals of case study research. First of all, we discuss the research functions underlying research questions (i.e. exploratory and explanatory). Different types of explanatory research questions catering to the research functions are discussed next. Depending on the focal variable, these questions are termed X-centered (focusing on the independent variable X), Y-centered (focusing on the dependent variable Y), and X&Y centered (focusing on X and Y). The importance of the context (Z) is discussed afterwards. The logical reasonings underpinning case study research (i.e. induction, deduction, and abduction) are also discussed. The chapter also addresses some common (mis)conceptions regarding the research functions, research questions, research context, and logical reasoning.

This chapter establishes the strong link between coherence and legal reasoning. In so doing, it draws three main conclusions. A first conclusion is that legal reasoning is an instance of practical reasoning and practical deliberation. What this means, ultimately, is that when one reasons and argues about the content of the law one does not seek to discover truth in the same sense as when forming an opinion about the way things are in nature. Rather, the aim is to formulate a reasoned opinion and commit oneself to a specific course of action given the presence of a legal problem. A second conclusion is that, when understood as practical reasoning, legal reasoning exhibits certain coherence-related features. These are: (i) a web-like structure; (ii) the fact that rationality in legal reasoning does not depend only on logic but also on plausibility (or fit); and (iii) a purposive nature. A third conclusion is that coherence acts as a substantive and a methodological principle during legal reasoning, thus further confirming the dual dimension of coherence identified in Chapter 1.

The category of ‘human rights law’ is sometimes limited to bills and charters of rights on the model of the Universal Declaration of Human Rights and to the case law of courts interpreting and applying these legal measures. This chapter argues that the measures that realise human rights in the law are the everyday, unremarkable measures that make up the full corpus of legal materials directing what may, must, and must not be done. The argument explores how all sound positive law finds its source in the human goods through one of two modes of derivation: deduction or specification. These are the same two modes of positive law’s derivation from natural law, for the reach of human rights law is more or less coextensive with the reach of positive law and the human goods from which are derived human rights law are the same human goods from which are derived natural law’s practical principles and precepts.

Pufendorf’s method comprised three distinguishable strains: a humanistic deployment of diverse sources, especially from classical antiquity; an eclectic demand to choose and fashion such materials anew; and a scientific insistence on observational evidence, systemic coherence, and procedural rigor. Each of these resisted disciplinary capture, authoritarian control, and subservience to extraneous, extra-philosophical interests – appealing instead to a rational and thus potentially universal audience. In Pufendorf the third strain became dominant and involved the others as auxiliary procedures. Like other early modern instances of “mathematical” or scientific method, it aspired – in principle, and within its characteristic domain of free, human action – to probative certitude and intellectual authority while remaining exposed to challenges and demands for articulation, thereby claiming the participatory assent of other, unbiased reasoners. Despite eschewing metaphysical foundations in favor of merely empirical supports, it claimed the peculiar force or authority animating explanatory and normative legality alike. It was, in short, rational and empirical at the same time, attempting to control the pull of these counter-tendencies toward more abstract, vacuous, and irreconcilable extremes. This aim was achieved by combining broadly prudential analyses of both human and divine intent, nourished by a realistic or pragmatic assessment of historical (actual and recorded) experience.

This introduction has three goals: to locate this book’s arguments in contemporary scholarship on Parmenides, to outline its methodology and structure, and to establish the stakes of the project as a whole. The first considers Parmenides’ invention of extended deductive argumentation and the practice of demonstration – the central topic of this book – as a relic of the ‘Greek Miracle’ paradigm; it also addresses discussions of Parmenides’ use of poetry and his relationship to Homer. The second addresses distinctions between actors’ and observers’ categories and between reasoning and discourse, and explores the Foucauldian discourse analysis that anchors the book’s treatment of the relationship between Parmenides and Homer. The third requires setting out what this book does not intend to do in order to specify its main contribution: providing an account of how Parmenides’ use of the image of the hodos helps him invent extended deductive argumentation and the practice of demonstration. The Introduction sketches out the three axes of the book’s argument: an exploration of the physical reality of archaic and classical Greek roads, a discussion of the semantics of the word hodos, and an articulation of the relationship between Parmenides’ and Homer’s poems.

This chapter pivots to Parmenides’ poem by examining at a more general level the close intertextual connections with Odyssey 12. I then examine in close detail how the krisis or exclusive, exhaustive disjunction in Parmenides’ Fragment 2 bears a close resemblance to the exclusive, exhaustive disjunction in the hodos that Circe spells out in Odyssey 12; I also detail important differences between Parmenides’ and Homer’s uses of this disjunction. Finally, I explore the importance of this disjunction for Parmenides’ groundbreaking extended deductive argument and, especially, its role in the practice of demonstration.

This chapter is in many ways the culmination of the book. It applies the analysis of chapters 3 and 4 to the structure of Parmenides’ Fragment 8, and shows how Parmenides uses the blueprint of Circe’s hodos in Odyssey 12 to craft what we would call an extended deductive argument; in this, it develops the discussion of Chapter 5. It cashes out the implications of Chapter 1 by showing how Parmenides takes advantage of rut road imagery to articulate what we would call a notion of logical necessity, and by showing how the durative and telic components of the word hodos define the teleological shape of his arguments. Building on Chapter 2, I set out the traditions Parmenides developed by creating a discursive structure that is both systematic and argumentatively rigorous. I also examine how the poem’s complex relationships between story, plot, and the time of narration plays a crucial role in bestowing on Parmenides’ arguments, and on demonstration more generally, an ostensibly timeless quality. Finally, I assess my conclusions about Parmenides’ invention of deductive argumentation in relation to other scholars’ discussions of his arguments, and clarify what my argument does not claim to offer – and what it insists on.

Chapter 1 points to two problems with the deduction of the principle of the purposiveness of nature in the Introduction to the Critique of the Power of Judgment. The first is that it assumes that empirical knowledge must take the form of a comprehensive hierarchical taxonomy of empirical concepts – but does not explain why. Second, Kant creates high expectations by employing the demanding term "deduction" and promising to seek the grounds of the principle of the purposiveness of nature in the “sources of cognition a priori” – but appears simply to declare that finding a hierarchical system of empirical laws is a need of the understanding and that although we have no a priori insight into its existence “such a unity must still necessarily be presupposed and assumed” by the power of judgment. The Introduction further emphasizes the importance of the notion of pleasure and its relation to our successful attempts to discover the conceptual order of nature. It also argues that the introduction of the aesthetic and logical aspects of the purposiveness of nature gives us good reason to think that the two principal parts of the book are concerned with the latter notion and its transcendental role.