Transreal logical space of all propositions

Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

Legitimacy

This chapter examines the importance of legitimacy for international organizations, and their efforts to legitimate themselves vis-à-vis different audiences. Legitimacy, which for decades barely featured in the scholarly analysis of international organizations, has since the late 1990s been an increasingly important lens through which the processes, practices, and structures of international organizations have been examined. The chapter makes three main arguments. First, it argues that in most international organizations the most important actors engaging in legitimation efforts are not the supranational bureaucracies, but member states. This has important implications for our understanding of the purposes of seeking legitimacy, and for the possible practices. Second, legitimacy and legitimation serve a range of purposes for these states, beyond achieving greater compliance with their decisions, which has been one of the key functional logics highlighted for legitimacy in the literature. Instead, legitimacy is frequently sought to exclude outsiders from the functional or territorial domains affected by an international organization’s authority, or to maintain external material and political support for existing arrangements. Third, one of the most prominent legitimation efforts, institutional reforms, often prioritizes form over function, signalling to important and powerful audiences to encourage their continued material and political support. To advance these arguments, the chapter is divided into four sections. The first develops the concept of legitimacy and its application to international organizations, and then asks why their legitimacy has become such an important intellectual and political concern in recent years. The second part will look in more detail at the legitimation practices of international organizations, focusing on who engages in these practices, who the key audiences are, and how legitimation claims are advanced. The third section will look in more detail at one of the most common forms of legitimation – institutional reform – through the lens of two such reforms in international organizations: efforts towards greater interoperability in NATO, and the establishment of the African Peace and Security Architecture in the African Union (AU). The chapter will conclude with some reflections of the contribution that a legitimacy perspective has made to our understanding of the practices of international organizations.