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This chapter analyzes the different ways to describe brain behaviour with the goal to provide a basis for an informed discussion of the nature of decisions and actions that humans perform in their lives. The chapter is organized as follows. Section 2 outlines a number of concepts exhibiting how many subtle details and distinctions lie behind the broad notions of determinacy and stochasticity. These details are necessary for a discussion, in Section 3, of particular aspects relevant for the characterization of brain states and their dynamics. The descriptions of brain behaviour currently provided by neuroscience depend on the level and context of the descriptions. There is no clear-cut evidence for ultimately determinate or ultimately stochastic brain behaviour. As a consequence, there is no solid neurobiological basis to argue either in favour of or against any fundamental determination or openness of human decisions and actions.

Given that the generalist element of international legal doctrine has been virtually silent on the problem and implications of the effectiveness and determinacy of international legal regulation, this study examined the material accumulated in doctrine and practice for the past several decades, including the relevant jurisprudence of all major international tribunals. Effectiveness in interpretation serves the more general principle of completeness, determinacy and effectiveness of legal regulation. The methods of interpretation are aimed at preserving the original consent, will, and intention behind the relevant legal instruments and thus at ensuring the determinacy of the relevant provision by enabling its application to facts. These methods are consistently aimed at confronting claims as to the indeterminacy of treaty provisions.

I fulfils its referential function in the deictic mode. Deictic terms fulfil their referential role by the action of making an individual salient. That is the genus to which demonstration, utterance-relative uniqueness, and leading candidature belong as species. I fulfils its referential role by making an individual salient. Salience is the determinant of the term.

This concluding chapter sums up the key findings of this study about intentional content. The findings suggests that there are not intentional norms in nature because there are no biological norms in nature and that claims about function and content are claims about objective causal relations between natural items. The results also indicate that determinacy objection against a teleological approach to intentional explanation can be answered using the proposed account of the theory of functions.

‘Rule theory’, or the claim that a simple rule is sufficient to give the meaning of I, is a myth. Theorists have not shown that it is even possible to say what this rule is, what it means, what it determines, or what functions as its context. No such rule could be sufficient to give the meaning of I because there are areas which it does not cover, there are areas in which it applies but is insufficient, there are occasions on which it should not be applied, and there are occasions on which it cannot be applied.

The referential function of any singular term is to provide a positive answer to the question: ‘which individual is being spoken of?’, that is, to achieve determinacy of reference. What enables a singular term to carry out this function is the ‘determinant’ of the term. Demonstration is not the determinant of deictic terms because they can fulfil their referential function by appeal to utterance-relative uniqueness, or by leading candidacy given the surrounding discourse or perceptual environment.

Does the presence of a transfinitely iterable determinacy operator re-create the difficulties with stratified truth theories? This chapter argues that it does not. It begins by pointing out the many clear differences between what we have for determinacy and what we have with stratified truth theories. It goes on to consider some genuine costs, but argues that we can live with them. It ends by considering and rebutting some remaining worries about how revenge paradoxes might arise.

This chapter provides a simplified account of how vagueness arises in language and is manifested in the use of language. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall (or even short) with respect to professional basketball players. A person can be wealthy with respect to local business tycoons, but not wealthy with respect to CEOs of major software companies. The main feature of the present account is that the extensions (and anti-extensions) of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis of the view is that, in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts.

This chapter provides a technical model theory, using the resources of mathematical logic, for vagueness in some formalized languages. The system has a similar structure to the supervaluationist approach, employing the notion of a sharpening (or precisification) of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The model theory is much like that of the Kripke semantics for intuitionistic logic, except that both extensions and anti-extensions vary, in concert with each other, throughout a given frame. And the system does not rely on completely sharp interpretations.

Problems with the simplified account and some unnatural features of the model theory lead to refinements of the philosophical account, the model theoretic semantics, and perhaps the logic as well. This chapter deals with what passes for higher-order vagueness — vagueness in the notions of ‘determinacy’ and ‘borderline’. The philosophical picture is developed, by extending and modifying the account presented in Chapter 1. This is followed with the required modifications to the model theory, and the central meta-theorems.

This chapter returns to Wittgenstein’s proposals about ‘objects’ in order to reveal how they can also be seen as reflecting our failure to ascribe sense to the notion of the thinker ‘coming to’ or indeed already being ‘in contact with’ its world. We cannot make sense of deep worries about the capacity of ‘what we think about’ to be thought about: there are no questions to be raised in connection with the referents of the terms of the ultimate analyses of our propositions, about ‘their existence’, ‘their composition’, or ‘how they can combine to form facts’. But that points not to how the world must be constituted in order for thought to be possible, but to a confusion at the root of the idea of ‘thought being possible’.

This chapter sets the goal: a theory without excluded middle with ‘naïve truth and satisfaction’, that is, satisfying the full Tarski schemas and Intersubstitutivity Principle. A semantic framework is sketched, involving a deMorgan valued semantics with an additional operator for the conditional. There are different ways to fill out the framework — Lukasiewicz semantics is one of them — and the trick will be to find one in which the goal of naïve truth and satisfaction can be achieved. In all ways to fill out the framework, we can define a determinateness operator, and iterate it through the transfinite. But to achieve ‘naïvety’, this hierarchy can never collapse. This is also required if the theory is to be useful for vagueness.

This chapter describes the foundations of (significant parts of) the American law of restitution. It argues that this body of law can, and therefore should, be read as a contextual application of our commitments to autonomy, utility, and community in various situations of benefit-based liability or benefit-based recovery. LER shows that, because different restitutionary doctrines involve differing categories of interpersonal relationships, they invoke different interpretations and different balances of these values. And yet, maybe unsurprisingly, LER also demonstrates, at least at a high level of generality, how these core liberal values serve (or should serve) as the normative underpinnings of the law of restitution in its entirety. Since LER's publication in 2004, a number of review essays and book reviews have appeared. Reviewers have suggested interesting insights and several intriguing critiques. This chapter appreciates these challenges, and has addressed them in order to rethink and, in some cases, defend some of LER's main propositions more successfully. Not all the points raised in these reviews have been covered and the chapter has not been able to do justice to all their subtleties. The discussion has been confined to several recurrent themes focusing on LER's jurisprudential premises. These premises are legal realist, at least according to the chapter's reconstruction of this school's lessons. Some of the critics argue that LER fails because it is too infused with realism; others complain that LER is not loyal enough to the realist legacy. The chapter discusses both sides. Before embarking in a dialogue with critics, however, it outlines an understanding of legal realism, it explains the ways in which LER is indeed an exercise in legal realism, and provides a summary of LER's analysis of the law of mistakes.

This chapter focuses on a number of contexts where the policy-abundant indeterminate notions are included in treaties with the effect of impacting the rights and duties of States. These contexts relate to indeterminate margin of appreciation policy notions under the European Convention on Human Rights and the WTO law, ‘self-judging’ clauses of treaty termination under trade, investment and disarmament treaties, and the concept of the threat to the peace under Article 39 of the UN Charter. The principal findings of the chapter relate to the ways of eliminating subjective judgment in interpretation, and to the criteria of locating the observable elements of indeterminate ‘political’ notions included in treaties. The role of judicial review is also addressed to help interpreting indeterminate notions.

For any x there can be nothing y such that there is no fact that x = y and at the same time no fact that x ( y. For if there were, then y would differ from x in this respect: that there is no fact that x is it and no fact that x is not it. In this case there is a fact that x ( y. In short, identity is always determinate. This argument is defended at length against the most developed response to date, that of Terence Parsons. The proof is also contrasted with a similar proof due to Gareth Evans.

Second-order languages, canonically understood, allow quantification over all sets of objects in the range of the first-order variables. In this chapter two arguments are given against the suitability of using second-order consequence (defined in the Tarskian way) as the consequence relation of axiomatic theories. According to the first argument, second-order languages are inadequate for axiomatizing set theory because of the strong set-theoretic content coded by second-order consequence. The second more general argument is directed against the determinacy of second-order consequence, that is, against the assumption that this is a definite relation. Only taking a strong realist view of set theory can one maintain that it is.

The axiom of choice leads to a considerable simplification of the arithmetic of cardinals, but even so it leaves some questions in this domain unsettled. This chapter focuses on these issues. Topics discussed include the arithmetic of alephs, counting well-ordered sets, cardinal arithmetic and the axiom of choice, the continuum hypothesis, the axiom of determinacy, and the generalized continuum hypothesis.

This chapter demonstrates that it is artificial to distinguish between rights according to their correlative duties. All rights give rise to both duties of restraint and positive duties. It then asks whether positive duties are sufficiently determinate to be normative. It is argued that positive duties are best understood by using Alexy's concept of principles. A principle is a norm which must be realized to the greatest extent possible given the legal and factual possibilities. Principles do not lose their prima facie binding force when outweighed by other principles. This explains why positive duties retain their normative force even when not immediately fulfilled. Nor is it necessary to specify precise standards to be determinate: it is sufficient to meet specific parameters, namely, effectiveness, participation, accountability, and equality. This analysis helps resolve the controversy over the minimum core obligation. The chapter concludes by examining the relationship between the right-holder and the duty bearer.