The value of actual outcomes or states of affairs often depends on what could have been. Such dependencies create well-known “paradoxes” for decision theory, the best-known perhaps being the so-called Allais Paradox. The primary aim of this PhD thesis is to enrich decision theory such that it includes counterfactual prospects in the domains of desirability (or utility) functions, and show that, as a result, the paradoxes in question disappear. Before discussing the way in which counterfactual propositions influence the desirability of actual outcomes, I discuss the way in which the truth of one factual proposition influences the desirability of another. This examination leads me to reject the Invariance assumption, which states that the desirability of a proposition is independent of whether it is true. The assumption plays an important role in David Lewis’ famous arguments against the so-called Desire-as-Belief thesis (DAB). The unsoundness of Lewis’ argument does of course not make DAB true. In fact, I provide novel arguments against different versions of DAB, without assuming Invariance. To justify the assumptions I make when extending decision theory to counterfactual prospects, I discuss several issues concerning the logic, metaphysics and epistemology of counterfactuals. For instance, I defend a version of the so-called Ramsey test, and show that Richard Bradley’s recent Multidimensional Possible World Semantics for Conditionals is both more plausible and permissive than Bradley’s original formulation of it suggested. I use the multidimensional semantics to extend Richard Jeffrey’s decision theory to counterfactuals, and show that his desirability measure, extended to counterfactuals, can represent the various different ways in which counterfactuals influence the desirability of factual propositions. And I explain why the most common alternatives to Jeffrey’s theory cannot be similarly extended. I conclude the thesis by using Jeffrey’s extended decision theory to construct an ethical theory I call Modal Consequentialism, and argue that it better satisfies certain entrenched moral intuitions than Non-Modal Consequentialism (such as classical utilitarianism and welfare economics).

This thesis consists of five chapters: 1.The Mechanical View, 2.Social Machines, 3.The FCC Auction Machine, 4.Self-Interested Knaves, and 5.Self-Interested but Sympathetic. In the first three chapters, I advance a methodological account of current design and engineering in economics and political science, which I call methodological mechanicism. It is not ontological or literal; it relies on a technological metaphor by describing market and state institutions as machines, and the human mind as consisting of a number of mechanisms. I introduce the Mechanical view on scientific theories as distinct from the Syntactic and the Semantic views. The electromagnetic theories from the nineteenth century are used to illustrate this view as well as the use of minimal and maximal analogies in model-building in normal and revolutionary science. The Mechanical view is extended to the social sciences, particularly to mechanism design theory and institutional design, using the International Monetary Fund, the NHS internal markets and the FCC auction as examples. Their blueprints are evaluated using criteria such as shielding and power for calculating joint effects as well as libertarian, dirigiste, egalitarian and inegalitarian properties; and the holistic and piecemeal engineering they adopt. Experimental parameter variation is introduced as a method complementing design. Any design assumes a particular moral psychology, so in chapters four and five I argue that the moral psychology of universal self-interest from Bernard Mandeville, and the related ideas on design and engineering, should be chosen over the moral psychology of self-interest, sympathy and sentiments of humanity from David Hume. Hume finds no solution for knavery in politics and civil society. He accepts egalitarianism as useful and consistent with utilitarian principles; however he rejects it because of some difficulties with its implementation. I show how those difficulties may be overcome, and I explain why his objections are unbalanced and not sufficiently justified.

This thesis investigates the prospects for an interpretivist account of practical reasons. The proposed account identifies practical reasons with sets of propositional attitudes from which certain actions follow, given the constraints of interpretable functioning. Following Davidson, these constraints are taken to be enumerated by formal decision theory and formal semantics. Thus the account of practical reasons is framed in terms of what rationally follows from agents' beliefs and desires. The hope is that an account of practical reasons of this kind can explain the existence of practical reasons without invoking irreducible normative properties or relations. This outcome depends upon the availability of a theory of (radical) interpretation which is free from prior normative commitments. It is argued that a non-normative reading of Davidson's theory of radical interpretation is available, such that the account of practical reasons can meet this requirement. Although the proposed account of practical reasons does not admit of the possibility of categorical reasons for action, the ensuing objection that it fails to allow for the possibility of moral reasons for action is resisted. It is suggested that a plausible account on which moral reasons are hypothetical in kind can be provided. In particular, an account of moral reasons which is framed in terms of the motivations associated with a capacity for empathic affect is advanced. More generally, the aspiration of the thesis is to provide an account of practical reasons framed in terms of the requirements of interpretable functioning which will be regarded as an interesting and credible naturalistic option.

This thesis is about dialetheism and the problem of revenge. More broadly, it is about truth and what the logical paradoxes tell us about the logical behaviour of truth. One of the driving forces behind the contemporary study of truth and paradox is the problem of revenge: that many, perhaps all, available theories of truth, give rise to further paradoxes, invoking central notions of those theories, which demonstrate that the theory cannot express those notions. This sort of expressive limitation, especially if it involves the very notion invoked to diagnose what goes wrong in paradoxical sentences, would normally be thought a decisive point against a given theory of the paradoxes, were it not for the fact that the problem is so pervasive that every currently available theory has, at some point, been argued to suffer from it. Dialetheism, the view that some contradictions are true, has often been thought to be the only view which has a reasonable chance of avoiding the problem. Indeed, the surge of interest in the view since the first publication of Priest’s In Contradiction, in 1987, defending dialetheism, is probably due in large part to the seeming immunity to the revenge problem that Priest’s view possesses. Its virtue, in respect of revenge, is that its ability to accept, without collapse into incoherence, contradictions, allows it to accept any further revenge paradoxes as merely giving more sound arguments for dialetheia (true contradictions). This thesis argues that this appearance of revenge-immunity is mistaken. Dialetheism, too, has its revenge problems. The seeming virtue of dialetheism, that it can accept the contradictions generated by revenge paradoxes without incoherence, also has its drawbacks. This is because dialetheists are not only able, but compelled to accept the contradictions arising from the semantic paradoxes. This means that contradictions can arise in certain areas where they are undesirable. In particular, there are notions which seem to require consistency in order to be expressible. If we can demonstrate, using revenge paradoxes, that, on dialetheism, predicates putatively representing these notions would have to behave inconsistently, then we can demonstrate that dialetheists cannot express the notions. There are many ways one might wish to carve up the different varieties of dialetheism available. I have separated the view into two broad kinds: metatheoretically paraconsistent dialetheism, on the one hand, and metatheoretically consistent dialetheism, on the other. This distinction decides to which variety of revenge problem the version of dialetheism in question is subject. I take each in turn, and argue that they are each subject to expressive limitations brought about by revenge paradox.

This thesis defends the 'true-futurist' view, according to which statements about the future are either true or false, even if the future is open and unsettled in some robust, objective and mind-independent sense. A general argument for the validity of the principle of bivalence in the open future is advanced. The key feature of such argument is the 'principle of retrospective determinacy', stating that, for any proposition p, if it is now the case that p, then it was true that p would be the case. Different possible objections are discussed and dismissed. Second, two true-futurist theories are presented and shown to meet all the relevant desiderata of a true-futurist theory. In particular, much attention is devoted to the 'problem of counterfactual evaluation', concerning the truth-value of future-contingent statements in merely counterfactual scenarios. In addition, it is argued that that the choice between the two true-futurist theories depends upon which metaphysical picture of time is assumed as true. Some notable theoretical commitments of True-Futurism are examined. In particular, it is argued that True-Futurism is incompatible with two different ideas. The first one being that future-contingent statements (although bivalent) have an indefinite truth-value. The second one being that there are true 'counterfactuals of openness', stating that a certain future-contingent statement would have had a specific truth-value, had different circumstances obtained.

This thesis studies pricing and hedging barrier and other exotic options in continuous stochastic volatility models. Classical put-call symmetry relates the price of puts and calls under a suitable dual market transform. One well-known application is the semi-static hedging of path-dependent barrier options with European options. This, however, in its classical form requires the price process to observe rather stringent and unrealistic symmetry properties. In this thesis, we provide a general self-duality theorem to develop pricing and hedging schemes for barrier options in stochastic volatility models with correlation. A decomposition formula for pricing barrier options is then derived by Ito calculus which provides an alternative approach rather than solving a partial differential equation problem. Simulation on the performance is provided. In the last part of the thesis, via a version of the reflection principle by Desire Andre, originally proved for Brownian motion, we study its application to the pricing of exotic options in a stochastic volatility context.

In this thesis, we study Parisian excursions, which are defined as excursions of Brownian motion above or below a pre-determined barrier, exceeding a certain time length. Employing a new method, a recursion formula for the densities of single barrier and double barrier Parisian stopping times are computed. This new approach allows us to obtain a semi-closed form solution for the density of the one-sided stopping times, and does not require any numerical inversions of Laplace transforms. Further, it is backed by an intuitive argument which is premised on the recursive nature of the excursions and the strong Markov property of the Brownian motion. The same method is also employed in our computation of the two-sided and the double barrier Parisian stopping times. In turn, the resultant densities are used to price Parisian options. In particular, we provide numerical expressions for down-and-in Parisian calls. Additionally, we study the tail of the distribution of the two-sided Parisian stopping time. Based on the asymptotic properties of its distribution, we propose an approximation for the option prices, alleviating the heavy computational load arising from the recursions. Finally, we use the infinitesimal generator to obtain several results on other variations of Parisian excursions. Specifically, apart from the length, we are interested in the number of excursions and the maximum height achieved during an excursion. Using the same generator, we derive the joint Laplace transform of the occupation times of the Brownian motion above and below zero, but only starting the clock each time after a certain length.

There are reasons for us to act in certain ways and think certain things. We can recognise those reasons for what they are and respond to them accordingly. This thesis is an investigation of that phenomenon. In particular, it constitutes an attempt to resist certain ways in which our understanding of it can be distorted by letting our account of it be informed by bad cases of responding to reasons: cases in which one takes something to be a reason and responds accordingly by acting or thinking in the way it seems to one to recommend, even though one fails (blamelessly) to act or think for a genuine reason. I examine and reject three ways in which the possibility of bad cases might distort our thinking about the phenomenon at issue. First, we should reject the thought that the subject is able to act or think for the reason that p in both bad cases and good, so that acting or believing for a reason cannot simply be identical to the success condition of responding to a genuine reason. Second, we should reject the thought that the reasons for which we act and think are psychological features of ourselves, because that must be so in bad cases, and what goes for bad cases goes across the board. Finally, we should reject the thought that acting in response to a genuine reason involves only a rationalising explanation of the same type as that which is present in the bad case. The result is a vindication of the position promoted by Raz (2011): responding to reasons is a matter of acting or thinking in a way than manifests one's knowledge of the reasons there are for one to so act or think, so that the reasons in question, which are usually facts about the external world, explain why one does so qua reasons. Bad cases are a different kind of thing entirely.

The present thesis considers the relation between Jacques Derrida and G.W.F. Hegel. In his Positions Derrida noted that differance is ‘at a point of almost absolute proximity to Hegel,’ and that he had ‘attempted to distinguish [differance] from Hegelian difference at the point at which Hegel, in the greater Logic, determines difference as contradiction only in order to resolve it.’ Nevertheless, scholarship on the relation between the two thinkers has largely neglected the detailed consideration of the relation of Derrida’s thinking to Hegel’s logic of essence, where the categories of difference and contradiction are located. This has often led to a simplification, from both Hegelian and Derridean perspectives, of the relation between Hegel and Derrida. Through a reading of Hegel’s logic of essence and of Derrida’s early texts in particular, the thesis first aims to determine the nature and degree of the proximity indicated by Derrida and then considers the manner in which the two thinkers depart from one another. The proximity between Hegel and Derrida is drawn out through an analysis of Hegel’s notion of reflection and his logic of identity and difference. This logic is compared with the ‘graphics’ of identity and difference elaborated by Derrida in his Limited Inc. I claim that Derrida departs from Hegel in thinking difference as the displacement of opposition. Nevertheless, I claim that in relating Hegel and Derrida to one another, it cannot be a question of simply comparing two logics or two philosophies, for Derrida does not and cannot have a general logic or ‘philosophy’ of ‘differance.’ Derrida thus departs from Hegel also insofar as he puts into question the possibility of, and the desire for, a general onto-logic.

Plural Logic is an extension of First-Order Logic with plural terms and quantifiers. When its plural terms are interpreted as denoting more than one object at once, Plural Logic is usually taken to be ontologically innocent: plural quantifiers do not require a domain of their own, but range plurally over the first-order domain of quantification. Given that Plural Logic is equi-interpretable with Monadic Second-Order Logic, it gives us its expressive power at the low ontological cost of a first-order language. This makes it a valuable tool in various areas of philosophy. Some authors believe that Plural Logic can be extended into an even more expressive logic, Higher-Level Plural Logic, by adding higher-level plural terms and quantifiers to it. The basic idea is that second-level plurals stand to plurals like plurals stand to singulars (analogously for higher levels). Allegedly, Higher-Level Plural Logic enjoys the expressive power of type theory while, again, committing us only to the austere ontology of a first-order language. Were this really the case, Higher-Level Plural Logic would be a very useful tool, extending and strengthening some of the applications of Plural Logic. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with scepticism. The main objection raised against them is that higher-level plural reference is unintelligible. This has been argued, among others, on the grounds that there are no higher-level plurals in natural language and that, if there were any, they could be eliminated. In this thesis, after introducing the debate on plurals in Chapters 1 and 2, I turn to defending the legitimacy of the notion of higher-level plural reference. To this end, in Chapter 3, I present and elucidate the notion. Next, in Chapter 4, I show that some natural languages clearly contain these expressions and that they do so in an ineliminable manner. Finally, in Chapters 5 and 6, I develop a semantics for higher-level plurals that employs only devices previously well-understood by English speakers. To finish, in Chapter 7, I describe an application of Higher-level Plural Logic: a strengthening of the neo-Fregean programme. After describing my proposal, I turn to the issue of the logical status of this formalism and defend an optimistic take on the matter.