Let \(\char{cmmi10}{0x54}\) : \(\char{cmmi10}{0x58}\) → \(\char{cmmi10}{0x58}\) be a function from a countably infinite set \(\char{cmmi10}{0x58}\) to itself. We consider the following problem: can we put a structure on \(\char{cmmi10}{0x58}\) with respect to which \(\char{cmmi10}{0x54}\) has some meaning? In this thesis, the following questions are addressed: when can we endow \(\char{cmmi10}{0x58}\) with a topology such that \(\char{cmmi10}{0x58}\) is homeomorphic to the rationals \(\char{msbm10}{0x51}\) and with respect to which \(\char{cmmi10}{0x54}\) is continuous? We characterize such functions on the rational world. The other question is: can we put an order on \(\char{cmmi10}{0x58}\) with respect to which \(\char{cmmi10}{0x58}\) is order-isomorphic to the rationals \(\char{msbm10}{0x51}\), naturals \(\char{msbm10}{0x4e}\) or integers \(\char{msbm10}{0x5a}\) with their usual orders and with respect to which \(\char{cmmi10}{0x54}\) is order-preserving (or order-reversing)? We give characterization of such bijections, injections and surjections on the rational world and of arbitrary maps on the naturals and integers in terms of the orbit structure of the map concerned.

This thesis, which is divided into five papers, explores biased decision making in naturalistic environments and its implications for the efficiency of financial markets and forecasts of competitive event outcomes. Betting markets offer a valuable real world decision making context, allowing analysis that is not possible using regular financial market data. The first paper surveys studies that have employed betting markets to investigate biased decision making and discusses why the extent of these biases is significantly less than in the laboratory. The second paper addresses unresolved issues relating to noise trading and herding in financial markets, by showing that noise trading is associated with increased market efficiency, that the extent of herding differs depending on the direction and timing of changes in market prices, and that this results in an economically significant inefficiency. The findings of this paper have important policy implications for wider financial markets: regulatory measures to protect investors from the destabilizing effects of noise appear to be self-defeating and herding is particularly prevalent when uninformed traders perceive that informed traders are participating in the market. The third and fourth papers address the favourite-longshot bias (FLB), where market prices under-/over-estimate high/low probability outcomes. These papers demonstrate that previous explanations of the bias are inconsistent with evidence of trading in UK betting markets by developing and testing the predictions of models that explain the bias in terms of competition between market makers and the demand preferences of bettors. Moreover, it is definitively shown that, when no market maker is involved, the bias is due to cognitive errors of traders rather than their preference for risk, because only prospect theory, and not risk-love, can explain a reduced FLB in events with strong favourites. The final chapter explores methodological concerns relating to estimates of forecast accuracy in models of discrete choice, and arrives at a much more rigorous understanding of the value of these estimates.

This thesis explores the development of Bertrand Russell‘s theory of definite descriptions. It aims at demonstrating the connection between Russell‘s views on the subject of denoting and his attempt, in the period 1903-05, to develop a solution to 'the Contradiction' (i.e. the Russell Paradox). The thesis argues that the discovery of the theory of descriptions, and the way in which it works, are best understood against the backdrop of Russell‘s work on the paradoxes. A new understanding of Russell‘s seminal paper 'On Denoting' is presented, including a novel interpretation of the notorious 'Gray‘s Elegy Argument', in which Russell argues against his earlier theory of denoting. That Russell‘s work on denoting is connected to his work on the paradoxes is reasonably well-known: the nature of the connection has not, however, been adequately brought out in the literature. This is addressed through demonstrating the relationship between Russell‘s work on denoting and his development of the 'substitutional theory' of classes and relations. This theory eliminates classes and propositional functions in favour of matrices and substitutions. The role of the theory of descriptions in the development of the substitutional theory is commonly supposed to be merely that the theory of descriptions facilitates the ontological elimination of classes. But this elimination was equally possible on Russell‘s earlier theory of denoting (which he had rejected in the Gray‘s Elegy Argument). In the thesis it is suggested that the theory of descriptions brings with it a new conception of analysis, and that it is through the introduction of this new form of analysis—rather than through the elimination of classes—that the theory of descriptions facilitates the substitutional approach.

“Being with oneself in the other” is Hegel's famous definition of freedom, and, I argue, it is also the key topic of his entire Science of Logic. Hegel's Logic is an ontological analysis of the underlying relational structure of everything: the structure of thinking as much as the structure of the world. Hegel proposes at the beginning of the Logic that this structure must display the form of “being with oneself in the other”, i.e. consist in a relation of identity and difference between a totality and its elements. After presenting the different forms of “being with oneself in the other” developed in the Logic, I will offer a new interpretation of the Philosophy of Right and the Philosophy of History in the light of my interpretation of the Logic. This serves to show how exactly Philosophy of Right is the exposition of the existence of freedom and how it is grounded in the Logic. While the connection between Hegel's Logic and social philosophy has often been taken to have authoritarian and anti-individualist implications, I will show that this is not the case and that this connection instead highlights the republican aspects in Hegel's theory.

In this thesis I investigate the notion of experience in German Idealist Philosophy. I focus on the exploration of an alternative to the transcendental model notion of experience through Schelling's insight into the notion of logogrif. The structural division of this project into two sections reflects the two theoretical standpoints of this project, namely the logic and the logogrif of experience. The first section - the logic of experience - explores the notion of experience provided in Kant's Critique of Pure Reason, Critique of Judgement and Fichte's Science of Knowledge. I argue that Kant's fundamental question about the possibility of synthetic a priori judgements succeeds in thematising the aporia of cognitive experience but results in a subject-oriented, representational model which radically confines the notion of experience to the constitutive laws of the understanding or to the normative precepts of Reason. Experience is founded upon a sharp division between faith and knowledge, will and logic, desire and reflection, absolute and finitude. Fichte's endeavour to articulate a non-representational account of experience, does not succeed in extricating itself from the representational model, so long as experience is reduced to the ever-producing deeds of the self-positing ego. Despite the serious differences between Kant's and Fichte's notions of experience, both accounts, so long as they unfold from a transcendental standpoint, attempt to resolve experience into conceptual laws or determinations of the ego's absolute will. Experience is transformed into an object of the subject's cognitive or volitional faculties. The paradoxes of man's interaction with the world are intended to be accommodated either by the law-giving spontaneity of the understanding and the Architectonic of Pure Reason or by the overpowerful primordial act of the self-positing ego. This implies the conceptualisation of the self in terms of constant identity-through-time, or sheer self-determination. However, this conceptualisation remains at the normative or prescriptive level, which in turn is projected upon the world. The latter, though appears as the subject's property, essentially remains alien and opaque, confirming the radical limitations of the ego rather than its order-giving authority. Moreover, this notion of experience is ultimately founded upon a radical expulsion of the divine from the world, the de-spiritualisation of the sensual and the de-sensualisation of the spiritual, the sharp juxtaposition between absolute and finitude. This results in a self-defeating subjectivity, whose firm identity and rule-giving authority does not rescue it from its perennial unattainability to 'organise the conditioned' or 'conquer the unconditioned'. In Kant's and Fichte's thought, however, I detect elements that potentially transgress their transcendental account of experience. These are found in Kant's concept of spontaneity and free play between understanding and imagination, and Fichte's concept of productivity. I argue that these elements lose their potential dynamism, so long as they are absorbed by the transcendental demands for the solution of the aporias of logic. However, these elements point to the need for a radical re-conceptualisation of the notion of experience. This is provided by means of Schelling's logogriflic approach, which constitutes the theme of the second section. The second section - the logogrif of experience - attempts to articulate a different approach towards the notion of experience, through an exploration of Schelling's versatile and provocative thought. This section focuses on Schelling's original insight into the notion and act of logogrif, which opens the dialogue between logos and mythos, cosmic becoming and human soul, cosmic imagination and human reflection, faith and knowledge. This section attempts to illuminate Schelling's fascinating philosophical investigations and discoveries that have been rather overlooked, possibly, due to Hegel's overwhelming critique. This section, after a brief critical examination of the Identity Philosophy, attempts to elucidate Schelling's notion of experience through his middle works, Of Human Freedom, Ages of the World, The Deities of Samothrace, which are treated as a self-developing trilogy. Schelling re-addresses the aporias of logic not as part of Reason's self-interrogation but as part of the cosmic paradoxes and living experiences. In this way, Schelling resets the scene of the debate on the conditions of possibility for cognitive experience by putting on the stage the enigmas of the cosmos and life rather than the Tribunal of Reason. Logic itself is conceived as a potency in the cosmic becoming, and consequently can no longer attempt to establish the transcendental conditions for the possibility of cognitive experience. Cosmic becoming, in which man is an active part, is conceived as the process of the movement, the interaction, the transformations and transmutations of multiple potencies. These, far beyond any mechanical conceptualisation, appear as self-moving and yet interdependent, unknown yet familiar, inscrutable and yet manifest powers, describing the mystery of life itself. The latter is depicted as an ever-recurrent act of longing for self-expression as active unity. Experience is conceived as the lived process of a network of living potencies, which may not only resist rational powers but may also puzzle and seize them. In this context, reflection acquires a plastic dimension, as opposed to its rigidity in the representational model of experience. Reflection depicts cosmic longing's self-formation, whose man is part. This self-bending formation partially illuminates the nature of longing, and from this standpoint is the logic of the longing. However, this formation is movable, transmutable and mostly ineffable, and from this standpoint is the logic of a riddle: a logogrif. Logogrif is the transitive term that attempts to describe the transition of experience from its enacted phase to its allusive conceptual utterance, and in this sense the term itself participates in both phases, as both form of thought and form of life. The logogrific approach to experience in turn transposes us as from the realm of pure concepts to the realm of the mystery of life, from pure thought to acts of longing, from the Architectonic of Pure Reason to Cosmic Theurgy. The latter term attempts to grasp the paradox and dynamism of cosmic and non-cosmic becoming by means of multiple, vanishing and ever-recurring, transmutable potencies, or in Schelling's terms 'the magic of insoluble life'. Schelling's logogrific account consists in a powerful voice for the re-enchantment of the world, the introduction into the notion of experience of the imminence of the divine. This is not suggested in terms of the adoption of old religious doctrines but by means of the discovery and re-discovery of the theurgy of life, through the intensification of our artistic mood, the creative expansion of our deeds. This notion of experience allows for the reconsideration of the notion of the self, in terms of a dynamic, conflictual process between conscious and unconscious powers and the critical revaluation of the accounts of subjectivity which reduce it to the sphere of self-consciousness. The thesis concludes with the need for an investigation into the relation between logos and mythos, which only tangentially has been introduced by the present project. In this context it will be possible to re-appraise the potential that the logogrific approach opens for an alternative to both logical and traditional mythological patterns of thinking.

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This thesis analyzes the direction of time problem in the framework of philosophy of science. The radiation arrow, Newtonian arrow, thermodynamic arrow and quantum mechanical arrow have been studied in detail. The importance of the structure of space-time concerning direction of time is emphasized.

The main purpose of the present study is to show that scientific realism is still worth advocating despite its vulnerability in the face of anti-realist objections. For, it does not seem possible to &lsquo / do science&rsquo / without realist commitments. The second purpose of this study is to investigate the plausibility of the novel versions of realism in the sense that whether they can satisfactorily respond to the anti-realist objections. Regarding the main purpose, I try to show that theoretical terms are neither reducible to observables nor they can be dispensed with. Hence in scientific theories there always remains a metaphysical part. Regarding the second purpose I discuss ontic structural realism which holds the individualistic attributions responsible for the metaphysical parts in theories and suggests that non-individualistic interpretation of theoretical terms is possible. The legitimacy of Ontic structural realism&rsquo / s suggestion, as its advocates claim, lies within quantum facts.

As early as 1958 John McCarthy stressed the importance of formulating common sense knowledge, and common sense reasoning, in a rigourous manner. Today, this is considered to be the central problem in Artificial Intelligence (AI). A strong advocate of this view is Patrick Hayes, who in 1974 argued that fuzzy logic was not a useful mechanism for representing vague terms, and suggested a better formalism could be developed using Zeeman's Tolerance Geometry. Five years later, Hayes complained about AI's emphasis on toy world's and suggested that a suitable project would be to formalise our common sense knowledge of the (everyday) physical world. A project now known as Naïve Physics (NP). In this project, Hayes discussed his attempts at describing the intuitive notion of objects touching using topological techniques, and indicated that Tolerance Geometry would be a better framework for capturing this notion. This thesis investigates Hayes' suggestion of developing Tolerance Geometry into a formal framework in which one can capture such intuitive terms as bodies touching, and characterising such vague terms as being tall. The analysis in this thesis begins with a (formal) investigation of the Sorites paradox. This puzzle is singled out because it clearly illustrates the problems raised by any formal analysis of vagueness in any language. The analyses of vagueness indicate that vague predicates possess continuous interpretations, and thence demonstarte the need for a spatial structure to be incorporated into the formalised metalanguage. This metalanguage then provides the framework for the proof that the Sorites is insoluble in a logic with a truth-set given by {0,1}, but consistent in a logic with truth-set given by {0,u,1}. Furthermore, this investigation reveals that Zadeh has confused the notions of continuity and the continuum, and therefore his theory of fuzzy sets rest on a mistaken assumption.

This thesis aims to throw an illuminating light on the as yet neglected concept of nothing in Kant’s system, a concept which is taken into consideration, by Kant, in accordance with the guiding thread of the categories of the understanding. My main argument is that Kant has a fourfold division of nothing and each has a transcendental function in his system. This function is basically a limiting one; setting up negative determinations without which Kant’s system would have never been constituted as it is now. It is shown in the thesis that the concept of nothing is divided basically into four: first, nothing as ens rationis that limits and thereby protects knowledge, secondly nothing as nihil privativum that defines the boundaries of phenomenal reality, thirdly nothing as ens imaginarium that makes possible the unity of experience and finally, nothing as nihil negativum that draws the lines of logical thinking. All make, in the last resort and by being the concepts of the opposite, experience possible. The thesis consists of four chapters. The first chapter is an exposition of all four divisions of nothing, the second is the display specifically of the concepts of ens rationis and nihil negativum, and the third is of the concepts of ens imaginarium and nihil privativum. The auxiliary argument of the thesis is that while Hegel makes a strong charge of externality against and thereby severely criticizes the Kantian concept of the thing-in-itself, - the concept of which I propose to be contained under the concept of ens rationis- Kant has equally convincing arguments against such a charge. This is the topic of the fourth and final chapter which has an implicit aim of creating the image of a powerful critical Hegel but on the other hand an equally enduring and war-like Kant. Kant is presented as a philosopher who has powerful responses to institute a balance between himself and his opponent. When Kant’s differing concepts of nothing are taken into account, Hegel’s attack of externality, it is maintained, appears not to have taken into account the full measure of the resources of the Kantian position. Even when it is said that the attack is against one specific concept of the thing-in-itself alone, Kant still seems to have enough resources for toleration and defence indeed.