Radicals, like other functional groups, may be classed as nucleophiles or electrophiles depending upon their character. Much has been done in the past to determine the· nucleophilicity or electrophilicity of a wide ra~ge of radicals, but it .. does not appear that the philicity ofthe aryl radical has yet been determined. A competitive cyclisation of an aryl radical to one of two alkyl chains containing olefins ofdiffering electron density was undertaken to determine aryl radical philicity. Prior to cyclisation, synthesis of the precursors was required, starting from simple commercially available aromatic compounds. A wide range of allyloxy aromatic compounds with different substituents on the two olefins was synthesised. In the course of the required multi-step synthesis many previously unreported compounds were isolated and fully characterised, including crystal X-ray diffraction studies where crystals were obtained. To investigate the effects of different electron density in the aryl ring a further range of competitive cyclisation precursors were synthesised with an ester group para to the site where the aryl radical is formed. Studies into the synthesis of a competitive cyclisation precursor with olefin bearing side chains with no heteroatom were also undertaken. The procedure for the cyclisation reactions and subsequent work-up was optimised under both conventional and microwave methodology. Analysis of the products was performed using both quantitative and qualitative analytical techniques. Quantitative analysis was performed using gas chromatography, IH NMR spectroscopy with an internal standard and isolation of products. Qualitative analysis was performed using both ID and 2D NMR spectroscopy. Analysis of the results of the competitive cyclisation reactions show beyond reasonable doubt that the aryl radical is nucleophilic in character.

There seems to exist a tension between our metaphysical and phenomenological commitments in the free will debate. On the one hand, I argue that at the metaphysical level we cannot coherently defend the belief that we are morally responsible in the sense that we deserve to be rewarded and punished for our actions, where desert-entailing moral responsibility is the primary understanding of moral responsibility presupposed in the free will debate. I argue that we are responsible for our actions but only in the weaker sense, termed ‘attributability’ by Gary Watson. On the other hand, we are allegedly unrenounceably committed at the phenomenological level to conceiving of, and treating, ourselves and one another as morally responsible beings in the desert-entailing sense. P. F. Strawson famously defends this claim in his seminal work, ‘Freedom and Resentment’. In my thesis I will set out this tension by exploring both commitments in turn. I then aim to show that the tension can be dissolved by arguing, contra P. F. Strawson, that our phenomenological commitment is not in fact unrenounceable. The dissolution of this tension entails, I argue, that we must examine our conception of self and other. We must explore the implications of adopting a position which denies that we are morally responsible beings for our life-hopes, personal feelings, inter-personal relationships and projects. Most importantly, I argue that we must renounce our current retributive condemnatory practices which are based on the unjustified belief that we are morally responsible beings.

Doctor of Philosophy / Department of Mathematics / Ivan Blank / In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such operator L and at any point [chi]₀ in the domain, there exists a nested family of sets { D[subscript]r([chi]₀) } where the average over any of those sets is related to the value of the function at [chi]₀. Although it is known that the { D[subscript]r([chi]₀) } are nested and are comparable to balls in the sense that there exists c, C depending only on L such that B[subscript]cr([chi]₀) ⊂ D[subscript]r([chi]₀) ⊂ B[subscript]Cr([chi]₀) for all r > 0 and [chi]₀ in the domain, otherwise their geometric and topological properties are largely unknown. In this work we begin the study of these topics and we prove a few results about the geometry of these sets and give a couple of applications of the theorems.

This thesis shows the ways in which the concepts of freedom and responsibility are related, and how indeed they illuminate each other. In Part One, it is shown that both are based on a concept of action, and it is thus with an analysis of action that a theory of freedom and responsibility must begin. Actions are first differentiated from events, so that conditions which must obtain from an event to be an action are specified. The concept of responsibility may then be used to illuminate action by showing how excuses indicate ways in which actions can fail. From this analysis, an analysis of action in the full sense emerges, namely, that an action in the full or unqualified sense is that to which no excuses are applicable. Action in the full sense is thus linked to responsibility in the full sense. The analysis of action shows that the breakdown of an action is the loss of control over its effects, and action in the full sense thus obtains where no breakdown occurs. Conscious control over an action is the control of an action's effects, which is the realization of intentions, and the control of intentions, which is what may be analyzed as rationality. Conscious control over an action, or agency, constitutes freedom on the plane of individual action. Thus, from the concept of responsibility emerges a concept of action and of agency which indicates what freedom is. Yet, it is the actual structure of action upon which the action of responsibility rests. The theory of freedom is defined in Part Two against the incompatibilist position that if determinism is true, neither freedom nor responsibility exist. It is shown that causal determinism does not rule out actions being free in the sense required for an individual to be responsible; for them as a theory of action shows that it is not an action's being caused but the nature of its causes which makes it free or unfree. If the action is caused so that it is in the conscious control of the agent, it is free. The rest of Part Two examines moral practices such as praise and blame in light of the limits determinism places on them. It is necessary to show what rational or justifiable grounds there could be for practices such as praising and blaming in any theory of freedom and responsibility. Part Three shows that agency, or control over an action, is extendable over the values upon which actions are based. Control over values is achieved by the individual consciously choosing values in awareness of being responsible for those choices and values. What the Existentialists call "Authenticity" is thus a fuller degree of freedom and of agency. This analysis of authenticity does not focus on how authenticity is a response to a value question posed by nihilism; but on how authenticity is an extension of our regular concepts of freedom and responsibility. It is shown that authenticity, when it is accompanied by full agency (as that notion is developed in Part One) is freedom and responsibility in the highest degree. / Arts, Faculty of / Philosophy, Department of / Graduate

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<p> This thesis deals with the construction of Free Lattices on various sets of generators, ranging from a set of unordered generators to a countable set of chains. It also considers sublattices of the structures presented.</p> / Thesis / Master of Science (MSc)

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