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.

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In my thesis, I address the question ʽWhat normative status does logic have?', to argue that logical normativity is of a weak sort, and that its constraining power is similar to that of recommendations. The thesis first discusses the notion of logical validity and logical formality, then asks whether logic is a priori and whether it can provide a priori norms for thinking. Subsequently, the issue of the bridge principles linking formal logic to informal reasoning is addressed, jointly with a brief discussion of the deontic operators included in the bridge principles. Then, the thesis addresses three criticisms of the normative role of logic with respect to rational reasoning. The first criticism is discussed in the fourth chapter; it starts from the consideration of the cognitive limitations of human agents and discusses a model of rationality that takes those limitations into account. The second criticism is analyzed in the fifth chapter; it is motivated by the empirical studies in the psychology of reasoning, and discusses human reasoning from a descriptive point of view, lending support to the model of rationality presented in the fourth chapter. The third criticism, presented in the sixth and final chapter, addresses the normative role of logic from an a priori point of view, showing how the epistemic paradoxes are crucial for determining what normative import logic has on rational reasoning. The final chapter defends the main thesis that logic has a weak import on our reasoning, which resembles a recommendation rather than an obligation.

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A project report submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. / Up to now the benefits and problems with fuzzy control have not been fully identified and its role in the control domain needs investigation. The past trend has been to show that a fuzzy controller can provide better control than classical control, without examining what is actually being achieved. The aim in this project report is to give a fair comparison between classical and fuzzy control. Robustness, disturbance rejection, noise suppression" nonminimurn phase and dead time are examined for both controllers. The comparison is performed through computer simulation of classical and fuzzy controlled plant models. Fuzzy control has the advantage of non-linear performance and the ability to capture linguistic information. Translating quantitative information into the fuzzy domain is difficult; therefore when the system is easily mathematically modelled and linear, classical control is usually better. Which controller should be used depends on the application, control designer and information available. / Andrew Chakane 2018

A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Master of Science in Mathematics. 26 August 2016. / In this thesis we analyse the issue of decidability for two modal logics which contain least binders. Towards this goal, we begin the work with a brief survey of modal logic, PDL, the modal -calculus and algebraic filtrations as exposited by Conradie et al. The first such modal logic we analyse is the fragment of the modal -calculus corresponding to PDL; the second logic is the equational theory of the class of -algebras (motivated by the least root calculus of Pratt). We offer a new, algebraic, proof for the decidability of PDL by showing that PDL has the finite model property with respect to the class of dynamic algebras. We then show that the equational theory of the class of -algebras has the finite model property with respect to the class of -algebras; this is based on the proof of Pratt but differs in an important detail. The finite model property results for these two modal logics are achieved by an algebraic filtration method based on that of Conradie et al. / LG2017

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