My thesis is an exposition and defence of Aristotle's philosophy of mathematics. The first part of my thesis is an exposition of Aristotle's cryptic and challenging view on mathematics and is based on remarks scattered all over the corpus aristotelicum. The thesis' central focus is on Aristotle's view on numbers rather than on geometrical figures. In particular, number is understood as a countable plurality and is always a number of something. I show that as a consequence the related concept of counting is based on units. In the second part of my thesis, I verify Aristotle's view on number by applying it to his account of time. Time presents itself as a perfect test case for this project because Aristotle defines time as a kind of number but also considers it as a continuum. Since numbers and continuous things are mutually exclusive this observation seems to lead to an apparent contradiction. I show why a contradiction does not arise when we understand Aristotle properly. In the third part, I argue that the ontological status of mathematical objects, dubbed as materially [hulekos, ÍlekÀc] by Aristotle, can only be defended as an alternative to Platonism if mathematical objects exist potentially enmattered in physical objects. In the fourth part, I compare Aristotle's and Plato's views on how we obtain knowledge of mathematical objects. The fifth part is an extension of my comparison between Aristotle's and Plato's epistemological views to their respective ontological views regarding mathematics. In the last part of my thesis I bring Frege's view on numbers into play and engage with Plato, Aristotle and Frege equally while exploring their ontological commitments to mathematical objects. Specifically, I argue that Frege should not be mistaken for a historical Platonist and that we find surprisingly many similarities between Frege and Aristotle. After having acknowledged commonalities between Aristotle and Frege, I turn to the most significant differences in their views. Finally, I defend Aristotle's abstractionism in mathematics against Frege's counting block argument. This whole project sheds more light on Aristotle's view on mathematical objects and explains why it remains an attractive view in the philosophy of mathematics.

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Legalism, as one of the most useful philosophies of government, has attracted a great deal of scholarly attention. The work of Han Fei—one of the most influential proponents of Legalism—has been scrutinized and critiqued for centuries as immoral. I intend to show Legalism, especially the Han Feizi, is moral through focusing on four aspects of Han Fei’s work. First, his understanding of human nature. Han Fei states people are born with a hatred of harm and a love of profit. This understanding of human nature can never lead to a cognitive distortions in governing. So it is a moral basic of a philosophy. The second element is a focus on the context of Han Fei’s writings. If his works are read in detail back to his age, one cannot reach an immorality conclusion. Then, based on his understanding of subjects and his correspondingly suggested strategies, his goal is moral because he wants to built a peaceful and stable society, which was unobtainable at that time. Finally, Han Fei’s conception of punishment, which has been thought of immoral, actually is a moral tool to protect the majority of subjects who are innocent.

In this thesis I try to answer the question of what attitude the ancient sceptics had towards the notion of belief. I concern myself exclusively with Pyrrhonic scepticism, as it was described by Sextus Empiricus in his book Pyrrhoniai hypotyposeis. Pyrrhonic scepticism was an epistemological system with ethical ramifications, that questioned most of the conventional wisdom of the time, I begin by evaluating two infleuntial readings, by Michael Frede and Casey Perin. I then go on to make my own assessment. Ultimately, I show why Frede's view is the more plausible; the sceptics allowed themselves to hold beliefs about reality, not just appearance.

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Nesta investigação tenho por fim estudar a translatio da lexicografia conceitual que parte do verbo grego ser (einai) chegando ao verbo latino ser (esse) à luz do de Hebdomadibus de Boécio. Neste percurso me deparo com a embriologia da doutrina dos transcendentais, na qual ser, bem e um são convertíveis ou coextensivos, como também me deparo com uma metafísica do bem, herdada pela Escolástica, pela qual tento especular Boécio em seu exercício filosófico, que consiste em tentar esclarecer o modo pelo qual as substâncias são boas nisto que são, contudo não são bens substanciais. / The aim of this study is the translatio of the conceptual lexicography following the Greek verb be (einai) through the Latin verb be (esse) in light of Boethius de Hebdomadibus. Throughout this journey I find myself facing the embriology of the doctrine of transcendentals, in which being, goodness and one are convertible or co-extensive, and I also face a metaphysics of goodness, inherited by the Scholastics, through which I then try to speculate Boethius in his philosophical endeavour, consisting in trying to clarify how substances are good in that they are, though they are not substantial goods.

This is a study of love (erōs) in Plato’s Symposium. It’s a study undertaken over three chapters, each of which serves as a stepping stone for the following and addresses one of three primary aims. First: to provide an interpretation of Plato’s favored theory of erōs in the Symposium, or as it’s referred to here, a theory of Platonic love. This theory is understood to be ultimately concerned with a practice of living which, if developed correctly, may come to constitute the life most worth living for a human being. On this interpretation, Platonic love is the desire for Beauty, ultimately for the sake of eudaimonic immortality, manifested through productive activity. Second: to offer a reading of the Symposium which attends to the work’s literary elements, especially characterization and narrative structure, as partially constitutive of Plato’s philosophical thought on erōs. Here it’s suggested that Platonic love is concerned with seeking and producing truly virtuous action and true poetry. This reading positions us to see that a correctly progressing and well-practiced Platonic love is illustrated in the character of the philosopher Socrates, who is known and followed for his bizarre displays of virtue and whom Alcibiades crowns over either Aristophanes or Agathon as the wisest and most beautiful poet at the Symposium. Third: to account for how to love a person Platonically. Contra Gregory Vlastos’ influential critical interpretation, it’s here argued that the Platonic lover is able to really love a person: to really love a person Platonically is to seek jointly for Beauty; it is to work together as co-practitioners in the art of love. The art of Platonic love is set up in this way to be explored as a practice potentially constitutive of the life most worth living for a human being.

Thesis (MPhil)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The definition and function of Socratic irony has been much disputed in contemporary scholarship. This thesis identifies some methodological difficulties in interpreting and defining Socratic irony and attempts to narrow the field of interpretation in order to facilitate the formulation of a new definition of the concept. With reference to the primary texts of Plato, Xenophon and Aristophanes, as well as some fragments, the different types of irony as employed by Socrates are identified as verbal, in the form of self-deprecation and knowledge disavowal, and physical. A review of late 18th, 19th and 20th century philosophical scholarship on the topic is done in order to gain a better understanding of the perceived functions of Socratic irony. On the basis of this, as well as the opinions of prominent classical scholars, it is argued that the function of Socratic irony in its verbal form is primarily heuristic, while the physical form is a political mode of being designed to criticise 5th-century Athenian politics. Socratic irony is then redefined to allow for these forms and functions, which are shown to be much more complex than previously thought. / AFRIKAANSE OPSOMMING: Daar word baie gedebatteer oor die definisie en funksie van die Sokratiese ironie in die onlangse navorsing. Hierdie tesis identifiseer sommige metodologiese probleme in die interpretasie en die definisie van Sokratiese ironie en poog om die veld van interpretasie te beperk ten einde die formulering van 'n nuwe definisie van die begrip te fasiliteer. Met verwysing na die primêre tekste van Plato, Xenophon en Aristophanes, asook 'n paar fragmente, word die verskillende vorme van ironie soos deur Sokrates gebruik, geïdentifiseer as verbaal, in die vorm van self-afkeuring en ontkenning van kennis, en fisies. ʼn Oorsig van die laat 18de-, 19de- en 20ste-eeuse filosofiese navorsing is gegee ten einde 'n beter begrip te verkry van die waargenome funksies van Sokratiese ironie. Op grond hiervan, asook die menings van vooraanstaande klassici, word aangevoer dat die funksie van die Sokratiese ironie in sy verbale vorm hoofsaaklik heuristies is, terwyl die fisiese vorm 'n politieke bestaanswyse is, met die doel om die 5de-eeuse Atheense politiek te kritiseer. Teen hierdie agtergrond word Sokratiese ironie dan herdefinieer om voorsiening te maak vir bogenoemde vorme en funksies wat blyk baie meer kompleks te wees as wat voorheen gemeen is.

This thesis analyses the method, purpose, and results of Aristotle's treatment of a select number of Presocratic and Platonic theses about the soul within the context of De Anima 1. Contrary to a prevalent interpretation of De Anima 1 which sees Aristotle's treatment of his predecessors' psychological views as dialectical, I argue that Aristotle treats his predecessors as having offered potentially viable hypotheses about the nature of the soul, and that these hypotheses are treated as attempts to explain the soul's basic powers. I further show that, in order to test the explanatory limits of these theories, Aristotle uses a version of the scientific method of inquiry advertised in the Prior and Posterior Analytics, which consists in setting out the basic psychological phenomena which psychology should explain, and then testing the extent to which his predecessors' definitions of the soul are able to accomplish this task. This thesis argues that, by demonstrating where his predecessors' first principles fall short, Aristotle is able to make theoretical progress towards establishing his own 'hylomorphic' first principle of soul, that soul is the 'first fulfilment of a natural instrumental body', and towards the idea that soul operates in the body of living beings as a formal, final, and efficient cause.