Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1991. / Includes bibliographical references (p. 72-74).

Thesis--Bonn. Extra t.p. with thesis statement inserted. / Includes bibliographical references (p. 45).

Thesis--Bonn. Extra t. p. with thesis statement inserted. / Bibliography: p. 45.

I argue the science of medicine and medical analogy in Plato provides the grounds for Plato’s formulation of his metaphysics, epistemology, psychology, and ethics. The metaphysics of the Forms, as known by the argument from the sciences, can be derived from medical analogy when accompanied by knowledge of ancient Greek medicine. Plato’s realism regarding non-spatiotemporal objects and his understanding of them as explanations for identities, functions, and ends are thoughts obtainable to one who reflects on the contemporaneous science of medicine. Similarly, Plato’s psychology, namely his parts of the soul doctrine, psychological egoism, and nonrationalism, can all be explained economically by light of medical analogy. Thus, if one traces the motivation for these arguments in medical analogy back to their source in the science of medicine, one gets the result that Plato’s big ideas stand on the science of medicine as his intellectual forbearer. Plato, just like the rest of us, thinks by means of the technologies of his day. This situates Plato’s philosophy in the technologies and sciences that surround him in a way previously unexplored.

We investigate the action of the Atkin operator on spaces of overconvergent p-adic modular forms. Our contributions are both computational and geometric. We present several algorithms to compute the spectrum of the Atkin operator, as well as its p-adic variation as a function of the weight. As an application, we explicitly construct Heegner-type points on elliptic curves. We then make a geometric study of the Atkin operator, and prove a potential semi-stability theorem for correspondences. We explicitly determine the stable models of various Hecke operators on quaternionic Shimura curves, and make a purely geometric study of canonical subgroups.

This dissertation is a study of the ontological foundations of true and false speech in Plato’s Sophist. Unlike most contemporary scholarship on the Sophist, my dissertation offers a wholistic account of the dialogue, demonstrating that the ontological theory of the “communing” of forms and the theory of true and false speech later in the dialogue entail one another. As I interpret it, the account of true and false speech in the Sophist is primarily concerned with true and false speech about the forms. As Plato sees it, we can only make true statements about spatio-temporal beings if it is possible to make true statements about the forms. Statements about the forms, however, make claims about how forms “commune” with other forms, that is, how forms are intelligibly related to and participate in one another. If forms stand in determinate relations of participation to other forms, however, then forms, as the relata of these relations, must compose structured wholes. Yet if they compose structured wholes, there must be a higher order normative principle that explains their structure. This creates a regress problem. In order to ground the structure of spatio-temporal beings, forms must be the highest explanatory principles. The theory of the “communing” of forms, however, makes it seem as if the forms require further explanation. This dissertation argues (1) that in the Sophist Plato solves the regress problem and (2) that, by doing so, he is able to ground true and false speech about the forms. I demonstrate that he solves the regress problem by differentiating a form’s nature from a form qua countable object. Then I show that this distinction between a form’s nature and a form qua countable object explains how true and false statements about the forms are possible.

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[pt] A tese pretende investigar a ontologia defendida pelo personagem Sócrates nos diálogos platônicos. Em oposição à interpretação majoritariamente aceita, que atribui ao personagem Sócrates a adesão a duas ontologias distintas, defendo a hipótese de que o Sócrates dos diálogos platônicos argumenta consistentemente a partir de uma única proposta ontológica. Esta proposta consiste na postulação de entidades inteligíveis realmente existentes que atuam como causa das propriedades dos objetos sensíveis. A tese divide-se em duas partes. Na primeira parte, começo por analisar as particularidades da composição platônica, assim como a formação do paradigma atual de leitura das obras de Platão. Em um segundo momento, tomo como foco os diálogos iniciais e defendo que a ontologia subjacente à argumentação de Sócrates nestas obras é a mesma que encontramos nos diálogos médios. No último capítulo da primeira parte, apresento a argumentação socrática dos diálogos médios e demonstro como, nestas obras, a ontologia dos diálogos iniciais é apresentada de maneira explícita e mais informativa. A segunda parte da tese consiste em uma análise das críticas à Teoria das Ideias que encontramos no diálogo Parmênides. No primeiro momento desta segunda parte, argumento que o Sócrates do Parmênides está, novamente, defendendo a mesma proposta ontológica dos diálogos médios e iniciais. Posteriormente, demonstro como as críticas formuladas pelo personagem Parmênides são válidas e realmente apresentam problemas relevantes para teoria socrática. / [en] This dissertation aims to investigate the ontology proposed by the character Socrates in the Platonic dialogues. In opposition tothe mostly accepted interpretation which attributes to the character Socrates the adoption of two distinct ontologies, I defend the hypothesis that the Socrates of the Platonic dialogues consistently argues from within a single ontological theory. This theory consists in the postulation of real and existing intelligible entities that act as the cause of the properties of sensible objects. The dissertation is divided in two parts. In the first part, I analyze the particularities of the Platonic composition as well as the construction of the actual reading paradigm of the Platonic works. In a second moment, I start investigating the first dialogues and claim that the ontological theory that underlies Socrates arguments in these works is the same as the one we can find in the middle dialogues. In the last chapter of the first part, I expose the Socratic arguments from the middle dialogues and I show how, in these woks, the underlying ontology of the first dialogues is more explicitly and informatively presented. The second part of the dissertation consists in an analysis of the critiques of the Theory of Forms that we find in the Parmenides dialogue. In the first moment of this second part, I argue that the Socrates from the Parmenides is again defending the same ontological theory from the middle and first dialogues. Afterwards, I show how the critiques constructed by the character Parmenides are valid and do present significant problems to the ontological theory of Socrates.

Cette recherche se propose de montrer l’existence de ce que nous appelons des « niveaux psychologiques » chez Platon, en empruntant à la théorie des types logiques, formulée par B. Russel et A.N. Whitehead, puis revisitée par l’anthropologue G. Bateson au sein du mouvement cybernétique. Par « niveaux psychologiques », nous entendons des états psychiques d’être en relation avec le réel sur le mode analogique. Nous défendons la thèse selon laquelle la théorie platonicienne des formes n’oblige pas à penser des degrés de réalité de la chose mais bien un processus de réalisation de l’objet en soi par le sujet de l’expérience. En tant que tels, les niveaux psychologiques correspondent donc à des niveaux d’apprentissages de la réalité. Ainsi, la méthode dialectique utilisée par Socrate accompagne le progrès de l’âme, pilotée par l’intellect, au moyen de la raison qui relie et distingue les phénomène sensibles. Cette double fonction caractérise l’exercice du langage et rend compte du mouvement de la pensée. La succession et la répétition des ajustements opérés à partir de l’expérience conduisent ainsi à une meilleure définition de la forme de l’objet en soi, i.e. une saisie plus nette de ce qui, de l’intelligible, passe dans le sensible. De ce fait, la théorie platonicienne de la connaissance apparaît comme une théorie du processus et non comme une théorie du contenu de savoir, qui mène du théâtre intérieur de nos représentations, limitées par le temps d’une vie et l’espace d’un corps, au spectacle de l’infini. En outre, parce qu’il existe un seul chemin pour penser ce qui est réellement, l’examen psychologique des causes de soi rejoint nécessairement la recherche philosophique sur les causes du monde, dans une cosmologie. / This research intends to demonstrate the existence of what we call "psychological levels" in Plato's philosophy, taking from the theory of logical types, formulated by B. Russel and A.N. Whitehead, then restyled by the anthropologist G. Bateson, inside the cybernetic movement. By "psychological levels", we mean psychic states of being in relation with reality under an analogical scheme. We defend the argument that Plato’s theory of Forms does not imply degrees of reality in the thing but a process of realization of the object in itself through the subject experiencing it. As such, psychological levels refer to levels of learning what is reality. Thus, the Socratic dialectical method accompanies the soul’s progress, driven by the intellect, thanks to reason which relates and distinguishes the sensible phenomena. This double function characterizes what language is and gives reason for the movement of thought. Succession and repetition of the adjustments made from the experience of the thing lead to a better definition of the Form of the object in itself, i.e. a clearer acquisition of the intelligible part of the thing that is passing through its sensible expression. Hence, Plato’s theory of knowledge stands like a process theory more than a content theory, by conducting the search for truth from the inner theatre of our representations, limited by a lifetime and the space of a body, to the spectacle of the infinite. Furthermore, since there is only one path in order to think what exists in reality, the psychological research into the causes of thyself necessarily fits in the philosophical research into the causes of the world — a cosmology.

摘要 本篇論文的討論起點來自柏拉圖如何面對靈魂能夠認知真理的這個可能性。柏拉圖設立那與變動的感覺現象完全分離的「不變動的『相』」作為知識得以成立的條件，這個歷史緣由可從亞里士多德的記載當中知道：一方面，柏拉圖認同克拉梯樓斯與赫拉克利圖學派所主張的感覺現象的永遠流動、無一停留，並因此認為絕不可能有關於感覺現象的知識，然而，另一方面，那致力於倫理事物研究的蘇格拉底則堅持必定有那可被定義的知識對象得以被思考與認知；由於受到這兩方所堅持的信念，柏拉圖則在為了拯救現象並使思考與知識得以可能的情況下，他設立了那必須與變動的感覺現象完全分離的相來作為感覺現象之所以如此存在的原因，並在透過那分有相的感覺現象當中，靈魂得以思考並回憶起關於相的知識，而由此拯救現象並保全靈魂得以思考且獲得知識的可能性。 然而，柏拉圖的分離相論卻有可能引發諸多困難，這主要可由《巴曼尼德斯篇》裡的少年蘇格拉底所遭遇到的三個困境所表現出來：○1少年蘇格拉底對於是否有卑下者的相的存在，顯得猶疑不定；○2由於無法回答相與現象之間到底是如何分有，以致於分有成為不可能；○3更進一步地，正是由於相與現象彼此的完全分離，以致於原本肩負拯救現象這使命的相，到頭來卻反而根本無法拯救現象，而且也面臨無法為人所知的這個最大困境。 這三個困境其實正是柏拉圖真理之路---愛智者如何能擁有那與現象完全分離的相的知識？---所蘊含的兩個一體兩面的論題：第一，思考與知識的可能性如何成立？也就是，相如何拯救現象？第二，愛智者要以什麼樣的方法才能正確地獲得相的知識以成為真正的哲學家？關於第一個論題，筆者認為，柏拉圖在《巴曼尼德斯篇》第二部分的八組推論當中提出一種具有數特徵的存有論，這個存有論綿密、細緻地論說《蒂邁歐篇》裡的宇宙生成論以及「未成書研究」裡的原理論，在這當中，相拯救現象的可能性乃在於---神以其意願與叡智將相形塑於這個數存有的世界並因此使那些在場域裡生滅變化的現象獲得一致性，如此，神的意願（i.e.善）乃作為相得以拯救現象的最具統馭力的原因與原理；關於第二個論題，那能使少年蘇格拉底獲得真理以成為哲學家的訓練，正是那以合理論說所掌握的相為對象的訓練，筆者認為，柏拉圖在這個訓練當中，試圖透過假設法的運用，使得愛智者能緊守在對「是」（i.e.相）的追求上，並得以在一步步的往上探求當中，在最後能以最終的決定性原因---善---來束縛住所有的相，如此，當愛智者能在「善」的指導下以合理論說來正確地指出每個相的真實本質時，這個愛智者也就成為真正的哲學家。 在這樣的解決方式當中，柏拉圖證成了靈魂能夠認知真理的可能性，為自己的真理之路尋得一個合理的立足點。柏拉圖在這當中所奮力搏鬥的，主要並不是亞里士多德在《物理學以後諸篇》A 6.987a33-b10所提及的這些哲學家，而是歷史上的這位伊利亞哲學家---巴曼尼德斯：柏拉圖分離相論的核心來自巴曼尼德斯其毫無生滅變動的「完滿的是」，然而，柏拉圖拯救現象以及保全思考與知識的可能性的這個企圖，卻又是必須對巴曼尼德斯的「完滿的是」提出批判。而在柏拉圖藉由這兩個假設與八組推論來與巴曼尼德斯奮力搏鬥當中，柏拉圖所完成的不僅僅只是解決分離相論所可能引來的困境，而更是走上一條不同於巴曼尼德斯的真理之路，因為現象的拯救是柏拉圖所主要異於巴曼尼德斯的地方，而那使得現象得以被相所拯救的最具統馭力的原因與原理乃在於---宇宙父親的意願與叡智，而這乃作為柏拉圖自己的真理之路的最終磐石。 關鍵詞：相論，分離，分有，善，假設法，柏拉圖，巴曼尼德斯，〈未成書研究〉，《巴曼尼德斯篇》，《蒂邁歐篇》。 / Abstract The aim of this thesis is to show that how Plato might deal with the possibility for soul of knowing the truth. The historical reason for Plato positing the invariable Forms, which are totally apart from the variable sensible things, is remarked by Aristotle that: on the one hand, having been agreed with Cratylus and the Heracllitean doctrines that all sensible things are always in a state of flux and that no science of them exists, yet on the other hand, taking into account the Socrates’ efforts to find general definitions of ethical terms, Plato, having been inspired by both views, thinks that there must be some invariable things, i.e. Forms, which are totally apart from the variable sensible things and could only be thought with logos（or reasonable account）, as the causes of the sensible things. Therefore, the soul could recollect and think of Forms by perceiving these sensible things, which participate in the corresponding Forms. Hence, Plato saves the phenomena and secures the possibility for soul of thinking and knowing the truth by his theory of Forms. However, there might be many problems that arisen from Plato’s theory of Forms. These problems are shown mainly by the three perplexities, which are encountered by the young Socrates in the Parmenides. First, the young Socrates is undecided about whether the base things could have their Forms, second, having been unable to solve the problem of the sharing between the sensible things and Forms, the young Socrates finally has to accept the impossibility of sharing, third, further, just owing to this totally separation that is between the sensible things and Forms, Forms finally could not save the phenomena and could not be known by anyone. Actually, the three perplexities are the two topics of Plato’s way of truth, which is that how the lover of wisdom could know the Forms that are totally separate from the sensible things. The first topic is that, in what way the possibility of thinking and acquiring knowledge could be secured. That is, how the phenomena could be saved by Forms? The second topic is that, in what way the lover of wisdom could acquire the truth and becomes the real philosopher. As for the first, I think that Plato claims a kind of ontology, which has numerical character, in the second part of the Parmenides. This ontology provides deliberately the cosmogony of the Timaeus and the theory of the Principles in the Unwritten Doctrines that could justify the possibility of the phenomena that are saved by Forms. This possibility lies in the god’s nous and will, i.e. the world that has numerical character is fashioned by the god with Forms as model, and then the becoming phenomena that cling to the receptacle are saved and intelligible. Therefore, the god’s will is the supremely valid cause and principle of this possibility. As for the second, this exercise that can make the young Socrates as a real philosopher if he takes it into practice is the training, which takes Forms as its objects and be practiced in hypothetical method. I think the reason for Plato of using the hypothetical method is that this hypothetical method can make the lover of wisdom to cling to Forms when he is putting this exercise into practice, and in this upward process systematically, finally, he can fasten all the Forms with the final cause, i.e. the good. Therefore, when the lover of wisdom could show the real essence of each Form with reasonable account under the guidance of the good, he at that time is a real philosopher. Under this solution, Plato justifies the possibility for soul of knowing the truth, and makes his way of truth possible. In this fighting, those with whom Plato fights are not those philosophers that are remarked by Aristotle in Metaphysics A 6.987a33-b10, but the philosopher of Elea, Parmenides. On the one hand, the key point of Plato’s theory of Forms is coming from Parmenides’ concept of Being, which is ungenerated and imperishable, yet on the other hand, the attempt for the possibility of saving the phenomena and for soul to know the truth is urging Plato to put Parmenides’ claim to the question. Then what Plato has done in this fighting, which mainly occurs in the second part of the Parmenides, is that as he is solving these perplexities, he at the same time is stepping upon another way of truth, which is different from Parmenides. In this fighting, saving phenomena is the main difference between Plato and Parmenides. The god’s nous and will is the supremely valid cause and principle of the saved phenomena and this most supreme cause is the coping-stone for Plato’s way of truth. Keywords: Plato’s theory of Forms, separate, participate, the good, the hypothetical method, Plato, Parmenides, the Unwritten Doctrines, the Parmenides, the Timaeus.