The dissertation investigates the relations between philosophy and mathematics in Plato’s thought through a close examination of the corpus of mathematical examples, that is mathematical analogies, similes, images and digressions introduced in order to explain and develop a broad array of philosophical issues. Sometimes extremely obscure, sometimes ostentatiously elementary, most mathematical examples are rather odd and puzzling, and perplex and fascinate common readers as well as scholars. Some of them constitute invaluable sources for historians of ancient science working on pre-euclidean mathematics and provide hints on the progresses of mathematics in the Academy. In addition, they allow a reconsideration of central issues of Plato’s philosophy of mathematics, such as the ontological status of mathematical entities, the methods and the epistemological status of mathematics, and its function. Complementarily, they perform a pivotal function on the philosophical dimension because they clarify, and often problematize, central problems of Plato’s reflection. By focusing on exempla, the dissertation aims at investigating both their mathematical content and their philosophical significance. The connection between Plato and mathematics has been thoroughly investigated by scholars of ancient philosophy and historians of ancient mathematics. Despite the voluminous literature on this topic, most studies are devoted to few selected passages. As a result, a number of examples have been neglected, both because they seem too bizarre to be taken seriously or because they contain elementary mathematical theories which seem not to deserve a serious attention. By appreciating, beside the most well-known passages, also these apparently irrelevant examples, the research aims at casting light on their mathematical as well as on their philosophical relevance. Furthermore, in many reconstructions examples are often isolated from their argumentative and dramatic context. By taking seriously into account the context and by stressing the intersections between the philosophical and the mathematical dimension, the research aims at establishing what function do mathematical examples have in their philosophical framework, that is trying to define to what extent and in which sense they are endowed with an exemplary function. The dissertation is divided into two main parts. The first part addresses methodological considerations as well as aims and objectives of the research (1.1). Furthermore, it contains a literature review on Plato’s account of mathematics and on mathematics in Plato’s time (1.2) and outlines the research’s innovative aspects with respect to the state of the art (1.3). The second part consists in a systematic commentary on a number of mathematical examples. The commentary is structured as follows: after a brief introduction and a translation, each passage is placed in its argumentative and dramatic context. Then specific textual problems are addressed, devoting particular attention to mathematical terminology, which is in most cases ambiguous and cryptic. Finally, each passage is interpreted trying to shed light both on its function in the clarification of the philosophical issues under discussion and on its relevance for the history and philosophy of mathematics.
Paradeigmata: Esempi e modelli matematici in Platone
MARONGIU, LAURA
2019-06-18
Abstract
The dissertation investigates the relations between philosophy and mathematics in Plato’s thought through a close examination of the corpus of mathematical examples, that is mathematical analogies, similes, images and digressions introduced in order to explain and develop a broad array of philosophical issues. Sometimes extremely obscure, sometimes ostentatiously elementary, most mathematical examples are rather odd and puzzling, and perplex and fascinate common readers as well as scholars. Some of them constitute invaluable sources for historians of ancient science working on pre-euclidean mathematics and provide hints on the progresses of mathematics in the Academy. In addition, they allow a reconsideration of central issues of Plato’s philosophy of mathematics, such as the ontological status of mathematical entities, the methods and the epistemological status of mathematics, and its function. Complementarily, they perform a pivotal function on the philosophical dimension because they clarify, and often problematize, central problems of Plato’s reflection. By focusing on exempla, the dissertation aims at investigating both their mathematical content and their philosophical significance. The connection between Plato and mathematics has been thoroughly investigated by scholars of ancient philosophy and historians of ancient mathematics. Despite the voluminous literature on this topic, most studies are devoted to few selected passages. As a result, a number of examples have been neglected, both because they seem too bizarre to be taken seriously or because they contain elementary mathematical theories which seem not to deserve a serious attention. By appreciating, beside the most well-known passages, also these apparently irrelevant examples, the research aims at casting light on their mathematical as well as on their philosophical relevance. Furthermore, in many reconstructions examples are often isolated from their argumentative and dramatic context. By taking seriously into account the context and by stressing the intersections between the philosophical and the mathematical dimension, the research aims at establishing what function do mathematical examples have in their philosophical framework, that is trying to define to what extent and in which sense they are endowed with an exemplary function. The dissertation is divided into two main parts. The first part addresses methodological considerations as well as aims and objectives of the research (1.1). Furthermore, it contains a literature review on Plato’s account of mathematics and on mathematics in Plato’s time (1.2) and outlines the research’s innovative aspects with respect to the state of the art (1.3). The second part consists in a systematic commentary on a number of mathematical examples. The commentary is structured as follows: after a brief introduction and a translation, each passage is placed in its argumentative and dramatic context. Then specific textual problems are addressed, devoting particular attention to mathematical terminology, which is in most cases ambiguous and cryptic. Finally, each passage is interpreted trying to shed light both on its function in the clarification of the philosophical issues under discussion and on its relevance for the history and philosophy of mathematics.
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