Plato and the Method of Analysis (original) (raw)
Related papers
Plato's Use of Geometrical Logic
2003
Socrates’ brief mention of a complex problem in geometrical analysis at Meno (86d-87c) remains today a persistent mystery. The ostensible reason for the reference is to provide an analogy for the method of hypothesis from the use of hypotheses in analytic geometry. Both methods begin by assuming what is to be demonstrated and then show that the assumption leads to a well-founded truth father than something known to be false. But why did Plato pick this particular problem in analysis and why at this particular place in the inquiry? For those of us who view the dialogues as pedagogical puzzles for readers of all time to “scour” out the subtle and complicated details, this is an unquiet mystery that demands further examination. In this paper I will defend the claim that Plato had developed a powerful new heuristic method for the clarification and resolution of a broad range of philosophical problems. This method, based on the techniques of inquiry used in geometry, was a kind of concep...
Mathematical reasoning in Plato’s Epistemology
2014
4 Introduction 5 Aims of the thesis 7 Statement of Terminology 9 Section One: The Republic 31 Chapter One: Introducing the Sun, Line and Cave 33 Chapter Two: Readings of the Allegories in Context 44 i. Knowledge, Belief and Gail Fine 44 ii. Propositions or Objects: Gonzalez on Fine 56 Chapter Three: My Reading 68 i. How Seriously Should We Take the Allegories? 68 ii. Ascending the Scale 78 iii. Noēsis and the Role Definition in Plato’s Epistemology 109 Chapter Four: A Closer Look at dianoia 112 i. The Dianoectic Image 113 ii. The Hypothesis 134 iii. Theaetetus: Hypothesis and Image in the Search for a Definition 146 Section Two: The Meno 152 Chapter One: Definition in the Meno 155 a. Meno’s Definitions 156 b. Socrates’ Definitions 159 c. What is Plato’s preferred answer? 162 ii. What role do definitions play in Plato’s epistemological scale? 169 a. Definition and Essence 170 b. Gail Fine and the Meno 171 Chapter Two: Aporia and the Psychology of Mathematics 181 i. What is aporia? 18...
The philosophical use of mathematical analysis
2000
This dissertation defends the thesis that Plato's employs methods of philosophical analysis that are akin to and based upon mathematical analysis. It identifies and describes three kinds of ancient mathematical analysis, rectilinear, dioristic, and poristic.
Plato, Mathematics, and the Forms: The Perceptual Foundation of Platonic Theory
That Plato was fascinated with mathematics and saw in it the basis for the theory of the Forms is a truism. Most commentators argue that this linkage was based on a rational deduction discovered through argument or dialectic. In other words, the philosopher-kings were able to apprehend the Forms or Ideas as a result of their ability to reason. The Forms themselves were simply the product of a rather mechanical process which the philosophers were taught. This exposes Plato to severe criticism, however, since it is not clear that such a process cannot be widely taught. If that is true, then his reservation of political authority to a select group of philosophers has struck many as fairly arbitrary and likely a mask for more sinister motives—most famously for Karl Popper, making Plato the originator of the totalitarian impulse. I wish to suggest that Plato’s Forms were based, not on a process of rational reflection, but on a kind of perception that I shall term “mathematical visualization.” Instead of being a product of a reflective process, they are akin to what mathematicians and others “see” when they consider problems and relationships. I consider the implications of this suggestion for Plato’s justification for philosophic rule in the Republic.
Amicus Plato sed...': Fowler's New Mathematical Reconstruction of the Mathematics of Plato's Academy
Ann Sci, 2002
He knew perfectly well that what you call criticism is engendered by respect and aVection, not by any feelings of aversion. (Peter Ustinov)1 Like the Druzes, like the moon, like death, like next week, the distant past is one of those things that can enrich ignorance. It is in nitely malleable and agreeable, far more obliging than the future and far less demanding of our eVorts. It is the famous season favored by all mythologies. (Jorge Luis Borges)2 Professor Ryle has produced a biography in which almost none of the central facts and events has ever appeared in writing before.. .. What cannot be re ected in short compass is the intricacy and ingenuity with which it is all pieced together out of hints, echoes, incongruities and inconsistencies. For there is not one explicit ancient textual basis for a single one of the substantive statements. 'We have to make do with straws,' writes Professor Ryle. True, but though we know all about making bricks without straw, this must be the rst serious attempt in history to make them with straw alone.. .. The fact is that the materials are lacking for a biography of Plato. And, though it comes oddly from a historian to a philosopher, I suggest that it doesn't much matter. (Moses I. Finley)3 'This is an updated second edition of a very well received and controversial book, in which the author presents a highly original interpretation of early Greek mathematics', brags the publisher on the dust cover of the new edition. It is an essentially true claim, although, for the sake of accuracy, I would have moved 'very' and placed it before 'controversial'; but there is no question that the interpretation, in its fullness and detailed speci city, is highly original, even if drawing on ideas put forward in