Download or read book Plato s Theory of Forms and Cantor s Theory of Sets written by John Acheson Faris and published by . This book was released on 1968 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Structure of Being written by International Society for Neoplatonic Studies and published by SUNY Press. This book was released on 1982-01-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neoplatonism has sometimes been seen as a species of mysticism. This volume shows that Neoplatonism has, on the contrary, a characteristic and definable structure. It presents the logic of Neoplatonism and carefully distinguishes it from the logic of other forms of philosophy.
Download or read book Reforging the Great Chain of Being written by Simo Knuuttila and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sports reporter might say that in a competition all the participants realize their potentialities or possibilities. When an athlete performs far below his usual standard, it can be said that it was possible for him to do better. But the idea of fair play requires that this use of 'possible' refers to another com petition. It is presumed that the best athlete wins and that no real possibility of doing better is left unrealized in a competition. Here we have a use of language, a language game, in which modal notions are used so as to imply that if something is possible, it is realized. This idea does not belong to the general presuppositions of current ordinary usage. It is, nevertheless, not difficult to fmd other similar examples outside of the language of sports. It may be that such a use of modal notions is sometimes calculated to express that in the context in question there are no real alternative courses of events in contradistinction to other cases in which some possible alternatives remain unrealized. Even though modal notions are currently interpreted without the presup position that each genuine possibility should be realized at some moment of the actual history, there are contemporary philosophical models of modalities which incorporate this presupposition. In his book Untersuchungen tiber den Modalkalkiil (Anton Hain, Meisenheim am Glan 1952, pp. 16-36), Oscar Becker presents a statistical interpretation of modal calculi.
Download or read book Plato and Socrates RLE Plato written by Richard McKirahan and published by Routledge. This book was released on 2012-11-12 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This valuable work of reference provides a comprehensive bibliography on all scholarly work that was published on Plato and Socrates during the years 1958-73. It thus forms an important addition to Harold Cherniss’s bibliography, which covered the years 1950-7. The author has sought to include all materials primarily concerned with Socrates and Plato, together with other works which make a contribution to our understanding of the two philosophers. The bibliography is arranged by topic and there are cross-references at the end of each section. The works in each category are arranged chronologically and then alphabetically (by author) within each year. An effort has been made to distinguish when a book has had more than one edition and when an article has been reprinted. Additionally the author has listed reviews of books and dissertations as these have come to his attention.
Download or read book Plato s Euthyphro and the Earlier Theory of Forms RLE Plato written by R E Allen and published by Routledge. This book was released on 2012-11-12 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato’s Euthyphro is important because it gives an excellent example of Socratic dialogue in operation and of the connection of that dialectic with Plato’s earlier theory of Forms. Professor Allen’s edition of the dialogue provides a translation with interspersed commentary, aimed both at helping the reader who does not have Greek and also elucidating the discussion of the earlier Theory of Forms which follows. The author argues that there is a theory of Forms in the Euthyphro and in other early Platonic dialogues and that this theory is the foundation of Socratic dialogue. However, he maintains that the theory in the early dialogues is a realist theory of universals and this theory is not to be identified with the theory of Forms found in the Phaedo, Republic, and other middle dialogues, since it differs on the issues of ontological status.
Download or read book Encyclopedia of Mathematics Education written by Louise Grinstein and published by Routledge. This book was released on 2001-03-15 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.
Download or read book Plato s Forms written by William A. Welton and published by Lexington Books. This book was released on 2002 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "theory of forms" usually attributed to Plato is one of the most famous of philosophical theories, yet it has engendered such controversy in the literature on Plato that scholars even debate whether or not such a theory exists in his texts. Plato's Forms: Varieties of Interpretation is an ambitious work that brings together, in a single volume, widely divergent approaches to the topic of the forms in Plato's dialogues. With contributions rooted in both Anglo-American and Continental philosophy, the book illustrates the contentious role the forms have played in Platonic scholarship and suggests new approaches to a central problem of Plato studies.
Download or read book The Logic of the Articles in Traditional Philosophy written by E.M. Barth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the original Dutch version of this book was presented in 1971 to the University of Leiden as a thesis for the Doctorate in philosophy, I was prevented by the academic mores of that university from expressing my sincere thanks to three members of the Philosophical Faculty for their support of and interest in my pursuits. I take the liberty of doing so now, two and a half years later. First and foremost I want to thank Professor G. Nuchelmans warmly for his expert guidance of my research. A number of my most im portant sources were brought to my attention by him. During the whole process of composing this book his criticism and encouragement were carried out in a truly academic spirit. He thereby provided working conditions that are a sine qua non for every author who is attempting to approach controversial matters in a scientific manner, conditions which, however, were not easily available at that time. In a later phase I also came into contact with Professors L. M. de Rijk and J. B. Ubbink, with both of whom I had highly stimulating discussions and exchanges of ideas. The present edition contains some entirely new sections, viz. 1-9, IV-29, V-9, V-20, VII-14 (iii), (iv), VII-17 (i), VIII-22, IX-17, IX-19, X-9 and XI-8. Section X-9 was inspired by a remark made by Professor A.
Download or read book Plato s Theory of Ideas written by William David Ross and published by Greenwood. This book was released on 1976 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plato s Arguments for Forms written by Robert William Jordan and published by Cambridge Philological Society. This book was released on 2020-08-30 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: If we are to understand why Plato had a theory of Forms, we must explain, firstly, why he thought it necessary to depart from the ontology of the Socratic dialogues; secondly, why he then posited the existence of entities that have the characteristics that he ascribes to Forms (entities that are 'unmixed', 'unchanging', 'in every way being' and so on); and thirdly, why Plato took this course when other philosophers have not done so (and even he himself and his immediate pupils were later to modify or abandon the theory). In this study, Robert William Jordan discovers an answer to these questions where we might expect to find one - namely in the arguments Plato gives us in favour of the hypothesis that there are Forms. These arguments, on analysis, reveal not just a concern with the nature of knowledge and explanation, but an interest in the analysis of the apparent contradictions that Plato in his middle period thought to be presented to the intellect by the sensible world. These contradictions, he then thought, could not be resolved except by those with knowledge of the Forms.
Download or read book Mathematics and Art written by Lynn Gamwell and published by Princeton University Press. This book was released on 2016 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell's comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians' search for the foundations of their science, such as David Hilbert's conception of mathematics as an arrangement of meaning-free signs, as well as artists' search for the essence of their craft, such as Aleksandr Rodchenko's monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked "What is art?" in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.
Download or read book David Hume s Critique of Infinity written by Dale Jacquette and published by BRILL. This book was released on 2001 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new study of David Hume s philosophy of mathematics critically examines his objections to the concept of infinity, and his alternative phenomenalist theory of space and time as constituted by minima sensibilia or sensible extensionless indivisibles.
Download or read book The Philosophers of Greece written by Robert Sherrick Brumbaugh and published by SUNY Press. This book was released on 1981-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrations include a reconstruction of the first map.
Download or read book Plato Metaphysics and the Forms written by Francis A. Grabowski and published by Continuum. This book was released on 2008-06-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important new monograph on Plato's metaphysics, focusing on the theory of the forms, which is the central philosophical concept in Plato's theory.
Download or read book Philosophy of Mathematics written by and published by Elsevier. This book was released on 2009-07-08 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Download or read book Plato s forms mathematics and astronomy written by Theokritos Kouremenos and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-22 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato’s view that mathematics paves the way for his philosophy of forms is well known. This book attempts to flesh out the relationship between mathematics and philosophy as Plato conceived them by proposing that in his view, although it is philosophy that came up with the concept of beings, which he calls forms, and highlighted their importance, first to natural philosophy and then to ethics, the things that do qualify as beings are inchoately revealed by mathematics as the raw materials that must be further processed by philosophy (mathematicians, to use Plato’s simile in the Euthedemus, do not invent the theorems they prove but discover beings and, like hunters who must hand over what they catch to chefs if it is going to turn into something useful, they must hand over their discoveries to philosophers). Even those forms that do not bear names of mathematical objects, such as the famous forms of beauty and goodness, are in fact forms of mathematical objects. The first chapter is an attempt to defend this thesis. The second argues that for Plato philosophy’s crucial task of investigating the exfoliation of the forms into the sensible world, including the sphere of human private and public life, is already foreshadowed in one of its branches, astronomy.
Download or read book Resources in Ancient Philosophy written by Albert A. Bell and published by Metuchen, N.J. : Scarecrow Press. This book was released on 1991 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt: This guide covers all philosophers appearing in standard textbooks, from Thales (580 BC) to Augustine (400 AD). A brief introduction to each thinker or school summarizes their major themes and gives the nonspecialist some idea of the most important problems involved in studying that philosopher. Introductions are provided for each of Plato's dialogues and for various aspects of his thought and of Aristotle's views. The compilers include older books reprinted during this period, older articles included in anthologies, and bibliographies on each author, regardless of date of publication. Each of the more than 7,700 items is annotated. Cross-references and an index of terms are also included.
