This paper aims to show that the Middle Platonists’ appeal to the Timaeus was grounded in a complex and effective philosophical reasoning: the Middle Platonists conceived of Plato’s text as a web of passages which Plato himself had carefully established. Only a few of them were granted a qualified priority, namely, those offering a complete and comprehensive philosophical account of the key elements which the Platonists regarded as fundamental. This will allow us to show that the Middle (...) Platonists’ preference for the Timaeus does not depend on the fact that it is systematic. Rather it is systematic insofar as it proves capable of giving context to passages from other dialogues and provides them with an account that is philosophically sound. (shrink)

G. W. F. Hegel (1770–1831), the influential German philosopher, believed that human history was advancing spiritually and morally according to God’s purpose. At the beginning of this masterwork, Hegel writes: “What the history of Philosophy shows us is a succession of noble minds, a gallery of heroes of thought, who, by the power of Reason, have penetrated into the being of things, of nature and of spirit, into the Being of God, and have won for us by their labours the (...) highest treasure, the treasure of reasoned knowledge.” In his introduction to this Bison Book edition, Frederick C. Beiser notes the complex and controversial history of Hegel’s text. He makes a case that this English-language translation by E. S. Haldane and Frances H. Simson is still the most reliable one. (shrink)

'Middle' Platonism has some claim to be the single most influential philosophical movement of the last two thousand years, as the common background to 'Neoplatonism' and the early development of Christian theology. This book breaks with the tradition of considering it primarily in terms of its sources, instead putting its contemporary philosophical engagements front and centre to reconstruct its philosophical motivations and activity across the full range of its interests. The volume explores the ideas at the heart of Platonist philosophy (...) in this period and includes a comprehensive selection of primary sources, a significant number of which appear in English translation for the first time, along with dedicated guides to the questions that have been, and might be, asked about the movement. The result is a tool intended to help bring the study of Middle Platonism into mainstream discussions of ancient philosophy. (shrink)

A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical (...) objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist. (shrink)

The best known and most widely discussed aspect of Kurt Gödel's philosophy of mathematics is undoubtedly his robust realism or platonism about mathematical objects and mathematical knowledge. This has scandalized many philosophers but probably has done so less in recent years than earlier. Bertrand Russell's report in his autobiography of one or more encounters with Gödel is well known:Gödel turned out to be an unadulterated Platonist, and apparently believed that an eternal “not” was laid up in heaven, where virtuous logicians (...) might hope to meet it hereafter.On this Gödel commented:Concerning my “unadulterated” Platonism, it is no more unadulterated than Russell's own in 1921 when in the Introduction to Mathematical Philosophy … he said, “Logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.” At that time evidently Russell had met the “not” even in this world, but later on under the infuence of Wittgenstein he chose to overlook it.One of the tasks I shall undertake here is to say something about what Gödel's platonism is and why he held it.A feature of Gödel's view is the manner in which he connects it with a strong conception of mathematical intuition, strong in the sense that it appears to be a basic epistemological factor in knowledge of highly abstract mathematics, in particular higher set theory. Other defenders of intuition in the foundations of mathematics, such as Brouwer and the traditional intuitionists, have a much more modest conception of what mathematical intuition will accomplish. (shrink)

The first comprehensive account of Platonism in Antiquity, from the foundation of Plato's Academy in the fourth century BC to Late Antiquity. Written in a clear language, the book shows that Platonism is philosophically engaging and very influential in the history of philosophy. Useful for both students and scholars.

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument (...) for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct. (shrink)

This is the first monograph devoted to the genesis, aims, and argument of Berthold of Moosburg’s 14th-century _Commentary_ on Proclus’ _Elements of Theology_, the most extensive commentary on Proclus’ text in any language. It includes an English translation of the _Commentary_’s three fundamental prefaces.

Spiritual Taxonomies and Ritual Authority recounts how philosophers of the late third century C.E. organized the spirit world into hierarchies, positioning themselves as high priests in the process. By establishing themselves as experts on sacred matters, they fortified their authority, prestige, and reputation.

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.

Platonism, Ficino to Foucault explores some key chapters in the history Platonic philosophy from the revival of Plato in the fifteenth century to the new reading of Platonic dialogues promoted by the so-called ‘Critique of Modernity’.

This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does (...) this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy. (shrink)

Various criticisms have been brought against a Platonistic construal of the musical work: that is, against the view that the musical work is a universal or kind or type, of which the performances are instances or tokens. Some of these criticisms are: (1) that musical works possess perceptual properties and universals do not; (2) that musical works are created and universals cannot be; (3) that universals cannot be destroyed and musical works can; (4) that parts of tokens of the same (...) type can be interchanged and still yield tokens of that type, whereas we cannot interchange parts of performances of the same work and still get performances of the work. Of these claims, (1) and (2) seem to be true, but are not incompatible with a Platonistic construal of the musical work, whereas (3) and (4) just seem to be false and, therefore, of no concern to the musical Platonist. (shrink)

In this paper, we develop an alternative strategy, Platonized Naturalism, for reconciling naturalism and Platonism and to account for our knowledge of mathematical objects and properties. A systematic (Principled) Platonism based on a comprehension principle that asserts the existence of a plenitude of abstract objects is not just consistent with, but required (on transcendental grounds) for naturalism. Such a comprehension principle is synthetic, and it is known a priori. Its synthetic a priori character is grounded in the fact that it (...) is an essential part of the logic in which any scientific theory will be formulated and so underlies (our understanding of) the meaningfulness of any such theory (this is why it is required for naturalism). Moreover, the comprehension principle satisfies naturalist standards of reference, knowledge, and ontological parsimony! As part of our argument, we identify mathematical objects as abstract individuals in the domain governed by the comprehension principle, and we show that our knowledge of mathematical truths is linked to our knowledge of that principle. (shrink)

In this dissertation I examine the NeoFregean metaontology of mathematics. I try to clarify the relationship between what is sometimes called Priority Thesis and Platonism about mathematical entities. I then present three coherent ways in which one might endorse both these stances, also answering some possible objections. Finally I try to show which of these three ways is the most promising.

Thrasyllus, best known as the Roman emperor Tiberius' astrologist, figured prominently in the development of ancient Platonism. How prominently and to what effect are questions that have puzzled philosophers down to our day; Harold Tarrant's important new book attempts to answer them.

"This volume brings together articles by sixteen leading scholars on a cross-section of Platonists authors-Christian and non-Christian-from early through late Byzantium philosophy, including the Capaddocians, Cyril, Proclus, Damascius, Dionysius, George of Pisidia, Nicetas Stethatos, Nikephoros Choumenos, Psellos, and George Palamas. The reception of Byzantine thought in the Latin tradition is also considered. The articles collectively show development in the Greek East on ontological issues such as the doctrine of the soul, as well as theological concepts of the One/God and (...) Trinity within a hierarchical universe. The volume considers exegetical questions relating to the use of Plato and the Platonists by Byzantine Christian authors"--. (shrink)

"Aristotle versus Plato. For a long time that is the angle from which the tale has been told, in textbooks on the history of philosophy and to university students. Aristotle's philosophy, so the story goes, was au fond in opposition to Plato's. But it was not always thus."--from the Introduction In a wide-ranging book likely to cause controversy, Lloyd P. Gerson sets out the case for the "harmony" of Platonism and Aristotelianism, the standard view in late antiquity. He aims to (...) show that the twentieth-century view that Aristotle started out as a Platonist and ended up as an anti-Platonist is seriously flawed. Gerson examines the Neoplatonic commentators on Aristotle based on their principle of harmony. In considering ancient studies of Aristotle's Categories, Physics, De Anima, Metaphysics, and Nicomachean Ethics, the author shows how the principle of harmony allows us to understand numerous texts that otherwise appear intractable. Gerson also explains how these "esoteric" treatises can be seen not to conflict with the early "exoteric" and admittedly Platonic dialogues of Aristotle. Aristotle and Other Platonists concludes with an assessment of some of the philosophical results of acknowledging harmony. (shrink)

An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.