Plato: Exact Sciences

Plato's educational model (paidèia) differentiates the level of education according to the students' skills. Thus, a basic education includes, in addition to gymnastics and fighting (the exercise of the body), music (the exercise of the spirit), without being imposed by force because a free man must be free in the conquest of knowledge. If the student has skills, he is educated in mathematics to become a strategist, and in astronomy to raise the soul. From these, the best are selected to (...) become good leaders, studying philosophy and dialectics. Women will have the same rights and duties as men. According to Socratic principles, in order to do justice, one must know what is good, and this is best known to the philosopher. Plato detailed this concept, highlighting the distinction between the philosopher (who seeks the principles of truth without claiming to possess it) and the sophist (who lets himself be guided by opinion as the only valid parameter of knowledge). Plato considers philosophers to be ideal leaders for two main reasons: because they know what is right, and because they do not want to lead. -/- DOI: 10.13140/RG.2.2.17459.71200. (shrink)

This article concerns the so-called irrigation system in the Timaeus’ biology (77a-81e), which replenishes our body’s tissues with resources from food delivered as blood. I argue that this system functions mainly by the natural like-to-like motion of the elements and that the circulation of blood is an important case study of Plato’s physics. We are forced to revise the view that the elements attract their like. Instead, similar elements merely tend to coalesce with each other in virtue of their tactile (...) features as the atomists describe. The notion of attraction is replaced with this notion of mere coalescence. I begin by outlining how blood is made from food. I then argue that an understanding of health and disease compels us to read Plato as if he were an atomist and to abandon the popular scholarly interpretations according to which the elements attract each other. (shrink)

The principles governing elemental composition, variation, and change in Plato’s Timaeus appear to be incompatible, which has led commentators to prioritize some of the principles to the exclusion of others. Call this seeming incompatibility the problem of isomorphic variants. In this paper, I develop the theory of proportionate atomism as a solution to this problem. Proportionate atomism retains the advantages of rival interpretations but allows the principles of material composition, variation, and change to combine into an internally coherent and explanatorily (...) powerful atomic physics. (shrink)

I argue that Plato thinks that the soul has location, surface, depth, and extension, and that the Timaeus’ composition of the soul out of eight circles is intended literally. A novel contribution is the development of an account of corporeality that denies the entailment that the soul is corporeal. I conclude by examining Aristotle’s objection to the Timaeus’ psychology and then the intellectual history of this reading of Plato.

I argue that, according to Plato, the body is the sole cause of psychic disorders. This view is expressed at Timaeus 86b in an ambiguous sentence that has been widely misunderstood by translators and commentators. The goal of this article is to offer a new understanding of Plato’s text and view. In the first section, I argue that although the body is the result of the gods’ best efforts, their sub-optimal materials meant that the soul is constantly vulnerable to the (...) body’s influences. In the second section, I argue that every psychic disorder is a disruption of the motions of the inner psychic circles by the body; moreover, I defend my translation of 86b. In the final section, I argue that the goal of education is to restore the circles to their original orbits, and I disarm a possible objection that bad education is also a cause of psychic disorder. (shrink)

It is a notion commonly acknowledged that in his work Timaeus the Athenian philosopher Plato (_c_. 429–347 BC) laid down an early chemical theory of the creation, structure and phenomena of the universe. There is much truth in this acknowledgement because Plato’s “chemistry” gives a description of the material world in mathematical terms, an approach that marks an outstanding advancement over cosmologic doctrines put forward by his predecessors, and which was very influential on western culture for many centuries. In the (...) present article, I discuss inter-transformations among Plato’s four types (fire, air, water, and earth) as well as the interpretation they received in the literature. I find that scientists and scholars generally emphasized (and often misunderstood) mathematical aspects of these “reactions” over the philosophical ones. I argue that Plato’s “chemistry” in fact bears on crucial topics of his philosophical system, such as Forms, Becoming, causation and teleology. I propose that consideration of these doctrines help to understand not only the sense of his “chemical” reactions, but also the reason why their stoichiometry is by surface balance and is restricted only to types that come to be and pass away but not to those that provoke the inter-transformations. (shrink)

I argue that Plato believes that the soul must be both the principle of motion and the subject of cognition because it moves things specifically by means of its thoughts. I begin by arguing that the soul moves things by means of such acts as examination and deliberation, and that this view is developed in response to Anaxagoras. I then argue that every kind of soul enjoys a kind of cognition, with even plant souls having a form of Aristotelian discrimination (...) (krisis), and that there is therefore no completely unintelligent, evil soul in the cosmos that can explain disorderly motions; as a result, the soul is not the principle of all motion but only motion in the cosmos after it has been ordered by the Demiurge. (shrink)

In Mohist philosophy, the gnomon is a metaphor for the standard of valid arguments. This metaphor comes from the method of establishing due east and west by observing gnomon shadows at dusk and dawn. I argue that there is also an overlooked, implicit aspect of the gnomon metaphor that comes from its function of measuring the height of heaven indirectly through proportional calculation. The function of indirect measurement inspires a strategy of argumentation in Mohist ethics, which I call “analogical upscaling.” (...) Such an argument draws a parallel between small-scale and large-scale actions for the purpose of determining the Will of Heaven in a particular circumstance, just as the gnomon measures heaven’s physical height analogically. In the conclusion, I compare the epistemological status of light and shadow in the Mozi and Plato’s Republic. (shrink)

In this paper I argue that in several passages Plato sympathizes with the following view: sensible particulars undergo continuous, pervasive physical change; as a consequence, where there seems to be one and the same object which is identical through time, there is in fact a succession of impermanent objects numerically distinct from each other but similar to each other. I illustrate the difference between this view—which invites interesting comparisons with modern and contemporary theories—and other, superficially similar views which Plato criticizes. (...) I also suggest that this view might contribute to explaining Plato’s contention that sensible particulars lack being and are confined to coming to be. Finally, I show that my interpretation was well attested in antiquity; and I put forward the hypothesis that part of the aim of certain Aristotelian claims about substance might be to correct Plato in this respect. (shrink)

In his Republic Plato considers grasping the unity of mathematics as the ultimate goal of the mathematical studies in which the future philosopher-rulers must engage before they turn to philosophy. How the unity of mathematics is supposed to be understood is not explained, however. This book argues that Plato conceives of the unity of mathematics in terms of the mutually benefiting links between its branches, just as he conceives of the unity of the state outlined in the Republic in terms (...) of the common benefit for all citizens. Evidence for this view is provided by a discussion of his conception of astronomy as a propedeutic to philosophy, which can be best understood as hinting at a historically possible link between fourth-century-BC astronomy and solid geometry. The monograph also includes a detailed discussion of two well-known stories about Plato: not only he motivated Greek mathematicians to solve a difficult problem in solid geometry with his interpretation of a Delphic oracle given to the inhabitants of the island of Delos but he also posed the question which led to the development of the astronomical theory of homocentric spheres. It is argued that these stories are best understood as fictional episodes in Plato's life, constructed from passages in his works. (shrink)

The article defends the thesis that interpreting Plato’s natural philosophy it is useful to take the terms horatos and aoratos in two distinct meanings: “observable” and “unobservable”, and “visible” and “invisible”. This approach helps to perceive new sides of Plato’s ideas, implicitly present in the “Timaeus”, which allows interpreting it in both anthropomorphic and anti-anthropomorphic senses.

No agreed-upon account of mirror reversal is currently available although it has been discussed for more than two thousand years since Plato. Mirror reversal usually refers to recognized left-right reversal of a mirror image. Depending on the nature and layout of a reflected object, however, top-bottom reversal may be recognized instead of left-right reversal; no reversal at all may be recognized; and the presence or absence of reversal may not be decidable. Takano (1998) proposed a psycho-optic theory to explain all (...) these cases of mirror image recognition in a consistent manner. The proposed theory assumes different causes of mirror reversal depending on whether an object's left-right axis is parallel or perpendicular to a mirror's surface. This theory was later criticized in that it provided no explanation when the left-right axis is neither parallel nor perpendicular but at an intermediate angle between zero and 90 degrees with a mirror. This article completes the theory by presenting psycho-optic anal.. (shrink)

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

In Science before Socrates, Daniel W. Graham argues against the belief that the Presocratic philosophers did not produce any empirical science and that the first major Greek science, astronomy, did not develop until at least the time of Plato. Instead, Graham proposes that the advances made by Presocratic philosophers in the study of astronomy deserve to be considered as scientific contributions.

In this paper I ask how Timaeus explains change within the trianglebased part of his cosmos. Two common views are that change among physical items is somehow caused or enabled by either the forms or the demiurge. I argue for a competing view, on which the physical items are capable of bringing about change by themselves, prior to the intervention of the demiurge, and prior to their being turned into imitations of the forms. I outline three problems for the view (...) that physical things depend on the forms for their causal powers, and show how the view I propose solves each. I then add further arguments for my view, based on (a) statements by Timaeus that seem to favor my view directly, (b) implications of Timaeus’ positions that favor the view, and (c) Timaeus’ explanatory practice in the second half of his speech. (shrink)

Plato is the first scientist whose work we still possess. He is our first writer to interpret the natural world mathematically, and also the first theorist of mathematics in the natural sciences. As no one else before or after, he set out why we should suppose a link between nature and mathematics, a link that has never been stronger than it is today. Mathematical Plato examines how Plato organized and justified the principles, terms, and methods of our mathematical, natural science. (...) "Roger Sworder deserves our gratitude for drawing attention to the significance of mathematics in Plato's thought and writings. He lays the principal discussions out before us with clarity. He also presents Plato as a theorist of nature: of physics and not just metaphysics, to use Aristotle's distinction. Not all readers, we should admit, will be equally convinced of the usefulness of Plato's science for today, but they will all be led more deeply into Plato's vision of reality."--ANDREW DAVISON, Westcott House, Cambridge "Here is Plato for an anti-Platonic age. The author gives careful attention to some of the most important passages in the Platonic dialogues and offers new solutions to some of Plato's most famous mathematical puzzles. He then considers the implications of these penetrating studies for the philosophy of science, and the natural sciences especially. This is a book that revivifies the core themes of Platonism and restores science to worship. It shows Roger Sworder to be one of the foremost students of Plato writing today, and places him in the noble tradition of Thomas Taylor."--RODNEY BLACKHIRST, author of Primordial Alchemy and Modern Religion: Essays on Traditional Cosmology. (shrink)

I offer a comparison between Plato’s discussion of χώρα in the Timaeus at 48A–53C and Aristotle’s discussion of τόπος in Physics Book IV, arguing that the two accounts have more in common than has been suggested by Continental scholars. Τόπος and χώρα both signal what I call the impasse of place as the question of that which cannot be reduced to either the sensible or the intelligible, and which (un)grounds such categories. Identifying this impasse reveals Plato’s and Aristotle’s accounts of (...) “place” as strikingly dissimilar from the Newtonian category of Absolute Space; and it also suggests new ways of thinking the relationships between bodies, motion, place and nature. (shrink)

This paper aims to show that—and how—Plato’s notion of the receptacle in the Timaeus provides the conditions for developing a mathematical as well as a physical space without itself being space. In response to the debate whether Plato’s receptacle is a conception of space or of matter, I suggest employing criteria from topology and the theory of metric spaces as the most basic ones available. I show that the receptacle fulfils its main task–allowing the elements qua images of the Forms (...) to exist as sensible things by being that in which the elements appear, change and move–in virtue of being pure continuity. All further qualifications required for a full notion of space are derived solely from the content of the receptacle. (shrink)

A Russian translation of a chapter on astronomy from the famous book of Prof. Walter Burkert is prepared for the participants of educational project “ΤΕΧΝΗ. Theoretical foundations of Arts, sciences and technology in the Greco-Roman World". The chapter treats the structure of the world and planetary system; the theory of planetary movements; the cosmos of Philolaus; harmony of the spheres and astral immortality. Original publication: Weisheit und Wissenschaft: Studien zu Pythagoras, Philolaos und Platon ; prepared on the basis of the (...) revised English edition: Lore and Science in Ancient Pythagoreanism, tr. by E. Minar. (shrink)

Plato's dialogue the Timaeus-Critias presents two connected accounts, that of the story of Atlantis and its defeat by ancient Athens and that of the creation of the cosmos by a divine craftsman. This book offers a unified reading of the dialogue. It tackles a wide range of interpretative and philosophical issues. Topics discussed include the function of the famous Atlantis story, the notion of cosmology as 'myth' and as 'likely', and the role of God in Platonic cosmology. Other areas commented (...) upon are Plato's concepts of 'necessity' and 'teleology', the nature of the 'receptacle', the relationship between the soul and the body, the use of perception in cosmology, and the work's peculiar monologue form. The unifying theme is teleology: Plato's attempt to show the cosmos to be organised for the good. A central lesson which emerges is that the Timaeus is closer to Aristotle's physics than previously thought. (shrink)

This essay explores Leibniz's defense of teleology and teleological explanations in the domain of physics in general, and the roles that teleology plays in his studies of optics in particular. I argue first that Leibniz draws upon Plato's defense of final causes to introduce a novel research program intended to steer a middle course, on the one hand, between Aristotelian-Scholasticism and the new mechanical philosophy, and, on the other hand, between Cartesian rationalism and Gassendist empiricism. The implementation of this program (...) leads Leibniz to significant conceptual innovations, as he attempts to reconcile teleological and efficient explanatory frameworks, and important discoveries, as he tries to show how final causes can be used to achieve results in the study of the natural world. ;Having situated Leibniz's defense of final causes in the broader context of his general philosophy of physics, I turn to a more detailed investigation of the roles that teleology plays in his work in geometrical optics. Interest in final causes leads Leibniz to introduce his "Most Determined Path Principle" from which both of the central laws of geometrical optics may be derived. I argue that Leibniz uses the discovery of such principles to introduce a thin notion of final causation within the order of nature based on teleological laws that link prior events to subsequent events via the likely or expected outcomes of those events, and defend this view against objections made both by Leibniz's contemporaries and our own. I also argue that Leibniz uses the discovery of principles like Most Determined Path Principle to provide a novel connection within his system between considerations of divine perfection and the laws of nature. I defend the internal consistency of this connection, and explore its relations to Leibniz's mature physics, and to his view that the world is governed by two sets of equipotent laws, one teleological and one mechanical. (shrink)

This appears in a supplementary issue of the Bulletin of the Institute of Classical Studies, entitled "Ancient Approaches to Plato's Timaeus.".

Seeking to reassess Plato's views on how we might investigate and explain the natural world, this book argues that many of the common charges against Plato (disinterest, ignorance, dismissal of observation) are unfounded, and that Plato had a series of important and cogent criticisms of the early atomists and other physiologoi. His views on science, and on astronomy and cosmology in particular, develop in interesting ways. It also argues that Plato can best be seen as someone who is struggling with (...) the foundations of scientific realism, and that he has interesting epistemological, cosmological and nomological reasons for his teleological approach. (shrink)

There are a few isolated passages in the Timaeus which an advocate might claim fore shadow modern scientific ideas. For example, 37c–38d seems to anticipate the concept of the “block” Universe as formulated by modern philosophers of science, and 52b similarly the Kantian notion of space. The “triangles” of 53d–57c might be regarded as a quasi-molecular theory of matter, and 67b makes a striking comment about the relation of frequency to perceived pitch. But I suspect much of this is coincidence. (...) Overall, Plato’s speculations on the nature of the physical world do not have much in common with the answers given by modern science. Rather it is his questions that often have a modern resonance, and it is these which I shall address in this paper. In this context, the most interesting passages are probably 27d–38b, on the isotropy and uniqueness of the Universe and the nature of time, 47c–52d on nous (reason) versus anankê (necessity), the idea of the hypodochê (usually translated as “receptacle”), sameness and difference, kinematics versus dynamics, necessity versus contingency, and finally, the discussion from 69a onward about the relation of the physical Universe to human existence and perceptions. Just about all these issues are still alive, either explicitly or implicitly, in modern physics and cosmology. (shrink)

Though the two-world interpretation of Plato's metaphysics is no longer uncontested the question of the expendability of the physical world still predominates current discussions. Against this tendency the article suggests that Plato neither intended to dispose of sensory evidence altogether nor to locate the Forms in a separate realm of pure understanding. The Forms should rather be understood as the ideal principles determining the proper function of each entity. Such a 'functional view' of the Forms is discussed explicitly in Book (...) X of the Republic, but it can easily be extended to account for Plato's use of the Forms elsewhere. (shrink)

The figure of the cordial host of the Academy, who invited the most gifted mathematicians and cultivated pure research, whose keen intellect was able if not to solve the particular problem then at least to show the method for its solution: this figure is quite familiar to students of Greek science. But was the Academy as such a center of scientific research, and did Plato really set for mathematicians and astronomers the problems they should study and methods they should use? (...) Our sources tell about Plato's friendship or at least acquaintance with many brilliant mathematicians of his day (Theodorus, Archytas, Theaetetus), but they were never his pupils, rather vice versa -- he learned much from them and actively used this knowledge in developing his philosophy. There is no reliable evidence that Eudoxus, Menaechmus, Dinostratus, Theudius, and others, whom many scholars unite into the group of so-called "Academic mathematicians," ever were his pupils or close associates. Our analysis of the relevant passages (Eratosthenes' Platonicus, Sosigenes ap. Simplicius, Proclus' "Catalogue of geometers", and Philodemus' "History of the Academy", etc.) shows that the very tendency of portraying Plato as the architect of science goes back to the early Academy and is born out of interpretations of his dialogues. (shrink)

Plato's comments on astronomy and the education of the guardians at Republic 528e ff have been hotly disputed, and have provoked much criticism from those who have interpreted them as a rejection or denigration of observational astronomy. Here I argue that the key to interpreting these comments lies in the relationship between the conception of enquiry that is implicit in the epistemological allegories, and the programme for the education of the guardians that Plato subsequently proposes. We have, I suggest, been (...) too eager to stress the similarities here, when recognition of the differences may supply us with the tools required for a better understanding of 528e ff, one that to a large extent disarms the anti-empirical critique. My discussion proceeds in three stages. Firstly, Plato takes great care to place his comments on astronomy in the context of the preceding epistemological allegories. Is there any evidence here, where Plato might be thought to discuss enquiry in general, that he rejected or denigrated observation? I argue that even if Plato advocated a 'Two Worlds' (TW) ontology, he still envisaged a dynamic process of enquiry, interrelating sensibles and intelligibles, the investigation of each being necessary but not sufficient to achieve the overall aim. Secondly, Plato appears to be deriving how we ought to go about educating the guardians from how we ought to conduct our enquiries. While the two are intimately related there are important differences, recognition of which turns the supposed rejection of observation into an affirmation of the need for an initial empirical approach. I contend that this makes good sense of the internal structure of 528e ff, and of its relations to other parts of the Republic. Thirdly, I discuss the Republic in relation to the evidence offered by later works on the question of astronomy and observation, and raise the question of whether Plato's views on the imperfection of the sensible world necessarily lead to the denigration of careful and prolonged empirical work. (shrink)

This article expands a traditional pedagogic interpretation of Plato’s reasons for urging trainee rulers to study astronomy. It argues, primarily, that they need to become familiar with astronomy because it teaches them about cosmic harmony. This harmony indeed models a “personal harmony,” which will prevent them from becoming tyrants, and informs them about the analogous social harmony— which it will be their special duty to create and maintain. In Plato’s view, indeed, astronomy shows that social harmony requires obedience on the (...) part of the lower orders and that social goods are best distributed in accordance with a special antidemocratic principle of equality. (shrink)

Since 1961, the experimental exploration at the fundamental level of physical reality has surprised physists by revealing to them a highly geometric scenery. Like Einstein's (classical) theory of gravity, the “standard model,” describing the strong, weak, and electromagnetic interaction, testifies in favor of Plato's reported allegation.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

In one of the most disputed passages of Greek literature Plato in the Republic, 7. 528e–530c prescribes astronomy as the fourth study in the education of the Guardians. But what sort of astronomy? According to one school of thought it is a purely speculative study of bodies in motion having no relation to the celestial objects that we see. While this interpretation has rejoiced the hearts of Plato's detractors, who regard him as an obstacle to the progress of science, it (...) has dismayed his admirers. Another school of thought holds that what Plato meant was that astronomers must get to know the real motions of the heavenly bodies as opposed to their apparent motions as seen by us on earth. The opposed interpretations may be set out in the following representative citations from Sir Thomas Heath and John Burnet. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Notes and Discussions ARISTOTLE'S "DE MOTU ANIMALIUM" AND THE SEPARABILITY OF THE SCIENCES In contrast to Plato's vision of a unified science of reality and with a profound effect on subsequent natural science and philosophy, Aristotle urges in the Posterior Analytics and elsewhere that scientific knowledge is to be pursued in limited, separable domains, each with its own true and necessary first principles for the explanation of a discrete (...) range of phenomena, that is, accepted observations and beliefs, from which its investigations are launched (An. Pr. 46al7ff.; An. Post. 74b25, 76a26-3 o, 84b14-18, 88a31; Cael. 3o6a6ff.; Gen. An. 748a7ff.). In an early introduction to a course of lectures on the natural sciences, Aristotle also indicates the order in which those sciences ought to be presented (Mete. 338a2o-~9, 339a5-9; cf. Cael. 268al6, Part. An. 644b~2ff.). The plan is to start with a general discussion of change and motion, then progress to studies of specific natural phenomena, ending with the many species of plants and animals. In the theory of demonstration in Posterior Analytics 1, which is concerned with the organization, justification, and teaching of a finished science, Aristotle maintains that terms cannot ordinarily cross genera; for example, geometry cannot provide demonstrations of truths of arithmetic or aesthetics. Demonstration of a theorem of some one science by means of another can be accomplished when and only when the sciences are related as "subordinate " to "superior" (75b14-17), for example, as harmonics to arithmetic or optics to geometry. A superior science may supply the "reason" for a "fact" known to obtain in the subordinate science (78b34-79a6). Evidently at least part of what he has in mind is the relation between pure and applied sciences.' Aristotle's practice as well as a number of methodological remarks ' See ThomasAquinas,In Post. An. 50.1,15.131, 50.1.25,as wellasJ. Barnes'snoteson An. Post. 78b34,in Aristotle'sPosteriorAnalytics (Oxford:OxfordUniversityPress,1975).For relevant background see Ian Mueller,"Ascendingto Problems:Astronomyand Harmonicsin Republic VII," inJohn Anton,ed., Scienceand the Sciencesin Plato (Albany:StateUniversityof NewYork Press, 1979). [65] 66 HISTORY OF PHILOSOPHY suggest also that the strictures of the Posterior Analytics are not intended to prohibit the heuristic use of material from other disciplines in research (see e.g., Top. 1.14; Part An. 639b17ff., 641a6-14, 642alo-14, 645b15-2o; Ph. 192b8-34, 199a8-21, 199a33-b5). The requirements for science laid down here are very strict, and it is sometimes maintained that Aristotle violates them himself to some degree in other works, but it is not usually believed that he ever denies the separability of the sciences in general. Martha C. Nussbaum has recently presented a lively challenge to this concensus? She argues that Aristotle's late, little known work De Motu Animalium represents a radical but "deliberate and fruitful" rejection of his earlier philosophy of science as enunciated in the Organon and not seriously questioned in other, subsequent writings. Her claim is that in his mature thought about the sciences Aristotle arrives at a significantly "less departmental and more flexible picture of scientific study" (p. 113) and comes to hold that "no inquiry is genuinely separable from a whole group of interlocking studies, and no being can be extensively studied without an account of its placement in the whole of nature" (p. 164). Nussbaum's conclusion is probably not intended to be as Platonic as it may appear at first blush, for she seems actually to be speaking only of connections between sciences of different substances. There is no suggestion that the study of beauty or health or geometry, say, is on a par with the sciences of substances. Nor does she suggest that Aristotle wavers in his conviction that there are fundamental cleavages between the practical and theoretical sciences, which will make a full-blown science of ethics-politics look very different from the demonstrative science of meteorology, for example. Nevertheless, even if limited to the natural sciences of substances, her claim remains an important and interesting one. She holds, more specifically, that Aristotle departs from his earlier position as follows: (1) He recognizes that the biological study of various modes of local motion... (shrink)

This little book contains lectures given by Vlastos in the summer of 1972 in the Danz Lectures series of the University of Washington. His theme relates to that often rather paternalistic exercise of plotting out the extent to which Science was Revealed to the Greeks. In his view, "it was not given to them... to grasp the essential genius of the scientific method." However, they did discover "the conception of the cosmos that is presupposed by the idea of natural science (...) and by its practice". This discovery, an intellectual "revolution," was of the view, upheld by the Presocratic physiologoi, that the world is characterized by "unbreachable regularities" which make the world a "cosmos," which "constitute the order of nature and, if known, would yield the ultimate explanation of every natural phenomenon". This was revolutionary since it rejected the traditional belief in an unlimited area of possible divine supernatural intervention in the world, a belief which made perception of the universe a perception of an "irrational universe". Thus, "for the first time in history", man achieved, with Presocratic physiologia, "a perception of a rational universe". In the remaining two chapters of the book, Vlastos examines Plato, represented as a "fierce opponent" of the revolution who appropriated the newly discovered cosmos, refashioning it "on the pattern of his own idealistic and theistic metaphysics". This interpretation of Plato is developed mainly through a study of the Timaeus and especially of the "Theory of Celestial Motions" and of the "Theory of the Structure of Matter". Plato appears as opposed to the "impiety" of the physiologoi, proposing himself in the Timaeus a transcendent god as his primary cosmological principle. At the same time, the Timaeus reflects, as Vlastos shows in a brief survey of earlier and contemporary Greek astronomy, an awareness of the "empirical facts" established by the astronomers and Plato’s desire to reconcile these facts with his metaphysical, theological, a priori convictions. This reconciliation involved postulating a system of celestial circular motions, a theory whose "scientific value" Vlastos does not doubt, despite its dependence on a "metaphysical scheme". Vlastos concludes that although Plato fully acknowledged a supernatural power in the universe, he guaranteed the regularities of nature against divine intervention. There is an unfailing natural law. However, its ground for Plato is not natural but supernatural. In examining the "Theory of the Structure of Matter", Vlastos again finds that Plato’s world-order resembles very much that of the physiologoi and, like theirs, is "safe from supernatural interference". The "elementarism" of the Timaeus is shown to be indebted to the Atomists, but also to innovate by opening the way to the intertransformability of elementary corpuscules. What "scientific value" does this theory of the transformation of elements have? It is neither entailed nor contradicted by observation. Vlastos suggests rather that its grounds are "aesthetic". At any rate, Vlastos concludes that although Plato opposed the physiologoi in reintroducing supernatural agency, he annexed their conception of cosmos. In his "perversely original way," he thus "sustained the faith that our world is cosmos. He gave rational men a pious faith to live by in two millennia all through which science was more prophecy than reality". Some of Vlastos’ more extensive footnotes are collected in an Appendix, which is followed by a Bibliography and Indices. (shrink)

Socrates, in the Republic , uses the symbol of a divided line to illustrate the distinction between the Visible and Intelligible Worlds, and between the kinds of perception appropriate to each. This paper will present a new hypothesis: that the proportions of the line are derived from optical theory. The construction of the Divided Line is described as follows: Socrates asks his interlocutors to represent the Visible and Intelligible Worlds by a line divided into two unequal segments. The ratio in (...) which the division is to be made is not specified, and it seems that any ratio is acceptable provided that one segment is longer than the other. Socrates then tells them to cut each part again according to the same ratio as the original division. After describing the division of the line thus into four parts, Socrates goes on to explain the philosophical significance of each part. For the purposes of this paper the following brief identification of each segment of the line will suffice. (shrink)

Socrates, in the Republic, uses the symbol of a divided line to illustrate the distinction between the Visible and Intelligible Worlds, and between the kinds of perception appropriate to each. This paper will present a new hypothesis: that the proportions of the line are derived from optical theory. The construction of the Divided Line is described as follows: Socrates asks his interlocutors to represent the Visible and Intelligible Worlds by a line divided into two unequal segments. The ratio in which (...) the division is to be made is not specified, and it seems that any ratio is acceptable provided that one segment is longer than the other. Socrates then tells them to cut each part again according to the same ratio as the original division. After describing the division of the line thus into four parts, Socrates goes on to explain the philosophical significance of each part. For the purposes of this paper the following brief identification of each segment of the line will suffice. (shrink)