Berkeley: Space and Time

Berkeley in his Introduction to the Principles of Human knowledge uses geometrical examples to illustrate a way of generating “universal ideas,” which allegedly account for the existence of general terms. In doing proofs we might, for example, selectively attend to the triangular shape of a diagram. Presumably what we prove using just that property applies to all triangles.I contend, rather, that given Berkeley’s view of extension, no Euclidean triangles exist to attend to. Rather proof, as Berkeley would normally assume, requires (...) idealizing diagrams; treating them as if they obeyed Euclidean constraints. This convention solves the problem of representative generalization. View HTML Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.Berkeley and Proof in GeometryVolume 51, Issue 3RICHARD J. BROOK DOI: https://doi.org/10.1017/S0012217312000686Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. Berkeley and Proof in GeometryVolume 51, Issue 3RICHARD J. BROOK DOI: https://doi.org/10.1017/S0012217312000686Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. Berkeley and Proof in GeometryVolume 51, Issue 3RICHARD J. BROOK DOI: https://doi.org/10.1017/S0012217312000686Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

Berkeley’s general tenet about immaterialism is presented and discussed. I examined apart the several theses that concur to the immaterialist theory. After that, the general argument is presented and discussed. In particular, I stress Berkeley’s assumption that a world without matter and a world with matter would be indistinguishable from the point of view of the content of perceptions, natural science. I stress that this assumption depends on a relative account of circular motion, generating the centrifugal forces, as Newton shows (...) in his bucket experiment. In spite of the efforts by Leibniz and Huygens, such a relative account of rotational motion was never presented. So the thesis about the scientific and perceptual identity between worlds with and without matter remains a simple case of wishful thinking in need for a justification. (shrink)

Berkeley doesn't use the Time-Gap Argument, as Leibniz does, to prove either that we immediately see only ideas or that we see physical objects mediately. It may be doubted whether he was even aware of the time-gap problem that gives rise to the argument. But certain passages in the Three Dialogues and elsewhere suggest that Berkeley would have had cogent answers to anyone who claimed that this argument, construed as being in aid of the conclusion that we only perceive ideas, (...) is unsound. Discussing points made by Bertil Belfrage, Len Carrier, John Foster, A. C. Grayling, Howard Robinson, A. D. Smith, Tom Stoneham, and Colin Turbayne, I try to show that the Time-Gap Argument can be expanded into a strong argument for Berkeleian Idealism. I also idnicate how the latter provides a solution to J. J. Valberg's "puzzle of experience" and disarms James Cornman's argument in Perception, Common Sense, and Science that Berkeley, too, faces a time-gap problem. (shrink)

I consider two arguments about the nature of space that occur in George Berkeley which I think are not sufficiently discussed. The first concerns the phenomenology of space, the second its physics. The first is the "mite" argument and the second concerns Isaac Newton's two thought experiments about absolute space, the "bucket" thought experiment and the "balls" thought experiment. The former suggests that there is no such thing as objective size. Berkeley's position is more confusing on the second experiment, but (...) I argue that the clash between absolutist and relationist spatial intuitions can be reconciled only by an idealist approach to space. (shrink)

The author considers two arguments concerning the nature of space which occur in Berkeley and which he thinks are not sufficiently discussed. The first one concerns the phenomenology of space, the second the physics of space. The first one is the “mite” argument, while the second draws from Newton’s two thought experiments concerning absolute space: the “bucket” experiment and the “balls” experiment. The author’s aim is to support the idealist approach to space.

The report is dedicated to modern understanding of the correlation between science and religion that is based on the analysis of certain ideas formulated by Newton, Berkeley and Mach. Newton proceeded from the existence of infinite (absolute) Space that he interpreted as the Sensory of the intelligent omnipresent Being (God) who sees things themselves intimately, and throughly perceives and comprehends them. Human being also has his little “Sensoriums” perceiving the images of things, the Order and the Beauty of their arrangement. (...) Mach emphasized that since Newton’s period space and time have become “immaterial substances that form the most important basis of our sensual world outlook”. Apparently, this “immateriality of substances” manifests itself in the way Machinterprets our perceptions, conceptions, will, feelings, i.e. all inner and outer world, which he understands as small number of homogeneous elements called sensations (Empfindungen). These sensations are compared in the report to what Berkeley called ideas while he denied the existence of the real absolute noncreated space that is part, or attribute, of God. If we accept the idea that beside space and time inseparable from matter as it is scientifically comprehended, there exist absolute space and time as Newton interpreted them, then these space and time must exist outside our universe or parallel to it. This brings us to the panentheistic model (Eduard I. Sorkin, ХХIst World Congress of philosophy, Abstracts 2003, pp. 374‐375). According to Mach the law of causality is separated from space and time while the laws of nature are just limitations that our experience dictates to our expectations. The report shows that if the Mach’s concept had been supplemented by the “idealistic” views of Newton and Berkeley, it would have been more convincing – something contrary to fideism. (shrink)

The problem of whether perception is direct or if it depends on additional, cognitive contributions made by the perceiving subject, is posed with particular force in an Essay towards a New Theory of Vision. It is evident from the recurrent treatment it receives therein that Berkeley considers it to be one of the central issues concerning perception. Fittingly, the NTV devotes the most attention to it. In this essay, I deal exclusively with Berkeley's treatment of the problem of indirect distance (...) perception, as it is presented in the context of that work. (shrink)

In the chapter “The Geometry of Visibles” in his ‘Inquiry into the Human Mind’, Thomas Reid constructs a special space, develops a special geometry for that space, and offers a natural model for this geometry. In doing so, Reid “discovers” non-Euclidean Geometry sixty years before the mathematicians. This paper examines this “discovery” and the philosophical motivations underlying it. By reviewing Reid’s ideas on visible space and confronting him with Kant and Berkeley, I hope, moreover, to resolve an alleged impasse in (...) Reid’s philosophy concerning the contradictory characteristics of Reid’s tangible and visible space. (shrink)

Berkeley's immaterialism has more in common with views developed by Henry More, the mathematician Joseph Raphson, John Toland, and Jonathan Edwards than those of thinkers with whom he is commonly associated (e.g., Malebranche and Locke). The key for recognizing their similarities lies in appreciating how they understand St. Paul's remark that in God "we live and move and have our being" as an invitation to think to God as the space of discourse in which minds and ideas are identified. This (...) way of speaking about God, adapted by Karl Barth and Paul Tillich, opens up new ways to think about the relation between God and finite minds. (shrink)

Berkeley and Helmholtz proposed different indirect mechanisms for size perception: Berkeley, that size was conditioned to various cues, independently of perceived distance; Helmholtz, that it was unconsciously calculated from angular size and perceived distance. The geometrical approach cannot explain size-distance paradoxes (e.g., moon illusion). The dorsal/ventral solution is dubious for close displays and untestable for far displays.

This paper examines Berkeley's attitude toward our perception of spatial relations on the two- dimensional visual field. This is a topic on which there has been some controversy. Historians of visual theory have tended to suppose that Berkeley took "all" spatial relations to be derived in the way our knowledge of depth is: from association of more primitive sensations which are themselves in no way spatial. But many philosophers commenting on Berkeley have supposed that he takes our awareness of two- (...) dimensional visual layout to be directly perceived. I argue that Berkeley's position on this issue is deeply ambivalent and that neither alternative sits well with the rest of his philosophy. (shrink)

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work.

The dissertation is a study of Berkeley's ideas on mathematics in which an evaluation is made of their merit and of their possible relevance to present day studies on the subject. ;The study is divided in five chapters and four appendices, in which the following subjects are discussed: Berkeley's arguments against infinite divisibility; his ideas on arithmetic and algebra, plus an appendix on the several views on numbers held by philosophers and mathematicians contemporaneous to or of about Berkeley's time. A (...) third chapter deals with Berkeley's ideas on geometry; I add two appendices: one on Berkeley and the Pythagoreans, where I consider with some detail problems which arise within Berkeley's perceptual geometry and irrational magnitudes; the second one, on Berkeley and Epicurus on minima, where I argue that Berkeleyan minima have to be extended, and I show that this view was held also by Epicurus, whom I take as a strong influence on Berkeley's thought. Chapter four is a schematic survey of the historical of the calculus, from its Greek origins to the eighteenth century, underlining the several methods used by the mathematicians to obtain their results, methods which will come under attack in Berkeley's Analyst. Finally, in chapter five I study Berkeley's attack to the foundations of the calculus as is put forth in The Analyst. I conclude the dissertation with a brief appendix on A. Robinson's work on infinitesimals, which sheds light both on why infinitesimals were so useful to XVIIth and XVIIIth century mathematicians, and why they were so difficult to be subjected to a systematic treatment by means of the mathematical tools then available. ;My overall appraisal of Berkeley's work is not uniform: there are points where he was ahead of his time, in his views on arithmetic and algebra; at other points, in geometry, say, he did not have a clear view of what was the aim of the mathematicians. As regards the calculus, I consider his criticism pointed in the right direction and was an important element in moving the mathematicians to look for sounder foundations for their discipline. (shrink)

Since both berkeley and hume are committed to the view that a line is composed of finitely many fundamental parts, They must find responses to the standard geometrical proofs of infinite divisibility. They both repeat traditional arguments intended to show that infinite divisibility leads to absurdities, E.G., That all lines would be infinite in length, That all lines would have the same length, Etc. In each case, Their arguments rest upon a misunderstanding of the concept of a limit, And thus (...) are not successful. Berkeley, However, Adds a further ingenious argument to the effect that the standard geometrical proofs of infinite divisibility misread the unlimited representational capacity of geometrical diagrams as a substantive feature of the objects that these diagrams represent. The article concludes that berkeley is right on this matter, And that the traditional proofs of infinite divisibility do not show what they are intended to show. (shrink)

Ce texte examine les arguments de Leibniz et de Berkeley contre la théorie de l'espace absolu, que Newton avait tenté de prouver au moyen de l'expérience connue sous le nom d'expérience du seau. Selon Leibniz, l'espace absolu ne peut exister parce que cette existence serait contraire au principe des indiscernables et au principe de raison suffisante. L'espace euclidien est en effet un ensemble de points doués des mêmes propriétés qualitatives; dans un tel espace, chaque monde possible appartiendrait à une classe (...) infinie de mondes indiscernables. En revanche, la critique de Berkeley résulte de prémisses empiristes : nous ne pouvons observer que des mouvements relatifs et des positions relatives, c'est-à-dire des relations entre les corps ; l'espace substantiel est une abstraction. Ainsi le rationalisme de Leibniz et l'empirisme de Berkeley aboutissent au même résultat, c'est-à-dire au relationisme. Leibniz et Berkeley refusent la thèse de Newton parce quelle est incompatible avec leurs présupposés ; l'un et l'autre conçoivent le monde comme un ensemble de relations entre des êtres immatériels. La fin du texte tente de montrer que, d'un point de vue classique, les théories relationistes ne sont pas entièrement fondées. This text provides a survey of Leibniz's and Berkeley's arguments against the theory of absolute space, that Newton had tried to prove by the so-called « bucket experiment ». According to Leibniz, absolute space cannot exist because its existence could be conformable neither to the principle of the identity of indiscernibles, nor to the principle of sufficient reason. Then Euclidean space is a set of points which have the same qualitative properties ; in such a space, every possible world would belong to an infinite class of indiscernibles worlds. On the other hand, Berkeley s criticism follows from empiricist premises : we cannot observe anything but relative motions and relative locations, i. e. relations that bodies bear to one another; substantival space is an abstraction. Hence, Leibniz's rationalism and Berkeley's empiricism come round to the same issue, i. e. relationism. Leibniz and Berkeley deny Newton's thesis because it is incompatible with their postulates ; both conceive the world as a set of relations that immaterial beings have to one another. In the end of the text, the author tries to show that, from a classical point of view, relationist theories are not entirelv well-grounded. (shrink)

In his Essay Towards a New Theory of Vision Berkeley argues that it is only a happy accident that we are aware of space and objects in space by means of vision, and that the logically primary way in which we are aware of space is by touch. Berkeley 's argument is that all connections between the visual and the spatial properties of things are contingent. Thus we may judge an object's distance from us by noting the number and size (...) of intervening objects, by the sensations arising when we turn our eyes to it, from the confused appearance of the object, or from the straining of our eyes ; but in each case there is only a contingent connection between the method used and the distance of the object from the observer. Similar considerations apply to the judgements we make by sight of magnitude and situation. If this is so then clearly we must have some other way of making spatial judgements, for how else could we establish the various contingent links between what we see and space? This other method must, of course, be by touch, but then touch cannot be merely contingently related to space, for then we would need a third method and so on. Berkeley is therefore led to maintain that there are necessary connections between touch and space. For Berkeley, then, it is impossible for us to make spatial judgements, judgements of the distances between objects and of the magnitudes and positions of objects, by means of sight alone, whereas it is possible to make such judgements on the basis of information obtainable from touch alone. It is this joint claim that I wish to consider. (shrink)

Berkeley held space to be relational. On the other hand, He took extension to be composed of absolute minima. This paper offers an analysis of berkeley's views on the nature of minimum visibles and space and related notions, E.G., Distance, Extension, And figure. The difficulties in his theory are clearest in the analysis of figure where it is argued that minima can have neither figure nor extension and that, Contrary to berkeley's view, Extension and figure cannot be composed of such (...) minima. The paper concludes by arguing that the "esse est percipi" doctrine is false, Since it entails that there are minimum visibles and that distances be specifiable in terms of minimum visible distances. (shrink)

Independently of any eighteenth century work on the geometry of parallels, Thomas Reid discovered the non-euclidean "geometry of visibles" in 1764. Reid's construction uses an idealized eye, incapable of making distance discriminations, to specify operationally a two dimensional visible space and a set of objects, the visibles. Reid offers sample theorems for his doubly elliptical geometry and proposes a natural model, the surface of the sphere. His construction draws on eighteenth century theory of vision for some of its technical features (...) and is motivated by Reid's desire to defend realism against Berkeley's idealist treatment of visual space. (shrink)

Berkeley's essay on vision was published in the spring of 1709. It was recognised at once as a book of considerable importance, and there was a second edition within the first year. The author was still only 24. His design, he wrote, was to show the ‘manner we perceive by sight the distance, magnitude and situation of objects’. Hitherto, writers on optics had ‘proceeded on wrong principles’.

The topic of thesis was not selected at random. In the last two years or so I have become increasingly interested in that broad complex of problems traditionally grouped together under the name of the 'Mind - Body' problem, and have become increasingly convinced that the solution of this problem is one of the most exciting, and certainly one of the most difficult, problems confronting modern science.