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$Math 121 Test #1 Spring 2012$

$Math 121 Test #2 Spring 2012$

8REVIEWSJesseph is on different ground in dealing with The Analyst.He is prepared to make stronger philosophical claims for it. It ispresented as an essential pan of our understanding of Berkeley'saccount of science and mathematics and Jesseph claims that it isindependent of immaterialism (however still no discussion ofthis). He forays into the heady world of Berkeley scholarship indiscussing the possible identity of the 'infidel mathematician'attacked in the text. His presentation of the mathematicalbackground is detailed in comparison to his discussion of themechanical background to De Motu and his discussion of theelements of the infinitesimal calculus and Newton's calculus offluxions is clear, as is his account of Berkeley's arguments againstthese. The 'outline analysis' of The Analyst is useful for thoseunfamiliar with that work. Once again the discussion of responsesto Berkeley's position is scanty, as is the note on the text.As an introduction to the two texts it serves well - but noBerkeley novice would buy so expensive a work (Â£51.00)Specialists in Berkeley gain no great insights from theintroductory material and no detailed interpretative strategy ispresented. Issues which could be addressed are sidestepped, suchas the immaterialism issue, the relation of theory of meaning toontology, etc.. It (rightly) claims no superior status for itstranslation of De Motu or the text of The Analyst over preexistingversions. What is puzzling about this book is who mightconstitute its intended readership.Paul O'CradyTrinity College Dublin9REVIEWSVision: Variations on Some Berkeleian Themes. Robert Schwartz,Oxford, Basil BIackwell, 1994, Pp. 162.This relatively short book, in four chapters, addresses some keyissues in the theory of vision: the manner in which we perceivedistance and size. and the nature and relevance of inference in theperceptual process. These issues are presented in the context ofBerkeley's seminal work on vision and throughout the book theauthor is at pains to present an impartial account of Berkeley'swork in the light of subsequent research. Appropriately, the bookconcludes with a comparison of Berkeley's position with that of J.1. Gibson.Perhaps one of the most engaging qualities of the book is thefairness with which Schwartz treats not only Berkeley but all ofthe other "vision theorists", psychologists, and philosophers whopopulate the pages. Indeed, it is the willingness to attempt to see"what was really meant" in Berkeley's writings, rather than beingcontent with the (often incorrect) interpretations of others, whichcontinually provides one with the motivation to carry on readingeven when one disagrees with Schwartz's perspective. Given thatBerkeley's writings are very often misunderstood, this is a verywelcome characteristic. Indeed, as a companion to Berkeley's owntext, this book would play a very useful role in keeping a reader'sprejudices at bay whilst coming to an understanding of Berkeley'sintended message. Nonetheless Schwartz is no apologist forBerkeley; rather he provides an impartial assessment ofBerkeley's position on vision, an altogether more comfortableendeavour.
inREVIEWSREVIEWS11From a Berkeleian perspective, Chapter 1 of Schwartz's bookis undoubtedly the most interesting and compelling. It takesBerkeley's position on distance and views it from the differentperspectives of subsequent vision theorists. If I can pick out onesingle detail for mention, it is the problem of calibrating one'sperceived distance (or "egocentric distance") with absolutedistance (or "ecocentric distance"). For Berkeley, this isaccomplished by learning, through association of the perceiveddistance and the actions of the perceiver in his environment. Thatis, it is achieved through the association of proprioceptiveinformation with exteroceptive information. This is an issue ofgreat contemporary interest in psychology, epistemology, andcomputational perception, and Schwartz does no small service inreminding us that it is not a new problem. He also provides avery well presented discussion on the nature of binocularstereopsis and, in particular, on the relevance of stereopsis toBerkeley's position. Contrary to common belief, stereopsis doesnot damage in the least Berkeley's case for the indirectness of theperception of distance and it is instructive to read Schwartz'saccount of this.Chapter 2 treats the perception of size and, inter alia, how itis we perceive given objects to have a constant size irrespective oftheir distance from us and in spite of the consequent variation inthe size of the image which is projected onto the retina.Berkeley's position on this issue is that the perception of size isachieved through the association of the tangible size of objectswith (a) the visible size of an object - the tangible size beingproportional to the visible size: (b) the relative blur of the visualappearance - tangible size being inversely related to the degree ofblur; and (c) the intensity of the visual appearance - the tangiblesize being inversely related to the intensity. Unfortunately, mostof the chapter is given over to a discussion of a position thatBerkeley himself rejects: the so-called 'taking account of distance'thesis. This thesis posits that the magnitude of an object isperceived by the prior estimation of its distance from theobserver and by exploiting this information with a knowledge ofthe visual angle subtended by that object at the retina of the eye.Chapter 3 on perceptual inference introduces manyinteresting issues, not the least of which is Schwartz's observationthat Berkeley's theory of vision can be construed as a thesis thatthe perceptual process is like linguistic undertanding. That said,very little of chapter 3 addresses overtly Berkeleian issues. Thisis not surprising given that Berekeley argued strongly that visualperception does not involve any sort of deliberate inferential (orreasoning) process. This is no criticism of the book for, as Schwartzpoints out, a great deal of modern vision theory presumes thevalidity of the inferential position. Again, the service whichSchwartz does is to assess this purported validity in a balancedmanner. In doing this, Schwartz notes a distinction (as he doeselsewhere in the book) between organic or physiological processesof visual sensing, on the one hand, and psychic or psychologicalprocesses, on the other. Schwartz's point is that it is very difficultto say with any confidence where one should draw this distinctionin the first place. Arguments for the validity of perceptualinference are often based, for example, on some inadequacy ininformational content which results from purely physiological
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