Bishop Berkeley Exorcises the Infinite: Fuzzy Consequences of Strict Finitism

Hume Studies 18 (2):511-536 (1992)
  Copy   BIBTEX

Abstract

In lieu of an abstract, here is a brief excerpt of the content:Bishop Berkeley Exorcises the Infinite: Fuzzy Consequences of Strict Finitism1 David M. Levy Introduction It all began simply enough when Molyneux asked the wonderful question whether a person born blind, now able to see, would recognize by sight what he knew by touch (Davis 1960). After George Berkeley elaborated an answer, that we learn to perceive by heuristics, the foundations ofcontemporarymathematics wereinruin. Contemporary mathematicians waved their hands and changed the subject.2 Berkeley's answer received a much more positive response from economists. Adam Smith,in particular, seizedupon Berkeley's doctrine that welearn to perceive distance tobuild anelaborate system in which one learns to perceive one's self-interest.3 Perhaps because older histories of mathematics are a positive hindrance in helping us understand the importance of Berkeley's argument against infinitesimals,4 its consequences for economics have passed unnoticed. If infinitesimal numbers are ruled out, and we wish to maintain an algebra, then we rule out infinite numbers. This implication of Berkeley's argumenthas a dramatic implication for our understanding ofthe history ofideas about rule-directed action. Let me motivate this claim with a well-known historical problem. The social doctrine set forth by John Locke outside the Two Treatises depends critically upon individual belief about possible states of infinite pain or pleasure. The critical issue for the intolerance of atheism in Locke's system is his claim that without beUefin the infinite bliss of heaven forgone by a criminal, there is no reason to think a calculating individual will avoid crime.5 Locke's discussion is so different from the discussion of religion by David Hume and Smith. Here, questions of the substance of belief—the infinite worth of Heaven—have largely vanished.6 What happened between Locke and Hume-Smith? One answer is Pierre Bayle and Bernard Mandeville. Berkeley's doctrine that only the finite is perceived is, I think, a better answer. Out of sight, out ofmind. In this paper I propose to give a close look at the content and consequences ofBishop Berkeley's once famous Towards a New Theory ofVision. While there are other aspects ofBerkeley's work that attract Volume XVIII Number 2 511 DAVID M. LEVY attention from historians ofeconomics,7 1 shall claim that Berkeley's insight into human perception in the Theory of Vision is central to Adam Smith's attempt to found economic behaviour on the self-awareness of systematic illusion. There is no doubt that Smith finds that much ofhuman behaviour is characterized by illusion.8 The difficulty arises, or so it seems to me, from modern unwilUngness to beheve that illusion can be systematic. There are four pieces to my argument. First, we consider Berkeley's statementofwhat we shall call his doctrine ofstrict finitism in perception.9 Berkeley puts forward two postulates: 1) there exists some minimum perceptible quantity, and 2) distance is not perceived directly but by experience. Second, we define strict finitism and demonstrate that it translates into the claim that perception is fuzzy in a technical sense. If Berkeleian perception is fuzzy, then some modern criticism of Berkeley's strict finitism is based upon a simple misunderstandingofthe propertiesoffuzzyrelations. Thisis quite easy to set right. (Getting right the doctrine of those who implicitly take perception to be fuzzy—Adam Smith is my prime candidate—will be muchharder.)Third, wereconsiderBerkeley's dispute withMandeville on the role ofinfinite gain in choice. Here, we find Mandeville putting forward the Berkeleian position that if infinite amounts mattered, people would not behave as they do. Berkeley's position against Mandeville, however, seems to depend upon the supposition that infinite distance is sensible.10 Earlier, however, the position that Mandeville argued for was defended by Berkeley. Fourth, we ask why all this isn't well known. The debate between Berkeley and Mandeville has been well studied, as has been the link between Berkeley and the Scots. In fact, our work focuses on one aspect of Berkeley's work that led to his challenge of the contemporary foundations of the calculus. If sense is a matter of perception, and infinitesimals cannot be perceived, then they are quite literally nonsense. Armed with this insight, Berkeley refuted contemporary mathematics. Nevertheless, the calculus was too...

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Berkeley and Irish philosophy.David Berman - 2005 - New York: Thoemmes Continuum.
Bishop Berkeley.Joseph M. Hone - 1931 - New York,: Macmillan. Edited by Mario M. Rossi.
The solipsism of Bishop Berkeley.Denis Grey - 1952 - Philosophical Quarterly 2 (9):338-349.
Bishop Berkeley and his message.George H. Mead - 1929 - Journal of Philosophy 26 (16):421-430.
The Works of George Berkeley, Bishop of Cloyne. [REVIEW]E. T. - 1956 - Review of Metaphysics 9 (3):515-515.

Analytics

Added to PP
2011-02-21

Downloads
34 (#407,456)

6 months
3 (#447,120)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

The Molyneux Problem.John W. Davis - 1960 - Journal of the History of Ideas 21 (1/4):392.
Utility-Enhancing Consumption Constraints.David Levy - 1988 - Economics and Philosophy 4 (1):69.

Add more references