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===Berkeley and infinitesimals===
===Berkeley and infinitesimals===
In 1734 Bishop Berkeley published a tract called ''The Analyst''. In this, the new [[calculus]] of [[Newton]] and [[Leibniz]] was attacked and especially the concept of "fixed infinitesimal" set forth by Isaac Newton in the [[Principia]] and in an appendix to the [[Opticks]]. Since the concept of  an infinitely small, and yet finite, quantity was  still fairly muddled and confused, Berkeley, although not a mathematician by training, made an extremely effective attack. His arguments provoked controversy among mathematicians and led to the clarification of central ideas underlying the new theory.
In 1734 Bishop Berkeley published a tract called ''The Analyst''. In this, the new [[calculus]] of [[Newton]] and [[Leibniz]] was attacked and especially the concept of "fixed infinitesimal" set forth by Isaac Newton in the [[Principia]] and in an appendix to the [[Opticks]]. Since the concept of  an infinitely small, and yet finite, quantity was  still fairly muddled and confused, Berkeley, although not a mathematician by training, made an extremely effective attack. His arguments provoked controversy among mathematicians and led to the clarification of central ideas underlying the new theory.
<ref>George Berkeley (1734)[http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.html THE
ANALYST;] or, a discourse addressed to an Infidel Mathematician wherein it is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith</ref>


== External links ==
== External links ==

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George Berkeley (12 March 1685 – 14 January 1753), also known as Bishop Berkeley, was an Irish philosopher. He is best known for developing an early form of idealism, according to which the only things which exist are minds and the ideas which they perceive. The University of California, Berkeley, and the city that grew up around it were both named after him.

"Philosophy being nothing else but the study of wisdom and truth, it may with reason be expected that those who have spent most time and pains in it should enjoy a greater calm and serenity of mind, a greater clearness and evidence of knowledge, and be less disturbed with doubts and difficulties than other men. Yet so it is, we see the illiterate bulk of mankind that walk the high-road of plain common sense, and are governed by the dictates of nature, for the most part easy and undisturbed. To them nothing that is familiar appears unaccountable or difficult to comprehend. They complain not of any want of evidence in their senses, and are out of all danger of becoming Sceptics. But no sooner do we depart from sense and instinct to follow the light of a superior principle, to reason, meditate, and reflect on the nature of things, but a thousand scruples spring up in our minds concerning those things which before we seemed fully to comprehend. Prejudices and errors of sense do from all parts discover themselves to our view; and, endeavouring to correct these by reason, we are insensibly drawn into uncouth paradoxes, difficulties, and inconsistencies, which multiply and grow upon us as we advance in speculation, till at length, having wandered through many intricate mazes, we find ourselves just where we were, or, which is worse, sit down in a forlorn Scepticism." From 'A Treatise Concerning the Principles of Human Knowledge' (1710).

[1]

Contributions to philosophy

Berkeleyan idealism

"But, say you, surely there is nothing easier than for me to imagine trees, for instance, in a park [. . .] and nobody by to perceive them. [...] The objects of sense exist only when they are perceived; the trees therefore are in the garden [. . .] no longer than while there is somebody by to perceive them."

The central thesis of Berkeley's idealism was that only minds and the ideas which they perceive exist. This committed him to immaterialism, the position that there are no material substances, where a substance is something which could exist even if nothing else did. According to Berkeley, objects like trees and chairs existed, but they could not exist independently of being perceived by a mind. He summarised this position with his famous dictum, "Esse est percipi" ("To be is to be perceived").

This thesis has been commonly expressed as "If a tree falls in a forest and no one is there to hear it, does it make a sound?" Berkeley's ultimate answer to this was that there is always a mind that perceives it - the mind of God.

Berkeley and infinitesimals

In 1734 Bishop Berkeley published a tract called The Analyst. In this, the new calculus of Newton and Leibniz was attacked and especially the concept of "fixed infinitesimal" set forth by Isaac Newton in the Principia and in an appendix to the Opticks. Since the concept of an infinitely small, and yet finite, quantity was still fairly muddled and confused, Berkeley, although not a mathematician by training, made an extremely effective attack. His arguments provoked controversy among mathematicians and led to the clarification of central ideas underlying the new theory. [2]

External links

References

  1. George Berkeley (1710) A Treatise Concerning the Principles of Human Knowledge
  2. George Berkeley (1734)[http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.html THE ANALYST;] or, a discourse addressed to an Infidel Mathematician wherein it is examined whether the Object, Principles, and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith