CALCULUS Understanding Its Concepts and Methods
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George Berkeley (1685--1753)--- Historical Sketch
The University of California's first campus was founded in Berkeley. Here is a quote from the Home Page of that city:
"In 1878, twenty-eight years after California became the Union's 31st State, a small town nestled on San Francisco Bay's eastern shore was incorporated as the City of Berkeley. Previously part of a larger area known as Oceanview, Berkeley was named after philosopher Bishop George Berkeley, born near Thomastown, Ireland in 1685.
George Berkeley's reputation as an esteemed graduate of Trinity College in Dublin and his seemingly tireless efforts to establish a college of Christianity in the American Colonies prompted his intimate friend, Alexander Pope, to declare him "possessed of every virtue." Bishop Berkeley resided in Rhode Island for nearly four years, exhausting much of his own fortune as he waited for funds promised by the British government. Ultimately, he was compelled to return to Europe, never having received the necessary capital to see his dream to fruition. He died January 14, 1753, at Oxford, England."
George Berkeley, an Irish philosopher, criticized Newton's calculus in The analyst: or a discourse addressed to an infidel mathematician in 1734, the same year he was made Bishop of Cloyne. This critique of the foundations of calculus was very influential in the subsequent development of mathematics.
As a young man, George Berkeley (pronounced bark-lee) theorized that we cannot know if an object is, we can only know if an object is perceived by a mind. We can't think or talk about an object's being. All that we know about an object is our perception of it. Berkeley is perhaps best known for his motto, esse is percipi, "to be is to be perceived."
Berkeley disdained abstraction, and mathematics is certainly abstract. He particularly aimed his sights at Newton and the basic ideas of calculus. Of the derivative, he said in his above-mentioned tract, "And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities? " He was here referring to derivatives of functions (fluxions) and the defining equation where of course the limit is taken as goes to While Berkeley's criticisms of Newton and his ideas were based on his religious revulsion of Newton's ideas of a mechanistic universe, his attack on Newton and his development of calculus had a good effect in that it prompted mathematicians to clarify and establish a logical foundation for calculus.
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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.