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  • 1/10/2004

George Berkeley


George Berkeley studied divinity and later lectured at Trinity College, Dublin. In 1734 he was appointed bishop at Cloyne, in which office he devoted himself to the social and economic plight ofIreland.
An eminent metaphysician, Berkeley is best known for his attack on the logical foundation of the calculus as developed byNewton. In his tractThe analyst: or a discourse addressed to an infidel mathematician he tried to argue that although the calculus led to true results its foundations were no more secure than those of religion.
He declared that the calculus involved a logical fallacy of a shift in the hypothesis. He described derivatives as follows:

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?

Berkeley's criticisms were well founded and important in that they focused the attention of mathematicians on a logical clarification of the calculus. He developed an ingenious theory to explain the correct results obtained, claiming that it was the result of two compensating errors.

De Moivre,Taylor,Maclaurin,Lagrange,Jacob Bernoulli andJohann Bernoulli all made attempts to bring the rigorous arguments of the Greeks into the calculus.Maclaurin inTreatise on fluxions gave the best response to Berkeley.

Article by: J J O'Connor and E F Robertson

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