Berkeley

George Berkeley

Born: 12 March 1685 in Dysert Castle (near Thomastown), County Kilkenny, Ireland
Died: 14 Jan 1753 in Oxford, England

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Berkeley is best known for his attack on the logical foundation of the calculus as developed by Newton.

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 of Ireland.

An eminent metaphysician, Berkeley is best known for his attack on the logical foundation of the calculus as developed by Newton. In his tract The 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 and Johann Bernoulli all made attempts to bring the rigorous arguments of the Greeks into the calculus. Maclaurin in Treatise on fluxions gave the best response to Berkeley.

References elsewhere in this archive:

Tell me about Berkeley's part in the rise of calculus

Other Web sites:

Clarke University, USA

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. A A Luce, The Life of George Berkeley, Bishop of Cloyne (1968).
  4. J M Hone and M M Rossi, Bishop Berkeley: His Life, Writings, and Philosophy (1931).
  5. J Wild, George Berkeley: A Study of His Life and Philosophy (New York, 1962).
  6. W Doney, Berkeley on Abstraction and Abstract Ideas (1989).
  7. F Cajori, A history of the conceptions of limits and fluxions in Great Britain from Newton to Woodhouse (Chicago, 1919), 57-95.
  8. W Breidert, George Berkeley 1685-1753 (Basel, 1989).
  9. D M Jesseph, Berkeley's philosophy of mathematics (Chicago, 1993).
  10. H Pycior, Mathematics and philosophy : Wallis, Hobbes, Barrow and Berkeley, Journal of the History of Ideas 48 (1987), 265-287.
  11. J Dancy, Berkeley, an Introduction (1987).
  12. A A Luce, Berkeley and Malebranche: A Study in the Origins of Berkeley's Thought (1988). 
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JOC/EFR February 1996