By Douglas M. Jesseph
Jesseph starts off with Berkeley's radical competition to the acquired view of arithmetic within the philosophy of the past due 17th and early eighteenth centuries, whilst arithmetic used to be thought of a "science of abstractions." given that this view heavily conflicted with Berkeley's critique of summary rules, Jesseph contends that he was once pressured to come back up with a nonabstract philosophy of arithmetic. Jesseph examines Berkeley's special remedies of geometry and mathematics and his recognized critique of the calculus in The Analyst.
By placing Berkeley's mathematical writings within the standpoint of his greater philosophical undertaking and interpreting their influence on eighteenth-century British arithmetic, Jesseph makes an incredible contribution to philosophy and to the heritage and philosophy of science.
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Extra info for Berkeley's Philosophy of Mathematics
He imagines that "although we can be absolutely sure that the proof would apply to right triangles of any color whatever, we have no right to conclude, from the lone fact that no mention is made of the relative sizes of the three angles and sides, that the proof would apply to triangles of any determinate shape whatever" (Pitcher 1977, 76). This is unconvincing, however. Pitcher overlooks the fact that representative generalization requires that the result be generalized only to cover those figures which share the properties which are used in the course of the demonstration.
S. or applicable copyright law. • 35 • Abstraction and the Berkeleyan Philosophy of Mathematics problems in the sciences, especially mathematics. In later chapters we will be concerned with the influence of this theory on Berkeley's philosophy of mathematics. In particular, I will argue in the second chapter that when he developed his alternative to the theory of abstract ideas, Berkeley's views on the nature of geometry underwent a significant change. I will also consider whether this theory is as free from abstraction as Berkeley imagined but will postpone this discussion until the end of chapter 3, as it ties in with some difficulties relating to the prospects for a purely nominalistic theory of arithmetic.
See especially Weinberg (1965) and Winkler (1989, chapter 2) for different presentations of it. The anthology edited by Doney (1988) contains essays addressing various aspects of Berkeley's case against abstraction. ; Berkeley's Philosophy of Mathematics Account: ns148561 Copyright © 1993. University of Chicago Press. All rights reserved. S. or applicable copyright law. • 22 • Chapter One impossible cannot be conceived, would suffice to refute the doctrine of abstraction. For the argument to succeed, Berkeley must show that the doctrine of abstraction characterizes abstract ideas in such a way that they must be ideas of things which cannot possibly exist.
Berkeley's Philosophy of Mathematics by Douglas M. Jesseph