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By Vanini Giulio Cesare

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Berkeley's Philosophy of Mathematics Account: ns148561 Copyright © 1993. University of Chicago Press. All rights reserved. S. or applicable copyright law. • 27 • Abstraction and the Berkeleyan Philosophy of Mathematics Indeed, the tactic of quoting Locke's discussion of the abstract idea of a triangle as a means of "clarifying" the doctrine of abstract ideas was Berkeley's favorite weapon in his polemics against abstraction. For example, in the New Theory of Vision Berkeley, declaring the abstract idea of a triangle "altogether incomprehensible," facetiously recommends consulting Locke's Essay to clarify the matter because "if anyone were able to introduce that idea into my mind, it must be the author of the Essay concerning Humane Understanding; he who has so far distinguished himself from the generality of writers by the clearness and significancy of what he says" (Theory, § 125).

Indeed, it gives a perfectly acceptable explanation of why such fallacious inferences are mistaken. ; Berkeley's Philosophy of Mathematics Account: ns148561 Copyright © 1993. University of Chicago Press. All rights reserved. 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.

In fact, there are moderate versions of the abstractionist thesis which are close to his own view, so that his claim to have refuted all varieties of the doctrine of abstract ideas is rather overblown. This can best be seen by presenting his central argument and noting how a defender of the doctrine of abstract ideas could avoid much of its force. " 10 It is intended to show that to frame an abstract idea would be to frame an idea of an impossible object that cannot be consistently described. This claim, in co~unction with the principle that what is (logically) 10.

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