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530 HISTORY OF PHILOSOPHY Berkeley's Philosophy o/Science. By Richard J. Brook. International Archives of the History of Ideas, 65. (The Hague: Martinus Nijhoff, 1973. Pp. 210) Although Berkeley's philosophy of science is emphasized in A. D. Ritchie's George Berkeley A Reappraisaland creatively illuminated in C. M. Turbayne's The Myth of Metaphor , Professor Brook's new volume is the first to deal exclusively with Berkeley's philosophy of science and the first to span all of Berkeley's scientific interests. Ritchie's book contains a profound and lively treatment of the theory of vision and the philosophy of physics. Turbayne's volume represents a unique approach, elaborating on the theory of vision in the context of an extended language metaphor. Brook's approach is more analytic than Ritchie's, less novel than Turbayne's, and more comprehensive than either. The first of five chapters deals with the theory of signs which sets the tone for the next three chapters on the theory of vision, physics, and mathematics. The fifth chapter is a summary of preceding material concentrating on Berkeley's relationship to Newton. Brook seems well equipped to handle his material, displaying some technical expertise in mathematics and a wide ranging acquaintance with Berkeley's works. As a straightforward, analytic approach to the whole of Berkeley's scientific thought, Brook's volume is a welcome addition to the literature. Perhaps the most significant part of the book is the chapter on mathematics, for this aspect of Berkeley's thought has been relatively neglected. Brook sees Berkeley's philosophy of mathematics as a paradigm for the application of the theory of signs to the sciences. Berkeley's account displays what Brook correctly views as the significant features of the language metaphor: the contingent relation between sign and designatum, the importance of order, syntax, and formalism relative to reference, and the manner in which particulars are rendered general. The problem of general terms and the theory of measurement dominate Brook's discussion of arithmetic and geometry in which he draws from the Principles and the Essay. He notes that Berkeley's nominalism precludes the "idea" of number as a universal so that number terms have divided reference. He rejects intuitionism, arguing instead that Berkeley's view of arithmetic is closer to modem formalism as represented by Hilbert: arithmetic is a manipulation of perceptual objects, i.e., strokes on a page and other signs lacking any extra-systematic reference. In connection with geometry Brook claims Berkeley confuses the general significance of a particular figure with the necessary truth of propositions demonstrated from that figure. In the case of measurement he argues that the application of geometry assumes some empirical domain which satisfies the axioms. But the doctrine of sensible minima, along with Berkeley's view that geometry is the science of perceived extension, preclude the assignment of magnitude to certain objects and poses problems in demonstrations such as the bisection of a line. In The Analyst Berkeley levies a number of criticisms at the Newtonian fluxional calculus . Brook discusses one of these in detail, the method of "compensation of errors" later advanced also by Lagrange. He argues that it is not a mathematically valid substitute for Newton's method of differentiation which is also invalid. Brook shows an appreciation of Berkeley's contributions to the development of the calculus. He points out that Berkeley exposed the need to clarify some of Newton's basic concepts such as "the ultimate ratio of evanescent increments" (which Berkeley describes as "the ghosts of departed quantities "). Brook's treatment is not a historical study but an analytic comparison of Berkeley and Newton. Whatever the ultimate merits of his analysis prove to be, Professor Brook has performed a service in calling more attention to Berkeley's criticism which Cajori describes in his History o/ Mathematics as "the most spectacular mathematical event of the eighteenth century in England." The attention given to Berkeley's theory of signs in the first chapter of the book is of special interest. Against Turbayne, Brook argues that Berkeley's theory of phenomenal BOOK REVIEWS 531 language cannot be extended beyond a mere metaphor into a model for the sciences...


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