By Douglas M. Jesseph
Jesseph starts with Berkeley's radical competition to the obtained view of arithmetic within the philosophy of the overdue 17th and early eighteenth centuries, while arithmetic used to be thought of a "science of abstractions." seeing that this view heavily conflicted with Berkeley's critique of summary principles, Jesseph contends that he was once pressured to come back up with a nonabstract philosophy of arithmetic. Jesseph examines Berkeley's certain remedies of geometry and mathematics and his well-known critique of the calculus in The Analyst.
By placing Berkeley's mathematical writings within the point of view of his better philosophical undertaking and analyzing their effect on eighteenth-century British arithmetic, Jesseph makes an enormous contribution to philosophy and to the background and philosophy of science.
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Extra resources for Berkeley's Philosophy of Mathematics
Early on, Berkeley saw the rhetorical advantage to be gained by using Locke's own words as a way of discrediting the theory of abstract ideas. In the Philosophical Commentaries Berkeley declares, "If men did not use words for Ideas they would never have thought of abstract ideas. These include a contradiction in their nature" (Commentaries, 561, dismissing Essay IV, vii, 9). g. in the matter of Abstraction to bring Lockes general triangle at the last" (Commentaries, 687). Thus, while the argument in §13 of the Introduction may not be a direct application of the argument from impossibility to the kinds of abstract ideas characterized in §§7 -9, this is really irrelevant to Berkeley.
But, alternatively, the line could be thought of as an abstraction in which a perceived object's length is considered while its breadth is disregarded. 15 In this case, abstraction does not form a new mental object, but features of a pre14. Kenelm Digby draws a distinction between these two kinds of abstraction in the second of his Two Treatises, where he declares that "[abstraction] we do two severall wayes; the one, when our manner of apprehension determineth us to one precise notion, which is so summed up within it selfe, as it not only abstracteth from all other notions, but also quite excludeth them, and admitteth no society with them.
S. or applicable copyright law. • 33 • Abstraction and the Berkeleyan Philosophy of Mathematics straight lines, which form three angles where they meet, without thinking in any way of the measure of these angles or of the lengths of their sides. (Leclerc 1711, 81-82) He concludes that the faculty of pure intellection is the only true source of geometric knowledge, and that Berkeley's attempt to reduce geometric knowledge to sensation and imagination has confused the issue. 18 Moreover, even if the distinction between intellect and imagination is granted, Berkeley argues that the object of geometry must be an idea of the imagination, since "it nevertheless seems to me that the pure intellect is entirely concerned with spiritual things known by the mind's reflection on itself, but [pure intellect] could in no way deal with the ideas arising from sensation, such as extension" (Works 8: 50).
Berkeley's Philosophy of Mathematics by Douglas M. Jesseph