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Title: De Motu and the Analyst: A Modern Edition, With Introductions and Commentary (New Synthese Historical Library Texts and Studies in the History of Ph) by George Berkeley, Douglas M. Jesseph ISBN: 0-7923-1520-0 Publisher: Kluwer Academic Publishers Pub. Date: 01 February, 1992 Format: Hardcover Volumes: 1 List Price(USD): $176.00

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Average Customer Rating: 5 (1 review)

Rating: 5
Summary: Very worthwhile.
Comment: This is an expensive item, and it obviously is not for everyone. That said, it is a valuable work and should be considered an adjunct to Fraser's "Works of George Berkeley." In Jesseph's book, he presents two of Berkeley's essays - "De Motu", and "The Analyst", to which he provides extensive introductions and references. Both essays (and Jesseph's supporting material) will be reviewed in turn.

"De Motu" (On Motion) was originally written in Latin. Jesseph's first service is that he provides an English translation along with the Latin version. In this essay, Berkeley described and critiqued then-contemporary theories on the nature of motion. Jesseph does the reader a great service by introducing 17th century physics to the reader, explaining terms, and tracking down Berkeley's references.

What makes "De Motu" something other than a period piece is Berkeley's methodology. In "A Treatise Concerning the Principals of Human Knowledge", Berkeley laid out an argument against terms denoting entities which could not be experienced or imagined. An example of such a thing was Newton's absolute space. In "De Motu", Berkeley wrote:

"And so let us imagine that all bodies have been destroyed and reduced to nothing. What remains they call absolute space, all relation which arose from the position and distances of bodies having been removed along with the bodies themselves. Now this space is infinite, immobile, indivisible, insensible, without relation and without distinction. That is, all of its attributes are privative and negative: it seems therefore to be merely nothing. ... Therefore let us take from absolute space just the words, and nothing will remain in the sense, imagination, or intellect; therefore they designate nothing, except pure privation or negation, that is, merely nothing."

While Berkeley granted that such terms could be useful in calculation, he argued that they led only to meaningless wrangling when imagined as real. He held up a difference between Newton and Torricelli on force as an example:

"Newton says that impressed force consists solely in action, and it is the action exerted on a body to change its state, nor does it remain after the action. Torricelli contends that a certain accumulation or aggregate of impressed forces is received by percussion in a mobile body, and that the same remains and constitutes impetus. ... And in truth, though Newton and Torricelli seem to disagree, nevertheless, each advances a consistent account, and the matter is adequately explained by both. For all forces attributed to bodies are ... mathematical hypotheses. Mathematical entities, however, have no stable essence in the nature of things: they depend on the notion of the definer: whence the same thing can be explained in different ways."

In sum, "De Motu" is valuable both as a general critique of science and as a fascinating application of Berkeley's epistimological ideas and is well worth reading on that basis.

The other Berkeley essay Jesseph covers is "The Analyst". This essay attacked the soundness of the mathematical foundations of Newton's calculus. Because Newton's notation, method, and terminology are no longer in use, the essay is difficult for the modern reader to follow. Jesseph's introduction to "The Analyst" is a fine piece of scholarship and immensely helpful, even necessary, to full understanding of Berkeley's essay.

"The Analyst" was motivated by apologetic purposes. Berkeley was annoyed at the contrast set up by "free thinkers" between religious belief and math and the sciences, and he sought to demonstrate that mathematics has its mysteries as much as religion. His target was Newton's calculus: in particular, fluxions. Fluxions were infinitesimal quantities, which Berkeley attacked as being literally inconceivable, following his general principals of meaning, and further that Newton did not handle them consistently - sometimes rounding them to zero, and other times not, with the only criterion being whichever was necessary to make the answers come out right.

"The Analyst" set off a firestorm among mathemeticians. Berkeley's acid style led to angry responses, but the mathematical problems Berkeley had attacked were real, and the defenders of Newton offered very different (and incompatible) approaches to resolving the problems Berkeley had raised, and they soon began attacking each other. It was only in the nineteeth century that the problems surrounding the foundations of Calculus were finally settled.

Certainly, "The Analyst" is of interest as a part of the history of mathematics, but it is also of interest as an application of Berkeley's general approach. The paragraph below on infinitesmals, for example, clearly follows the same approach as that on absolute space quoted previously:

"Now to conceive a Quantity infinitely small, that is, infinitely less than any sensible or imaginable Quantity, or than the least finite Magnitude, is, I confess, above my Capacity. But to conceive a Part of such infinitely small Quantity, that shall be infinitely less than it, and consequently though multiply'd infinitely shall never equal the minutest finite Quantity, is, I suspect, an infinite Difficulty to any man whatsoever...Nothing is easier to devise Expressions or Notations, for Fluxions and Infinitesimals of the first, second, third, fourth and subsequent Orders, proceeding in the same regular form without end or limit ... dx, ddx, dddx, ddddx, &c. These Expressions indeed are clear and distinct, and the Mind finds no difficulty in conceiving them to be continued beyond any assignable Bounds. But if we remove the Veil and look underneath, if laying aside the Expressions we set ourselves attentively to consider the things themselves, which are supposed to be expressed or marked thereby, we shall discover much Emptiness, Darkness, and Confusion..."

The last thing worth noting about "The Analyst" is that Berkeley wrote two follow-on essays in response to Newton's defenders, both of which are available in Fraser's "Works".