The Analyst, Or, A Discourse Addressed To An Infidel Mathematician: Wherein It Is Examined Whether The Object, Principles, And Inferences Of The Modern Analysis Are More Distinctly Conceived, Or More Evidently Deduced, Than Religious Mysteries And Poin...

by George Berkeley

It hath been an old remark, that Geometry is an excellent Logic. And it must be owned that when the definitions are clear; when the postulata cannot be refused, nor the axioms denied; when from the distinct contemplation and comparison of figures, their properties are derived, by a perpetual well-connected chain of consequences.

Genres: Philosophy, Mathematics

Hardcover

First published June 1, 2004

About the author

George Berkeley (/ˈbɑːrklɪ/;[1][2] 12 March 1685 – 14 January 1753) — known as Bishop Berkeley (Bishop of Cloyne) — was an Anglo-Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism" (later referred to as "subjective idealism" by others). This theory denies the existence of material substance and instead contends that familiar objects like tables and chairs are only ideas in the minds of perceivers, and as a result cannot exist without being perceived. Berkeley is also known for his critique of abstraction, an important premise in his argument for immaterialism.

Librarian note: There is more than one author in the Goodreads database with this name.

George^Berkeley

Reviews

[Rutger Smit · Rating 4 out of 5]

The year is 1734. Bishop Berkeley tears the "infidel" (freethinkers, like Edmund Halley) mathematicians and physicists of the time a new one in this ruthless attack on the theory of fluxions that was popular back then. These fluxions, the "ghosts of departed particles", expose that despite its rigourous surface and efficient applications, the theory of calculus in the 18th century was full of nonsense. It was not until more than a hundred years later that this crisis in the foundation was resolved by the notation and methods introduced by Cauchy and Weierstrass.

I quote from the Bishop:

"Though I am a Stranger to your Person, yet I am not, Sir, a Stranger to the Reputation
you have acquired, in that branch of Learning which hath been your peculiar Study; nor to
the Authority that you therefore assume in things foreign to your Profession, nor to the
Abuse that you, and too many more of the like Character, are known to make of such undue
Authority, to the misleading of unwary Persons in matters of the highest Concernment, and
whereof your mathematical Knowledge can by no means qualify you to be a competent Judge.
Equity indeed and good Sense would incline one to disregard the Judgment of Men, in Points
which they have not considered or examined."

Berkeley was not afraid to attack the percieved authority of mathematicians as geniuses in matters other than mathematics.

"The Method of Fluxions is the general Key, by help whereof the modern Mathematicians unlock the secrets of Geometry, and consequently of Nature. And as it is that which
hath enabled them so remarkably to outgo the Ancients in discovering Theorems and solving
Problems, the exercise and application thereof is become the main, if not sole, employment
of all those who in this Age pass for profound Geometers."

For Berkeley, the Greek geometry was devine and undoubtable an account of the works of God. What these infidel mathematical contemporaries where doing was an affront in many ways. Greek geometry, carried from the Elements by Euclides, allows nothing to be neglected. Every detail must be accounted for. The new mathematics, by Leibniz and Newton, requires neglect of infinitely small particles and quantities. The attack is fiery and ruthless, and warns the mathematician not to intrude into the devine mathematics, untill he has found a solid ground for his theory. Mathematicians are no different from any supersticious confident individual.

This was not the end of the discussion, as is well known. Later, Bayes (who himself was a Presbyterian minister) wrote a response, defending the theory of fluxions. The essay from the Bishop had clearly shaken the world of philosophy, religion and mathematics. Berkeleys work was seminal in stimulating discourse on the foundations of mathematics at the time, and might even directly have motivated the later epsilon-delta motivations as we know them.

Reading the work of the Bishop hundreds of years later, it is as witty and biting as ever.

[Joe Molenaar · Rating 3 out of 5]

epic diss track on newton and leibniz

[Arron · Rating 4 out of 5]

Short little biting critique of the sloppy thinking that underlay Calculus for centuries. It's helpful especially for students to understand why the limit definitions of derivatives and integrals are necessary and not just ugly rigor for its own sake.

Especially helpful as a counterpoint to Thompson's Calculus Made Easy.

[Rounak · Rating 4 out of 5]

This was savage af

[Ian · Rating 5 out of 5]

It had been said that “Berkeley’s criticisms of the rigor of the calculus were witty, unkind, and — with respect to the mathematical practices he was criticizing — essentially correct.” All these points are true. In reading The History of the Calculus and its Conceptual Development, I came across mention of this little work by George Berkeley. From the advent of the Modern period of mathematics (before Newton, perhaps starting from the time of Galileo) to the nineteenth century, calculus didn't rest on a solid logical foundation, but contained manifest contradictions that mathematicians of the time were uncomfortable with but tolerated because of the Calculus's utility. However, it is not a valid mathematical demonstration to argue from the truth of the conclusion to the truth of the premises, so the Calculus was unjustified. And yet some mathematicians considered mathematics to be of a different kind than theology and metaphysics, which Berkeley wrote to defend. This he imputes to mathematicians the same reliance on faith as a theologian or metaphysician. At the time, he was correct to do so. The question is, does the mathematics of today require the same faith? I haven't finished reading the History of Calculus, but I how to find out when I do. And then I may go on to investigate Robinson's nonstandard analysis, which claims to reintroduce infinitesimals, but with a justified exposition (something which postdated 1949 history book).