The Analyst

The Analyst, subtitled "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 Points of Faith", is a book published by George Berkeley in 1734. The "infidel mathematician" is believed to have been Edmond Halley. Some have thought Sir Isaac Newton (Burton 1997, 477) was intended, but such a reading is disproved by this passage, which appears toward the end of the book: "Query 58: Whether it be really an effect of Thinking, that the same Men admire the great author for his Fluxions, and deride him for his Religion?" Here Berkeley ridicules those who celebrate Newton (the inventor of "fluxions", roughly equivalent to the differentials of later versions of the differential calculus) as a genius while deriding his well-known religiosity. Since Berkeley is here explicitly calling attention to Newton's religious faith, he cannot have meant his readers to identify the "infidel (i.e., lacking faith) mathematician" with Newton. Kirsti Andersen (2011) showed that Berkeley's doctrine of the compensation of errors contains a logical circularity. Namely, Berkeley relies upon Apollonius's determination of the tangent of the parabola in Berkeley's determination of the derivative of the quadratic function.