The Constructible and the Intelligible in Newton's Philosophy of Geometry

Abstract

In the preface to the Principia (1687) Newton famously states that “geometry is founded on mechanical practice.” Several commentators have taken this and similar remarks as an indication that Newton was firmly situated in the constructivist tradition of geometry that was prevalent in the seventeenth century. By drawing on a selection of Newton's unpublished texts, I hope to show the faults of such an interpretation. In these texts, Newton not only rejects the constructivism that took its birth in Descartes's Géométrie (1637); he also presents the science of geometry as being more powerful than his Principia remarks may lead us to believe.

The debate between Peletier and Clavius on superposition

“…See also [Panza, 2011, 74-91]. Although one might see some similarity between Peletier and Descartes as to their use of the term "mechanical", since this term, in Peletier's commentary on Euclid as in Descartes's Geometrie, is opposed to "geometrical" and aims to qualify, in both contexts, a constructive process, or a motion, that is not rationally determinable (such a motion, for Descartes, would indeed not produce lines that may be measured with exactness, contrary to the rotations that generate circles, for example), it should however be noted that Descartes, in reinterpreting Pappus's classification of curves, also distinguished geometrical and mechanical curves by their algebraic expression (the former being expressible by a first-or second-degree polynomial equation, unlike the latter) [Domski, 2003[Domski, , in part. 1114[Domski, -1118.…”

How physics flew the philosophers' nest

“…which of the force laws explored by rational mechanics pertains in the behaviors of actual bodies), and then we seek the causes of these forces. For discussion of the role of mechanics in Newton's Principia seeDomski (2003) andGabbey (1992).…”

Idealizing Space in Newton’s Rational Mechanics

“…Oni mogu našim osjetilima biti predstavljeni materijalnim predmetima, ali sami su proizvoljni proizvodi naših misli.« 48 U suvremenim razmatranjima, ovaj problem poprimio je oblik pitanja: je li Newtonova pozicija bliska matematičkom konstruktivizmu? 49 Još atraktivnije pitanje postavlja se s obzirom na ideju savršene preciznosti u bavljenju racionalnom mehanikom, ali i znanošću uopće. Newtonova pretpostavka, da je moguće vršiti apsolutno precizna mjerenja i matematičke konstrukcije zahtjeva posebnu tematizaciju u odnosu spram pojma znanstvene istine i greške u znanstvenoj spoznaji.…”