(Oldroyd, pp. 78-84)

Works:

Principia Mathematica (1687)

Opticks (1704)

Principia

Begins with the three laws of motion and certain definitions; this serves as the starting point for a deductive (synthetic) system which results in "a host of 'theorems' in mechanics which could find application to specific physical problems."(78)

Included here is the postulate that gravity is a ubiquitous force in nature (i.e., it is found everywhere), and its action is described by the inverse square law -

M₁ X M₂

F = (G) x -------------

D²

Law of intertia (first law of motion) further requires assumption of vacuum - contra Descartes

Opticks

Despite the apparently deductive character of Newton's model of science - notice that " to a large extent Newton did not actually deduce the theorems directly from the definitions and axioms alone, for he frequently found it necessary to have recourse to experiments in order to carry through the arguments successfully."(79)

Newton further claims here that his conclusions regarding light can be reached without reference to any hypothetical commitments as to the nature of light (whether it is made of particles - 'corpuscular' - or of waves): that is, he claims that "I frame no hypotheses." We will see that this is just not true.

Clearly relies on the classical arch of knowledge - see p. 80.

General comments

Newton clearly wants to distinguish between his program of science and anything "merely" hypothetical (i.e., involvin the use of hypotheses, such as the instrumentalist approach of Renaissance astronomy.) In slightly different terms, he is after certainty - and here he agrees with Descartes regarding the goal of any science. Unlike Descartes, however, Newton seems to think that certainty in his project derives from the fact that "the principles were drawn directly from experiments and observations..."(81). Notice that this shows that Newton stands firmly in the English "empiricist" tradition, stretching back through Francis Bacon and to Roger Bacon - in contrast with the "idealist" tradition emphasizing the role of the conceptual (in particular, mathematics) that is most strongly expressed by Descartes.

Embedded in his use of the arch of knowledge is the claim that he moves from "phaenomena" (observed events, features, etc.) by a process of analysis or induction to general principles at the peak of the arch.

This raises the "notorious 'problem of induction,' - of how it is that we can justify moving from a series of particular cases to a general principle, and then expect that general principle to be necessarily true for a further series of particular cases. As Oldroyd points out, this problem is raised most forcefully only by Hume. While it's not "fair" to expect Newton to have seen or dealt with the problem - be advised that there is a serious problem here that is about to explode Newton's comfortable empiricist assumptions.

Newton further assumes the uniformity of nature - a critical assumption in any science - and one stretching back to the original assumption of ancient Greek philosophy/science that the universe is ordered (i.e., a kosmos).

Oldroyd objects that Newton claimed more for his science than can be justified - in particular, as a science that is supposedly devoid of hypothesis and based solely on observation.

The first law of motion - that bodies continue to travel in a straight line until affected by some external force - "referred to the behavior of objects that had never actually been observed - bodies moving uniformly in straight lines totally free from the influence of any external forces."(81) This law, therefore, cannot be said to be derived from "induction from phenomena."(ibid) It is rather an initial assumption or hypothesis - just as Newton elsewhere assumed "theoretical constructs" (the basic building blocks of a theory or model, which may or may not have any direct reference to sensory experience), such as the notion of light as a ray, and the notion of matter as built out of atoms, for which there was precious little evidence.(81f.)

His 'Rules of Reasoning' include a version of Ockham's razor - but again, we have seen that this is an assumption that ultimately turns on Aristotle's metaphysical claim that nature is simple.

Newton further believed in the doctrines of absolute space and absolute time - "that there was a frame of reference against which all motions and times could be determined, located in God's 'sensorium.'"(82) But it turns out that this assumption is clearly "metaphysical." For the purposes of actual science, relative points of reference in space/time had to be used - a point that Einstein hammers home. As Oldroyd says:

He had no practical access to absolute space and time, and these were for practical purposes quite useless for Newton's science. They were, to be sure, of paramount importance in his metaphysics and system of natural theology, but if he had followed his own 'First rule of reasoning,' [i.e., the principle of parsimony] he should perhaps have excised them.(83) [We will see, in fact, that Einstein will eliminate the Newtonian assumption of absolute space and time - both because they are not necessary (and thus to be eliminated under the principle of parsimony or Ockham's razor) and because there is no empirical verification of their existence.]

Other points to notice -

Primary qualities are not simply mathematically-oriented.

Oldroyd raises the major problem - "Why should an axiom system have anything to do with the real world?...What was the nature of the 'hook' linking Newton's theoretical science with the real world?"(84) For Newton, of course, the 'hook' was the inductive step from phenomena to general principle - but as Oldroyd points out, this claim is fundamentally implausible today.