2.6.1 Newton’s Methods

His "Rules of Reasoning in Philosophy"

Although his presentation was geometrical in the extreme, Newton rejected the traditional view of geometry as a purely deductive body of knowledge derived from the application of logic to Euclid’s axioms. Newton’s geometry was grounded in reality. He observed that “...geometry is founded in mechanical practice, and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring” [[i]]. In Newton’s work, the ties between the facts of reality and the mathematical abstractions are clear and unmistakable. The remarkable mathematical tools Newton introduced were not ends in themselves, but rather tools to the end of understanding physical reality.

By these examples, one can see that Newton did not treat his theoretical ideas as Platonic abstractions; rather he went to great effort to painstakingly ensure that his conclusions corresponded with the real world. In Newton’s own words, his procedure was “...from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena....” [[ii]]. In a lengthier discussion of his discovery of gravity at the end of Book III of the Principia, Newton said:

...[W]e have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power....  I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses ... have no place in experimental philosophy.  In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.  ...[A]nd to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea [[iii]].

Newton not only established the laws of physics we take for granted today, but also pioneered the methods of science itself. Book III of his Principia leads off with Newton’s “Rules of Reasoning in Philosophy” [[iv]].

Figure 2.28: Manuscript illustration of William of Ockham (1287–1347). The inscription reads “frater Occam iste,” or, “this is Brother Ockham” [[v]].

Rule I. We are to admit no more causes of natural things than such as art both true and sufficient to explain their appearances.

Newton’s first rule is a restatement of the principle of parsimony. Attributed to the English Franciscan friar, William of Ockham (1287–1347). This rule suggests that we should seek the simplest explanation that fits the available evidence.

Parsimony does not logically prohibit a more complicated explanation from being true, but it does suggest we should consider and attempt to rule out the simpler explanations first.

Rule II. Therefore to the same natural effects we must, as far as possible, assign the same causes.

Newton’s second rule appeals to the universality of physics, suggesting that one common explanation is needed to explain the same phenomenon in different contexts. Newton offers the examples of “respiration in a man and in a beast,” and “the descent of stones in Europe and America.” Clearly, Newton’s adherence to this rule was critical in his assigning a common cause to the fall of an apple as well as the motion of the Moon.

Rule III. The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

Newton’s third rule argues for the generalizability of physical conclusions. The conclusions we draw for how matter behaves in our experiments we must accept as the consistent and universal behavior of matter in general, given similar contexts. “We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising;” argued Newton, “nor are we to recede from the analogy of Nature, which is wont to be simple, and always consonant to itself.”

Rule IV. In experimental philosophy we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

Newton’s fourth rule recognizes the contextual truth of physical conclusions – that we must accept the truth of inductive conclusions until such time as we acquire new evidence to broaden our context of knowledge. “This rule we must follow,” Newton advises, “that the argument of induction may not be evaded by hypotheses.”

Certainly, Newton did entertain a great many speculative ideas. Newton referred to these as “indigested” notions [[vi]]. Throughout his investigations, with few exceptions, the facts of reality were always central and controlling. Newton only accepted those principles that he was satisfied could be rigorously inferred from the phenomena of nature. Newton’s policy of recognizing the primacy of existence places his work squarely in the Aristotelian camp.

Many of Newton’s successors took his conclusions for granted while ignoring his methods. In so doing, they subverted and undermined Newton’s vision. We can see how when considering Newton’s legacy, next week.

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References

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[i]  Sir Isaac Newton, Op.Cit., p. xvii.

[ii]  Sir Isaac Newton, Op.Cit.  The quotation is from Newton's preface to the first edition.

[iii]  Sir Isaac Newton, Op.Cit., pp. 546-547.

[iv]  Newton, Isaac, Op.Cit., Book III, pp. 398.

[v] Ockham - from a manuscipt of Ockham's Summa Logicae, MS Gonville and Caius College, Cambridge, 464/571, fol. 69r}. Sketch labelled 'frater Occham iste.' See: Occam's razor - Wikipedia

[vi]  See Cajori p. 675.  Letter to Robert Boyle.