Newton’s Principia

Isaac Newton Philosophiæ Naturalis  Principia Mathematica Motte 1728 (1687 in Latin)

This is sometimes informally referred to as the ‘principia mathematica’, but as the full title makes clear, it is about ‘natural philosophy’ (physics) from a ‘mathematical’ viewpoint, establishing physics, and particularly mechanics and cosmology, in a recognizably modern form.

 Rules of Reasoning in Philosophy

Book 3 from the 3rd (1726) edition includes the following rules, resembling Ockham’s razor.

Rule 1: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

Rule 2: Therefore to the same natural effects we must, as far as possible, assign the same causes.

Rule 3: The qualities of bodies, which admit neither intensification 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.

Rule 4: In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypothesis that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

This rule we must follow [:] that the argument of induction may not be evaded by hypotheses.

Comment

It seems to me that many ‘practical people’ and engineers follow something like Newton’s rules even outside physics, and that they often regard them as ‘mathematical’. Now, there is obviously some analogy between physics and finance, and so it might seem reasonable to claim that in applying something like Newton’s rules 1-4 during the period 200-2007 mainstream finance was following ‘mathematical principles’ or a ‘scientific method’. But some objections are obvious:

  • Finance (and other engineering) are not about ‘natural things’ in Newton’s sense, and so we cannot rely on his theory.
  • There are significant differences between finance and physics. For example, Newton’s things and causes have an existence and rules behaviours independent of the experimenters. In contrast, financial instruments have behaviours that depend on our expectations.
  • Newton’s general induction only really makes sense when one is considering all relevant phenomena, as Newton was. As in finance, engineering failures often occur because relevant data has been ignored.
  • Newton’s conclusions were eventually modified (by Einstein).

It is also notable that by ‘general induction’ Newton seems to considering induction on the properties of some set of similar things ‘in general’, and is not considering the extrapolation of the behaviour of a singular thing. Thus it is argued that a planet will continue to move in a particular way not because it has always behaved in that way, but because the widest possible observations have been made of planets ‘in general’, these all follow certain rules, which when applied to the particular planet ‘predict’ the particular behaviour. Thus Newton’s induction is dependent on adequate classification.

Perhaps we should consider a modified rule 4:

a. That the result of induction should be regarded as ‘true to the observations’ rather than ‘absolutely true’.
b. That it is pragmatic to regard the result as a good working hypothesis, provided that the observations are sufficiently testing and numerous. For example, the application of a rule should be more suspect when the conditions are outside of the experience base for the induction of the rule.
c. That nonetheless, the potential for error and the adequacy of the observations should be reviewed periodically. The results should never be consider as absolutely and unconditionally ‘true to reality’.

See Also

My notes on reasoning generally, science and mathematics. (These cover induction.)

Dave Marsay

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