The Simplest Law

We need notice at the moment only that the choice of the simplest law that fits the facts is an essential part of procedure in applied mathematics, and cannot be justified by the method of deductive logic. It is, however, rarely stated, and when it is stated it is usually in manner suggesting that it is something to be ashamed of. We may recall the words of Brutus,

But 'tis a common proof
That lowliness is young ambition's ladder,
Whereto the climber upwards turns his face;
But when he once attains the upmost round,
He then unto the ladder turns his back,
Looks in the clouds, scorning the base degrees
By which he did ascend.

It is asserted, for instance, that the choice of the simplest law is purely a matter of economy of description or thought, and has nothing to do with any reason for believing the law. No reason in deductive logic, certainly; but the question is, Does deductive logic contain the whole of reason? It does give economy of description of past experience, but is it unreasonable to be interested in future experience? Do we make predictions merely because those predictions are the easiest to make?

Jeffreys H., Theory of Probability, Oxford Univ. Press, 1961




Lastly, numbers ae applicable even to such things as seem to e goverened by no rule, I mean such as depend on chance: the quantity of probability and proportion of it in any two proposed cases being subject ot calculation as much as anything else. Upon this depend the principles of game. We find sharpers know enough of this to cheat some men that would take it very ill to be thought bubles; and one gamester exceeds anothe, as he has a greater sagacity and readiness in calculating his probability to win or lose in any particular case. To understand the theory of chance thoroughly, requires a great knowlede of numbers, and apretty competent one of Algebra.

cited in:
Geoffrey Grimmett, Probability and Random Processes, OUP, 2005