### On Some Corrections to the History of Actuarial Science : No academician ever showed that there were any deficiencies in Keynes’s Logical Theory of Probability and/or Principle of Indifference

#### Abstract

Craig Turnbull’s 2020 book, *Some Notes on the Methodology of Actuarial Science*, is to be highly recommended, in general. However, from a historical perspective, one particular section of chapter one ,on methodology, needs to be corrected in a future edition. The section is section 1.3 ,which deals with logical theories of probability ,in general, and Keynes’s logical theory ,specifically. There are two areas of confusion that have been ongoing for over 100 years that appear in this section.

The first area concerns Keynes’s revisions to the Bernoulli-Laplace version of the Principle of Indifference(POI), originally called the Principle of Non Sufficient Reason .

The second area concerns the foundations for the measurement of probability, which for Keynes was an improved version of Boole’s upper-lower probability intervals ,which Keynes called either non numerical probabilities ,inexact measurement or approximation. All three names refer to the technical derivation of upper-lower probability intervals, which in modern times is called imprecise probability. This name would be a better name to use than those used by Keynes, as it also incorporates Keynes’s decision weighting creation, his conventional coefficient of weight and risk, c ,which is the first such decision weight approach formulated in history.

Thus, the claim, that Keynes’s logical theory of probability has no way of measuring probability ,has no support , as Keynes’s method is the same as Boole’s.

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