Hailperin demonstrates how Boole's very difficult technique for solving problems in probability logic can be easily solved by using a linear programming approach , such as parametric and integer-mixed integer techniques.This approach makes the computation of Boolean probabilistic intervals straightforward.An additional benefit of Hailperin's solutions repertoire is that Keynes's improved technique for solving probabilistic interval estimate problems ,formally discussed by Keynes in chapters 15 and 17 of his A Treatise on Probablity in 1921(the actual work in this area was done by Keynes in 1907 and 1908,respectively,in two Cambridge University fellowship theses)and applied in chapters 20 and 22 of the TP on pp.234-237 and pp.255-257,respectively,can also be solved using Hailperin's approach although Hailperin himself appears not to realize this. Unfortunately,Hailperin's work on probability interval estimate techniques,as well as Boole's and Keynes's earlier contributions,have been completely overlooked by contemporary economists and philosophers still laboring under the misbelief that all probabilities used by rational decision makers must be unique,single number answers that add to one.

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