On Friday, September 13, 2013 9:31:56 AM UTC-4, Bruno Marchal wrote: > > > On 12 Sep 2013, at 17:47, Craig Weinberg wrote: > > Which reasoning is clearly false? > > Here's what I'm thinking: > > 1) The conclusion "I won't be surprised to be hanged Friday if I am not > hanged by Thursday" creates another proposition to be surprised about. By > leaving the condition of 'surprise' open ended, it could include being > surprised that the judge lied, or any number of other soft contingencies > that could render an 'unexpected' outcome. The condition of expectation > isn't an objective phenomenon, it is a subjective inference. Objectively, > there is no surprise as objects don't anticipate anything. > > 2) If we want to close in tightly on the quantitative logic of whether > deducibility can be deduced - given five coin flips and a certainty that > one will be heads, each successive tails coin flip increases the odds that > one the remaining flips will be heads. The fifth coin will either be 100% > likely to be heads, or will prove that the certainty assumed was 100% wrong. > > I think the paradox hinges on 1) the false inference of objectivity in the > use of the word surprise and 2) the false assertion of omniscience by the > judge. It's like an Escher drawing. In real life, surprise cannot be > predicted with certainty and the quality of unexpectedness it is not an > objective thing, just as expectation is not an objective thing. > > Or not? > > > That's not to bad. In fact to get the paradox you need to assume that the > teacher (for the unexpected exam) is rational, but it can't be. > > Bruno > > > Thanks Bruno!