The scenario goes like this. The predictee agrees to do one of two pre-specified actions. The predictor must communicate to the predictee which of the two actions the predictee will do before the predictee does it. Let the predictee appear like a typical human, and let one of the two actions be either the raising of its right arm or the raising of its left arm.
The paradox invoker is thinking that when the predictor communicates to the predictee that the latter will raise its right arm, all the predictee has to do is raise its left arm, and likewise inversely. To that paradox invoker, any predictor, including an omniscient predictor (what the paradox turns on), is unqualified to be labeled 'the predictor'.
The scenario shall require an additional element to help persuade the paradox invoker that it might be possible for the scenario's ontology to subsume a consistent label-worthy predictor in a way that's still interesting.
Let the predictor appear like a typical human. Let the additional element be the predictor putting its arms behind its back, hands duly hidden from the predictee, and indicating a prediction, simultaneously with communicating to the predictee a prediction, by extending the index finger from the fisted hand of the corresponding predicted action.
The communicated predictions won't always correspond with the hidden predictions. The communicated predictions will either never or sometimes – likely sometimes, given the predictee's understanding of the situation – correspond with the predictee's actions.
After, say, a trillion trials, it's possible – without paradox and in a way that's hopefully still interesting with respect to the perceived problem – for the predictor to be, in fact, a consistent label-worthy predictor, by having been correct in every single one of its hidden predictions.
[editing note: tried to improve clarity]
Edited by eirenicon, 05 December 2006 - 04:09 AM.
