the probability a length-N statement is undecidable practically surely goes to 0 or 1 when N-->infinity... but it depends on the precise language you permit for statements. E.g. if the statement was either an AND of many statements, or an OR of many statements, prob(decidable) would go to 1 and the truth value would almost surely be 0 or 1 respectively. So it is fairly difficult to cook up a language for statements in which this kind of obvious thing does not happen. A related question would be, given a random length-N input for some universal Turing machine, what is the probability it will halt when N-->infinity? In this case, I think the {0,1}-only law is avoided. This suggests that Turing machines actually are pretty special. For a lot of other things like Cellular Automata, tiling, diophantine equations, Kolmogorov optimal-compressedness, etc, I bet the limit probabilities of undecidability ---> 0, but for Turing machines I think it is positive.