> most sentences are neither true nor false. Nothing interesting has a probability of 0.000 or 1.000.
I'll start by observing that surely you're talking about propositions, not sentences, nor utterances. Or at least you ought to be.
But more significantly, I'll note that most propositions are either true or false (under a given interpretive framework), but that as epistemologically-unprivileged observers, we must assign empirical propositions probabilities that are higher than 0 and lower than 1. Propositions like "I am a fish" or "You hate meat" or "If Rosa hates meat then Alexis is a fish" are either true or false, under any given set of meanings for the constituent words (objects, predicates, etc). I'm curious what probability you think applies to propositions like "2 + 2 = 4" and "All triangles have 3 sides" and "All triangles have less than 11 sides". I think there are very many interesting propositions that differ from these only in degree of complexity (e.g. propositions about whether or not certain code, run on certain hardware, under certain enumerable assumptions about the runtime, will do certain things).
Based on your very strange claim that all interesting sentences have non-zero non-unity probability, perhaps you're saying that you find theorems uninteresting, and moreover are only interested in statements of empirical belief, such as "I put the odds of the sun failing to rise tomorrow lower than one in a billion." In that case, I cannot imagine what statement interest would qualify as a paradox, except perhaps insofar as some empirical statements of belief are "beyond strange".
"This sentence is false" is a paradox under pretty much everyone's notion of a paradox.
