Does Cantorian Set Theory Have Limitations for Evaluating the Size of Sets?      Cantorian set theory would have us believe that all countable infinites are the same size (or at least, that's the conceptual metaphor commonly used.)  I will try and argue that this makes little sense, in at least one significant case.      Let's look at classical propositional logic from the semantic point-of-view.  There exist three classes of well-formed formulas (hereafter formulas): tautologies, contradictions, and contingencies.  The class of tautologies is well known to be countably infinite, given countably many infinite variables, so via negation the class of contradictions is also countably infinite.  Though I don't know how to demonstrate it, the class of contingencies also seems countably infinite.      But, it does not make much sense to believe contingencies as big as tautologies.  Nor does it make much sense to believe contingencies as big as contradictions.  I will say that I do believe that a skilled set theorist could sufficiently describe two bijections: one between contingencies and tautologies, and another between contingencies and contradictions (and negation gives us a bijection between tautologies and contradictions).      However, if we had a machine which gave us propositional formulas at random, I assert that the class of contingencies would have the greatest frequency of occurrence after a sufficiently large amount of time (if needed, we might postulate 10 billion propositional formulas as enough.  My idea here goes that we have enough propositional formulas so that it becomes all too unlikely that the frequency distribution will change much when getting more propositional formulas at random.)  This would seem, at the very least, to imply the class of contingencies as greater than the class of contradictions.  It also would imply the class of contingencies greater than the class of tautologies.  Of course, that does not say that the frequency of contingencies obtained at random would come as greater than the class of tautologies and the class of contradictions combined.  That said, truth tables might seem to suggest this also, since there exist 14 truth functions of two variables which are contingencies, but only 2 which are either tautologies or contradictions, only 2 truth functions of three variables which are tautologies or contradictions and the rest of the truth functions of three variables are contingencies, and in general only 2 truth functions of n-variables and the rest of the truth functions of n-variables are contingencies.