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Could there be more than a countably infinite number of propositions?

If I remember correctly, and I may well not, David Lewis explicitly argues that there are uncountably many propositions in Plurality of Worlds and uses this as an argument against any view that would try to reduce propositions to sentences. At the very least, he does consider this issue. So here's an argument that I think I remember from that book that we can consider, anyway. It is based upon the claim that, for any real number x , there ought to be a proposition---a possible content of thought---that I am shorter than x inches tall. Indeed, each such proposition could be expressed by a sentence. All we have to do is give the real number x a name, say, "Fred", and then the proposition will be expressed by the sentence "I am shorter than Fred inches tall". But if so, then there are at least as many propositions as there are reals. The key to this argument, note, is the observation that the claim "For every proposition p , there could be a sentence S that expressed it" is...

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