- #76

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it does not follow.

you defined T, the set of all true propositions:

T={p| p is true}

then it seems that you "defined" another set, U.

you first defined it as the power set of T (the set of all subsets of T)

U1 has of course a greater cardinality than T- as you mentioned.

however, you then re-defined U as the set of all true conjunctions (by redefining "combination" as "logical conjunction") - I'll call this set U'.

out of the blue, you jumped a gap and transferred properties U to U', you stated that the second U' has a greater cardinality than T. this is false as U'⊆T and the demonstration is trivial:

the conjunction of true propositions is a true proposition. q.e.d.

U' is a subset of T, it is impossible for U' to have a greater cardinality than T.

Then you concluded that if we assume that the set of all true propositions exists, we get the result that U' is both a subset of T and not a subset of T.

How exactly is U' not a subset of T? you didn't demonstrate that part... what you demonstrated is that T is a subset of U not U'. the power set of a set is not identical with the set of the conjunctions of true propositions... you mixed definitions.