A program can’t pick out arbitrary subsets of an infinite set either. Programs can’t do uncountably many things, even if you give them an infinite amount of time to work with.
As is written, g(var) picks out one arbitrary subset of the infinite set. There are 2^Aleph_null possible subsets g(var) can produce, thus, g(var) can (not does) produce uncountably infinite many true propositions.
Ok, I see what you’re trying to do now (though the pseudocode you wrote still doesn’t do it successfully). It’s true that with randomness, there are uncountably many infinite strings that could be produced. But you still have no way of referring to each one individually, so there’s little point in calling them “propositions”, which typically refers to claims that can actually be stated.
A program can’t pick out arbitrary subsets of an infinite set either. Programs can’t do uncountably many things, even if you give them an infinite amount of time to work with.
As is written, g(var) picks out one arbitrary subset of the infinite set. There are 2^Aleph_null possible subsets g(var) can produce, thus, g(var) can (not does) produce uncountably infinite many true propositions.
Ok, I see what you’re trying to do now (though the pseudocode you wrote still doesn’t do it successfully). It’s true that with randomness, there are uncountably many infinite strings that could be produced. But you still have no way of referring to each one individually, so there’s little point in calling them “propositions”, which typically refers to claims that can actually be stated.