I meant that the paradoxical nature is not resolved by simply formalizing the statement into first order logic the following way:

"I have 2 children. Exists child where (Born_on_tuesday(child) and Boy(child))."

(Some other paradoxes completely disappear when you try to write the statement into first order logic. It is not the case here.)

This is what I wanted to say.

You see, the problem is that even your latest attempt to describe the question is ambiguous - the solution depends on how 'I' was selected. And if ever you describe that in a non-ambiguous manner, I suspect that the answer would no longer seem paradoxial. In other words, ambiguity in language is at the very heart of this problem.