Correct, it's not conceivable. The liar's paradox is a statement paradox. You add a second sentence and the paradox is resolved. As with most paradoxes the ability to add elements removes the constraints of the paradox.
I don't see the connection to paradoxes exist, therefore non-contradiction is false. The problem is that it necessarily must be true or arguments are useless to make.
Non-contradiction, cannot be true most of the time it has to be true all the time or it's false. One example of non-contradiction being false and the whole shit house falls.
He's the deal, if you put forth an argument that ends in a paradox, you did not make a deductive argument.
I really don't see the problem since the premises in a deductive argument lead to a single conclusion....Even in your cosmological example, the supposed two conclusions are repetitions of one another.
If you put forth an argument that can have 2 contradictory conclusions, then your argument is really very bad. The point is to come to a single conclusion to the exclusion of all others, if your not doing that you aren't doing deduction.