The verb ‘argue’ should be used with care.

Followed by an appropriate preposition, it could mean standing on one side of an argument or the other — for example: ‘She argued for the existence of God,’ and ‘He argued against the existence of God’ respectively mean that she provided arguments for, and he provided arguments against the particular proposition at hand.

However, without a preposition, the verb ‘argue’ just implies the action of argument, without any implication of the direction of the argument — for example, in describing the above situation, an observer, O, might exclaim, “I heard them with my own ears. They argued the existence of God!”

So, unless it is absolutely clear from the context, I think the above should be respected — The verb should be used with an appropriate preposition if one of two opposing stances is to be implied, and without preposition only in the case where one is describing the act of arguing.

Imagine, if you will, that O had reported the above statement to a second observer, M, who piped in, “but we all know God exists!”

To which O replied, “Well, you can’t argue that.”

Now, to me, O couldn’t have been more ambiguous. Or could she?

Ignore for a moment my earlier proposition about the use of prepositions — by show of hands, who thinks O meant to say
a) “You (the general you, i.e. everyone) can’t provide an argument against that statement.”
b) “Silly you, You (the general you, i.e. everyone) can’t provide an argument for that statement.”
c) “But wait, You (the general you, i.e. everyone) can’t provide arguments neither for nor against this statement. That is to say, this statement is not one to be affirmed or falsified by arguments.”
d) something else. hmm but what?

Now, the second part of the question is thus: if you had taken my earlier proposition to heart, what would have been your answer? (is it different from before?)