Is it true to say that "it's not logically possible to prove something can't be done"? A friend of mine asked me if I could explain this statement: "It's not logically possible to prove that something can't be done". The actual reason is the understanding of this strip: 

Since I'm not an expert on logic, but at least know the basics, I told him that the statement is false. To prove it I gave him the counterexample of the impossibility of trisecting an angle by using only straightedge and compass, which was proved by Pierre Wantzel. This shows clearly that it's possible to prove that something can't be done.
When I told him this, he explained to me that this is sort of naive because Asok, the guy who makes the statement, is a graduate from IIT and also I read that he's always a brilliant character in the strip.  
Can you guys please tell me what you think about this? Also I'd like to know how you would interpret this dialog.  

Scott Adams may have intended something different, but in the given context and with the given wording, Dan is right and Asok is wrong.
Imagine Asok writing a piece of software that crucially depends on deciding the halting problem (or any other property covered by Rice's theorem), then Dan is right: The halting problem is not decidable and therefore the software will never work. And Dan can indeed prove it, because the undecidability of the halting problem is provable.
