The only counter-argument is that even arbitrary precision is fixed-precision because computer memory is finite. But that's kind of a silly argument, because then you are arguing that computers can never reason, because they have finite memory, and moreover humans cannot reason either, because there is a finite number of brain cells.
In the end it all depends on what your definition of reasoning is, which you did not provide.
My argument carries through for any piece of software so if you think software can think and reason then you can remain unconvinced by my argument.
In any case, I have to drop out of this thread.