Now i'm no rocket scientist, but this just sounds like flat-out incorrect information. (Remember, i am NOT a rocket scientist. I'm waiting to be be corrected, not proved wrong as i have only moderate confidence in my answers.)
In order for motion to occur an object must be either moving to where it is or where it is not.
How exactly can something move towards where it already is? Unless you wrote that out wrong, we seem to have a problem already.
If you chose an instant in time to view the path of travel of an object
If you freeze time, you can't view the path of travel of an object, unless it leaves a visible trail.
it can't move to where it is since it's already there, but it can't move to where it is not because no time has elapsed for it to do so.
It can't move because there is no time to do so. Success. We have no discovered that something can't move if the clock isn't ticking.
therefore of something doesn't happen in one instant in time, it can never happen
Not from my observation, no. Something cannot 'happen' in one instant of time, but it CAN 'happen' over a period of time.
So motion is not possible.
Not quite... i wouldn't have been able to type this had this been true. This seems less a paradox, more a way to blow the mind of a first grader.
As Mr. Horse once said: No sir, i don't like it.