Why did Jose give Cole the gun?

This is one of the few movies that actually identifies a time travel reality. You cannot change events in your own timeline (baring parallel universes). One should look up the John Titor hoax for a good explanation of that type of time travel. Please stay with me on this, I'm veering from the movie so I can explain why I think Gilliam did what he did, then I'll get back to the movie: Personally I think Titor's explanation of time travel to alternate universes leaves too many holes. Sure, if you travel to a parallel universe you can make all the changes that you want, but if there is one of you time traveling and you make a paradoxical error (i.e. kill your own father before you're conceived) then surely there are others of you making this same error in other dimensions. In fact, the number of alternate you's could be as countless as the grains of sand on a beach. Just because there are parallel dimensions does not negate the shear truth of paradox because if you make this mistake they are also very likely making this same mistake, too much of a chance for a crossover. My thought is that if you did go back in time and you tried to kill your grandfather, well you obviously didn't succeed so your gun must have jammed. Intend all you want, you will not succeed because you cannot change events that have passed. Now, back to the movie- (hopefully you can see how that connects, because no matter what James does he cannot change anything). One thing that doesn't make sense with the explanations given in this forum is in the very end where the astrophysicist states "I'm in insurance." One person stated (as the reason why they wanted James dead) "and they could not allow [James] to disturb the past any further." I don't think you can change anything in the timeline and leaving him in the past wouldn't affect anything, so that explanation has a hole in my opinion (unless the scientists do actually believe you can make changes). It seems to me that she was there to be insurance in case James failed, therefore I don't think they planned on exploiting James into doing something to kill himself. Consider this, perhaps the movie acknowledges that you cannot change time, but the scientists in the movie may be under different assumptions, therefore they give James the gun to try to change history. At the same time other people have made a good point, this was an ancient gun so why would they give him that particular gun if they wanted him to succeed? Also, the mission is to get the virus, not to stop the virus, so when she states she is in insurance my gut tells me she had no plans on killing him or stopping the spread.

Then again, I come back to the gun, why the gun? So, ultimately here is my answer to the OP's question: This whole issue seems to be paradoxical in nature and maybe paradox in the plot is the point. This is from the same guy who brought you Brazil and The Zero Theorem, and he likes to be vague, as well as make the point you cannot really make changes (haven't seen Zero, but consider in Brazil the whole escape is a dream and the system remains intact).