Presumable there's some kind of mortar there holding the bricks together....
I'm not an architect or engineer, so I invite corrections from anyone that's an actual expert, but I doubt even modern mortar could suspend heavy stones horizontally like that -- certainly not for centuries. Real arches are held together by compressive forces.
I suppose there could be reinforcement rods inside, but then we should see them protruding in places where the stones have been stripped away. In any event, I think reinforcement rods (rebars) are a fairly recent innovation.