I would say that assuming they stack at all, that you would get a +1 for each for a total of +2. I'm a little dubious of the archtypes being compatible, but I don't have a reference for them. What book are they from?
So if one of them wasn't called trapfinding, but was called (for the sake of an example) clever explorer instead, they would stack? That seems slightly odd considering that nothing has been changed but the name, but I suppose stranger things have happened.
The rules say bonuses from the same source don't stack, and if they had different names they might stack by RAW, but you have to look at context also. If the devs noticed one slipped by, they would likely just make an FAQ saying they don't stack.
PS: If the ability also references another ability with regard to how they work they also might not stack depending on the specific circumstance.
They aren't the same source though. If you actually read though the abilities, you notice it. One 'adds 1/2 his alchemist level' and other 'adds 1/2 his level'. The Crypt Breaker bonus comes from level so it should go up even if you multiclass out.
Rogue Trap Sense:Trap sense bonuses gained from multiple classes stack
So it would make sense if they stacked
They aren't the same source though. If you actually read though the abilities, you notice it. One 'adds 1/2 his alchemist level' and other 'adds 1/2 his level'. The Crypt Breaker bonus comes from level so it should go up even if you multiclass out.
That is a distinction without a difference. In class and archetype descriptions, references to "level" are assumed to mean "level in class being described" unless the class or archetype description specifically says otherwise.
Class features refer to the parent class unless otherwise stated so due to the overlapping it still won't be gained twice. It is like climbing two five foot ladders at the same time. You can do it but you won't get any higher.