So this seems like a better definition until you run into a problem, which you do pretty quickly: "casuality" isn't the easiest thing to define.

The best definition I think I've seen is to view the universe as a partially ordered set of events, meaning that you can only order events (in time) if they're within each other's cones of causality. Outside of that you cannot say which happened first. That's the partially ordered part.

But even that is incomplete and arguably even self-referential. What's a "cone of causality" (without relying on causality)?

Also, there's the issue of what exactly time is and whether events are time-symmetric or not. Many physicists seem to view time as an emergent rather than fundamental property of our Universe.