We don't.

What we do know is this:

1. There are ways that are inherently unable to get you to the speed of light. For example, the acceleration of an object having mass will never get you there, because the closer you get the greater your mass becomes. To get to the speed of light you need infinite energy, so getting faster would require more than infinite energy.
2. FTL inherently allows you to set up situations in which you can go back in time and change the past. This is anathema to many people, including physicists.
3. There are things faster than light. Spacetime can expand at a rate faster than light, for example.

However, we do not know for certain that FTL isn't possible for, say, that object having mass mentioned before. What we do know is that it cannot *accelerate* to such a velocity and that it could violate causality if it found another way to get to that velocity.