How do I know if anything is right?

Q: Why do you think that the world is round?

A1: It has to be round as we can travel from one point in any direction and return to the same point without leaving the surface.

A2: It is round because we have seen it from space.

Which of these two answers is most convincing?

We like to see things for ourselves and that is perhaps some of the strongest evidence (there are plent of optical illusions and magicians to show that we can sometimes not believe our eyes). Everyday experience says that the world is flat. So we depend on the ideas of a shared experience, after all we cannot all experience everything and there are many things we do not want to experience at all. For example we do not want to have to experience poisons or toxic chemicals.

The other answer is perhaps more interesting as it is more abstract but more revealing. It shows how we can create an artificial model in our minds that can take into account all possible worlds - all possible realities and we can show that it is true for all of these cases. This is part of the reason there is such a strong connection between mathematics and knowledge.