This one took me a while to come to terms with. The gist of it is that you don't know for certain that the world around you is real, and you can never know that, no matter what philosophical argument you might come up with or what evidence you might encounter. It's impossible. Let's start with a question, the "Cartesian evil spirit problem": isn't it possible that the world around you is an illusion and your mind is just being fed these perceptions by a spirit (or a neurologist if you prefer) who wishes to deceive you? This might sound ridiculous at first, but think about it. What exactly is implausible about this?
Did you answer 'god is good and he wouldn't allow me to be in such essential error'? Because he would. And he does. Look at the world around you and tell me whether there are people called 'materialists' who believe that god doesn't exist and that everything is material. God's not stopping them from being in such essential error. He could prove his existence to them, but he doesn't. So what makes you think he would treat you any differently?
The only remaining answer is that nothing is implausible about the cartesian evil spirit scenario. And nothing ever will be, because any evidence you uncover about the world around you can be handwaved by saying you're being fed illusions by an evil spirit. So you can never know that the world around you is real. Everything you know about the world rests on an open assumption that can never be proven.
That doesn't mean you shouldn't act as if the world is real. It's still at least possible that it is, so we have to treat the other people in it like they exist, since there's no moral drawback to doing so. And, ultimately, life is pretty meaningless if I'm the only person that exists. Therefore I choose to believe that I am not, no matter what evidence I have to the contrary.