Ok, this one is going to be a roller-coaster, but stick with me. I believe that reality as we experience it is true, but I cannot prove it. In fact, I would argue that it is unproveable. We could be living in a matrix-like reality but we would never know.
I compare to The Matrix deliberately, because they actually had a grasp on the way it could be. Everything we know and experience comes to us through our senses. We take these sensory inputs and process them into impressions of the reality around us, and then into memories. we interpret the sensory inputs through our memories, meaning that they are no more than another sensory input. In fact, our understanding and interpretation of "now" and what we are currently experiencing is simply a set of neurological stimuli.
"OK," you say, "I know some biology, and this is all stored in our brains. so what?" The thing is, all of the biology you know has come via your senses, all of the knowledge that we have, all of the scientific explanation of the reality around us we obtain comes via our senses. We cannot actually know whether our interpretation of reality is accurate, because we have no external frame of reference to explore it from. All we know is that every source of data input into what we know as our consciousness presents a consistent picture that we call reality, and that we can rely on. There is no way that we can know whether this is because it is an external reality or because our interpretation of a generation form of reality is consistent. What is more, because we have a predilection for consistency, it is very hard to know whether even our individual perception of reality is consistent, or whether we simply interpret the reality that we are presented with in a way that is consistent.
What we do find, as we study the way the human mind works is that our ability to impose our personal worldview on the sensory input we receive is quite remarkable. What we find is that any data that doesn't fit in with our worldview - or explanatory picture of how reality is - we tend to reject. This is why it is very difficult to convince somebody that they are wrong in a basic way - that their faith, for example, is mistaken. It is why we often find people stay in abusive situations stay there, because to reject them or get out is a challenge to their worldview. When they do, it can be very damaging to them, because their view of how reality is has been challenged and it takes time to restore this.
The question of whether what we experience is true or not is disturbing to some people. I don't find this, because it doesn't actually make a lot of difference. We can behave as if what we experience is real. But it is useful sometimes to sit back and consider if this core principle is actually one we can demonstrate or not - and it turns out that we are really taking it as a core principle - that is, on faith. Everything else builds on the assumption that the reality we experience has something more concrete than simply our neurological responses to it. But it may not.
There are two points to all of this. Firstly, there is an acknowledgement that our interpretation of reality is based on our own sensory inputs. This understanding is crucial, because, even assuming that the reality we perceive has an existence beyond ourselves, OUR individual reality may differ from another persons. In fact, it will, because it is ALWAYS mitigated by our consciousness.
Secondly, it means that we cannot escape from the possibility that reality is as consistent as it is because it is our own creation. The consistency of reality is important - we can predict and interpret what is going on in other galaxies because we are certain that all of reality follows the same core laws and principles. What we cannot be certain of is whether this consistency is because reality is consistent, or because reality is all our own interpretation.
This is where the matrix references come back full circle. Red pill or blue pill? If you take the red pill, then reality is, you are a human being living in it, and everything is exactly as it was before. You believe what you want. If you take the blue pill, though, you realise that all we take for granted, all the certainties we thought we knew, are gone. It may not make much difference to how you actually behave, how you handle life. There is no way of getting beyond the matrix. But you know just how tenuous this reality is. If your mind survives.