Reality is what we perceive it to be. This is not an absolute statement. It is as close as we can get, as the following paragraphs explain.
Axiom: human perception is intrinsically subjective; objective perception is impossible for us. 
We can understand the concept of objectivity. We can formulate objective hypotheses. But we cannot objectively verify their truth (or not) in the world. So the pursuit of objective knowledge is pointless; the search for knowledge is not.
So what is left if we abandon objectivity? This is best answered with a brief thought experiment:
Consider a group of creatures living in a reality that has objective existence, whether the creatures know it or not. Select a creature at random. What does it know of the reality in which it lives? It learns of its environment from its perceptions. On what can they depend?
1. The reality in which the creature lives.
2. The mind of the creature.
3. The minds of one or more of its companions.
4. Some combination of the above.
5. None of the above.
Option 1 represents objective perception. What the creature perceives is dependent only on the external reality in which it lives. It has certain knowledge of its environment.
Options 2, 3 and 5 represent variations on the theme of solipsism. The creature’s perceptions have no connection with the reality in which it lives. It has no knowledge of its environment.
I believe that option 4 represents the position in which we (humans) find ourselves, that our perception depends upon our minds and on the reality in which we live. We have knowledge of our environment, but it isn’t certain (i.e. objective) knowledge. This, in my opinion, is the perceptual reality that lies in between Objectivity and Solipsism.
Abandoning our preoccupation with objectivity has benefits. For example:
 To affect certain knowledge of an objective world is self-deception that muddies our thinking. Such deliberate dishonesty would require strong justification, and I can see none.
The illusion of certainty masks other possibilities. Any significant and new discovery will probably contradict current wisdom. If we know we are right, we discount - or fail to recognise - indications to the contrary, preventing any such discovery. Being aware of the fallibility of our perceptions improves our perception.
 What we (subjectively) perceive has a probability of being correct. We can attempt to quantify that probability, perhaps using Beyesian statistics. (Initially, our attempts may be inaccurate, but this could improve with fine-tuning, using the real world as a guide).
Previously, it never occurred to us to consider such things: certainty is 100% probable. Learning to evaluate the accuracy of our perceptions will surely move our understanding forward.
So reality is what we perceive it to be. Probably.
 Axiom: an assumption or act of faith; a statement whose truth is accepted without proof.
 Objective: something whose truth is not dependent on people's opinions or conceptions.
 As axioms go, this one is quite safe. Consider:
Hypothesis: human perception is intrinsically subjective; objective perception is impossible for us.
Analysis: If the hypothesis is true, then it is impossible for a human to verify; there can be no objective proof of the hypothesis. If the hypothesis is false, then an objective refutation ought to be possible. The solipsist view - that "I" am the only real thing, and all else is a figment of my imagination - has remained objectively unassailable for millennia. If there were an objective refutation for the solipsist view, it would also invalidate our hypothesis. No such refutation has emerged.
Conclusion: The evidence is not conclusive. On the balance of probabilities, the hypothesis is probably true.
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