The empiricist approach to discerning reality is making sense of evidence that has been gleaned from the senses. Some philosophers – such as Kant – challenged this approach. They stated such things as that senses are imprecise, and that (in Kant) they only see the appearance of things – the “phenomenal” - but fail to see the things in themselves – the “noumenal.”
I want to make sense of the whole thing.
Now the senses are actually not imprecise. Incomplete yes, but imprecise no. We do not see the radio waves or the infrared radiation; we see the visible light. However the information that I get from seeing the visible light is not an erroneous one. If I see you, I am certain that I am actually seeing you – both the phenomenal you and the noumenal you. I can from this be certain that you are not Adolf Hitler.
In many cases, the things as they appear are very much the things as they are. If I am beholding an apple, I can be sure that I am holding an apple and not a frog. In this case the noumenal and the phenomenal are the same thing; and senses very much are a valid guide to reality.
Where Kant does have a point is in understanding people. People are very different inside from how they are on the outside. What a person looks like through the visual sense says absolutely nothing about the person's character or predispositions. In case of people, the Kantian argument has quite a lot of validity. To understand the person in-himself takes much different skills from discerning him in appearance. In this situation, the noumenal and the phenomenal very much differ from one another; and it takes different skills to understand each.
The empiricist view works with most of non-human reality. With human reality, Kant has a point. Do not discard physics or mathematics because of its empiricist origins. Do not judge what a person is on the inside from what he is on the outside. There is a place for both approaches, and it is instructive of all intelligence to recognize which – and where – to apply.