Do our eyes show us the truth or, does our eyesight contrive for us
'The truth' means: The real facts about a situation, event, or person.
You could ask yourself why we have more sense organs if our eyes can show the truth. If a man's eye could show as if he were looking through a concave lens or convex lens or a compound microscope, which one would you say, is true? what would be your conclusion..?
So, the answer to the first part of this question is,'No'; but the second part is, 'Yes'. For an explanation, you needn't seek the help of philosophy. Just remember the optical illusion, 'persistence of vision'. Many philosophies also agree with this ideas. E.g.: 'Maya'. Though this term is used in a higher level, any way we can say that the second part is true.
Can we even show that what we experience is more than a belief, even
as much as an approximation?
In the minutest level everyone's world or the 'world' created by everyone's mind is different. That is why we can't understand others fully. So, it is an approximation.
If I feel the ground beneath me then, does it exist? So, I theorize
that something exists and, I call it the ground. But, have I felt or
is it just that my expectation is met?
We cannot say that what one feels is true. Others also must be able to know/feel that; now or later in their life.
Keep in mind that, outside of your own existence, you can't really
"prove" anything at all, even that there is an outside reality. So
there is no fundamental truth. It's all belief.
We can't say sugar is sweet or there is a taste called sweetness until we taste it. Others also won't agree with it unless they also taste it. Most people might even scold such people who talk about the sweetness of sugar.
Likewise, "There is no fundamental truth. It's all belief"-- this (the last part) is a false belief. This last statement is not true in the case of the Ultimate truth.
See the Bhagavad Gita 13.18
If these verses are true most of us must be in darkness. That is the reason for our such belief.