True and False Perceptions

I apologize, but you have brought not a strictly and firm compare here. "What color numbers are?" isn't the same as mine question.

Ok, let you've got right, so the perceptions are true? How&why? Maybe they're neither true or false? Then, what is that such a phenomenon as phantom pain? Or how do we know whether we're sleeping?

I think even perceiving something we can be wrong. The matter is perceiving itself being unaware of it – it's only possible, not necessary. What if our perceptions are recursive as the mirrors?

Let's say we compare these things:

x and y
bread and butter
1 and 2
water and the transparent liquid

it might be that x and y are the same like in a case when x=1 and y=1. Bread and butter are never the same even being able to co-exist. 1 and 2 are not the same (in many respects, except for being numbers, but being numbers is not the same as being 1 or being 2). The water can be equal or can match with the transparent liquid like in a case of the distilated H20, but not in all the cases. As we see, then 1=2, then it is a false statement, and even if I have an opinion that 1=2, then I'm wrong. But if I have an opinion that the water is the transparent liquid, I might be right or wrong depending on the conditions. 

And by the way, you're saying about some actual demonstrating the truth? So what is kind of demonstration actually can demonstrate something to be true? Would this definition be true?

Maybe I confused something, so I apologize for it.

Perceptions can have value since they've got forms. In other words, one's attempts to get perceptions without any registration of it will fail. Either we're aware of the perceptions, or not.

It doesn't mean my thought of how the perceptions work is absolute. It depends on the sides of the contradiction.

There are at least two types of contradiction: logical and physical. The last one is closer to common: for a thing x is impossible to occupy a certain place P¹ and P² at the same time. A logical one – is to: acting without or beyond axioms.

(Actually, there's a Hegel's one, it's about the reason or the mind itself, but it's not so clear, so that's why it's not obvious how can it be used.)

If we've got a set of things, and dividing it into classes or groups can be done deliberately, then it's not straight to say that one class of them contradicts to another one. Alternatively, it would be a free from necessity separation.

The content of perception is similar to the above: P_ is "perception of _", and Px is "perception of x". x belongs to a domain of just things. Or we don't know what a perception contains until we will extract it.

This is a common view. People think that Pa and Pb cannot be in contradiction since a and b are freely divided area. And there's no way to be sure whether a contradicts to b or not.

However, Pa must have logical value, or the claim like "my perceptions doesn't register anything" has to be true.

In a more deep level, any act of perception is a chemistry between elements. So, while a is in certain relations with b, the perception occurs. And since this can be, it's also possible that Pa might contradict to Pb. The fact of it is the evidence that the perceptions have logical values.