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Faith fills the space that is temporarily inaccessible to reason. There is a domain of knowledge and a domain of ignorance. The area of ignorance is divided into two parts: one believes in the fabrications of the first part, and one does not believe in the fabrications of the other. The area of faith and knowledge does not overlap in any way.
I will take the liberty of quoting one of the respondents to the questioner's question.
“Faith fills the space that is temporarily inaccessible to reason.”
If this is so, then our scientific luminaries are definitely strongly religious people, since there is much more that is inaccessible to their minds than the average person with a secondary education. Unavailable due to a much larger problem horizon. They know this for a fact, because there are many more hypotheses in the scientific world than discoveries.
It is a different matter if we define it this way: “faith fills the space that is not occupied by knowledge.”
Thus, faith is present in the human mind like any other phenomenon or event. One person, as a result of clinical death, experienced firsthand that he could see himself lying breathless on the operating table and hear doctors talking. After being brought back to life, he will not have faith, but knowledge. Those who have not passed this experience will remain in a state of faith ( unbelief).
A developed mind has much greater cognitive capabilities than an undeveloped one. This mind, in harmony with intuition, will give him the knowledge ( not final, but relative, but still), and, therefore, the experience that a person has truly divine abilities. In particular, to see a thousand kilometers away and communicate with the same person on the other side of the Earth. For an ordinary believer, this is the area of believe not believe. Church officials will naturally attribute this phenomenon to the tricks of Satan. Although, if the priests themselves did this, it would be a fact of divine inspiration.
Proof is a personal matter for everyone. Everyone must prove it first of all to themselves. It is impossible to prove something to someone who stands on a different worldview platform. Proof is just as much a dialectical process as cognition. And since there is no limit to knowledge, there is also no limit to proof.
The sacramental “EVERYTHING” (to prove everything) is not real.
Faith is a belief in the authenticity of a particular fact. If you delve into how our brains work , ultimately all we know is faith.
Take an object in your hand, stretch your arm out in front of you and let go of the object – it will fall. Repeat this several times and you will see that the phenomenon is static and always manifests itself. And now you already have the belief that all objects fall down if you let them go.
And so, all our knowledge is faith. At first, in childhood, we are convinced of elementary things that become predictable for us. We believe our senses, we believe our eyes.
But the mind… If you quote Wikipedia, this is the highest type of thinking activity, the ability to think universally, the ability to analyze, abstract and generalize.
In fact, the mind is something inseparable from the language (spoken), because it is our language that allows us abstractions, generalizations. But the mind operates with knowledge and evaluates the reliability of information or creates a new one based on the known one.
So, the answer to the first question is that they are inextricably linked and reason does not exist without faith. The mind also sets the criteria for evaluating information: when it turns for us from a belief into an irrefutable fact.
And the answer to the second question, in my opinion: no, you can't prove everything.
All the information in a person's head is taken on faith.
We believe that objects fall down because we know that there is a law of universal gravitation and in fact all objects are attracted to each other, and the Earth is very large in comparison with them, and therefore everything falls down while we are standing on the Ground. And we also know that the Sun is a big ball of plasma, and the Earth also falls in orbit on the Sun. Because the Sun is just huge compared to the Earth. This force is called the force of attraction, and this force arises because space itself bends under the weight of matter… And why does it bend, and not vice versa? What exactly is it in the composition of matter that causes it to attract and why does it repel at the micro level? Why do molecules repel closer than a certain distance? But just because it is… I've never even seen the molecules themselves. We just believe in what we were taught 🙂
And similarly with any other phenomena – if we analyze the details, we will come to the moment when we do not know the causes of the phenomenon and there is only one thing left – the belief that it is so, and not otherwise.
And as a result, the least costly for the brain is the evaluation of information based on the authority of the source. This is easier and faster than digging the whole point down to the level where you don't understand it anyway. We study any phenomenon exactly to the point where the degree of knowledge becomes satisfactory for us and our tasks.
Faith and Reason are an ambiguous combination. They can be allies. For example, my faith in my Mind helps me achieve my goals. Or vice versa, when my blind Faith deprives my Mind of motivation to achieve goals. As long as we believe that the process of learning is eternal. This means that scientists will always have a job to do. The world is dynamic, we know it, and it changes at the same time… It is important that the object of our Faith does not hinder the Mind. So that our Faith changes with the achievements of Reason and is its ally.