Something to believe
You know that the Earth is "round." This idea is also a paradigm of the progress of science today. But the path to the paradigm has been long and complex.
XIX. At the end of the 20th century, for example, navigator Joshua Slocum encountered cultural people who believed the Earth to be flat. And he had problems with them because Slocum was claiming that on a sailboat he went around the world. Today no one doubts Slocum's achievement, but from that historical perspective people's doubt is understood.
We can do a test. How do we know that the Earth is not flat? Why has anyone argued or perceived it? In our environment, is there no alternative that the Earth is "round"? There is proof of this. But if someone has not presented us, would we be able to become aware of those trials? For most people, the answer is probably negative.
In general, science works like this. The smartest scientist cannot prove it all either. You should trust other scientists. You must accept concepts that you cannot demonstrate. The question is that those others also have to accept what others have done, etc. How long? For there comes a time when you do not have to accept an idea demonstrated by anyone else. We must accept something that cannot be demonstrated. These are basic ideas and principles we call axioms.
Why
The easiest thing is to give an example. And a good way to find examples is to use the question why, as children do.
Why is the Earth round? Because it has a lot of matter and, due to gravity, all this matter is oriented towards the center of the Earth. And why does gravity influence? Because matter attracts itself (that is gravity). Yes, but why do you feel attracted to matter? Right now we have a problem, it is difficult to explain why, but Einstein did it through general relativity: "because matter distorts the surrounding space and time," said the prestigious scientist. However, this does not end the questionnaire. Why does matter distort surrounding space and time?
There comes a time when the only possible answer is: "Because it is so." And perhaps science will clarify why it is so in the future, but it can also wonder why. We have to believe something we have to accept without proof. We have reached an axiom.
Some axioms are not as hard as Einstein's relativity. One of the axioms that science admits is, for example, that an experiment will give the same result anywhere. A chemical reaction under the same conditions will yield the same result in Brazil and Thailand. And done today or within five years. If it does not yield the same result, we recognize that conditions were not the same in both, but we do not conclude that chemical principles are different in those two regions or change over time. One Brazilian and one Thai electron are exactly the same and do not change over time. It cannot be demonstrated for all places and times, but science accepts this idea. It is an axiom.
All branches of science also use a set of axioms of their own. Plato himself realized that they are fundamental in mathematics. Others have defined mathematical theories by saying that it is a group of axioms and the direct consequences (theorems) of these axioms. Some axioms are obvious, for example 1=1 is an axiom. Obvious. Hence it is an axiom. It cannot be shown that 1=1 but we consider it true.
Although it seems extremely obvious, the definition of these simplifications is very important, since the axiom is the basis of theories, and if one of these bases is not correct, all the science built on being thrown away. In some branches, there is also an intense debate on what axioms are and what not, for example in the theory of natural selection.
And keep in mind that some of the axioms have been proven wrong. The discovery of America, for example, stirred up some axioms of botany and zoology until then, and years later, precisely, they were able to demonstrate that the Earth is round: One of the great European axioms was suspended.
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