## One Answer

1. yakub_harabet says:

In the strict sense of the word, proof is possible only where there is a system of axioms, for example, in mathematical logic or in geometry. Moreover, the statement is proved only in this system of axioms and in no other. The previous speaker gave a definition of proof.

In real life, there is no proof, because there is no system of axioms and rules of inference with which everyone would agree and within which it would be possible to prove, for example, that Ivan Ivanovich stole Ivan Petrovich's wallet, or that it is harmful to eat sugar. Instead of evidence, arguments are given that one side tries to convince the other of the correctness of their beliefs. The situation is as follows. Each agent (for simplicity, a person) has a set of beliefs. They are very diverse, come from different sources (and most of them – from the ceiling :)) and relate to all possible areas of our life. For example, “the earth is round”, not “with verbs written separately”, “we should wash hands before eating,” “uncle nick was a kind and decent man,” etc. When one agent wants to convince another of the truth of his thesis, he resorts to arguments, among which, besides the logical inference is also an example, analogy, and other tools. What is called evidence in court is a special case of an argument, the difference is that arguments in court should be as reliable as possible (apparently, that's why they are called evidence).

In the natural sciences, oddly enough, there is also no evidence in the logical sense of the word. Scientific theories can be confirmed or refuted by experience or observation. Of course, science uses logical inference. However, the only significant difference between inference and proof is that the premises in the proof are absolutely true statements (axioms), and in the conclusion – any, not necessarily true. We don't know if a given theory is true (after all, this is what we want to find out), and we use logical inference to getconsequences from it that can be verified experimentally or by observation. However, the experiment itself cannot be called a proof for two reasons:

1. We are convinced of the truth of the consequences, and the truth of the consequences does not imply the truth of the premises (anecdote about Chapaev and vobla).

2. No experiment gives absolutely reliable results. Imperfection of sensory organs, devices, the influence of random unforeseen factors. Therefore, a series of experiments or a series of observations is usually performed. Taken together, they should give a sufficiently high (but not absolute) degree of confidence in a certain thesis.