10.1 Proof and refutation The concept of evidence and its structure Definition of evidence Proof in a broad sense

The concept of evidence and its structure

It is impossible to overestimate the importance of evidence in our lives and especially in science. And yet, the evidence is not as common as we would like. Sometimes, evidence is issued that is not at all. Everybody resorts to evidence, but rarely anyone thinks about what it means to “prove”, why the evidence “proves”, whether any statement can be proved or disproved, whether everything needs to be proved, etc.

Definition of evidence

Our idea of ​​evidence as a special intellectual operation is formed in the process of carrying out concrete evidence. By studying different areas of knowledge, we assimilate and relevant evidence. On this basis, we gradually draw up - most often imperceptibly to ourselves - a general intuitive idea of ​​the evidence as such, its general structure, independent of the specific material, the goals and the meaning of the proof, etc.

A special role is played by the study of mathematics. From time immemorial, mathematical reasoning has been considered the generally accepted standard of proof. Wanting to praise anyone's argument, we call it mathematically rigorous and flawless.

The study of evidence on its specific samples is both interesting and useful. But it also requires familiarity with the basics of the logical theory of evidence, which speaks of evidence irrespective of the scope of their application. Practical skills of proof and an intuitive idea of ​​it are sufficient for many purposes, but not for everyone. Practice here, as usual, needs a theory.

The logical theory of proof is basically simple and accessible, although its specification requires a special symbolic language and other sophisticated techniques of modern logic.

The proof in logic is understood as the procedure for establishing the truth of a statement by bringing in other statements, the truth of which is already known and from which the first follows.

In the proof, the thesis is different - the statement that needs to be proved, the basis (arguments) - those statements with the help of which the thesis is proved, and the logical connection between the arguments and the thesis. The concept of proof always implies, therefore, an indication of the premises on which the thesis rests, of the logical rules according to which the statements are transformed during the course of the proof. In normal practice, we rarely formulate all used assumptions and, in essence, never pay attention to the rules of logic that we apply.

One of the main tasks of logic is to give an exact meaning to the concept of proof. But although this concept is almost the main thing in logic, it does not have an exact, strictly universal definition applicable in all cases and in any scientific theories.

“The concept of proof,” writes the Russian logician and mathematician V. A. Ouspensky, “in its entirety, belongs to mathematics no more than psychology: after all, proof is just a reason, convincing us so much that with its help we are ready to convince others.”

Proof is one of many ways to persuade. In science, this is one of the main methods. It can be said that the scientific method of persuasion is, above all, a method of rigorous and accurate evidence. The requirement for evidence of scientific reasoning determines the “general illumination” that modifies the colors that fall within its scope of action. All other requirements for scientific reasoning are permeated with this “general lighting”. Without it, it inevitably degenerates into an unsubstantiated set of general declarations and teachings, an appeal to faith and emotions.

Each of us has the “burden of proof” of the provisions being put forward. It is important to constantly think about the content side of things. At the same time, it is also essential that the unity of pithiness and evidence be always ensured. No artificial methods, no eloquence can help if there are no well-grounded ideas and convincing evidence.

The task of the proof is to fully approve the validity of the thesis to be proved.

Since the proof is about full confirmation, the link between the arguments and the thesis must be deductive . In its form, evidence is a deductive conclusion or a chain of such conclusions leading from true premises to a provable position.

An old Latin proverb says: "Evidence is appreciated but for quality, not for quantity." In fact, deduction from truth gives only truth. If the correct arguments are found and the provable position is deductively deduced from them, the proof has taken place and nothing more is required.

Proof in the broad sense

Often, the concept of proof has a broader meaning. In this case, the proof is any procedure for substantiating the truth of the thesis, including both deduction and inductive reasoning, references to the connection of the proposition being proved with facts, observations, etc. A broad interpretation of the evidence is common in the humanities. It is found in experimental, based on observations reasoning.

As a rule, evidence is widely understood in everyday life. To confirm the idea put forward, there are actively involved facts that are typical in certain respects, phenomena, etc. There is no deduction in this case, of course, it can only be about induction. But, nevertheless, the alleged rationale is often referred to as evidence.

The widespread use of the term “proof” does not in itself lead to misunderstandings. But only under one condition. It is necessary to keep in mind constantly that inductive generalization, the transition from particular facts to general conclusions, gives not reliable, but only probable knowledge.

Many of our statements are neither true nor false. Evaluations, rules, tips, requirements, cautions do not describe the situation under consideration. They indicate what it should be, in which direction it should be transformed. We are entitled to demand that the descriptions be true. But good order, advice, etc. we characterize as effective, expedient, but not as true.

The standard definition of evidence uses the concept of truth. To prove a thesis is to logically derive it from other true propositions. But there are claims that are not related to truth. It is also obvious that, by operating with them, one can and should be both logical and demonstrative.

Thus, the question arises of a substantial extension of the concept of proof. They should cover not only descriptions, but also statements such as estimates, requirements.

The task of redefining the proof is successfully solved by modern logic. Its sections such as the logic of assessments and the logic of norms convincingly show that arguments about values ​​and norms are also subject to the requirements of logic and do not go beyond the scope of logic.