11.3 Indirect Confirmation

In science, and not only in it, direct observation of what is said in the verified statement is rare. The most important and at the same time universal method of confirmation is the derivation from the substantiated position of logical consequences and their subsequent verification. Confirmation of the consequences is assessed as evidence in favor of the truth of the situation itself.

Here are two examples of this confirmation.

The one who thinks clearly speaks clearly. The touchstone of clear thinking is the ability to transfer your knowledge to someone else, possibly far from the subject under discussion. If a person possesses this ability and his speech is clear and convincing, this can be considered a confirmation that his thinking is also clear.

It is known that a strongly cooled object in a warm room is covered with dew drops. If we see that the person who entered the house immediately misted his glasses, we can conclude with sufficient confidence that it is freezing outside.

In each of these examples, reasoning goes according to the pattern: “the second follows from the first; the second is true; it means that the first one is also, in all likelihood, true ”(“ If it’s freezing outside, the person who entered the house gets fogged up; the glasses are really fogged up; it means that it’s cold outside ”). This is not deductive reasoning, the truth of the premises does not guarantee here the truth of the conclusion. From the premises “if there is the first, that is, the second” and “there is the second” conclusion “there is the first” follows only with a certain probability (for example, a person who has glasses sweated in a warm room could cool them, say, in a refrigerator, so that then inspire us like a freezing cold outside.

The derivation of the consequences and their confirmation, taken by itself, can never establish the validity of a substantiated position. Confirmation of the consequences only increases its likelihood.

The greater the number of consequences found confirmation, the higher the probability of the assertion being verified. From here - the recommendation to deduce from positions put forward and demanding the reliable base as much as possible logical consequences for the purpose of their check.

What matters is not only the number of consequences, but also their character. The more unexpected the consequences of a provision are confirmed, the stronger the argument they give in its support. Conversely, the more expected in the light of the corollaries of the already obtained corollaries, the less his contribution to the substantiation of the checked position.

A. Einstein’s general theory of relativity predicted a peculiar and unexpected effect: not only the planets revolve around the sun, but the ellipses that they describe must rotate very slowly relative to the sun. This rotation is the greater, the closer the planet is to the Sun. For all planets except Mercury, it is so small that it cannot be caught. The ellipse of Mercury, the closest planet to the Sun, performs a complete rotation in 3 million years, which can be detected. And the rotation of this ellipse was really discovered by astronomers, and long before Einstein. No explanation for this rotation was found. The theory of relativity did not rely, when formulated, on the data on the orbit of Mercury. Therefore, when the conclusion about the rotation of the Mercury ellipse that turned out to be true was derived from its gravitational equations, this was rightly regarded as an important evidence in favor of the theory of relativity.

Confirmation of unexpected predictions made on the basis of a situation significantly increases its plausibility. However, no matter how large the number of corroborating consequences is, and no matter how unexpected, interesting or important they may be, the situation from which they are derived still remains only plausible. No effect can make it true. In principle, even the simplest assertion cannot be proved on the basis of one confirmation of the corollaries arising from this statement.

This is the central point of all reasoning about empirical evidence. Direct observation of what is said in the statement gives confidence in the truth of the latter. But the scope of this observation is limited. The corollary is a universal trick applicable to all statements. However, a technique that only enhances the credibility of the statement, but does not make it reliable.

The importance of empirical substantiation of assertions cannot be overestimated. It is primarily due to the fact that the only source of our knowledge is experience. Knowledge begins with living, sensual contemplation, with what is given in direct observation. Sensual experience connects a person with the world, theoretical knowledge is only a superstructure over an empirical basis.

At the same time, the theoretical is not completely reducible to the empirical. Experience is not an absolute and undisputed guarantee of the irrefutable knowledge. It can also be criticized, monitored and reviewed. “In the empirical basis of objective science, writes K. Popper, there is nothing“ absolute ”. Science does not rest on a solid foundation of facts. The rigid structure of its theories rises, so to speak, over the swamp. It is like the knowledge erected on stilts. These piles are driven into the swamp, but do not reach any natural or "given" base. If we stopped piling further, it was not at all because we had reached solid ground. We stop just when we are convinced that the piles are strong enough and capable, at least for a while, to withstand the weight of our structure. ”

Thus, if we limit the range of ways to substantiate statements to direct or indirect confirmation in experience, it will be incomprehensible how we can still move from hypotheses to theories, from assumptions to true knowledge.