## 12 Border Design For Students

The knowledge of separate subjects, their properties occurs by means of forms of sensory perception (feelings and perceptions). We see that this house is not completed yet, we feel taste of bitter medicine and so on. This truth is not subject to the special proof, they are obvious.

The most known and, perhaps, the most interesting of all logical paradoxes is the paradox "Liar". There are various options of this paradox, many of which only to all appearances are paradoxical.

The certified isolated facts. To sorts to arguments so-called actual material, that is statistical data on the population, the state territory, quantity of arms, testimony, signatures of the person on the document, scientific these scientific facts belongs. The role of the facts in justification of the put-forward provisions, including scientific, is very great.

This way of a denial consists that shows mistakes in the form of the proof. The most widespread mistake a yavlyaetsyapodbor of such arguments from which the validity of the disproved thesis does not follow. The proof can be constructed incorrectly if any rule of conclusion is violated or "hasty generalization" is made.

In the first case the mistake arises when instead of one true thesis try to prove other, stronger thesis, and thus the second thesis can be false. If from and follows, but from would not follow and, the thesis and is stronger, than the thesis. For example, if instead of proving that this person did not begin the first a fight, will start proving that he did not participate in a fight, will be able to prove nothing if this person really fought and somebody saw it.

Mistakes in inductive conclusions. One of such mistakes — "hasty generalization", for example the statement that "all witnesses give biased evidences". Other mistake is "after that — means, because of it" (for example, loss of a thing is found after arrival to the house of this person, so it carried away it). All superstitions are based on this logical mistake.

It is necessary to highlight that criterion of the validity is practice. If practice confirmed the validity of judgment, the further proof is not necessary. Practice - criterion of the validity of any theory.

Sometimes people in the performance, the written statement, the scientific article, the report, lecture cannot accurately, clearly, unambiguously formulate the thesis. At meeting some acting cannot accurately formulate 2-3 theses, and then is powerful, with deep arguments to state them before listeners.

The theory of the proof and denial is in modern conditions means of formation evidence-based belief. In science scientists should prove the most different judgments, for example judgment that existed B.C., the subjects found at archeological excavations about the atmosphere of planets of Solar system, about stars and galaxies of the Universe, about theorems of mathematics, about the direction of development of the COMPUTER, about implementation of long-term weather forecasts, about secrets of the World Ocean and space belong to what period. All these judgments have to be scientifically reasonable.

denial by the facts - the valid events, the phenomena, statistical yielded have to be given, results of experiment, scientific data which contradict the thesis, that is the disproved judgment;

The thesis — this judgment, which validity should be proved. Arguments — it is those true judgments which use at the proof of the thesis. A proof form, or demonstration, the way of logical communication between the thesis and arguments is called.

Mistake in conclusion by analogy. Mistakes by analogy can be illustrated with examples of false analogies (so-called vulgar analogies), including analogies of alchemists. A main goal of alchemy — finding of so-called "philosophers' stone" for transformation of ignoble metals into gold and silver, receiving an elixir of longevity, universal solvent, etc. Together with it also the positive role of alchemy is noted.

In the mathematician, the mechanic, theoretical physics, mathematical logic and other sciences except definitions enter axioms. Axioms are judgments which are accepted as arguments without proof as they are confirmed with centuries-old practice of people.