for curious and
not quite smart people


Table of contents
1. Knowledge and Faith.
2. Scientific methods.
3. Logic.
4. Logic and Sophistry.
5. Laws of Logic.

Knowledge and Faith

This is a nice picture What is "Knowledge"? At first glance, everything is clear. It is what we know exactly, as opposed to assumptions, beliefs, and speculation. However, it is not so simple. In reality, there is no "Berlin Wall" between these antipodes. For example, they teach Archimedes' Law at school, which states, in particular: "The volume of liquid displaced by a body is exactly equal to the volume of the submerged part of the body." This statement is not doubted by anyone. Why? This idea came to Archimedes, it began to be tested, ...experimenting and calculating with all sorts of objects. And always received confirmation of this formula. But no one has ever done a test... for the whole variety of physical bodies. Scientists in this case believe (believe !!!), that this formula is universal. There are very good reasons for this, however some "reasonable" element of faith does exist. Methods of Scientific Methodology OBJECTIVITY Everyone wants to have a correct, objective judgment of the phenomena, events of our life. Why it is very difficult and what prevents it? Almost everything, unfortunately, interferes with it. Let's try to put some order into "everything". 1. Incorrect aequiomatics (initial basic assumptions) These are the assumptions that are taken for granted. That is, we take them to be true, with no evidence (within the theory in question) is not required. But what if the accepted axioms are wrong? Most likely, all further reasoning will also be wrong. Therefore, when choosing the foundation (axioms) for our wonderful reasoning and theories, one should be very careful and critical choice of axiomatics. Some assumptions may be implicit, i.e., they are not mentioned, but later on they are used as a "matter of course. This, of course, can lead to contradictions and errors in reasoning. 2. Stereotypes, clichés, prejudices. They can be realized (for example: in general, I have a worse attitude toward black people (they are stupid, impudent, and steal) than toward white people. I am aware of it; I know it is wrong, but nevertheless, this is my perception) or subconscious. 3. information problems The information base (data) can be inadequate. Today's information industry makes it possible to obtain an enormous amount of data. Which, on the one hand, increases chances of success, but on the other hand the problem of reception (selection) of high-grade, non-falsified, reliable information (see item 7) turns into a separate, extremely important task. 4. "You can't see the forest for the trees. When analyzing a problem, we get too deep into details that may be unimportant, and as a result we lose the big picture and get the wrong conclusions. 5. "The devil is in the details." Missing data, relationships that seem unimportant, in fact they may be very important. As a result, we again get the devil knows what.... 6. Problems with concepts (ideas). Concepts are thinking absolutely necessary tools. No matter how much we want to deal only with objective and real facts we need artificial models and fictional concepts anyway. This is where one of the most unpleasant and vicious dogs is buried. A model is a new object. It is different from the real object. In a model: 1. Any part of the object is discarded(Point 5). This happens either a. Consciously, because they seem unimportant, or b) unconsciously, because we haven't noticed them in our analysis of the object 2. Some components and connections between them are simplified a. consciously, because we believe that these are small details which do not influence the final result b. unconsciously, because we have not noticed them in the analysis of the object. The most important problem is that this is where this is where very "heavy" errors are generated. "Hard" because they are hard to find and, accordingly it is easy and joyful to get an erroneous result. 7. Perceptual selectivity. This is a rather subtle and curious aspect, having in particular to do with religion....... The essence of the problem is the so-called "observation selection process". That is, not all the facts are considered, but only some of them, selected for objective or subjective reasons. Let us explain with the help of an example. During World War II, German engineers observed fighter planes returning from flights to England. They examined them for bullet holes from enemy anti-aircraft guns in order to draw conclusions about the accuracy of British anti-aircraft guns. The result was strange: Bullet holes were found almost everywhere on the plane except for a precisely defined rectangle near the center of the plane. There had never been a single bullet there!!! Did the British anti-aircraft guns not want to hit this area of about 1.5 x 1.0 meters, or could they not have hit it? The answer was quickly found. The rectangle was exactly under the area where the fuel tank was located. If it was hit, the plane exploded and of course would not return. So simply observing the planes that came back (and therefore excluding all unreturned ones ) results in consciously or unconsciously limits the consideration of all possibilities. The result of the "objective" analysis about the accuracy of the British guns is not objective at all. LOGIC Suppose you have successfully dealt with the problems outlined above and are winning an intellectual battle with your adversary (points 1-7). If so, it means that you have mastered a tool called "Logic. Without any exaggeration: Logic is an absolutely essential tool in knowing the world and solving any mental problem. You can have the most reliable data, reasonable axiomatics, be able to highlight the main thing, avoid selective perception, etc., but if you make logical errors in your reasoning, you will get wrong conclusions and results. Such errors occur due to violations of the laws of logic. In ordinary, everyday terms, the term logic is used quite often. The fact is that not every set of concepts, judgments, inferences makes it possible to get a correct and effective process of thinking. Logical laws define the rules by which consistency, consistency, validity of statements and reasoning are ensured. Logic and Sophistry The foundations of formal logic were laid in ancient Greece. Slightly earlier than logic came the so-called sophistry, sophism. Sophistry in ancient Greek philosophy was the teaching of the sophists, teachers of eloquence and rhetoric. They believed that there are no one-size-fits-all answers to complex questions. All things can be looked at from opposite sides, and there is no ultimate truth. Sophists have the ability to conduct arguments by confusing and stumping their opponents, skillfully constructing sequential chains of reasoning that give the impression of being correct and logical. However, in essence, it is a technique of verbal fraud. Sophism translates as skill, cunning, contrivance, fabrication, subterfuge. Sophism is reasoning, which seems correct at first sight, but contains a hidden logical error. It is used to give the appearance of truth to a false statement. Sophistry came before logic as a formalized science, and it may have been sophists who encouraged philosophers to create logic as a tool to counter demagogy. Here are examples of sophisms. Laws of Logic. There are four fundamental laws in formal logic. law of identity the law of contradiction the law of the excluded third the law of sufficient grounds The first three were formulated by Aristotle. The fourth was "discovered" by the German mathematician and philosopher Leibniz in the 18th century. The law of identity Every thought and every term in the whole process of reasoning must have the same meaning. "" have more than one meaning is to have no meaning at all." Aristotle very wisely pointed out in his work Metaphysics. This means that the substitution of concepts in the course of reasoning is unacceptable. Unfortunately, this is an extremely common classical logical fallacy (or deliberate subterfuge). Example: "А. Sergeev is a very good person, modest and rides a bicycle to work. He would make an excellent assistant to the city's mayor on ecology!" In this example, the first part of the statement describes the person's personal qualities, while the second part concludes about his professional qualities - which, generally speaking, are quite different things. The Law of Contradiction Two contradictory judgments cannot be true at the same time. At least one of them is false. "... it is impossible that one and the same thing at the same time is and is not inherent in the same relation" (Aristotle, "Metaphysics") Example: Often there are these kinds of statements from officials: "The people of our country have repeatedly demonstrated their political maturity by casting their votes in presidential and parliamentary elections. At the same time, our people are not yet ready for the election of governors and other democratic changes." There is a clear contradiction: on the one hand, the people are politically mature, but on the other hand, they are completely dormant and not ready to elect local officials. The Law of the Excluded Third Two contradictory judgments cannot be both true or both false at the same time. "...nothing can be in the middle between two contradictory judgments about one thing; each separate predicate must either be affirmed or denied." (Aristotle, Metaphysics) The law of the excluded third implies that if A is true, then not-A is true, or vice versa, not-A is true and not-A is true. Here the letter A denotes an arbitrary statement. No third is given, nor is any B yet given, which would claim to be an expression of truth. Thus, the very name of the law expresses its meaning: Things are as the statement in question says, or as , as its negation says, and there is no third possibility. Example: 1. "Censorship is forbidden!" 2. "Censorship is permitted if it is in the interest of the state." Both of these statements about the same phenomenon cannot be simultaneously true or false. If an exception is made, as in the second statement, then the first statement is false-"there is no third possibility." The law of sufficient reason Every thought claiming to be "correct" must be conditioned by other thoughts whose truth has been proved. The essence of the law of sufficient reason - there must be clear, verifiable proof that a statement (inference) is true. Thus, the law of sufficient reason expresses the methodological requirement for the validity of all rational knowledge that claims to be an objective judgment. Example: "This person is not sick because he has no cough and a normal temperature." Clearly, the evidence of no cough and a normal temperature is not sufficient to conclude definitively that a person is healthy. The most important legal principle is based on this law: "Presumption of Innocence." "No one shall be declared guilty unless his guilt has been proved."
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