Logical errors

What is a Logical Error
A logical fallacy is, in logic, philosophy, and other sciences that study cognition, an error associated with a violation of the logical correctness of inferences.

An error is due to some logical flaw in the proof, which renders the proof wrong as a whole.


If a person who looks at the railroad tracks going away seems to think that they converge at one point on the horizon, he is mistaken. He is mistaken who thinks that the fall of a single grain on the ground does not make the slightest noise, that a fluff has no weight, etc.

Can we call these mistakes logical? No. They are errors of vision, hearing, etc., but they are errors of perception.

And logical errors relate to thoughts. And not to thoughts as such, but to the way one thought relates to another, to the relations between various thoughts.

Violation of the law of identity
One of the main laws of logic, the law of identity, is often violated in our daily lives. Take, for example, such a conversation.

  • Can I take your books?
  • Take them.
  • And I do not want to take them.
  • Then don’t take them.
  • He forbade me to take his books.

Here in the expression «do not take» two different judgments are mixed up: «do not take» in the sense of «you may not take» and «do not take» in the sense of «you may not take,» as a result of which the law of identity is broken and a misunderstanding inevitably occurs.

Often the smallest change in a phrase, such as the transfer of the accent, can completely change its logical meaning.

Recall the misunderstanding that arose in connection with the statement of Isaac Newton: «I do not concoct hypotheses. Many people were surprised that Newton (see interesting facts about Newton), despite this statement, himself put forward many hypotheses.

In fact, there is no reason for surprise, and those who see a contradiction here, simply violate the law of identity. In the above statement of Newton it is necessary to put the logical emphasis on the word «compose», and then it will make sense: «I do not compose hypotheses, but I put them forward on the basis of facts.

Some people interpreted it differently and, putting the logical emphasis on the word «hypotheses», put into this statement a completely different meaning: «I don’t make hypotheses, that is, I don’t create them at all». This led to the conclusion that Newton is an opponent of all hypotheses.

Violation of the law of the excluded third
It is also not uncommon to encounter logical errors associated with violation of the law of the excluded third. Here is a classic example.

In one bathhouse, the following notice is posted:

«The luggage room accepts:

money and valuables.
Not accepted for storage:

firearms and edged weapons,
combustible materials,
hammers and knives.
A citizen comes to the bathhouse and wants to deposit a bundle of books along with his clothes. The checkroom attendant refuses to take the books on the grounds that they are not on the list of items accepted for deposit. The citizen insists, referring to the fact that the list of items not accepted for storage does not include books.

Based on the above announcement, the judgment «books are accepted» is denied in the same way as the judgment «books are not accepted».

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