A tautology can be a redundant statement: "Go up."
Tautology is a term that comes from a Greek word and refers to the repetition of the same thought through different expressions . A tautology, for rhetoric, is a redundant statement .
It is common for tautologies to be considered an error in language or a lack of style. However, it is possible to appeal to tautologies to emphasize a certain idea. For example: the sentence “I can confirm that the accused is guilty since I saw the murder with my own eyes” presents an unnecessary clarification about the use of his eyes, since he could not have seen through any other means; Likewise, the emphasis on the word "own" may be completely omitted.
Other very common examples of tautology can be seen in the following sentences: “I'm going to go upstairs to look for a book and I'll come back,” “I have to go outside to water the plants.” Whenever you go up it is upwards; Likewise, leaving implies moving away from a place, which is why these clarifications are meaningless and unnecessary for understanding.
The tautology or truism
When tautology involves a redundant explanation that does not provide new knowledge, we usually speak of a truism or truism : “I am what I am.”
The expression in which redundant terms appear (such as “going up” or “going outside” ), on the other hand, is called pleonasm .
For logic, a tautology is the formula of a system that is true for all interpretation.
The concept in logic
In the field of logic , a tautology is a formula of a system that is true for any interpretation. In other words, it is a logical expression that is true for all possible truth values of its atomic components.
To find out if a given formula is a tautology, a truth table must be constructed.
Truth table and tautologies
The truth table (also known as the truth value table ) presents a compound proposition and its truth value for each of the possible combinations that can occur with its elements. Its author was the American philosopher and scientist Charles Sanders Peirce, also known as the greatest representative of modern semiotics, and he published it in the mid-1880s.
To configure a formal system, it is necessary to establish the definitions of each operator and the arguments must be presented in the form of logical-linguistic deductive reasoning, respond to a purely mathematical design and constitute a logical application that defines its input and output variables.
The two possible values that a truth table can return are: true , which is expressed by the letter "V" or the number "1" and indicates that the circuit is closed; false , represented by the letter "F" or the number "0", when a circuit is open. The propositions to be analyzed are the variables, and they are located at the top of the table, occupying the place that is commonly allocated to field names.
The operators used in a truth table are:
* negation : when executed on a given truth value , it returns the opposite (if it was originally true, it returns false, and vice versa);
* conjunction : used to operate with two truth values, generally from two different propositions, and returns true when both are true, and false for the rest of the cases;
* disjunction : similar to conjunction, but it is enough for one of the two propositions to have a true value to return such a result;
* conditional : also known as implication , it takes two statements and returns false only when the first returns true and the second returns false. For the remaining cases, its result is true;
* biconditional : operates on the truth values of two propositions and returns true if both have the same value and false otherwise.