A false and true statement is often used in language practice. The first assessment is perceived as a denial of truth (untruth). In reality, other types of assessment are also used: uncertainty, unprovability (provability), and insolubility. Arguing over for what number x a statement is true, it is necessary to consider the laws of logic.
The emergence of “multi-valued logic” has led to the use of an unlimited number of truth indicators. The situation with the elements of truth is confused, complicated, so it is important to clarify it.
Principles of theory
A true statement is the value of a property (attribute), always considered for a specific action. What is the truth? The scheme is as follows: “The utterance X has the truth value Y in the case when the utterance Z is true.”
Let's look at an example. It is necessary to understand for which of the following the statement is true: "The subject a has the characteristic B". This statement is incorrect in that the object has a sign B, and it is not true that a does not have a sign in. ” The term "false" in this case is used as an external negation.
Definition of truth
How is a true statement determined? Regardless of the structure of the utterance X, only the following definition is allowed: “The utterance X is true when there is X, only X”.
This definition makes it possible to introduce the term “true” into the language. It defines the act of accepting consent or expression with what it says.
Simple sayings
They have a true statement without definition. One may restrict oneself to the statement “He-X” by a general definition if this statement is not true. The conjunction "X and Y" is true if X and Y are true.
Statement Example
How to understand for which x the statement is true? To answer this question, we use the expression: “Particle a is in the region of space b”. Consider the following cases for this statement:
- it is impossible to observe a particle;
- can observe a particle.
The second option involves certain features:
- the particle is actually located in a certain region of space;
- it is not in the supposed part of space;
- the particle moves in such a way that it is difficult to determine its location.
In this case, one can use four terms of truth values that correspond to the given possibilities.
For complex structures, the use of more terms is appropriate. This indicates the unlimited value of truth. For what number the statement is true, depends on practical expediency.
Ambiguity principle
In accordance with it, any statement is either false or true, that is, is characterized by one of two probable truth values - “false” and “true”.
This principle is the basis of classical logic, which is called a two-valued theory. The ambiguity principle was used by Aristotle. This philosopher, arguing over for what number x a statement is true, considered it unsuitable for those statements that relate to future random events.
He established a logical relationship between fatalism and the principle of ambiguity, the provision on the predetermination of any human action.
In subsequent historical epochs, the restrictions imposed on this principle were explained by the fact that it significantly complicates the analysis of statements about planned events, as well as about non-existent (unobservable) objects.
Thinking about what statements are true, with this method it was not always possible to find a definite answer.
Emerging doubts about logical systems were dispelled only after modern logic was developed.
To understand which of these numbers is true statement, suitable two-valued logic.
Polysemy principle
If we reformulate a variant of a two-valued statement to reveal truth, we can turn it into a special case of polysemy: any statement will have one n value of truth, if n is either greater than 2, or less than infinity.
As exceptions for additional truth values (above “false” and “true”), many logical systems are based on the principle of polysemy. The two-valued classical logic characterizes typical uses of some logical signs: “or”, “and”, “not”.
The multi-valued logic that claims to be more specific should not contradict the results of a two-valued system.
The belief that the principle of ambiguity always leads to the establishment of fatalism and determinism is considered erroneous. The idea is also incorrect, according to which, multiple logic is considered as a necessary means of carrying out indeterministic reasoning that its adoption corresponds to the rejection of the use of strict determinism.
Semantics of logical signs
To understand for what number X a statement is true, one can arm oneself with truth tables. Logical semantics is a section of metalogy, which explores the relationship to designated objects, their content of various language expressions.
This problem was already considered in the ancient world, but in the form of a full-fledged independent discipline, it was formulated only at the turn of the XIX-XX centuries. The work of G. Frege, C. Pierce, R. Karnap, S. Kripke revealed the essence of this theory, its realism and expediency.
For a long time period, semantic logic relied mainly on the analysis of formalized languages. Only recently, much of the research began to be devoted to natural language.
In this technique, two main areas are distinguished:
- designation theory (references);
- theory of meaning.
The first involves the study of the relationship of various linguistic expressions to designated objects. As its main categories, one can imagine: “designation”, “name”, “model”, “interpretation”. This theory is the basis for evidence in modern logic.
The theory of meaning seeks an answer to the question as to what constitutes the meaning of linguistic expression. She explains their identity in meaning.
The theory of meaning has a significant role in the discussion of semantic paradoxes, in the solution of which any criterion of acceptability is considered important and relevant.
Logical equation
This term is used in metalanguage. Under the logical equation, we can write the entry F1 = F2, in which F1 and F2 are formulas of the extended language of logical statements. To solve such an equation means to determine those sets of true values of variables that will be included in one of the formulas F1 or F2, at which the proposed equality will be observed.
The equal sign in mathematics in some situations indicates the equality of the original objects, and in some cases it is placed to demonstrate the equality of their values. The entry F1 = F2 may indicate that we are talking about the same formula.
In the literature, quite often under formal logic is meant such a synonym as "language of logical utterances." The “right words” are formulas that serve as semantic units used to build reasoning in informal (philosophical) logic.
A statement appears as a sentence that expresses a specific judgment. In other words, it expresses the thought of the presence of a certain state of affairs.
Any statement can be considered true in the case when the state of affairs described in it exists in reality. In other cases, such a statement will be a false statement.
This fact became the basis of propositional logic. There is a division of statements into simple and complex groups.
In formalizing simple variations of sentences, elementary formulas of a zero-order language are used. Description of complex statements is possible only with the use of language formulas.
Logical connectives are needed to indicate alliances. When applied, simple statements turn into complex forms:
- "not",
- "It’s wrong that ...",
- "or".
Conclusion
Formal logic helps to figure out what name a statement is true for, involves the construction and analysis of the rules for converting certain expressions that preserve their true meaning, regardless of content. As a separate section of philosophical science, it appeared only at the end of the nineteenth century. The second direction is informal logic.
The main task of this science is to systematize the rules that allow us to derive new statements on the basis of proven statements.
The foundation of logic is the possibility of obtaining some ideas as a logical consequence of other statements.
Such a fact allows us to adequately describe not only a specific problem in mathematical science, but also to transfer logic into artistic creation.
Logical research involves the relationship that exists between the premises and the conclusions drawn from them.
It can be attributed to the number of initial, fundamental concepts of modern logic, which is often called the science of "what follows from it."
It is difficult to imagine without such reasoning the proof of theorems in geometry, an explanation of physical phenomena, an explanation of the mechanisms of reactions in chemistry.