False and true statements are 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), unsolvability. Arguing over for what number x the statement is true, it is necessary to consider the laws of logic.
The emergence of "multivalued logic" led to the use of an unlimited number of truth indicators. The situation with the elements of truth is confusing, complicated, so it is important to clarify it.
A true statement is the value of a property (attribute), which is always considered for a certain action. What is truth? The scheme is as follows: "Proposition X has a truth value Y in the case when proposition Z is true."
Let's look at an example. It is necessary to understand for which of the given statements the statement is true: "Object a has a sign B". This statement is false in that the object has attribute B, and false in that a does not have attribute B. The term "false" in this case is used as an external negation.
Determination of truth
How is a true statement determined? Regardless of the structure of proposition X, only the following definition is allowed: “Proposition 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 agreeing or speaking with what it says.
They contain a true statement without a definition. One can confine oneself to a general definition in the proposition "Not-X" if this proposition is not true. The conjunction "X and Y" is true if both X and Y are true.
How to understand for which x the statement is true? To answer this question, we use the expression: "Particle a is located in a region of space b". Consider the following cases for this statement:
- impossible to observe the particle;
- you can observe the particle.
The second option suggests certain possibilities:
- particle is actually located in a certain region of space;
- she is not in the intended part of space;
- particle moves in such a way that it is difficult to determine the area of its location.
In this case, four truth-value terms can be used that correspond to the given possibilities.
For complex structures, more terms are appropriate. This isindicates unlimited truth values. For which number the statement is true depends on practical expediency.
The ambiguity principle
According to it, any statement is either false or true, that is, it is characterized by one of two possible truth values - “false” and “true”.
This principle is the basis of classical logic, which is called the two-valued theory. The ambiguity principle was used by Aristotle. This philosopher, arguing over for what number x the 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 predestination of any human action.
In subsequent historical eras, the restrictions that were 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 (non-observable) objects.
Thinking about which statements are true, it was not always possible to find a clear answer with this method.
Emerging doubts about logical systems were dispelled only after modern logic was developed.
To understand for which of the given numbers the statement is true, two-valued logic is suitable.
Principle of ambiguity
If reformulatedvariant of a two-valued statement to reveal the truth, you can turn it into a special case of polysemy: any statement will have one n truth value if n is either greater than 2 or less than infinity.
As exceptions to additional truth values (above "false" and "true") are many logical systems based on the principle of ambiguity. Two-valued classical logic characterizes typical uses of some logical signs: “or”, “and”, “not”.
Multivalued logic claiming to be concretized should not contradict the results of a twovalued system.
The belief that the principle of ambiguity always leads to a statement of fatalism and determinism is considered erroneous. Also wrong is the idea that multiple logic is seen as a necessary means of carrying out indeterministic reasoning, that its acceptance corresponds to the rejection of the use of strict determinism.
Semantics of logical signs
To understand for what number X the statement is true, you can arm yourself with truth tables. Logical semantics is a branch of metalogics that studies the relation to designated objects, their content of various linguistic expressions.
This problem was considered already in the ancient world, but in the form of a full-fledged independent discipline it was formulated only at the turn of the 19th-20th centuries. Works by G. Frege, C. Pierce, R. Carnap, S. Kripkemade it possible to reveal 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 has the majority of research been devoted to natural language.
There are two main areas in this technique:
- notation theory (reference);
- theory of meaning.
The first involves the study of the relationship of various linguistic expressions to the designated objects. As its main categories, one can imagine: "designation", "name", "model", "interpretation". This theory is the basis for proofs in modern logic.
Theory of meaning deals with the search for an answer to the question of what is the meaning of a linguistic expression. She explains their identity in meaning.
The theory of meaning plays a significant role in the discussion of semantic paradoxes, in the solution of which any criterion of acceptability is considered important and relevant.
This term is used in metalanguage. Under the logical equation, we can represent the record F1=F2, in which F1 and F2 are formulas of the extended language of logical propositions. 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, under which the proposed equality will be observed.
The equal sign in mathematics in some situationsindicates the equality of the original objects, and in some cases it is set 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 the formal logic mean such a synonym as "the language of logical propositions". The “correct words” are formulas that serve as semantic units used to build reasoning in informal (philosophical) logic.
A statement acts as a sentence that expresses a particular proposition. In other words, it expresses the idea of the presence of some state of affairs.
Any statement can be considered true in the case when the state of affairs described in it exists in reality. Otherwise, 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.
When formalizing simple variants of statements, elementary formulas of the zero-order language are used. Description of complex statements is possible only with the use of language formulas.
Logical connectives are needed to denote unions. When applied, simple statements turn into complex forms:
- "it's not true that…",
Formal logic helps to find out for which name a statement is true, involves the construction and analysis of rules for transforming certain expressions that preserve themtrue value 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 you to derive new statements based on proven statements.
The foundation of logic is the possibility of obtaining some ideas as a logical consequence of other statements.
This fact makes it possible to adequately describe not only a certain problem in mathematical science, but also to transfer logic to artistic creativity.
Logical investigation presupposes the relationship that exists between 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 proving theorems in geometry, explaining physical phenomena, explaining the mechanisms of reactions in chemistry without such reasoning.