Frege's triangle: concept, logical model, semiotics and logic

2024 Author: Henry Conors | [email protected]. Last modified: 2024-02-12 02:41

What is semiotics? What is Frege's Triangle? The meaning, sign and meaning will be considered within the framework of the article. To understand the concept, it is not enough to read the definition of the term. You need to understand what exactly the creator of the idea was doing.

Who owns the authorship?

The idea known as Frege's triangle belongs to a German mathematician who also studied philosophy and logic. His name was Friedrich Ludwig Gottlob Frege. This man lived and worked at the turn of the 19th and 20th centuries.

A scientist was born in the family of a school teacher. Frege was educated at the University of Jena, and defended his thesis in Göttingen. After her defense, he returned to Jena, where he soon received the position of Privatdozent at one of the departments of the local university.

What is the significance of this scientist's work?

Frege's triangle is far from the only idea of the German logician and mathematician that was important for the development of philosophical thought. However, the recognitionreceived mainly due to the development and popularization of their students and followers. One of them was Rudolf Karnal, who did a lot to develop the philosophy and ideas of logical positivism.

The main significance of Frege's works is that in them the scientist revised a number of mathematical laws, approaching them from completely new positions. His work Begriffsschrift, which means "calculus of concepts" in Russian, which was published in 1879, practically became the beginning of a new era in the history of the development of logic.

Also, it was this scientist who first defined such concepts as “meaning”, “meaning” and described the difference between them. This is what is known in the modern world as Frege's semantic triangle.

What is this?

It is called differently - concept, theory, idea, term. Frege's triangle is a concept, a symbolic image, a definition, a direction, and even a scientific pattern at the same time.

This is a logical construction that explains the differences between the meaning and meaning of any concept. With the help of this "figure" you can consider any subject area. This formula is also applicable to art, sciences, the information field, languages and other things.

The essence of the concept and its graphic display

Logic of the Frege triangle - in mutual uninterrupted connection of three main components, called:

• value;
• meaning;
• sign.

These three components are the vertices of the figure, and the lines connecting them express the mutual influence of one onother.

What do vertex names mean?

The Frege triangle, whose semiotics is inextricably linked with its main elements, is a universal formula of constant regularities applicable to any field. Of course, depending on the scope, the essence of what is meant by the names of the vertices of a graphical symbolic display changes.

Meaning is a specific area associated with the name of the subject matter. The component in question itself is a sign or a name. The term "name" is often used in the analysis of the "Frege triangle" of people's activities in science, art or another field. It is also used to consider the so-called "animate phenomena".

Meaning is any specific, specific, separately taken aspect in the area under consideration, directly related to the subject of analysis.

What is the scientific significance of this formula?

Frege's Logical Triangle is a revolutionary discovery that has not yet been fully appreciated and has limitless potential.

The derivation of this regularity made it possible to combine mathematical laws, philosophy and logical construction and make their practical application possible in any sphere of life.

In addition, this discovery formed the basis of many scientific papers, the most famous of which are:

• incompleteness theorems by Kurt Friedrich Gödel;
• theorydescriptions of Bertrand Arthur William Russell.

Incompleteness theorems advance the understanding of mathematical logic, while Count Russell's work deals with philosophical questions.

What is semiotics?

This term is often used in a general context when it comes to Frege's triangle. Briefly, the concept of "semiotics" is rather difficult to imagine, since it is very voluminous and ambiguous.

As people say, in a nutshell, the term can be explained as follows. Semiotics is a general theory of the relationships between key elements in sign systems. It is with its help that the Frege triangle becomes a universal formula applicable to any area of human life or another area.

What is the relationship between the main elements?

As a rule, the relationship between the vertices of a triangle or the main elements of this formula is as follows:

• relation of the sign to the area under consideration, designation of the framework of the analysis;
• the influence of the same symbol on the concept of it, meaning.

That is, all relationships are based on a sign or a name. This vertex of the triangle is the starting point, the starting point for all other positions, conclusions, logical circuits and more.

In other words, the existence of the formula itself is impossible without a sign, this symbol is primary. However, the rest of the vertices have their own influence on it.

This feature, illustrating the interconnection of allthree main components can be seen in the use of pseudonyms by people. Let's say the name Mark Twain is taken as a sign in the formula. Of course, literature will act as a meaning, that is, an area associated or associated with a sign. The meaning will mean something related to the writer's contribution to it, the meaning of his works. However, if the name Samuel Langhorne Clemens is taken as a sign, then there will be no associative perception with literary activity. Accordingly, the concepts of "meaning" and "meaning" will be different. Although Clemens and Twain are the same person.

This feature is often called a "special case". Semiotics is used to eliminate errors in the application of Frege's formula due to such accidents.

What could be the relationship between the main elements?

Each of the three main, key elements or vertices in this triangle is both an independent concept that influences other components, and can act as an intermediary between its neighbors.

This means that each of the main elements ensures the existence of not only themselves, but also others. In other words, no phenomenon is considered without context, and it, in turn, affects the understanding of the cause that caused it.

An example of this would be a clear day, a natural phenomenon caused by the activity of the Sun. However, it would be unattainable on a single territory of the planet withoutrotation of the Earth around its axis.

More clearly and simplistically, these relationships between the key elements, the vertices of the triangle, look in ordinary life. For example, trade. For everyone, the correlation and mutual influence of such concepts as "demand", "supply", "opportunity" is obvious. And they also obey the laws verified by the German logistician, philosopher and mathematician.

Triangle reflects objective reality or not?

This question has been the subject of debate in scientific circles for more than a decade. Indeed, on the one hand, the Frege triangle is a mathematical formula based on simple, logical and completely objective laws. On the other hand, it has many variable aspects, nuances that affect the results and the content itself. And all the logical chains that make up relationships are not something that can be measured or touched. They are built in consciousness, that is, they are the fruit of the work of the brain, mental activity. Therefore, this formula has nothing to do with objective reality.

However, everything is not as simple as it seems at first glance. The thing, phenomenon, object or something else being considered, analyzed according to the triangle formula, is invariably an objective given that exists in reality. But a person comprehends this reality. That is, it examines and analyzes an object through its own idea of it, perception. This, in turn, is based on existing knowledge. Logical inferences are not builtonly on the basis of information about the analyzed phenomenon, but also taking into account life experience, cultural values and even mentality.

This means that with regard to the same phenomenon, for example, thunderstorms, different people will draw different conclusions, having similar initial data. They will build various logical chains in the mind. That is, the understanding of the essence of such a natural phenomenon as a thunderstorm will be different for a person living in the Stone Age, in biblical times and today.

This is the paradox of Frege's triangle. The practical application of this formula in various conditions invariably leads to special results. Moreover, they are always true for the conditions under which the formula was applied.

This is the main value, which is the regularity called the Frege triangle. It can be used in practice in any conditions, regardless of any social characteristics or level of development of society.