What is the prototype of Frege?Frige's prototype was the French Phrygian hat, which originated from the soft hat often worn by the Phrygian people in ancient Asia Minor. This hat was tightly attached to the head, with the tip bent forward and shaped like a triangular hat. During the French Revolution, it was one of the symbols of the revolutionary, representing freedom. It was also the hat that freed slaves and their descendants had the right to wear in ancient Rome. It was a symbol of freedom from tyranny. Its top drooped slightly forward, with hooded ears on both sides and drooping to the neck at the back. While watching the Olympics, you can also read the wonderful novels related to the Olympics!
Frege's logicalismFrege was one of the representatives of logicalism. He believed that all mathematics could be deduced from the basic laws of logic, and he believed that set theory had the nature of logic. He invented a set of complex logical symbols, transforming some of the contents of set theory into the definition and theorem of logic, and then defined natural numbers and deduced the entire theory of arithmetic.
Frege's work in the field of basic mathematics could be seen as a deepening of the theory of arithmetic based on Peano's axioms. When he and Husserl opposed the psychological explanation of mathematics, he emphasized the objective nature of mathematics, which was similar to the independent existence of concept entities. He acknowledged the existence of "class","concept" and "meaning".
Although the famous Russell's Parabola dealt a serious blow to Frege's idea of building mathematics on set theory, he laid an important foundation for the development of logicism. Russell inherited his ideas and continued to promote the development of logicism.
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Frege's Contribution to LogicsFrege made many important contributions to logic:
1. Creating a new logical system: He created some symbols to represent logical relationships. These symbols constituted a new logical system and became the foundation of modern logical semiotics.
2. [In-depth study of logical relations: Comparing the relationship between the deductive proposition A = A and the experiential proposition A = B. He has made important achievements in first-order predicative deduction, which has a profound impact on mathematical logic.]
3. ** Concepts related to logic:
- Distinguishing between logical things and psychological things, objective things and subjective things, emphasizing the objectively of truth, thinking that concepts and relations are abstract entities, ensuring the objectively of logic and mathematics, the propriety of logical discussion and proof, and advocating the close combination of logic and mathematics to provide a starting point for philosophy.
- Distinguishing between concept and object, it is clear that the object is the corresponding object of the proper name, which can be used as the reference of the main word, and the concept is the reference of the predicates, and there are differences between the two kinds of belonging relations between the object and the concept.
- The difference between meaning and reference was that a name referred to an object by meaning, and there was a corresponding relationship between a specific sign, meaning, and reference (object). The thought expressed by a sentence was meaning, and its truth value was reference, and a sentence could have meaning but no reference.
4. ** Expands the content of logic **: He created the logic of "quantum"(related to the categories of "all","some", and "none"), changing the situation where logic only studies the relationship between proposition and proposition.
5. ** Foundational contribution to mathematical logic **: He was one of the founders of mathematical logic. His work reignited people's philosophical interest in logic. He tried to find the "foundation" of arithmetic and proved that basic identities must be true by deduction. He invented a set of logical symbols, translated and transformed some contents of set theory into the definition and theorem of logic, and then defined natural numbers and deduced the entire arithmetic theory.
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Frege's Three PrinciplesIn different fields, Frege's Three Principles had different meanings:
1. The three principles in Frege's Basics of Arithmetic:
- He always made a clear distinction between psychological and logical, subjective and objective.
- You can't ask the meaning of a word in isolation, but only in the context of a proposition.
- He could not lose the distinction between concepts and objects.
2. There are three principles in social psychology (proposed by the American psychologist Joseph Frege in the 1950s):
- [Situation: The environment and situation in which both parties interact affects their speech and behavior.]
- Language: The tool for people to communicate, including voice, text, body language, and many other forms.
- Relationship: A relationship established between two parties that depends on each other and influences each other.
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What kind of animal is Frege?Frege was not an animal. It was the official mascot of the 2024 Paris Olympics and paralympics. It was made up of two dolls wearing red Frege hats. While watching the Olympics, you can also read the wonderful novels related to the Olympics!
Frege mascot picture stick figureYou can search for pictures by entering "2024 Olympic mascot, Frege's stick figure". These stick figures can help you intuitively understand the image characteristics of Frege's mascot. While watching the Olympics, you can also read the wonderful novels related to the Olympics!
Frege's Theory of Concepts and ObjectsFrege's discussion of concepts and objects has two distinctive features.
Firstly, starting from the " function " in mathematics, the structure of functions and self-variables was used to reveal the nature and relationship between concepts and objects, and this analysis of concepts and objects was combined with language analysis. In mathematics, there was a view on functions that said " a function of x refers to a formula containing x." Frege felt that this view was not satisfactory because it did not distinguish between form and content, symbols and what symbols represented. In fact," x " was an independent variable, which represented a kind of universal. The true nature of the function was in the common factor of the expression, that is, in the things that existed in addition to " x."
Secondly, there were two types of terms in language: concept and object. Concepts were a collection of things with common attributes, and the object was a single entity or individual. For example, the word " cat " could be divided into a concept part that represented the collection of all cats and an object part that represented a cat. At the same time, Frege's Ontological Analysis relies on the analysis of language. He believes that objects can be referred to by singular terms and concepts can be referred to by predicates. In sentence relations, concepts and objects interacted to form the meaning of language expression. Frege paid special attention to the problem of predictors in the proposition, which was used to describe the number of objects represented by the term. He also proposed the world's first formal theory of predictors.
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How much did Frege contribute to logic?Frege made a great contribution to logic.
He was the founder of mathematical logic and created some symbols to represent logical relationships. These symbols formed the foundation of modern logical semiotics and established a new logical system.
His work expanded the content of logic and created the logic of " quantum ", which was related to the categories of " all "," some ", and " none ". This achievement became the knowledge that modern philosophers were familiar with and used.
His 1879 book," Concept Words ", was the first to use logic to extensively discuss the concepts of existence and universal names. He also discussed the relationship between the proposition " there is at least one X, X is Y " and " all X is Y ", which supplemented the missing parts of the logic of Orthodoxy.
In addition, he distinguished logical things from psychological things, objective things from subjective things. This distinction emphasized the objective nature of truth and was of great significance to the development of logic.
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