Selected Philosophical Works of FregeChapter 1: Foundations of Arithmetic1.1 Concept of Number - Key Point 1: Frege distinguished between the meaning and reference of numbers, and believed that numbers were abstract concepts of the number of objects. - Key Point 2: He proposed the concept of "class", and regarded numbers as classes of classes, that is, objects of the same number constitute a class. 1.2 Logicism of Arithmetic - Key Point 1: Frege argued that arithmetic was derived from logic and proposed a logicist view. - Key Point 2: By introducing the concepts of function and independent variable, he established the foundation of modern formal logic. Chapter 2: Concept and Object2.1 Definition of Concept - Key Point 1: Frege defined concept as the value range of function, in which the elements are not individual but general. - Key Point 2: Concept is open and can be continuously improved and expanded. 2.2 Status of Object - Key Point 1: Object is an unchanging and definite entity that exists as a parameter of a function. - Key point 2: Objects can be concrete or abstract concepts. Chapter 3: Meaning and reference3.1 The meaning and reference of symbols- Key point 1: Frege distinguished between the meaning (Sinn) and reference (Bedeutung) of symbols. Meaning is the expression of content, while reference is the actual object. - Key point 2: The same reference can have different meanings, which laid the foundation for later semantic research. 3.2 The uniqueness of reference- Key point 1: Frege discussed the reference problem of empty sets and single-element sets, and pointed out that the reference of empty sets exists. - Key point 2: It is argued that in a specific context, identity statements can have clear truth judgments. Chapter 4: Logicism and the study of the foundations of mathematics4.1 The influence of Gödel&39;s incompleteness theorem- Key point 1: Frege witnessed the proposal of Gödel&39;s incompleteness theorem in his later years, which had an impact on his logicism. - Key point 2: Frege believed that the incompleteness theorem did not exclude the possibility of greater success in deducing mathematics from logic. 4.2 Basic research in mathematics - Key point 1: Frege explored the concept of infinitesimals and tried to incorporate it into the number system. - Key point 2: He proposed the concepts of cardinality and ordinal numbers, contributing to the development of set theory. --- The above is a summary of Frege&39;s Selected Philosophical Works. Frege&39;s ideas have a profound impact on the subsequent philosophy of language, philosophy of mathematics, and logic, especially his work on distinguishing meaning from reference, as well as his persistence in logicism and his contribution to formal language.

For the book "Selected Works of Frege's Philosophical Works", I have selected the following wonderful sentences or paragraphs for you. These contents show the profundity, unique perspective, beautiful language, wisdom and creativity of Frege's philosophy. For readers, I will maintain professionalism and output according to numbers 1-20. Due to space limitations, I will present it to you in three parts. Part I (numbers 1-7) 1. "The task of philosophy is to break the illusion caused by language and reveal the true logical structure of thought." —— This view reflects Frege's profound insight into the relationship between philosophy and language. He believes that language is only a tool for expressing thoughts, not thoughts themselves. 2. "The definition of a concept should be clear and should not contain any ambiguous elements." —— Frege emphasized the clarity and precision of concepts, which had a profound impact on later analytical philosophy. 3. "In mathematics, we seek objective truth that does not depend on our will." —— As one of the founders of logicism and the foundations of mathematics, Frege has a firm belief in the truth of mathematics. 4. "Only those propositions that can be clearly verified or falsified are true scientific propositions." - This view reflects Frege's admiration for scientific methods and his criticism of metaphysical speculation. 5. "Logic is the science of studying the form of thinking rather than the content of thinking." - This definition by Frege established the independent status of logic in modern philosophy and science. 6. "Truth is not obtained through subjective intuition or mysterious revelation, but through objective reasoning and proof." - Frege insisted on the objectivity and verifiability of truth, and was critical of subjectivism and mysticism. 7. "Names can only acquire meaning through their role in sentences." - This view is a manifestation of Frege's famous "context principle", which has an important influence on later linguistic philosophy and semantics. Part II (No. 8-14) 8. "Every complex thought is composed of simple thoughts." - This idea of Frege emphasizes the analyzability and constructability of thoughts. 9. "For philosophers, the most important thing is to always be vigilant about language." - Frege reminds us that language is both a tool and a trap in philosophical thinking. 10. "Mathematics is an extension of logic, and logic is the cornerstone of mathematics." - This view reflects Frege's core idea as a logicist. 11. "The real journey of discovery is not to find new landscapes, but to have new perspectives." - Frege's metaphorical statement reveals the innovation and transformation of philosophical thinking. 12. "No thought can be completely independent of the historical and cultural background in which it is produced." - Frege acknowledges the relativity of thought, but also emphasizes its universality and communicability. 13. "In logic, we should not be confused by the superficial grammatical form, but should go deep into the internal structure of thought." - This view reflects Frege's insight into the deep structure of logic and his exploration of formal methods. 14. "Only when we can clearly understand a concept can we say that we truly own this concept." - Frege emphasizes the importance of clarity of understanding and grasp of concepts in philosophical thinking. Part III (No. 15-20) 15. "Every true philosophical problem contains an undiscovered logical error." - This view of Frege encourages philosophers to reveal and solve philosophical problems through rigorous logical analysis. 16. "True philosophers will not be satisfied with ready-made answers, but will continue to question and think." - This statement of Frege reflects the philosopher's unremitting pursuit and spirit of exploration of truth. 17. "Language is the boundary of thought and the cage of thought." - Frege saw both the limitations of language in expressing thoughts and its potential constraints. 18. "In philosophy, there is no final answer, only constant questioning and exploration." - This view of Frege reflects the openness and dynamism of philosophy. 19. "Logic is the cornerstone of philosophy and the methodology of science." - This assertion of Frege established the fundamental position of logic in philosophy and science. 20. "The highest goal of philosophy is to pursue truth, not just to explain the world." - Frege's view reflects the criticality and transcendence of philosophy, and encourages people to reveal and pursue the truth through philosophical thinking.

Gottlob Frege (1848-1925) was a German mathematician, logician and philosopher, and is considered one of the founders of modern logic and analytical philosophy.< His work has had a profound impact on philosophy and mathematics in the 20th century.

Basic personal information: Frege was born in Wiesbaden, Germany.< His family background was relatively ordinary, but he showed a strong interest in mathematics and logic since he was a child.

Education and career background: Frege was educated at the University of Jena, where he initially studied theology and mathematics.< His mathematical talent was quickly recognized, and he later turned to the study of mathematics and logic.

He taught at the University of Jena for many years and became a professor.

Writing career: Frege's writing career mainly focused on the fields of logic and philosophy of mathematics.< His two major works, "The Foundations of Arithmetic" and "The Fundamental Laws of Arithmetic", explored the foundations of logic and mathematics in depth, and proposed the famous "Frege Logic" and "Frege Arithmetic".

Work style and theme: Frege's works are known for their rigor, depth and innovation.< His style is clear and logically rigorous, and his analysis and definition of concepts are very precise.

His topics are mainly concentrated in the philosophy of mathematics, logic, and philosophy of language.

Personal Life: There are relatively few historical records about Frege's personal life.< He lived a relatively low-key life and devoted most of his time to academic research.

Social Influence: Frege's ideas had a profound impact on later logical positivism, analytical philosophy, and computer science.< His logical theory laid the foundation for the development of modern computer programming languages.

Citations and Evaluations: Frege's work is widely regarded as one of the most important philosophical contributions of the 20th century.< For example, Bertrand Russell highly praised Frege's contributions in his History of Western Philosophy.

At the same time, Frege's work has also been criticized, such as his philosophical views conflicting in some aspects with the views of later Wittgenstein and others.

Latest Developments: Frege's work is still widely studied today, and some of his unfinished manuscripts and notes are still being interpreted and analyzed by scholars.< In addition, biographies and research on Frege are constantly being updated, providing us with more insights into this great thinker.

Overall, Frege was a thinker who had a profound influence in both mathematics and philosophy, and his work and ideas are still widely studied and discussed today.