フレーゲ『算術の基礎』──「1+1=2」はなぜ正しいのか｜数とは何か、論理学が数学を根拠づける瞬間

Philosophical Text Reading Series, Part 118: Foundations of Arithmetic "1 + 1 = 2"—everyone knows this is true. But why is it true? Can you explain the reasoning? This book thoroughly re-examines the concept of "number," which no one had ever questioned, rewriting the boundaries between mathematics, logic, and philosophy. It is a starting point for modern analytical philosophy. What is a number? Does the truth of arithmetic come from experience, or can it be proven solely through logic? This question, which Frege tackled, resonates deeply in today's world where AI "calculates" and the "correctness" of programs is questioned. From the grand system established by a solitary mathematician, to the glory and setbacks brought about by a letter from Russell— We will carefully unravel the essence of philosophy: "questioning the basis of the self-evident." ■ Contents of this video (Chapters) 00:00 Opening: Can you prove "1 + 1 = 2"? 04:22 Preface: Who Was Frege? – A Forgotten Revolutionary of Philosophy 09:45 Chapter 1: Three Basic Principles – Frege's Methodological Manifesto 14:35 Chapter 2: Where Does the Truth of Arithmetic Come From? – A Challenge to Kant 21:59 Chapter 3: What Numbers Are Not – A Rebuttal to False Number Theories 29:14 Chapter 4: What Are Numbers? – Frege's Revolutionary Definition 37:50 Chapter 5: The Contextual Principle – Where Does the Word "Number" Lie? 44:08 Chapter 6: Arithmetic is an A priori Analytical Truth – The Completion of Logicalism 50:35 Chapter 7: Russell's Paradox – Glory and Frustration 57:00 Chapter 8: Frege's Legacy – His Influence on 20th Century Philosophy 1:03:45 Summary: What "Foundations of Arithmetic" Asks ■ What you will gain from this video: • The depth of the question: Why is "1+1=2" correct? • Why are erroneous number theories such as psychologism and nominalism rejected? • A revolutionary definition of "number" through one-to-one correspondence • What is logicism, and why did it fail? • What Frege left behind in 20th-century philosophy, logic, and computer science. ■ Book discussed: Gottlob Frege, Foundations of Arithmetic https://amzn.to/43dSN5G ■ Previous video: Nietzsche, *Twilight of Idols*—A philosopher who re-examined the "basis of value" Just as Nietzsche questioned the basis of value, Frege questioned the basis of numbers. Watching both videos together will give you a more comprehensive understanding of the philosophical stance of "doubting the self-evident." ▶    • ニーチェ『偶像の黄昏』──哲学者たちの「嘘」を暴く ｜理性・道徳・宗教、すべての偶像...   ■ About the Channel This channel carefully analyzes philosophical texts from all times and places, one by one. We aim to present even the most difficult classics in the simplest language possible, without compromising on content. If you enjoyed the video, please give it a thumbs up and subscribe to the channel. Your support will empower us to analyze the next book. ■ Hashtags #Frege #FoundationsofArithmetic #Philosophy #Logic #AnalyticalPhilosophy #PhilosophyofMathematics #PhilosophicalBooks #Reading #Logicism #Russell'sParadox #SlowPhilosophy #Culture Transcript Blog Here https://jijigrammer.info/thought/%e5%... VOICEVOX: Ryusei Aoyama