Book contents
- Frontmatter
- Contents
- Introduction
- Historical remarks on Suslin's problem
- The continuum hypothesis, the generic-multiverse of sets, and the Ω conjecture
- ω-models of finite set theory
- Tennenbaum's theorem for models of arithmetic
- Hierarchies of subsystems of weak arithmetic
- Diophantine correct open induction
- Tennenbaum's theorem and recursive reducts
- History of constructivism in the 20th century
- A very short history of ultrafinitism
- Sue Toledo's notes of her conversations with Gödel in 1972–5
- Stanley Tennenbaum's Socrates
- Tennenbaum's proof of the irrationality of √2
Sue Toledo's notes of her conversations with Gödel in 1972–5
Published online by Cambridge University Press: 07 October 2011
- Frontmatter
- Contents
- Introduction
- Historical remarks on Suslin's problem
- The continuum hypothesis, the generic-multiverse of sets, and the Ω conjecture
- ω-models of finite set theory
- Tennenbaum's theorem for models of arithmetic
- Hierarchies of subsystems of weak arithmetic
- Diophantine correct open induction
- Tennenbaum's theorem and recursive reducts
- History of constructivism in the 20th century
- A very short history of ultrafinitism
- Sue Toledo's notes of her conversations with Gödel in 1972–5
- Stanley Tennenbaum's Socrates
- Tennenbaum's proof of the irrationality of √2
Summary
Husserl.
Conversation March 3, 1972. Husserl's philosophy is very different before 1909 from what it is after 1909. At this point he made a fundamental philosophical discovery, which changed his whole philosophical outlook and is even reflected in his style of writing. He describes this as a time of crisis in his life, both intellectual and personal. Both were resolved by his discovery. At this time he was working on phenomenological investigation of time.
There is a certain moment in the life of any real philosopher where he for the first time grasps directly the system of primitive terms and their relationships. This is what had happened to Husserl. Descartes, Schelling, Plato discuss it. Leibniz described it (the understanding or the system?) as being like the big dipper — it leads the ships. It was called understanding the absolute.
The analytic philosophers try to make concepts clear by defining them in terms of primitive terms. But they don't attempt to make the primitive terms clear. Moreover, they take the wrong primitive terms, such as “red”, etc., while the correct primitive terms would be “object”, “relation”, “well”, “good”, etc.
The understanding of the system of primitive terms and their relationships cannot be transferred from one person to another. The purpose of reading Husserl should be to use his experience to get to this understanding more quickly. (“Philosophy As Rigorous Science” is the first paper Husserl wrote after his discovery.)
Perhaps the best way would be to repeat his investigation of time. At one point there existed a 500-page manuscript on the investigation (mentioned in letters to Ingarden, with whom he wished to publish the manuscript).
- Type
- Chapter
- Information
- Set Theory, Arithmetic, and Foundations of MathematicsTheorems, Philosophies, pp. 200 - 207Publisher: Cambridge University PressPrint publication year: 2011
- 10
- Cited by