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
- References
Stanley Tennenbaum's Socrates
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
- References
Summary
Plato was not present on the day that Socrates drank hemlock in the jail at Athens and died. Phædo, who was, later related that day's conversation to Echecrates in the presence of a gathering of Pythagorean philosophers at Phlius. Once again, Plato was not around to hear what was said. Yet he wrote a dialog, “Phædo,” dramatizing Phædo's retelling of the occasion of Socrates' final words and death. In it, Plato presents to us Phædo and Echecrates' conversation, though what these two actually said he didn't hear. In Plato's account of that conversation, Phædo describes to Echecrates Socrates' conversation with the Thebian Pythagoreans, Simmias and Cebes, though by his own account he only witnessed that conversation and refrained from contributing to it. Plato even has Phædo explain his absence: “Plato,” he tells Echecrates, “I believe, was ill.”
We look to Socrates' death from a distance. Not only by time, but by this doubly embedded narrative, we feel removed from the event. But this same distance draws us close to Socrates' thought. Neither Simmias nor Cebes understood Socrates' words as well as Phædo did by the time he was asked to repeat them. Even Phædo failed to notice crucial details that Plato points out. Had we overheard Socrates' conversation, we would not have understood it. We look to Socrates' death from a distance, but to understand Socrates, we don't need to access him—we need Plato.
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- Chapter
- Information
- Set Theory, Arithmetic, and Foundations of MathematicsTheorems, Philosophies, pp. 208 - 225Publisher: Cambridge University PressPrint publication year: 2011
References
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