The Outer Limits of Reason
The Outer Limits of Reason is as far as I remember one of the best research essay that I have read so far. I definitely recommend the book to all inquiring minds around and to anyone who is too much confident about him/her-self knowledge.
Noson S. Yanofsky confirmed his knowledge page by page and with astonishing clarity explain hard topic such as Chaos, Relativity Theory and Quantum Mechanics. As a graduate student of Computer Science and Engineering I have found really well written explanations about theoretical computer science. Not for nothing Yanofsky is Professor in the Department of Computer and Information Science at Brooklyn College and The Graduate Center of the City University of New York.
Awards
Winner, 2013 American Publishers Award for Professional and Scholarly Excellence (PROSE Award) in Popular Science & Popular Mathematics, presented by the Professional and Scholarly Publishing Division of the Association of American Publishers
Quotes
Science is a human activity. It is created by finite, flawed human beings attempting to search for the ultimate truth.
The mathematics becomes abstract and about nothing in particular. Because these concepts are about nothing, they are about everything.
Rather than asking why the laws of physics follow mathematics, ask why there are any laws at all.
When we talk about the limits of scientific reasoning, we must keep in mind how we are observing the universe…the way we look at the universe is the way it will present itself to us.
Do not mistake the metaphor for reality.
SPOILER: Yanofsky conclusion thought
We human beings already live beyond reason. Real life has importance only when it includes ethics, values, and beauty. Reason is a powerful but nevertheless limited tool.
Table Of Contents
- Introduction
1 - Language Pradoxes
15- Liar! Liar!
15 - Self-Referential Paradoxes
19 - Naming Numbers
26
- Liar! Liar!
- Philosophical Conundrums
31- Ships, People, and Other Objects
31 - Hangin’ with Zeno and Gödel
41 - Bald Men, Heaps, and Vagueness
50 - Knowing about Knowing
57
- Ships, People, and Other Objects
- Infinity puzzles
65- Sets and Sizes
66 - Infinite Sets
69 - Anything Larger?
76 - Knowable and Unknowable
85
- Sets and Sizes
- Computing Complexities
97- Some Easy Problems
98 - Some Hard Problems
109 - They’re All Connected
121 - Almost Solving Hard Problems
129 - Even Harder Problems
131
- Some Easy Problems
- Computing Impossibilities
135- Algorithms, Computers, Machines, and Programs
136 - To Halt or Not to Halt?
139 - They’re All Connected
146 - A Hierarchy of the Unknown
152 - Minds, Brains, and Computers
157
- Algorithms, Computers, Machines, and Programs
- Scientific Limitations
161- Chaos and Cosmos
161 - Quantum Mechanics
175 - Relativity Theory
214
- Chaos and Cosmos
- Metascientific Perplexities
235- Philosophical Limitations of Science
235 - Science and Methamatics
252 - The Origin of Reason
272
- Philosophical Limitations of Science
- Mathematical Obstructions
297- Classical limits
298 - Galois Theory
304 - Harder Than Halting
309 - Logic
320 - Axioms and Independence
331
- Classical limits
- Beyond Reason
339- Summing Up
339 - Defining Reason
345 - Peering Beyond
349
- Summing Up
- Notes
355 - Bibliography
379 - Index
393