An introduction to Gödel's theorems /
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2013
Cambridge ; New York : 2013 Cambridge, England ; New York : 2013 |
| Edition: | 2nd ed |
| Series: | Cambridge introductions to philosophy
|
| Subjects: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 45 Proving the Thesis?
- Vagueness and the idea of computability
- Formal proofs and informal demonstrations.
- Machine generated contents note: 1 What Godel's Theorems say
- Basic arithmetic
- Incompleteness
- More incompleteness
- Some implications?
- The unprovability of consistency
- More implications?
- What's next?
- 2. Functions and enumerations
- Kinds of function
- Characteristic functions
- Enumerable sets
- Enumerating pairs of numbers
- An indenumerable set: Cantor's theorem
- 3. Effective computability
- Effectively computable functions
- Effectively decidable properties and sets
- Effective enumerability
- Another way of defining e.e. sets of numbers
- The Basic Theorem about e.e. sets
- 4. Effectively axiomatized theories
- Formalization as an ideal
- Formalized languages
- Formalized theories
- More definitions
- The effective enumerability of theorems
- Negation-complete theories are decidable
- 5. Capturing numerical properties
- Three remarks on notation
- The language LA
- A quick remark about truth
- Expressing numerical properties and functions
- Capturing numerical properties and functions
- Expressing vs. capturing: keeping the distinction clear.
- Note continued: Squeezing arguments
- the very idea
- Kreisel's squeezing argument
- The first premiss for a squeezing argument
- The other premisses, thanks to Kolmogorov and Uspenskii
- The squeezing argument defended
- To summarize
- 46 Looking back.