---
title: "Gödel | Mathematical logic | Thought Archive"
number: "062"
slug: "062-godel"
author: "Wenzi / 文子"
language: "en"
canonical: "https://tongzai.space/en/thought-archive/062-godel/"
is_primary_text: true
---

# Gödel（Mathematical logic）



## Common research question

**What do Gödel's incompleteness theorems actually establish?**

Gödel's incompleteness theorems concern sufficiently strong, effectively axiomatized formal systems under specified conditions. The first limits completeness for arithmetic; the second constrains an appropriate system's proof of its own consistency. They do not show that nothing can be proved, nor directly establish the impossibility of machine intelligence.

## Interpretive boundary

State the relevant assumptions about formal systems and consistency.

## Archive evidence

- [E-04 ｜ 1931 Proposition VI｜formal undecidability](#E-04)
- [E-06 ｜ 1931 Proposition XI｜consistency cannot be self-proved](#E-06)
- [E-01 ｜ 1930 “Completeness of the Functional Calculus”｜semantic validity and provability](#E-01)