History of logic - Godel's Incompleteness, Theorems, Mathematics

history of logic

Table of Contents

Introduction
Origins of logic in the West
- Precursors of ancient logic
- Aristotle
  - Categorical forms
  - Syllogisms
- Theophrastus of Eresus
- The Megarians and the Stoics
- Late representatives of ancient Greek logic
Medieval logic
- Transmission of Greek logic to the Latin West
- Arabic logic
- The revival of logic in Europe
  - St. Anselm and Peter Abelard
  - The “properties of terms” and discussions of fallacies
- Developments in the 13th and early 14th centuries
  - The theory of supposition
  - Developments in modal logic
- Late medieval logic
Modern logic
- The 16th century
- The 17th century
- Leibniz
- The 18th and 19th centuries
  - Gottfried Ploucquet
  - Johann Heinrich Lambert
  - Other 18th-century logicians
  - Boole and De Morgan
  - Charles Sanders Peirce
  - Gottlob Frege
  - Ernst Schröder
  - Georg Cantor
  - Other 19th-century logicians
Logic since 1900
- Propositional and predicate logic
- Principia Mathematica and its aftermath
- Set theory
  - Zermelo-Fraenkel set theory (ZF)
  - The continuum problem and the axiom of constructibility
  - The axiom of choice
  - Problems and new directions
- Theory of logic (metalogic)
- Syntax and proof theory
- Logical semantics and model theory
  - Completeness
  - Gödel’s incompleteness theorems
  - Development of model theory
- Interfaces of proof theory and model theory
- Theory of recursive functions and computability
  - Effective computability
  - The Turing machine
  - Applications of recursive-function theory

References & Edit History Related Topics

Images

Rembrandt: Aristotle with a Bust of Homer

Read Next

Spiral Galaxy type Sa-Sb or Sa/Sb in the constellation Virgo. The majestic Sombrero Galaxy Messier 104 (M104) or NGC 4594. The team took six pictures of the galaxy, stitched them together to create the final composite image. Photo from May-June 2003

9 Britannica Articles That Explain the Meaning of Life

Discover

A Factory Interior, watercolor, pen and gray ink, graphite, and white goache on wove paper by unknown artist, c. 1871-91; in the Yale Center for British Art. Industrial Revolution England

Inventors and Inventions of the Industrial Revolution

Person paying with a credit card using a credit card terminal. Cashless payment, credit card reader

What Is a Cashless Society and How Does It Work?

The Sun Was Eaten: 6 Ways Cultures Have Explained Eclipses

Eid al-Fitr

In this aerial photo, structures are damaged and destroyed October 15, 2005 in Balakot, Pakistan. It is estimated that 90% of the city of Balakot was leveled by the earthquake. The death toll in the 7.6 magnitude earthquake that struck northern Pakistan on October 8, 2005 is believed to be 38,000 with at least 1,300 more dead in Indian Kashmir. SEE CONTENT NOTES.

6 of the World’s Deadliest Natural Disasters

earthquake. Heavily damaged school in the town of Yingxiu after a major earthquake struck China's Sichuan Province on May 12, 2008.

The 6 Deadliest Earthquakes Since 1950

African Americans demonstrating for voting rights in front of the White House as police and others watch, March 12, 1965. One sign reads, "We demand the right to vote everywhere." Voting Rights Act, civil rights.

Timeline of the American Civil Rights Movement

It was initially assumed that descriptive completeness and deductive completeness coincide. This assumption was relied on by Hilbert in his metalogical project of proving the consistency of arithmetic, and it was reinforced by Kurt Gödel’s proof of the semantic completeness of first-order logic in 1930. Improved versions of the completeness of first-order logic were subsequently presented by various researchers, among them the American mathematician Leon Henkin and the Dutch logician Evert W. Beth. In 1931, however, the belief in the coincidence of descriptive and deductive completeness was shattered by the publication of Gödel’s paper “Über formal unentscheidbare Sätze der Principia ...(100 of 27062 words)

Access the full article

Help support true facts by becoming a member.