History of logic - Aristotle, Syllogism, Deduction

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

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Only fragments of the work of these thinkers are relevant to what is now considered logic. The systematic study of logic seems to have been undertaken first by Aristotle. Although Plato used dialectic as both a method of reasoning and a means of philosophical training, Aristotle established a system of rules and strategies for such reasoning. At the end of his Sophistic Refutations, he acknowledges the novelty of his enterprise. In most cases, he says, discoveries rely on previous labours by others. But then he adds: Aristotle’s logical writings comprise six works, known collectively as the Organon (“Tool”). The significance ...(100 of 27062 words)

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