Logic

From Mathematics

Logic involves the systematic study of valid methods of argument and inference. It can be seen as a subset of philosophy or mathematics, and provides the foundation of each discipline.

[edit] History

Although many ancient civilizations developed systems of argumentation and studied logical paradoxes, the history of modern logic is typically traced back to Ancient Greece and the writings of Aristotle (384–322 BC).^[1][2] His formulation of so-called Aristotelian logic was the dominant form of formal logic until the late 18th and early 19th centuries, during which the development of symbolic logic and mathematical logic introduced new paradoxes and more powerful techniques to deal with them.

[edit] Types

Informal logic 

Studies the nature of natural-language arguments, including logical fallacies and paradoxes.

Formal logic 

Systematizes modes of argumentation in terms of abstract rules.

Symbolic logic 

Further abstraction of systems of inference using symbols for statements and logical connectives ("and", "or", and so forth).

Major branches of symbolic logic include:

• propositional logic
• predicate logic

Predicate logic may be further subdivided into:

• first-order logic
• second-order logic
• third-order logic
• higher-order logic

Mathematical logic 

Extends symbolic logic into other areas including model theory, proof theory, set theory, and recursion theory.^[1]

• Set theory

Modal logic

[edit] References

1. ↑ ^{1.0 1.1} Wikipedia:Logic
2. ↑ Wikipedia:Aristotle