# Logic

Essays on the structure of language and rational argument

## What Is Logic?

Logic: from Greek logike "reasoning" and logikos "pertaining to speaking or reasoning"

Issues in Logic centre around two key disciplines:

1. formal systems (what sets of axioms and rules of inference function best?)
2. philosophical foundations (what is the relationship between logic, mathematics and ordinary language and are logical laws empirical?)

With formal systems, a number of types of formal logic have been developed that suit various purposes. These include:

• Propositional logic, also known as 'sentential logic', deals with the relationships between propositions, using logical operators such as 'and', 'or', 'not', 'if-then' and 'if and only if'.
• Predicate logic, also known as first-order logic, extends propositional logic by introducing variables that can represent objects and relations between them. Predicate logic can represent complex relationships between propositions, as well as handle quantifiers such as 'all', 'some', and 'none'.
• Modal logic extends propositional logic by introducing modal operators such as 'necessarily' and 'possibly'. Modal logic can represent statements about necessity, possibility, contingency and belief.

Below you will find Rational Realm essays of two types.

General Essays:
Short popular essays of a more general nature requiring no specialist knowledge
Specialist Essays:
Comprehensive referenced research papers on specialist subjects requiring a working familiarity with the subject

Rational Realm welcomes essay contributions for publication on our site. Please review our submission guidelines and contact us.

## General Essays

• Propositional Logic – A Primer

This tutorial is for beginners wanting to learn the basics of propositional logic; the simplest of the formal systems of logic. Leslie Allan introduces students to the nature of arguments, validity, formal proofs, logical operators and rules of inference. With many examples, Allan shows how these concepts are employed through the application of three different methods for proving the formal validity of arguments.

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