Definition:Logic

Definition

Logic is the study of the structure of statements and their truth values, divorced from their conceptual content.

It has frequently been defined as the science of reasoning.

According to Charles Peirce:

Nearly a hundred definitions of it have been given. ... It will, however, generally be conceded that its central problem is the classification of arguments, so that all those that are bad are thrown into one division, and all those which are good into another...

1965: E.J. Lemmon: Beginning Logic:

The best way to find out what logic is is to do some.

1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.)

Logic ... consists of deduction.

1993: Richard J. Trudeau: Introduction to Graph Theory:

... nothing but an etherealized version of the "common sense" we absorb from the culture as we grow up.

Matt Westwood:

Logic can be considered as being the rickety gangplank between the ship of natural language and the solid ground of mathematics.

Also see

• Definition:Aristotelian Logic, in which all statements have a truth value that is either true or false.

• Definition:Multi-Value Logic, in which it is admissible for a statement to have a truth value other than those two values.

• Definition:Symbolic Logic, in which the logical form of statements is analysed by using symbols as tools.

• Definition:Mathematical Logic, in which the foundations of the assumptions upon which rest mathematics itself are investigated and made rigorous.

• Definition:Propositional Logic, a sub-branch of symbolic logic in which the truth values of statements are investigated and analysed.

• Definition:Predicate Logic, an extension of propositional logic in which the internal structure of statements is analysed.

• Definition:Modal Logic, in which truth values are more complex than being merely true or false, and which distinguishes between different modes of truth.

• Results about logic can be found here.

Historical Note

The study of logic was begun by the ancient Greeks.

Their education system stressed the importance of competence in philosophy and rhetoric.

In order to excel in rhetoric, it was necessary to master logic.

Sources

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}.6$: Logical Constants
• 1951: Willard Van Orman Quine: Mathematical Logic (revised ed.) ... (previous) ... (next): Introduction
• 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (next): Preface
• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $1$ The Nature of Logic
• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (next): $1$ Introduction: Logic and Language: $1.1$: What is Logic?
• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems
• 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (next): $\S 1$: Informal statement calculus: $\S 1.1$: Statements and connectives
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): logic: 1.
• 1993: Richard J. Trudeau: Introduction to Graph Theory ... (previous) ... (next): $1$. Pure Mathematics: Games
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logic
• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): logic