# Definition:Logic

## Definition

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

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.*

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

## Branches of Logic

There are several branches of logic, for example:

- Aristotelian logic, in which all statements have a truth value that is either true or false.

- Multi-value logic, in which it is admissible for a statement to have a truth value other than those two values.

- Symbolic logic, in which the logical form of statements is analysed by using symbols as tools.

- Mathematical logic, in which the foundations of the assumptions upon which rest mathematics itself are investigated and made rigorous.

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

- Predicate logic, an extension of propositional logic in which the internal structure of statements is analysed.

- Modal logic, in which truth values are more complex than being merely true or false, and which distinguishes between different modes of truth.

## Also see

- Results about
**logic**can be found here.

## 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): $\S 1.1$: The Nature of Logic - 1975: T.S. Blyth:
*Set Theory and Abstract Algebra*... (previous) ... (next): $\S 1$ - 1973: Irving M. Copi:
*Symbolic Logic*(4th ed.) ... (next): $1.1$: What is Logic? - 1993: M. Ben-Ari:
*Mathematical Logic for Computer Science*(1st ed.) ... (next): $\S 1.1$: The origins of mathematical logic - 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson