# Definition:Symbolic Logic

## Definition

**Symbolic logic** is the study of logic in which the logical form of statements is analyzed by using symbols as tools.

Instead of explicit statements, logical formulas are investigated, which are symbolic representations of statements, and compound statements in particular.

In **symbolic logic**, the rules of reasoning and logic are investigated by means of formal systems, which form a good foundation for the symbolic manipulations performed in this field.

### Characteristics

According to the analysis of Clarence Irving Lewis, the three characteristics of symbolic logic are:

- $(2): \quad$ The use of the deductive method

- $(3): \quad$ The use of variables.

## Also known as

Some sources refer to this as **mathematical logic**, but it is generally preferred to reserve that term for its more specialised branch.

The term **logistic** can be seen for this branch of logic, but this can be confused with the (mathematical) science of logistics.

## Also see

Branches of **symbolic logic** include:

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

## Historical Note

The discipline of **symbolic logic** was invented, way before its time, by Gottfried Wilhelm von Leibniz, whose first forays failed to exert much infulence.

*If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, to sit down to their slates, and to say to each other (with a friend as witness if they liked): Let us calculate.*

While this idea made little headway at the time, it became the source of the symbolic logic developed by George Boole and then evolved by Alfred North Whitehead and Bertrand Russell.

## Sources

- 1946: Alfred Tarski:
*Introduction to Logic and to the Methodology of Deductive Sciences*(2nd ed.) ... (previous) ... (next): $\S \text{II}.6$: Logical Constants - 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (next): Chapter $\text I$ Introductory: $1$. Symbolic Logic and Classical Logic - 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.) ... (previous) ... (next): $1$ Introduction: Logic and Language: $1.4$: Symbolic Logic - 1980: D.J. O'Connor and Betty Powell:
*Elementary Logic*... (previous) ... (next): $\S \text{I}: 1$: The Logic of Statements $(1)$ - 2000: Michael R.A. Huth and Mark D. Ryan:
*Logic in Computer Science: Modelling and reasoning about systems*... (previous) ... (next): $\S 1.1$: Declarative sentences