Constant

Definition

A constant is a symbol with a fixed reference in a given system.

Example:

5

The symbol 5 refers to a specific number.

Another example:

Socrates

In a logical system, this may refer to one particular person.

A constant is a symbol whose reference is fixed in the current interpretation.

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Constant vs Variable

A variable can vary.

Example:

x

It may refer to different values depending on assignment.

A constant is fixed.

Example:

5

It does not become 7 in the same interpretation.

Variable = flexible reference. Constant = fixed reference.

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Constants In Expressions

Constants can appear inside expressions.

Example:

x + 5

Here:

x = variable
5 = constant

If x = 2, then:

x + 5 = 7

The variable changes by assignment.

The constant remains fixed.

Constants provide stable pieces inside expressions.

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Constants In Logic

In logic, a constant can name a specific object.

Example:

Human(Socrates)

Here Socrates is a constant symbol.

It refers to a specific object in the interpretation.

Compare:

Human(x)

Here x is a variable.

It can stand for different objects.

Logical constants name specific objects.

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Fixed Within A Context

A constant is fixed within a system or interpretation.

That does not mean the same mark must have the same meaning in every possible system.

Example:

pi

In mathematics, this usually refers to a specific constant.

But a badly defined system could use the same letters differently.

What matters is consistency inside the current interpretation.

Constant reference is fixed relative to a context.

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Final Summary

• A constant is a symbol with fixed reference in a system.
• A variable can vary; a constant stays fixed.
• Constants can appear inside expressions.
• In logic, constants can name particular objects.
• Constant meaning depends on the interpretation but must stay consistent within it.