Substitution

Definition

Substitution means replacing a variable with a value or expression.

Example:

x + 1

Substitute:

x = 5

Result:

5 + 1

Substitution replaces a symbol while keeping the surrounding structure.

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Why Substitution Matters

Variables make expressions general.

Substitution makes them specific.

General expression:

x + 1

Specific case:

5 + 1

Now the expression can be evaluated:

6

Substitution turns a general form into a particular instance.

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Substitution In Logic

Logical statements can also use substitution.

Example:

Human(x)

Substitute:

x = Socrates

Result:

Human(Socrates)

The structure of the statement remains.

Only the variable is replaced.

Substitution lets a general logical form apply to a particular object.

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Correct Substitution

Substitution must replace the intended symbol consistently.

Example:

x + x

Substitute:

x = 3

Correct result:

3 + 3

Incorrect result:

3 + x

If the same variable refers to the same value in the same context, every occurrence must be replaced.

Substitution must respect the variable's context.

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Substitution vs Evaluation

Substitution is not the same as evaluation.

Substitution:

x + 1
x = 5
5 + 1

Evaluation:

5 + 1 = 6

Substitution replaces symbols.

Evaluation computes the result.

Substitution prepares an expression; evaluation produces a value.

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Final Summary

• Substitution replaces a variable with a value or expression.
• It keeps the surrounding structure intact.
• It turns a general form into a specific instance.
• Substitution must be consistent within its context.
• Substitution is different from evaluation.
• In logic, substitution lets general statements apply to particular objects.