Tautology

Definition

A tautology is a proposition that is always true because of its logical form.

Example:

P OR NOT P

This is true whether P is true or false.

Tautology = logically always true.

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Truth Table Example

Truth table:

P      NOT P   P OR NOT P
true   false   true
false  true    true

Every row is true.

That makes the expression a tautology.

A truth table can show whether a statement is a tautology.

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Tautology Depends On Form

A tautology does not depend on the specific meaning of P.

Example:

P = "It is raining"

Then:

It is raining OR it is not raining.

The statement is true because of logical structure.

The content can change, but the form remains always true.

Tautology is truth by logical structure.

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Tautology vs True Statement

Not every true statement is a tautology.

Example:

2 + 3 = 5

This is true.

But it is not true merely because of the structure:

P OR NOT P

It depends on arithmetic interpretation.

Tautology is stronger than ordinary truth.

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Why Tautologies Matter

Tautologies reveal forms of reasoning that hold no matter what the content is.

They help separate:

truth from meaning

and:

truth from structure

This is useful because symbolic logic often studies structure directly.

Tautologies show truth guaranteed by form.

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Final Summary

• A tautology is true under every truth assignment.
• P OR NOT P is a basic tautology.
• Truth tables can identify tautologies.
• Tautology depends on logical form.
• A true statement is not always a tautology.
• Tautologies show truth guaranteed by structure.