# Understanding the law of identity in logic

In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are built on just these laws.

## What is an example of the law of identity?

The law of identity states that if a statement has been determined to be true, then the statement is true. In formulaic terms, it states that ‘X is X’. For example, if I make a statement that ‘It is snowing,’ and it’s the truth, then the statement must be true.

## Why is the law of identity important?

The concept of identity is important because it makes explicit that reality has a definite nature. Since reality has an identity, it is knowable. Since it exists in a particular way, it has no contradictions.

## What is the formula of law of identity?

If we go by how “Self-reference” is defined, then the Law of Identity (A=A) is its evident example: “Self-reference occurs in natural or formal languages when a sentence idea or formula refers to itself”. (

## Can you prove the law of identity?

In any “complete” logical system, such as standard first-order predicate logic with identity, you can prove any logical truth. So you can prove the law of identity and the law of noncontradiction in such systems, because those laws are logical truths in those systems.

## What is logical identity?

Given two propositions P and Q, the identity of P and Q, noted as P ⇔ Q or “P if and only if Q”, is the new proposition that is true if and only if the biconditional P ↔ Q is a tautology. The logical identity is also called logical equivalence and so the propositions P are Q are said to be equivalent.