What are the three traditional laws of thought?

In the philosophy of logic, the three traditional laws of thought are fundamental principles that have historically served as the foundation for logical systems. They are defined as follows:1

• The Law of Contradiction: This principle states that it is impossible for a proposition p and its negation (not p) to both be true at the same time and in the same sense. Symbolically, this is expressed as $~(p·~p)$.12
• The Law of Excluded Middle: Also known as the law of the excluded third, this principle asserts that for any proposition, either the proposition or its negation must be true; there is no middle ground. Symbolically, this is represented as $p\vee ~p$.31
• The Principle of Identity: This law states that a thing is identical with itself, or that a proposition where the subject and predicate are the same is true. It can be expressed as $F(x)\supset F(x)$ or simply as $x=x$.14

While these laws were traditionally viewed as sufficient foundations for logic, they have been challenged or modified in various systems, such as intuitionism and many-valued logics.1