Logical paradoxes are statements or propositions that lead to a contradiction or a situation that defies intuition. They often challenge our understanding of truth and reasoning. A classic example is the liar paradox, where a statement refers to itself in a way that creates a contradiction, such as "This statement is false." If it's true, then it must be false, and if it's false, then it must be true. These paradoxes are important in the study of philosophy and mathematics, as they reveal limitations in our logical frameworks. They encourage deeper exploration of concepts like truth, consistency, and the foundations of reasoning, prompting discussions about how we define and understand these ideas.