Logical truth

Logical truth is a statement which is true in all possible worlds or under all possible interpretations. Logical truths are a central concept in logic, philosophy, and mathematics. They are often contrasted with empirical truths, which are true based on observation and experience.

Characteristics of Logical Truth

Logical truths are characterized by their necessity and universality. They are true by virtue of their form and not because of any particular facts about the world. For example, the statement "All bachelors are unmarried" is a logical truth because it is true by definition.

Examples of Logical Truths

Some common examples of logical truths include:

• Tautologies: Statements that are true by their logical form, such as "It is raining or it is not raining."
• Mathematical truths: Statements in mathematics that are true by definition, such as "2 + 2 = 4."
• Logical axioms: Fundamental principles in logic, such as the law of noncontradiction, which states that a statement cannot be both true and false at the same time.

Importance in Philosophy

In philosophy, logical truths are important for understanding the nature of truth, knowledge, and reality. They are often used in arguments to demonstrate the validity of certain philosophical positions. Logical truths are also crucial in the study of metaphysics, where they help to explore the fundamental nature of being and existence.

Logical Truth in Mathematics

In mathematics, logical truths are foundational. They form the basis of mathematical proofs and theorems. The study of logical truths in mathematics is closely related to the field of mathematical logic, which investigates the formal properties of logical systems and their applications in mathematics.

Related Concepts

• Analytic proposition: A statement that is true by definition and whose truth can be determined by analyzing its meaning.
• Synthetic proposition: A statement whose truth depends on how the world is, rather than on the meanings of the words involved.
• A priori: Knowledge that is independent of experience.
• A posteriori: Knowledge that depends on empirical evidence.

See Also

• Logic
• Philosophy of logic
• Mathematical logic
• Tautology (logic)
• Law of noncontradiction
• Analytic-synthetic distinction