In formal logic, "validity" is a fundamental concept concerning the structure of arguments. An argument is considered valid if the conclusion logically follows from the premises. This means that if the premises are true, the conclusion must necessarily be true as well. Validity focuses strictly on the form or structure of the argument rather than the actual truthfulness of the premises or the conclusion. # Validity as a special case of Entailment One way to express validity is the following: $\varnothing \models A$ or just $\models A$ , this means that **independent of any premise**, the statement $A$ is **always valid**. See [[@WhatEntailmentSymbolic2020|What is Entailment?]].  ### Key Points about Validity: 1. **Formal Structure**: Validity is determined by the argument's form. The specific content of the premises doesn't matter for determining validity; what matters is how the conclusion follows from them logically. 2. **Logical Deduction**: A valid argument is one where it is impossible for all the premises to be true and the conclusion to be false. For instance, in a classic example of a valid argument: - Premise 1: All men are mortal. - Premise 2: Socrates is a man. - Conclusion: Socrates is mortal. In this case, if both premises are true, the conclusion must necessarily be true, demonstrating validity. 3. **Truth Independence**: An argument can be valid even if its premises and conclusion are false. Validity does not depend on the actual truth of the statements but on the logical connection between them. For example: - Premise 1: All birds can fly. - Premise 2: Penguins are birds. - Conclusion: Penguins can fly. This argument is valid because it correctly follows the logical form, even though the premises and the conclusion are factually incorrect. 4. **Contrast with Soundness**: While validity is purely about the form and logical structure of the argument, soundness is another property of arguments. An argument is sound if it is valid and all its premises are actually true. Thus, soundness is a stronger condition than validity. 5. **Use in Mathematical Logic and Philosophy**: In mathematical logic, validity is used to establish proofs and theorems. In philosophy, it helps analyze philosophical arguments and their logical consistency. Validity is a crucial tool in logical reasoning, allowing individuals to evaluate the coherence and potential correctness of arguments in a variety of disciplines, including mathematics, computer science, philosophy, and law. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Validity") or contains(subject, "validity") sort title, authors, modified, desc ```