[A06] Validity and Relevance

Introduction to Validity in Arguments

Understanding the concept of validity is essential in logic and argument analysis. Validity determines whether an argument's structure ensures that if the premises are true, the conclusion must also be true. This topic is foundational in critical thinking and philosophy, though it is not directly related to microeconomics.

• Definition of Validity: An argument is valid if and only if there is no logically possible situation where all the premises are true and the conclusion is false at the same time.

• Key Point: Validity concerns the logical structure of the argument, not the actual truth of the premises or conclusion.

• Example: If all humans are mortal, and Socrates is a human, then Socrates is mortal. This argument is valid because the conclusion follows logically from the premises.

§1. Circularity

Circular arguments are those in which the conclusion also appears as a premise. These arguments are always valid, but not necessarily good or persuasive.

• Definition: A circular argument is one where the conclusion is restated as one of the premises.

• Key Point: Circular arguments are valid because it is impossible for the premises to be true and the conclusion false at the same time.

• Example:

  • Premise: God exists. Premise: The moon is made of cheese. Conclusion: Therefore, God exists.

• Additional info: While circular arguments are valid, they are not considered strong arguments because they do not provide independent support for the conclusion.

§2. Necessarily True Conclusions

Arguments with necessarily true conclusions are always valid, regardless of the truth of the premises. This can lead to counterintuitive results.

• Key Point: If the conclusion is necessarily true (true in all possible worlds), then the argument is valid even if the premises are unrelated or false.

• Example:

  • Premise: The moon is made of cheese. Conclusion: 1+1=2.

• Additional info: This feature of validity shows that logical validity does not guarantee relevance or usefulness in real-world reasoning.

§3. Validity with Inconsistent Premises

Arguments with inconsistent premises (premises that cannot all be true at the same time) are always valid, because there is no situation where all premises are true and the conclusion is false.

• Key Point: If the premises are inconsistent, the argument is valid by definition, regardless of the conclusion.

• Example:

  • Premise: The moon is made of cheese. Premise: The moon is not made of cheese. Conclusion: Paris is the capital of France.

• Additional info: In practical reasoning, we usually avoid arguments with inconsistent premises, but understanding this property is important in formal logic.

Exercise: Testing Validity

Consider the following arguments and determine if they are valid:

• 1. John loves Mary. So John loves Mary.

• 2. John loves Mary. So Mary is loved by John.

• 3. 1+2=2.

• 4. All triangles have three sides. So all pigs have four legs.

• 5. All pigs have four legs. So all triangles have three sides.

• 6. All squares have three sides. So pigs have four legs.

• 7. All squares have four sides. So all triangles have three sides.

Note: These exercises illustrate the difference between validity and truth. Some arguments are valid due to their logical structure, even if the premises or conclusions are false or unrelated.