Overview
This lecture explains some counterintuitive consequences of the precise definition of validity in logic, focusing on circular arguments, necessarily true conclusions, and inconsistent premises.
Definition of Validity
- An argument is valid if there is no logically possible situation where all premises are true and the conclusion is false.
- Validity depends strictly on this logical definition, not on whether the argument seems convincing or sensible.
Counterintuitive Consequence #1: Circular Arguments
- A circular argument has a conclusion that is also one of its premises.
- Example: "The earth is flat. Therefore, the earth is flat."
- Circular arguments are valid because the conclusion cannot be false if the premises are true.
- There is no possible scenario where all premises are true but the conclusion is false in circular arguments.
Counterintuitive Consequence #2: Necessarily True Conclusions (Tautologies)
- A tautology is a statement that is true in all possible situations.
- Arguments with necessarily true conclusions are always valid, regardless of the premises.
- Example: "Rainbows are made of ice cream. Therefore, either it is raining here now or it is not raining here now."
- There cannot be a situation where the premises are true and the necessarily true conclusion is false.
Counterintuitive Consequence #3: Inconsistent Premises
- Inconsistent premises cannot all be true at the same time.
- Example: "Rocks have souls. Rocks do not have souls. Therefore, the moon is made of cheese."
- Arguments with inconsistent premises are valid, because there is no possible situation where all premises are true and the conclusion is false.
- No counterexample exists for arguments with inconsistent premises.
Key Terms & Definitions
- Validity — An argument is valid if it is impossible for all premises to be true while the conclusion is false.
- Circular Argument — An argument where the conclusion is also among the premises.
- Tautology — A statement true in every possible situation; a necessary truth.
- Inconsistent Premises — A set of premises that cannot all be true simultaneously.
Action Items / Next Steps
- Review the definition of validity and practice identifying whether arguments are valid based on this definition.
- Reflect on examples of circular arguments, tautologies, and inconsistent premises to solidify understanding.