Validity and soundness
From Chains of Reason
Contents |
The basic definition
A valid argument is an argument that uses unflawed logic, regardless of the truth of the premises on which it is based.
A sound argument is a valid argument based on true premises.
So, whereas the conclusion of a sound argument must be true, that of a valid argument may be true or false.
Examples
Validity without soundness
The following is an example of an argument that is valid but not sound:
- Premise 1
- Paris is located in France.
- Premise 2
- France is located on Mars.
- Conclusion
- Paris is located on Mars.
The argument is valid, even though the conclusion is false, because if the premises were both true, then the conclusion would be true. But it is not sound, because the second premise is actually false.
Soundness
The following is an example of a sound argument:
- Premise 1
- Paris is located in France.
- Premise 2
- France is located in Europe.
- Conclusion
- Paris is located in Europe.
The argument is valid - because if the premises were both true, then the conclusion would be true - and sound, because both the premises are also true.
True premises and conclusion without validity, and therefore soundness
The following is an example of an argument that has true premises leading to a true conclusion, and yet is still be invalid and therefore also unsound:
- Premise 1
- Paris is located in France.
- Premise 2
- The Eiffel Tower is located in France.
- Conclusion
- The Eiffel Tower is located in Paris.
Although the premises and the conclusion of the argument are all true, the conclusion does not follow from the premises - that is, the premises do not exclude the possibility that the Eiffel Tower is located in France but outside Paris.
Validity and true conclusion without soundness
The following is an example of a valid argument leading to a true conclusion, but which is unsound:
- Premise 1
- Paris is located in Germany.
- Premise 2
- Germany is located in Europe.
- Conclusion
- Paris is located in Europe.
The argument is valid - because if the premises were both true, then the conclusion would be true - and the conclusion is true, but the first premise is false - the truth of the conclusion is the result of accident, not sound logic.
