02 / 18 · Read the argument
True is not the same as valid
Distinguish statement truth, argument validity, and soundness.
Builds on What is the argument?
Go to practice ↓A question to keep in mind
Could an argument with a true conclusion still be a bad inference?
A deductively valid argument has no possible interpretation in which all its premises are true and its conclusion is false. Validity tests the link: if the premises hold, must the conclusion hold? It does not say the premises actually hold.
A sound argument is valid and has true premises. It therefore has a true conclusion. A true conclusion alone does not establish validity: a lucky guess can be true without the reasons guaranteeing it.
A counterexample to validity must preserve every premise while falsifying the conclusion. If even one premise is false, that situation does not show invalidity. Later we will represent these possibilities with truth assignments and finite models.
Work through an example
- All squares are circles. All circles are blue. Therefore all squares are blue.
- Read as set inclusion, the form is valid: anything in the first set must reach the third. Its geometry premise is false in the ordinary interpretation, so the argument is not sound there.
- 'The conclusion is true in my example' and 'there is no counterexample' are different claims.
Your turn
0 / 3An argument is valid, but one premise is false. What follows?
Read solution · does not award completion
It is not sound; the conclusion may be true or false.
Soundness combines two requirements. Failing one does not tell you that the other failed.
Which situation refutes an argument's validity?
Read solution · does not award completion
All true premises, false conclusion.
One genuine counterexample is enough. Many successful cases are not a general proof.
An AI answer reaches a factually correct result using an invalid inference. How should you review it?
Read solution · does not award completion
Keep the verified fact separate from the faulty justification.
A review should state what is true, what follows, and what remains unsupported separately.
Bring it back to your own work
Write a true claim supported by a bad reason. Explain why the reason fails without denying the claim.