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What is the difference between valid and sound argument? |
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A valid argument is an argument whose conclusion follows logically from the truth of the premises. It is impossible for the premises to be true and the conclusion false. An example of a valid argument is:
1. If Thales was right, then everything is made of water.
2. It's not the case that everything was made of water.
3. So, Thales wasn't right.
This argument has the form: If P then Q, ~Q, therefore ~P. The conclusion is derived using Modus Tollens. All of the premises are true, and so is the conclusion.
However, the validity of an argument does not entail the truth of its conclusion. Consider another example of a valid argument:
1. If Socrates was a Philosopher, then Socrates was a happy alligator.
2. Socrates was a Philosopher.
3. So, Socrates was a happy alligator.
This argument is valid: it is of the form If P then Q, P, therefore Q. The conclusion is derived using Modus Ponens (a rule for logical inference which preserves truth).
However, the conclusion is false. Because it is valid, one of the premises must also be false: and, we can see, premise 1 is the culprit. If we replace it with a better premise, such as "If Socrates was a Philosopher, then Socrates existed", we derive a different and true conclusion (that Socrates existed).
A sound argument is an argument with two features: (i) it is valid, and (ii) its premises are all true.
It is not clear whether we ought to include other features, like non-circularity, in the necessary conditions for soundness; convention has yet to determine it.
1. If Thales was right, then everything is made of water.
2. It's not the case that everything was made of water.
3. So, Thales wasn't right.
This argument has the form: If P then Q, ~Q, therefore ~P. The conclusion is derived using Modus Tollens. All of the premises are true, and so is the conclusion.
However, the validity of an argument does not entail the truth of its conclusion. Consider another example of a valid argument:
1. If Socrates was a Philosopher, then Socrates was a happy alligator.
2. Socrates was a Philosopher.
3. So, Socrates was a happy alligator.
This argument is valid: it is of the form If P then Q, P, therefore Q. The conclusion is derived using Modus Ponens (a rule for logical inference which preserves truth).
However, the conclusion is false. Because it is valid, one of the premises must also be false: and, we can see, premise 1 is the culprit. If we replace it with a better premise, such as "If Socrates was a Philosopher, then Socrates existed", we derive a different and true conclusion (that Socrates existed).
A sound argument is an argument with two features: (i) it is valid, and (ii) its premises are all true.
It is not clear whether we ought to include other features, like non-circularity, in the necessary conditions for soundness; convention has yet to determine it.
First answer by ID1272296671. Last edit by Fischlein. Contributor trust: 0 [recommend contributor]. Question popularity: 5 [recommend question].
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