What is the difference between a valid argument and a sound argument?

First, let's be clear what an argument is. An argument is a set of claims intended to establish the truth of another claim. The set of claims are the premises of the argument, and they are intended to establish the truth of the conclusion. For example: --- Argument 1 Premise 1: If there is a dog barking nearby, the cat won't go outside. Premise 2: There is a dog barking nearby. Conclusion: The cat won't go outside. --- An argument is valid if the truth of the conclusion follows from the truth of the premises. That is, an argument is valid if, when all the premises are true, the conclusion is necessarily true. The argument given above is valid, because if the two premises are both true, then the conclusion must be true. If it is true that the cat won't go outside when a dog is barking nearby, and also true that there is a dog barking nearby, then we cannot avoid the truth of the conclusion that the cat won't go outside. Therefore, the argument is valid. It is very important to recognise that the argument remains valid even if some or all of the premises are actually false. Let us say, for example, that Premise 1 is false, because the cat isn't at all bothered by dogs barking, and will go outside regardless. Or let us say that Premise 2 is false, because there isn't actually a dog barking nearby. Even if one or both of these premises are false, the argument remains valid, because it is still the case that if the premises were true, then the conclusion would necessarily be true. --- An argument is not valid, or is invalid, if the truth of the conclusion does not follow from the truth of the premises. That is, an argument is invalid if it is possible for all the premises to be true whilst the conclusion is false. The following is an example of an invalid argument: --- Argument 2 Premise 1: Honey is sweet. Premise 2: Bananas are yellow. Conclusion: The cat won't go outside. --- This argument is invalid because it is possible for the premises to be true without the conclusion being true. In other words, it isn't the case that the conclusion must be true when the premises are both true. --- An argument is sound if it is valid and the premises are all true. Argument 1 is valid, but will only be sound if both of its premises are true. If one or both of its premises are actually false, then it is unsound, even though it remains valid. Because Argument 2 is invalid, it will always be unsound, even if both of its premises are actually true.