Difference between valid and sound argument
An argument formed by a set of propositions of which one is the conclusion and the others are premises. An argument is valid when it is possible to adequately justify the conclusion through the premises and it is sound when, in addition to being valid, it also has true premises.
Consider the following example:
All spiders have twelve legs.
Every human being is a spider.
So every human has twelve legs.
Each of the propositions of the above argument is false. However, the argument as a whole is valid. This is because a valid argument is one that the conclusion necessarily follows from the premises. That is, if the premises are true, the conclusion will also be true.
Suppose the first and second propositions are true. If you accept that both are true, then you will have to accept that the conclusion is also true, because there is no possibility that the conclusion is false in this case.
Consider a second example:
The Annabelle cow has black and white fur.
The Betsie cow has black and white fur.
Therefore, all cows have black and white fur.
The premises of the argument are true, but the conclusion is false. That is, this is an invalid argument, since the premises are true and the conclusion is false.
Note: A valid argument is one that is impossible for the conclusion to be false if the premises are true. However, validity says nothing about the truth of the conclusion. It just says that the conclusion follows from the premises.
A valid argument can have a false conclusion. Therefore, the validity of an argument is no guarantee that that argument is a good one. In logic, there is another term used to refer to an argument that, besides being valid, has true premises and, therefore, the true conclusion: sound.
A sound argument is one that, in addition to being valid, has true premises.
When we are going to analyze an argument, we must ask two questions:
- Are the premises of the argument true?
- Is the argument valid, that is, does the conclusion necessarily follow from the premises?
As we saw in the examples above, it is not enough for an argument to be valid for it to be good. The first argument, while valid, had a false conclusion.
On the other hand, it is not enough for an argument to have its true premises for it to be a good argument. The second example, although it had true premises, led to a false conclusion.
Therefore, in the analysis of arguments, it is important to be aware of these two aspects: the content of the argument (if the premises are true) and its form (if it is valid). In order to have a good argument, which justifies its conclusion, it must be valid and have true premises.
Logic cannot tell us anything about the truth of an argument’s premises. If we are faced with the statement “a spider has twelve legs”, there is no point in using logic to find out if it is true or false. We will have to do an investigation looking at these insects and counting their number of legs.
The logic contributes to the analysis and evaluation of arguments showing which are valid and which are invalid. Throughout the history of logic, instruments have been developed for the analysis and evaluation of different types of arguments. The syllogistic logic and the propositional logic are two examples.
Walton, Douglas. Informal Logic: A Pragmatic Approach. Cambridge: Cambridge University Press, 2008.