# Question regarding sound argument [duplicate]

Sound argument is an argument which is both valid and it's premises are true.
But my question is, why do we mention in the definition of the sound argument that "it's premises are true" when we've already said it's valid?
Is not that true that when we say an argument is valid, we've already accepted it's premises are assumed to be true?so when the premises are true the conclusion must be true for the argument to be valid, thus, when we say an argument is valid, we've already confirmed the premises correctness.So I again say, why do we mention that "premises are true" in the definition of the sound argument?

All birds are green, My dog is a bird Therefore my dog is green

This is a valid argument because the conclusion follows from the premises. Yet the premises are false.

This is because validity and soundness don't exactly refer to the the same properties of an argument.

Consider the following conditions for validity and soundness from Philosophical Writing: An Introduction (Martinich 2005):

Validity: An argument is valid if and only if it is necessary that if all the premises are true, then the conclusion is true.

Soundness: A sound argument is an argument which is valid and which contains only true premises.

As you can see, the condition for validity doesn't state that all the premises are true, only that if they were true the conclusion would necessarily follow. Put differently, validity concerns an hypothetical situation where the premises are assumed to be true. If in that hypothetical situation the truth of the premises necessarily makes the conclusion also true we then say the argument is valid. Consider the following example:

``````P1: All pigs are birds.
P2: All dinosaurs are pigs.
C: All dinosaurs are birds.
``````

Premises P1 and P2 are false, but the argument is nevertheless valid because if P1 and P2 were true the conclusion C would necessarily follow. Validity is thus a property of the logical structure of the argument and doesn't depend on the truth of the premises. That means it's also possible to have an invalid argument containing only true premises. Consider the following example:

``````P1: All pigs are mammals.
P2: The Moon orbits around Earth.
C: All humans are mortal.
``````

Even though both premises are true and the conclusion is also true, the argument isn't valid because the conclusion doesn't logically follow from the premises. Therefore accepting the truth of the premises and of the conclusion doesn't imply accepting the validity of the argument.

Soundness, on the other hand, requires not only that the argument be valid, but also that the premises be actually true. It's not sufficient to assume that premises are true, they must be true in our world. Consider the following example:

``````P1: All mammals are animals.
P2: All pigs are mammals.
C: All pigs are animals.
``````

This argument is sound because it's valid and only contains true premises.

Because validity has nothing to do with having true premises.

An argument is valid if it is the case that were its premise true, then its conclusion must also be true.

See What is the logical form of the definition of validity? for a more thorough explanation of the difference.

Because the premises can be false and the form valid. For example:

P1: Hitler was a vegetarian and was evil. (T) P2: All vegetarians are like Hitler. (F) C: All vegetarians are evil. (F)

We an have an argument whose premises are true and whose conclusions are true, but which nonetheless is an awful argument:

• All men are mortal
• George Bush is mortal
• Therefore George Bush is a man.

This argument might possible sound good. It's premises are certainly true. It's conclusion is also true. Is it a good argument? Well, no, not really. Here's why:

• All blue bottomed baboons are mortal.
• George Bush is mortal.
• Therefore George Bush is a blue bottomed baboon.

Now this is obviously not true. It shows that even though the premises of the first argument were true and the conclusion was true, the conclusion wasn't true because the premises were true. If it was, then this last argument would also have had a true conclusion.

Because of this problem, we need to know whether a form of argument, or of type of argument, can be good or bad. In other words we need to be able to separate out whether an argument is good from whether it's conclusion and premises are true.

So this means that being true and being a good argument are different things. Consider the following argument.

• Bob's a Blarg or a Varg
• Bob's not a Blarg
• Therefore Bob's a Varg.

Now Blargs and Vargs don't exist, so it's not possible for Bob to be either a Blarg or a Varg. Nonetheless, we can see that this kind of argument, or deduction is a good type of deduction. If there were Blargs or Vargs, and Bob was one and he wasn't a Blarg, then he would indeed be a Varg. So we can see a property of this argument, which is that given true premises its conclusion is true. This doesn't mean that Bob actually is a Varg, however, because Vargs don't exist outside of my imagination. This property of being a good argument is called 'validity'. As we have seen it is not the same as being true.

So now we face a different problem when we see an argument. We may know that if the argument's valid then if the assumptions in the argument are true, the conclusion will be true. However, obviously this means that having a valid argument isn't good enough to guarantee a true conclusion. We need the further property of the assumptions of an argument being true to guarantee a true conclusion. The conjunction of these properties is soundness.

Notice that the premises in argument about the blue-bottomed baboon were true, but the argument wasn't valid. Similarly, the argument about Bob was valid; but it didn't have true premises. In each case we do not have a reliable argument in terms of being able to trust the conclusion because of the argument. For that we need both of the distinct qualities of having true premises and being valid - the quality of being sound!