In this paper, I will analyze the following argument in terms of validity and soundness: An argument is a syllogism only if it is valid. An argument has a true conclusion, if it is valid. If an argument has consistent premises, then it has a true conclusion. Thus, if an argument is a syllogism, then it has a true conclusion.
As we shall soon learn, this argument is valid but unsound.
I begin my analysis by providing a dictionary and putting the argument in standard logical form.
Here is my dictionary. Let ‘S’ stand for ‘an argument is a syllogism’ Let ‘V’ stand for ‘an argument is valid’ Let ‘C’ stand for ‘an argument has a true conclusion’ Let ‘P’ stand for the premises are consistent’ Here is the argument in standard logical form.
This argument is valid. My proof for validity can be found in my appendix at the end of the paper.
[And no, I am not going to provide an appendix for a sample paper].
Now that we know that the argument is valid, let us examine each statement in the argument. The first premise is S→V. This states that if an argument is a syllogism, then it is valid. This is false. An argument could be a syllogism yet be invalid. A syllogism is an argument that has two premises and a conclusion; but such an argument can be valid or invalid. Some poodles are dogs
Some elephants are not dogs
No elephants are poodles
This argument is a syllogism yet it still has an invalid form. [No, you don’t have to prove the form is invalid; but you better be correct]
The second premise is P→C. This states that if the premises are consistent, then the argument has a true conclusion. This premise is false. If the premises are consistent, then there is an interpretation where they are all true. But we know nothing about the conclusion.
P1 P2 P3 C
: : : :
T T T F
; ; ; ;
In this truth table, we see that our premise are consistent. There is an interpretation where all three are true. But in this interpretation, the conclusion is false. So, the argument is actually invalid. ( This is a relatively abstract truth table. You could also use a concrete example such as this: AvB
This argument has consistent premises but it is invalid. You will want to present both the argument and a truth table. Don’t make the reader guess what are the premises and conclusion from the table itself. Present the argument)
The third premise is V→C. This states that if an argument is valid, then it has a true conclusion. This is false. A valid argument can have a false conclusion. All dogs are cats
Some mice are dogs
Some mice are cats
As we can see from this example, a valid argument can have a false conclusion but only it if also has false premises.
Finally, let us examine the conclusion: S→C. This states that if an argument is a syllogism, then it has a true conclusion. This also is false. A syllogism can have either a true or false conclusion. Here is an example of a syllogism with a false conclusion. Some mice are cats
Some mammals are mice
No mammals are cats
A sound argument has both a valid form and true premises. While our argument had the valid form, it also had false premises. Thus, our argument is valid but unsound.