How can a valid deductive argument with a true conclusion be unsound?


Pr 1: All WVC students are dogs.

Pr 2: All dogs are human.

Conclusion:  All WVC students are human.


            For a deductive argument to be sound, it must have good logic (validity), and all the premises must be true.  First I’d like to explain the difference between how the words “true” or “false“ and “valid“ or “invalid“ are used [SAL1] when evaluating an argument.

            When evaluating an argument, the words “true” and “false” [SAL2] refer only to the statements and not to the argument as a whole.  The statements in an argument are the individual premises and conclusions.  In the example above, the premises would be “All WVC students are dogs.” and “All dogs are human.”  The conclusion that is inferred by the premises[SAL3]  in this argument is “All WVC students are human.”  Are all of these statements true?  No, the premises are false.  We know that no WVC students are dogs, and it’s impossible that all dogs are humans.  However, the conclusion is true because it is a fact that there is no other type of species enrolled at West Valley College besides humans.  We look at the statements in arguments as being true or false[SAL4] , not valid or invalid.

            The words “valid” and “invalid” pertain to the logic of an argument. If the logic contains no fallacies it[SAL5]  is valid.  For an argument to be valid the premises must support the conclusion.  It doesn’t matter whether the premises are true or false as long as the conclusion follows from the premises.  An argument can have false premises and a true conclusion, or true premises and a true conclusion, or false premises and a false conclusion.  An argument is not valid if it has true premises and a false conclusion because the truth of the premises guarantees the conclusion to be true[SAL6] .  Therefore, it is impossible for a conclusion to be false when both premises are true. [SAL7]  We would call an argument with true premises and a false conclusion invalid.  Is the above argument valid?  Yes, because even though the premises are false, the conclusion is true.  [SAL8] Another reason this is a valid argument is that the premises support the conclusion.[SAL9] 

            So how can a valid deductive argument with a true conclusion be unsound?  For an argument to be sound it must be valid and the premises must all be true.  The argument above is a big hint because it is very obvious that the premises are false.  Even though the argument is valid, it is missing the other characteristic needed for it to be sound. 

            Since this argument is valid but not sound, it is of no worth to us.  The best arguments are those that are valid and have true premises.  If an argument is sound we can rely on it to be accurate and truthful[SAL10] .

 [SAL1] 32 read this aloud – the difference between how the words are used?  HUH?

 [SAL2] Good punctuating here!  You know that when you talk ABOUT words, you put the words in quotes.

 [SAL3] 22, 44  Premises do not “infer”. People infer (draw conclusions).

 [SAL4] 32 I don’t understand.  Of course we look at the statements as true or false – that’s part of the definition of a statement (as opposed to, say, a question).

 [SAL5] 9 the logic? The argument?

 [SAL6] 32 This could be stated more clearly, no? For example, “Since a valid argument is one in which the premises, if true, guarantee the truth of the conclusion, no valid argument could ever have actually true premises and a false conclusion.”

 [SAL7] 44 You’ve got to be really clear here.  What you say is true only if the argument is valid – it’s certainly not IMPOSSIBLE for people to make invalid arguments .  E.g., “WVC is in Saratoga, and the moon orbits the earth.  Therefore Al Gore is the current President.”

 [SAL8] 44 It sounds like you’re saying that any argument with a true conclusion is valid.  That’s incorrect (see previous comment).

 [SAL9] 44 This is not “another reason” – it’s the ONLY reason. “Support” in logic simply means “the conclusion must be true IF the premises are true”.  “Support” does NOT mean the premises are actually true – just that IF they were, the conclusion would have to be.

 [SAL10] I think you almost understand this completely.  English-wise, this is very good.


Grade:  18 / 20