What is an argument?
An argument is a group of statements in which some of the
statements
(the premises) are claimed to provide support for another (the
conclusion).
All arguments have just one conclusion, but may have several premises
(at
least one premise is required).
Statements are sentences which have a truth value, which is to say, a sentence that is either true or false. "Watch your step!", for example, is a sentence, but it is not a statement because it is neither true nor false.
Arguments may be said to be valid or invalid, sound or
unsound.
They are not properly said to be true or false.
Statements may be said to be
true or false. They are not properly
said to be valid or invalid, sound or unsound.
Validity
Put most simply, if an argument is valid,
the truth of the premises
insures the truth of the conclusion. Otherwise put, if an
argument
is valid, there will be no
case in which all the premises are true and
the conclusion is false. The following argument, for example, is
valid:
All B are C
All A are B
All A are C
Think about the argument above. Could you substitute terms in for A, B, and C (substituting consistently, of course) such that the two premises come out true but the conclusion false? Experiment for a moment to see if you can do this. Eventually, you will be convinced that you can't. (And no, you cannot subsitute so as to have the same word but with two different meanings  e.g. "plant"  that's a particular kind of error called "equivocation" that we'll discuss later.)
An informal way to gauge the validity of an argument is to ask yourself the following question: IF the premises are true, MUST the conclusion also be true? Note that in any given case, the premises may or may not be true  but pretend for a moment that they ARE true, and ask yourself if their truth also insures the truth of the conclusion. If they do, then the argument is valid.
It will have occurred to you, then, that it is possible to have a valid argument in which some or all of the premises are false. It is even possible to have a valid argument with a false conclusion. The one case that is NOT possible in a valid argument is to have all true premises and a false conclusion.
Consider the following instances of the valid
argument form presented above:
#1:
All bats are
camels
(false)
All aardvarks
are bats
(false)
All aardvarks are
camels
(false)
#2:
All maples are dogs
(false)
All poodles are
maples
(false)
All poodles are
dogs
(true)
#3: All vertebrates are felines
(false)
All cats are vertebrates
(true)
All cats are
felines
(true)
#4: All bears are mammals
(true)
All animals are bears
(false)
All animals are
mammals
(false)
#5: All trees are plants
(true)
All oaks are trees
(true)
All oaks are plants
(true)
Again, all five of the arguments above are valid. That's because,
in each case, IF the premises were true, the conclusion would have to
be
true.
Now, what happens if the argument is invalid? Then you aren't guaranteed anything about the truth  or falsity  of the conclusion. Sometimes, invalid arguments have conclusions which just happen to be true, but not because their truth was supported by the premises. With invalid arguments, the premises may be true or false, and the conclusion may be true or false: all combinations are possible. Here, for example, is an invalid argument:
Some B are C
All A are B
All A are C
In this argument, the truth of the premises does not guarantee the truth of the conclusion. In other words, it will be possible to find instances of this argument form in which the premises are all true and the conclusion is false. Here is such a case:
Some Christians are Baptists (true)
All Catholics are Christians.
(true)
All Catholics are
Baptists.
(false)
It might have occurred to you by now that if you have an argument in which all the premises are true and the conclusion is false, then that argument must be invalid (remember  there is no such thing as a valid argument with all true premises and false conclusion).
But again, remember that all combinations are possible in an invalid
argument. For example, here is an invalid argument with a true
conclusion.
(It has the same form as the argument immediately above.)
Some canines are dogs. (true)
All poodles are canines. (true)
All poodles are dogs. (true)
Soundness
As we've just seen, just because an argument is valid doesn't
necessarily
mean that the conclusion is true. But if, in addition to knowing
that the argument is valid, you also know that the premises are true,
THEN
you know that the conclusion must be true. In this case the
argument
is said to be sound. In other words:
An argument is sound if and only if both of the following conditions
are met:
1. The argument is valid.
2. All the premises are true.
If the argument is sound, then the conclusion must be true.
Here is a quick selftest on some of the ideas presented so far:
True or False
1. You can have a valid argument with all false premises.
2. You can have a valid argument with some true premises and some false
premises.
3. You can have a valid argument with all false premises and a false
conclusion.
4. You can have a valid argument with all true premises and a false
conclusion.
5. You can have a sound argument with a false premise.
6. You can have a sound argument with a false conclusion.
7. You can have a sound argument that is invalid.
8. You can have a valid argument that is unsound.
9. You can have an invalid argument with all true premises and
a true conclusion.
10. You can have a false argument.
11. You can have a true argument.
12. You can have a valid statement.
Click here
for the answers.
Here is a summary table of
some of the ideas discussed above:
Valid Argument Example 
Invalid Argument
Example 

True Premises True Conclusion 
All
dogs
are mammals (T) All terriers are dogs (T) All terriers are mammals(T) 
All
dogs
are mammals (T) All terriers are mammals (T) All terriers are dogs (T) 
True Premises False Conclusion 
One doesn't exist! 
All
dogs
are mammals (T) All cats are mammals (T) All cats are dogs (F) 
False Premises True Conclusion 
All
mammals are fish (F) All barracuda are mammals (F) All barracuda are fish (T) 
All
mammals are dogs (F) All cats are dogs (F) All cats are mammals (T) 
False Premises False Conclusion 
All
terriers are cats (F) All mammals are terriers (F) All mammals are cats (F) 
All
dogs
are cats (F) All mammals are cats (F) All mammals are dogs (F) 
Mixed (both T and F) Premises True Conclusion 
All
mammals are dogs (F) All terriers are mammals (T) All terriers are dogs (T) 
All
mammals are dogs (F) All terriers are dogs (T) All terriers are mammals (T) 
Mixed
(both T and F) Premises False Conclusion 
All
terriers are dogs (T) All cats are terriers (F) All cats are dogs (F) 
All
terriers are dogs (T) All mammals are dogs (F) All mammals are terriers (F) 
Question: Which of the 12 argument examples above (highlighted in
white)
is/are sound? Why?