Valid/Invalid

"Your argument is invalid!" Perhaps you've heard this phrase before.  Perhaps you've used it yourself.

To most people, invalid is synonymous with wrong (i.e. false, not true) and it is wrong because I said so.  However, an invalid argument is not necessarily a false one.  By that I mean that the conclusion may be true even if the argument is invalid.  Likewise, an argument may be valid but have a false conclusion.

Consider an example of the first possibility:

1. All men are mortal.
2. Churchill is mortal.
3. Therefore, Churchill is a man.

Every one of these statements are true.  But the argument is not valid.  There is nothing about the first two statements that leads me to believe the third.

Consider an example of the second possibility:

1. All men are immortal.
2. Churchill is man.
3. Therefore, Churchill is immortal.

Since the first premise is not true, but the argument is valid, my conclusion is false as a result.  If all men were immortal, Churchill, being a man, would be immortal.  But not all men are immortal, and in fact, all men are mortal.

What is a valid argument?  A valid argument is one where if the premises are true and the terms unambiguous, the conclusion must be true.  Your choice is to believe the conclusion or be illogical.  Validity has to do with the form of an argument.  The structure of some arguments force you to believe the conclusion, just as the structure of some buildings force you to enter and leave a particular way (such as through a door rather than a window). We need valid arguments in order to think, debate, and reason clearly.  Otherwise, we are blindly stumbling looking for truth.

In the first example above, we see that all men are mortal and that Churchill is mortal.  But I do not know anything else about Churchill.  I can't conclude anything about him.  Churchill may be the name of my pet British bulldog, and hence not a man, rather than the British leader nicknamed the British Bulldog.  In the second, my knowledge of the first two statements leads me to my knowledge of the third.  I know that Churchill is mortal because he is a man and all men are mortal.

Consider a third possibility where an argument is valid and the conclusion true:

1. All men are mortal.
2. Churchill is man.
3. Therefore, Churchill is mortal.

When the structure, or form, of an argument is valid; the terms are unambiguous, for example, we know what mortal and men mean; and the premises are true; we must believe the conclusion.  We call this a sound argument.  It is impossible to disbelieve a sound argument and remain a rational thinker.