Convincingness, Truth, and Validity

I. An argument is a string of sentences intended to convince someone of something.

So to be a good argument is to be a convincing argument (for a typical rational person).

II. The two ingredients for being a convincing argument:

	1. The premise(s) must be true (or at least: accepted as true).
	
	2. The argument (as a whole) must be valid.

III. A valid argument is an argument such that, in any possible situation where the premises are true, the conclusion is also true.

In other words: a valid argument is an argument where true premises are always and everywhere accompanied by a true conclusion.

In other words: a valid argument is an argument where it’s impossible to have true premises without also having a true conclusion.

In other words: a valid argument is an argument where knowing that the premises are true guarantees that the conclusion is true as well.

(Validity is just a more formal version of the ordinary concept of “following from”: if an argument is valid, the conclusion follows from the premises.)

IV.  If there is even one possible situation where an argument has true premises without having a true conclusion, then that argument is not valid (it’s invalid).

So a possible situation where the argument has true premises but a false conclusion will demonstrate that the argument is invalid.  For this reason, such a situation is called an invalidating situation.  

An invalidating situation is a possible situation where the premises of an argument are true, but the conclusion is false.  (An invalidating situation is a possible situation which reveals the invalidity of the argument.)

V. Keep in mind: a valid argument is valid always and everywhere; an invalid argument is invalid always and everywhere.  (By contrast, the truth of some sentence in the argument can change from situation to situation.)