This article is from the Atheism FAQ, by mathew firstname.lastname@example.org with numerous contributions by others.
An argument is, to quote the Monty Python sketch, "a connected series
of statements to establish a definite proposition". There are three
stages to an argument: premises, inference, and conclusion.
Stage one: Premises
For the argument to get anywhere, you need one or more initial
propositions. These initial statements are called the premises of the
argument, and must be stated explicitly.
You can think of the premises as the reasons for accepting the
argument, or the evidence it's built on. Premises are often indicated
by phrases such as "because", "since", "obviously", "let's assume",
and so on.
(The phrase "obviously" is often viewed with suspicion, as it gets
used to intimidate people into accepting things which aren't true at
all. If something doesn't seem obvious to you, don't be afraid to
question it. You can always say "Oh, yes, you're right, it is obvious"
when you've heard the explanation.)
Stage two: Inference
Next the argument continues step by step, in a process called
In inference, you start with one or more propositions which have been
accepted. You then use those propositions to arrive at a new
proposition. The new proposition can, of course, be used in later
stages of inference.
There are various kinds of valid inference -- and also some invalid
kinds, but we'll get to those later. Inference is often denoted by
phrases such as "implies that" or "therefore".
Stage three: Conclusion
Finally, you arrive at the conclusion of the argument, another
proposition. The conclusion is often stated as the final stage of
The conclusion is affirmed on the basis the original premises, and the
inference from them. Conclusions are often indicated by phrases such
as "therefore", "it follows that", "we conclude" and so on.