1. What is an Argument?

Since arguments are at the heart of logic and argumentation it's natural to start with this question.

The first thing to say about arguments is that, as this term is used in logic, it isn't intended to imply anything like an emotional confrontation, like when I say that "an argument broke out at a bar" or "I just had a huge argument with my parents about my grades". In logic an “argument” is a technical term. It doesn't carry any connotation about conflict or confrontation.

Here's our definition. It will have three parts:

(1) An argument is a set of "claims", or "statements".

We'll have more to say about what a claim or statement is later, but for now it's enough to say that a claim is the sort of thing that can be true or false.

(2) One of the claims is singled out for special attention. We call it the "conclusion". The remaining claims are called the "premises".

(3) The premises are interpreted as offering reasons to believe or accept the conclusion.

That's it, that's the definition of an argument.

Now let's have a look at one:

1. All musicians can read music.
2. John is a musician.
Therefore, John can read music.

Premises 1 and 2 are being offered as reasons to accept the conclusion that John can read music.

This may not be a particularly good argument actually, since that first premise makes a pretty broad generalization about all musicians that isn't very plausible. I'm sure there are a few great musicians out there that don't read sheet music. But it's an argument nonetheless.

Now, notice how it's written. The premises are each numbered and put on separate lines, and the conclusion is at the bottom and set off from the rest by a line and flagged with the word "therefore".

This is called putting an argument in standard form and it can be useful when you're doing argument analysis.

In ordinary language we're almost never this formal, but when you're trying to analyze arguments, when you're investigating their logical properties, or considering whether the premises are true or not, putting an argument in standard form can make life a lot easier.

Now just to highlight this point, here's another way of saying the same thing:

"Can John read music? Of course, he's a musician, isn't he?"

This expresses the very same argument as the written in standard form above. But notice how much easier it is to see the structure of the argument when it's written in standard form. In this version you have to infer the conclusion, "John can read music", from the question and the "of course" part.

And you have to fill in a missing premise. What you're given is "John is a musician", but the conclusion only follows if you assume that all musicians, or most musicians, can read music, which is not a given, it's just a background assumption. The argument only makes sense because you're filling in the background premise automatically. You can imagine that this might become a problem for more complex arguments. You can't always be sure that everyone is filling in the same background premise.

So, standard form can be helpful, and we're going to be using it a lot.