Now, that we've identified arguments and we've also identified premises and
conclusions, we need to put them in order.
The actual word order doesn't always tell us the order of argument.
Compare these two sentences. Because I am a professor, I teach
classes. I teach classes because I am a professor.
In those two examples, the words I am a professor, in one instance, occur at the
beginning and at the other instance, occur at the end.
But they actually express exactly the same argument.
Namely, the fact that I'm a professor is a reason why I teach classes.
But contrast both of those with this example.
I teach classes, so I must be a professor.
The point there must be something like nobody but professors can teach classes.
And whether or not that's true, the point here is, that's a different argument from
the first one. And we need to represent the difference
between these two arguments very carefully.
In order to show what is shared by the first two examples, but is different than
the third example, we put the arguments in what's called
standard form. And it's really easy.
Basically, you put the premise down and if there's another premise, you put that
down. Then, you draw a line.
Then, you put what I call a dot pyramid. It's basically three little dots with two
at the bottom and one at the top. And then, you put the conclusion after
that. It's also useful, we'll see why later,
but its useful to number the premises and to number the conclusion, so that we can
refer back to the premise and conclusion with the number instead of having to
repeat it all the time. And that's all there is in a standard
form. You just put down the premises on
different lines, then you draw a line, put the little dot pyramid, and then
write down the conclusion and then number them all.
That's it. And this standard form accomplishes what
we wanted it to. Namely, it helps us show what's common to
the first two examples at the beginning of this lecture that distinguishes them
from the third example. So, the first two examples were, I teach
classes because I'm a professor. And because I'm a professor, I teach
classes. They are the sentences.
The premise that goes above the line is, I'm a professor.
And the conclusion that goes below the line and next to the dot pyramid is, I
teach classes. But the next example, the third example
at the beginning of the lecture was, I teach classes, so, I must be a professor.
Now, that means that I am a professor is the conclusion that goes below the line
next to the dot pyramid. And the premise is, I teach classes.
So, when you put these two in standard form right next to each other, it makes
it absolutely clear what the difference is and what's in common to the first two
that distinguishes them from the third one.
No matter how easy, I think it's still worthwhile to do a few exercises just to
make sure we've got it straight because this notion in standard form will become
important later.