Welcome back. We've covered stages one through three of
argument reconstruction namely, close analysis, get down to basics, and sharpen
edges. In this lecture, we'll cover stage four,
which is organized parts. because it's not enough to isolate the parts and
figure out what they are. We need to show how the fit together in a structure so
that they work together to support the conclusion of the argument.
To see how this works, let's start with an example.
Consider this example. That fertilizer won't help the roses bloom because there
is already a lot of nitrogen in the soil. So, the fertilizer will make the nitrogen
levels too high. Of course, so is a conclusion marker so
one conclusion is that, the fertilizer will make the nitrogen levels too high.
And then, you might think that one might have put the argument into standard form
goes like this. Premise one is that fertilizer won't make
the roses bloom. Premise two is the nitrogen levels in the
soil are already high. And then, the conclusion is that the
fertilizer will make the nitrogen levels too high.
But that doesn't really make any sense, if you think about it. How could the fact
that the roses won't bloom be a reason to believe that the nitrogen levels are too
high? This couldn't be a reason for that. So,
we might just have the wrong structure. However, there is another argument
marker. This time it's a premise marker, because.
And that indicates that the claim that there's already a lot of nitrogen in the
soil is a premise. But what is the conclusion for that
premise? That's supposed to show that the
fertilizer won't make the roses bloom. So, we've missed that part of the
structure if we put it in standard form, the way we first thought.
The trick here is that there are really two conclusions.
One conclusion is that the fertilizer won't help the roses bloom, and another
conclusion is that the fertilizer will make the nitrogen levels too high.
But each argument's just supposed to have one conclusion.
So, how are we going to put this into a structure?
The solution is that there are two arguments.
One is that the nitrogen levels in the soil are already high.
Therefore, adding the fertilizer will make them too high.
And the second argument is that, adding the fertilizer will make the nitrogen
levels too high, therefore the fertilizer will not make the roses bloom.
Now notice that one argument really builds on the other because the
conclusion of the first argument is really a premise in the second argument.
So, we can represent them as two separate arguments.
But we can also put them together in a chain.
So that the argument says, the nitrogen levels in the soil are
already high. Therefore, adding fertilizer will make
them too high. And therefore,
adding fertilizer will not help the roses bloom.
Now, if we take that whole structure and we try to represent it in a diagram, and
we represent each premise with a number, which is the number that was given in the
standard form, then we can simply have premise one with an arrow to premise two
indicating that premise one is a reason for premise two. And then, another arrow
going from premise two to premise three to indicate that two is a reason for
three. In a way, we've got two premises and two
conclusions because that one kind in the middle, number two, operates as a
conclusion in the first argument and a premise in the second argument.
But overall, I hope the diagram, its clear.
Well, I want to call this linear structure. When you have one premise
giving reason for a conclusion which is then premise for another conclusion, then
they form a line in the diagram them in the way that I am proposing.
Arguments can have other structures, too. In particular, sometimes there's more
than one premise associated with a single conclusion.
And this can happen in two ways. The first, we're going to call the
branching structure, and the second we're going to call the joint structure.
Here is an example of the branching structure.
I'm not going to go to the movie with you because I don't like horror flicks.
And besides, I'm too busy.
The word because is a premise marker. So that indicates that the conclusion is
that, I'm not going to go to the movie with you.
And there are two premises. One is, I don't like horror flicks,
and the other is, I'm too busy. Now, you might think that, that could
just be put in the old linear structure that we already saw.
But then, the argument's going to look like this.
I don't like horror flicks. Therefore, I'm too busy. Therefore, I'm not going to
go to the movie. But, wait a minute.
The fact that I don't like horror flicks doesn't mean I'm too busy.
That doesn't make any sense. Oh, maybe it's the other way around.
I'm too busy. Therefore, I don't like horror flicks. Therefore, I'm not going
to go to that movie with you. That doesn't make any sense either.
The fact that I'm too busy isn't why I don't like horror flicks.
The problem is, there are two premises here but neither one is a reason for the
other, as we saw in the linear structure.
Instead, in this branching structure, each premise is operating independently.
There's one argument. I don't like horror flicks, therefore I'm
not going to go to that movie with you. There's another argument.
I'm too busy, therefore I'm not going to that movie with you.
And each premise by itself is a sufficient reason not to go to the movie
with you. I mean, just think about it.
If I wasn't too busy, but I didn't like horror flicks, I wouldn't go to the
movie. But if I liked horror flicks, but I was
too busy, I still would go to the movie. So, each premise by itself is enough, and
they operate independently. That's what makes this a branching
structure instead of a linear structure. Let's diagram it and you'll see why we
call it a branching structure. One way to diagram it would be to simply
draw an arrow between premise one and the conclusion two.
And then, there's a separate argument, so you draw another arrow from one star,
another premise, to conclusion two. And that's okay.
But, notice that it doesn't show you that both premises are reasons for the same
conclusion. So, to capture that aspect of the
structure, that both Premise one and Premise one Star support the same
conclusion, namely two. It's better to diagram it so that there's
an arrow that runs independently from both premises to a single instance of
conclusion two, as you see on the diagram on the screen.
And that should show you why we're calling it a branching structure because
it kind of branches, it looks like the branches of a tree.
Okay. Well, it doesn't really look like the
branches of a tree, but you get the idea. We're going to call it a branching
structure. Next, we have to separate this branching
structure from what we're going to call the joint structure.
The difference is that in the branching structure, the premises provide
independent support for the conclusion. Whereas, in this joint structure, they
work together and they're not going to have force independent of each-other.
It's like the joint in your leg, which joins together the calf with the thigh.
And, if you didn't have both, it wouldn't work very well.
So, we're going to call it a joint structure.
Here's an example. For my birthday, my wife always gives me
either a sweater or a board game. This box does not contain a sweater. So,
this time she must have given me a board game.
Now, notice that the argent marker, so, indicates that the conclusion is, this
time she must've given me a board game. And it's got two premises.
And you might think that they got a linear structure, and the argument goes
something like this. My wife always gives me either a sweater
or board games. Therefore, this box does not contain a
sweater. Therefore, this time she gave me board
game. That doesn't make any sense,
right? I mean, the fact that she always gives me
either a sweater or board game is no reason to believe this box doesn't
contain a sweater. Well, okay.
Let's try it again. Maybe it's a branching structure.
That would mean that the argument looks like this.
My wife always gives me either a sweater or a board game.
Therefore, this time she gave me a board game.
And, as a separate argument, this box does not contain a sweater, therefore
this time she must have given me a board game.
Neither of those arguments makes any sense so it can't be a branching
structure. Instead, what we have here is the two
premises working together. She always gives me either a sweater or a
board game. And, the second premise, this box does
not contain a sweater. Those two premises have to work together.
It's only jointly working together that they can support the conclusion that,
this time she must have given me a board game.
How can we diagram this joint structure? We can put a plus sign between premise
one and premise two, then draw a line under them to show that they work
together jointly. And take a line from that line and draw
an arrow down to the conclusion, just like in the diagram.
And this is what we're going to call the joint structure.
So, we've seen the linear structure, the branching structure, and the joint
structure. And, we can combine more than one of
these structures into a single argument. To see how to do this, let's just do a
slight variation on the previous example. My wife always gives me either a sweater
or a board game. This is box is not contain a sweater
because it rattles when I shake it. So, this time she must have given me a
board game. This argument combines a linear structure
with a joint structure. There are two argument markers.
One is a conclusion marker, so, and that indicates that the eventual conclusion is
that she must given me a board game this time.
But there's also that new word, because, which indicates that the fact that it
rattles when I shake means that it's not a sweater.
So, the first stage of the argument in standard form looks like this.
Premise one, this box rattles when I shake it.
Therefore, conclusion, this box does not contain a sweater.
Stage two says, this box does not contain a sweater, my wife always gives me either
a sweater or a board game. So, the conclusion, this time, she must have
given me a board game. And, of course, the conclusion of that
first little argument is identical with the premise of the second argument, so we
can put them together into a chain. We can say," this box rattles when I
shake it, so it must not contain a sweater." My wife always gives me a
sweater or a board game, so this time she must have given me a board game.
That's how we get a linear structure combined with a joint structure.
And we can use our diagram methods to diagram this argument the same way we did
before. We simply start with premise one,
the box rattles when I shake it. Draw an arrow down to its conclusion.
Namely, the box does not contain a sweater.
That's two. An then, we show that those are joint by
adding a plus, premise three. Namely, my wife always gives me either a
sweater or a board game. Draw a line under them and an arrow from
those two together down to the eventual conclusion,
namely, four that this time she must have given me a board game.
The fact that the top arrow goes from premise one to two, but does not go from
premise one to three indicates that, that premises is a reason for two but is not a
reason for three. So when you use this method to diagram
arguments, you have to be careful where you draw the arrows. And draw them only
where there really is a rational connection.
That is, where one claim is being presenting as a reason for that
particular claim that the arrow is pointing towards.
Now, almost all arguments can be diagrammed using these three simple
structures. That is, the linear structure,
the branching structure, the joint structure,
and some combination of those three. You can add more premises because you can
always add one plus two plus three plus four if they're four premises operating
together in a joint structure. And, you can add extra arrows if you have
a branch with more than two branches. So, you can cover a lot of arguments
using these kinds of diagrams. The method can be described in general,
like this. You start by identifying the premises and
the conclusions, and you number them. So that you can just have numbers instead
of having to write out the whole sentence on the diagram.
Then, when they work together, you put a plus sign between them and draw a line
under it to indicate that they're working together.
They're functioning as a group. Then, you draw an arrow from the claims
that are reasons to the claims that they are reasons for.
And then, you move them around on the diagram so that they'll form a line when
it's a linear structure and branches when it's a branching structure. But, it will
be easy to rearrange them so as to show how all of the different premises and
conclusions work together in a single argumentative structure.
That's going to be enough to accomplish this stage of reconstruction.
Namely, to organize the parts and show how they work together in the overall
argument.