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. You need to show how they 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's 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 must have the wrong structure. However, there's 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's 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 is 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 is supposed to have just 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 it 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 claim in the middle, number two, operates as a conclusion in the first argument, and premise in the second argument. But overall, I hope the diagram makes it clear why I want to call this a linear structure. When you have one premise giving a reason for a conclusion, which is then a premise for another conclusion. Then they form a line when you diagram them in the way that I'm 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's 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 didn'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 on 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 go 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, then I still wouldn't go to the movie. So each premise itself, is enough and they operate independently. That's what makes this a branching structure, instead of a linear structure. Lets diagram it and you will see why we call it a branching structure. One way to diagram it would be simply draw an arrow between premise one and 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 in 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, 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 argument marker, so, indicates that the conclusion is this time she must have 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 give me a sweater or a board game. Therefore, this box does not contain a sweater. Therefore, this time she gave me a board game. That didn't make any sense, right? I mean the fact that she always give me a sweater or a board game gives me no reason to believe that 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 their conclusion this time she must have given me a board game. How can we diagram this joint structure. We can put, a plus sign between premiss one and premiss 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 slide variation on the previous example. My wife always gives me either a sweater or a board game. This box does not contain a sweater. Because it rattles when I shake it. So, this time she must have given me a board game. This argument combined a linear structure with a joint structure. There are two argument markers. One's a conclusion marker, so and that indicates that the eventual conclusion is that she must of 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 it, means that it's not a sweater. So the first stage if 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, drawn an arrow down to its conclusion, namely, the box does not contain a sweater. That's two, and then we show that those are joint by adding a plus premise three, mainly, 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 premise 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 presented as a reason for that particular claim that the arrow's 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 there are 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 form a line when it's a linear structure, and branches when it's a branching structure. That'll 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.
