Why Some Arguments are Stronger than Others

§1.5

Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then assess the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments enable us to tell that their conclusions are true. In doing so, they establish the conclusions as knowledge.

Map of epistemic status

If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called conclusive and is said to be a proof or to prove the conclusion.3 These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them worthless because they don’t do any of what an argument should do. Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. We can call this spectrum the proposition’s epistemic status.

Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you probably don’t know the proposition at all. At this point you have no idea who killed Carl, and no reason to suspect Natalie; you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale picture above. But the investigation proceeds and you learn more about Carl’s life and death, at some point you formulate the theory that Natalie murdered Carl because there is some evidence pointing to her. Perhaps at this point, it’s not much evidence. We certainly wouldn’t say that you know she killed him or even that you believe it (or have reason to believe it), but you now suspect her, so we wouldn’t say that you’re totally ignorant of her having murdered him either. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.

Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but you don’t know it yet. Finally, at a certain point you might get enough evidence to really be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it.

All the evidence that you accumulated along the way could be spelled out as arguments. And we can think of what arguments do as helping us advance along the scale from ignorance to knowledge. An argument that’s strong enough to take us all the way to knowledge is a conclusive argument or proof. An argument that doesn’t take us any of the way is worthless. But many arguments take us part of the way—they give us some reason to believe the conclusion without giving us conclusive reason.

Scale of epistemic status

Notice that in the scale for epistemic status, knowledge is represented by a range and not by a point. This is because, even among the things we know, we think of ourselves as knowing somethings better than others. For example, you probably think you know both that Trump is the 45th President of the United States and that twice two equals 4. But you might think that you know the second of these propositions better than the first, since you can probably imagine some bizarre scenario in which Trump isn’t really the president and you’re the victim of an elaborate hoax, but it’s hard to imagine any scenario in which you can be mistaken that twice two is four. Perhaps some of you think that you don’t really know that Trump is the 45th President because you think you can’t totally rule out this hoax scenario. We’ll discuss these sorts of skeptical worries later in the course. For now, my point is just that to saying that you know something is not to rule out the possibility that there are other things that you know even better. That’s why I’m representing knowledge as a range rather than as a point. Similarly, to say that an argument is conclusive is just to say that it’s enough to establish its conclusion as knowledge. It is not to say that there cannot be some other argument that is even stronger.

The two factors that contribute to the strength of an argument are its premises and its inferences. So, to assess an argument we need to assess each premise and each inference.

The strongest premises are ones that we know to be true independent of knowing the conclusion. In order for an argument to prove its conclusion all of its premises must be like this. On the other extreme if we have no reason at all to think that a premise is true (or if we know that it is false), then it will make any argument it is part of worthless. If, on the other hand, the premise has an intermediate epistemic status, an argument containing it could still support the conclusion to some extent, without proving it. This is illustrated in the map below.

Left