It's been a long and winding road, as the Beatles used to say. But we're finally at the last stages of reconstructing arguments. We've looked at stage one which is close analysis, stage two which is get down to basics stage three, which is, sharpen edges. Stage four, is organize parts. And now we're doing stage five, which is, fill in gaps. And we'll also get to stage six, which is, conclude. Stage five really consists of four separate steps. First, we need to assess the argument for validity. Then we need to add suppressed premises. Enough of them to make it valid. Then we need to assess those suppressed premises for truth or falsehood. And then we need to qualify the suppressed premises in order to make them true. And the whole goal is to make the suppressed premises both plausible for their truth and enough to make the argument valid. So these steps within the stage really do work in tandem together to try to make the argument good. We already learned how to assess validity. You simply ask is it possible for the premises to be true and the conclusion false and if so the argument is not valid and if not the argument is valid. And the way you figure out whether it's possible is, you try to tell a story or describe a situation. And if you can describe a coherent situation where the premises are true and the conclusion is false. Then that shows that the argument's not really valid. The main topic for today is what do you do. When you assess the argument for validity and you find out it's not valid. And the answer is you add suppress premises enough of them to make the argument valid. Now that might seem like cheating. I mean you'd start with an argument that's no good. It's not valid and then you just throw in some extra premises in order to make it valid. Why isn't that just distorting the argument, and making up something that wasn't there? The answer, is that it's not really bad. And if it were bad, we'd all be in bad shape, because in every day life, people always take things for granted. They make assumptions. We do it too. And if we didn't, boy, our arguments would be really long and boring. So there's something to be said in favor of suppressing premises, at least the obvious ones that people really do take for granted, but we can also get tricked. People can suppress premises that really are questionable and they just don't want us to see that they're making that assumption. It is useful to fill out the argument with suppressed premises to make sure it really is valid, because that brings those assumptions out into the open were we can access whether or not they're true of false. Another reason to fill in suppressed premises is to understand the argument better. Because, if people suppress premises, then they're showing us some of their footprints along the path, but, if we really want to know the full path that their reasoning followed, we've gotta see every single footprint. So, the goal of bringing out the suppressed premises is to let us trace exactly where their reasoning went. From one step to another. So there are two goals. One is to trace the full path every step, and the other goal is to see if there are any missed steps or they're trying to hide something from us by getting rid of one of their footsteps. So, that's the point of bringing out surpressed premises. To accomplish these goals is tricky. You have to find suppress premises that are just strong enough to make the argument valid but not so strong that they're going to be implausible. because you don't want to ascribe all kinds of suppressed premises to the person that they didn't really believe and that they didn't really need for their argument. So it's kind of like Goldilocks and the Three Bears. You want suppressed premises to be not too hot, and not too cold, but just right. Here's an example from a previous lecture. My wife always gives me either a sweater or a board game. This box does not contain a sweater because it rattles. When it's shaken. So this time, she must have given me a board game. And we put this in standard form, this way, first premise, this box rattles when I shake it, and that shows you it doesn't contain a sweater. Third, she always gives me either a sweater or a board game. Conclusion, this time she must have given me a board game. Now the first step of this argument is this box rattles when I shake it and the conclusion there is it doesn't contain a sweater, that's the part of the argument that we want to focus on here and ask whether that argument is valid. No. The argument's not valid, because it's possible for the premise to be true and the conclusion false. How can that happen? Well, my wife might be fooling me. She might know that I expect either a sweater or a board game, so she puts a sweater in the box, and then she puts little rocks around the outside, so when I shake it Well here is something. So thats possible, and that shows the argument is not valid. Well, how can we make the argument valid? The question here is, can we add a suppressed premise that will turn this invalid argument into a valid argument. Here's one that will do the trick. A box that contains a sweater. Doesn't rattle when shaken. The other argument looks like this. This box rattles when I shake it. A box that contains a sweater doesn't rattle when shaken. So this box doesn't contain a sweater. The explicit premise, is that this box rattles when I shake it. The suppress premise is that a box that contains a sweater doesn't rattle when shaken, and together they're supposed to support the conclusion that this box doesn't contain a sweater, but do they really support that conclusion? Is the argument valid? Well, it's valid only if there's no possibility that the premises are true and the conclusion is false. Without the suppressed premise, we saw that was possible, because my wife might be fooling me and putting rocks around the sweater. So let's see if that's going to ruin the validity of this argument. No, because, if the sweater's got rocks around it, so it makes noise when I shake it, then, the premise that says a box that contains a sweater doesn't rattle when shaken, turns out to be false. So that's not a case. Where the premises are true and the conclusion's false, because the premise is false in that case. So, by adding this premise, we actually succeeded in making the argument valid. The problem of course, is that validity is not enough for a good argument, as we saw several lectures ago. You can have a valid argument that's very bad when the argument's not sound. What we want really is soundness. So that's why we need the next step. Namely, check the suppressed premises for truth. Assess whether they're true or false, and if they're not true then you need to qualify them in order to make them true, because you don't want to claim that the person giving the argument was assuming this falsehood when they didn't have to. So let's see if there's some way to qualify this surpresssed premise in order to make it true. How can we qualify this premise to make it true? How are we going to do that, let me think, oh, what about that little word only? We can add that. We could say, a box that contains only a sweater doesn't rattle when shaken. But the word only what exactly does that mean? We need to clarify that. What exactly does the word only exclude? It excludes something. That's the function of the word only. But what does it exclude? Well. It probably excludes other things that might make the rattling sound. Like, if my wife put rocks in the box. So, we can clarify this premise by saying. A box that contains only a sweater and not anything else that might make a rattling sound when shaken, won't rattle when shaken. Well is that premise true? You might quibble about details but it's close enough for now. What we need to do though is to go back and determine whether when we put that suppress premise in, the argument's valid. And the argument now looks like this. This box does rattle when shaken. And a box doesn't rattle when shaken if it contains only a sweater and not anything else that makes a rattling sound. So this box doesn't contain a sweater. Is that valid? Well, no, for the same reason we saw before, because my wife might be a trickster who puts rocks around my sweater in the birthday present box, in order to fool me. Then, the premises can be true, and the conclusion, false. It's possible that the first premise is true, this box rattles when I shake it. The second premise is true, a box doesn't rattle when shaken if it contains only a sweater and nothing else that makes a rattling sound. But it's false. If this box doesn't contain a sweater, because it still does contain a sweater and it contains a sweater in addition to those pesky little rocks that make all that rattling noise. Well if the argument's not valid we got to back to that other step and add another suppressed premise. Remember how I told you that these different steps within this stage work in tandem. and what's happening is, you gotta check it for validity, add a suppressed premise, recheck it for validity, maybe add another suppressed premise in. That's what we're doing now. So what kind of suppressed premise could we add? Well, we could add, my wife's not a trickster. But basically that amounts to, she wouldn't put rocks in a birthday present with a sweater in order to fool me. So we can make that a little more explicit by making the suppressed premise something like this. If this box contains a sweater, then it contains only a sweater and it doesn't include anything else that would make a rattling sound when shaken. And now, we can stick that as an extra suppressed premise into the argument. Now the argument looks like this. This box, rattles when I shake it. A box doesn't rattle when shaken if it contains only a sweater and not anything else that makes a rattling noise when shaken. If this box contains a sweater, then it contains only a sweater, and doesn't contain anything else that rattles when shaken. So this box does not contain a sweater. Now we have an argument that's valid. And the surpressed premises are true at least given that my wife's not a trickster which she's not I assure you, and it looks like we have a sound reconstruction. Just what we were looking for. Admittedly this argument is a lot longer and more convoluted than the original. And that shows why people suppress premises instead of talk in the way this argument goes. And of course many people would be perfectly well convinced by the original argument because, they share the assumptions that are in the suppressed premises. So why do we go to all the trouble to go through this process and add the suppressed premises. Remember, the reason is that we want to understand the pathway between the premises and conclusion, we want to understand how the reasoning works step by step by step. And we want to do that because sometimes people are going to include suppressed premises that aren't true and we want to bring them out and make those assumptions explicit so that we can assess them for truth and falsehood. And when you're talking to somebody you trust, you might not have to do that. And it's okay to suppress premises, but when you really want to know whether the argument's any good that's when you want to fill it out with the suppressed premises. The point of going into detail on this example, is to illustrate this stage of reconstruction you want to assess the argument for validity, and suppress premises that make it valid, check them for truth. If they're not true, you qualify them. Then you go back and see whether that qualification made the argument not valid anymore. And then you go back and forth, and back and forth, until you've got a sound reconstruction. The same steps are going to apply to all kinds of suppressed premises. And sure enough, there are all kinds of suppressed premises. So let's go through a few examples a lot more quickly in order to show the variety of suppressed premises that are assumed in arguments. Here's one example. Abraham Lincoln turned 40 on February 12th, 1849. Therefore, Charles Darwin also turned 40 on February 12, 1849. Now, is that argument valid? No chance. Of course it's possible for the premise to be true and the conclusion false. So we have to add a suppressed premise. The suppressed premise is that Abraham Lincoln and Charles Darwin were born on the same day, and they were it happened to be February 12, 1809. So now we've filled out the argument. Abraham Lincoln turned 40 on February 12, 1849. Abraham Lincoln and Charles Darwin were born on the same day. Therefore, Charles Darwin also turned 40 on February 12, 1849. Now is the argument valid? No. It's still not valid. because Darwin might have died before 1849. So we have to add another suppressed premise namely that both Abraham Lincoln and Charles Darwin lived beyond 40. So now we have a fuller argument. Abraham Lincoln turned 40 on February 12th 1849. Abraham Lincoln and Charles Darwin were born on the same day. Both of them lived beyond the age of 40. Therefore, Charles Darwin also turned 40 on February 12, 1849. Now the argument looks pretty good. We had to have two suppressed premises, but we finally have a valid argument. And what this shows is that sometimes the suppressed premises are purely factual matters. In this case, that they were born on the same day. And that they both lived beyond 40. So sometimes we have factual suppressed premises. Here's another quick example. You ought to obey her because she's your mother. Here the premise is that she's your mother, and the conclusion's, you ought to obey her. Well, is that argument valid? No way. because it's possible that she's your mother, but it's false that you ought to obey her. When could that happen? Maybe she was like abusive, or stupid, or whatever. Then maybe you ought not to obey her, even though she is your mother. So, we have to add a premise. Namely, you ought to obey your mother. Now, we can say she's your mother, you ought to obey your mother, therefor you ought to obey her. But of course, that is the suppressed premise you ought to obey your mother is questionable because maybe she was abusive or stupid. So let's add another suppressed premise that your mother was not abusive or stupid. Of course, we also have to qualify that moral premise that you ought to obey your mother if she's not abusive or stupid. And now the argument looks like this. She's your mother. You ought to obey your mother if she's not abusive or stupid. Your mother was not abusive or stupid, therefore you ought to obey her. And notice that here, we added a moral premise about the that fact that you ought to obey your mother under certain conditions namely she's not abusive or stupid. And the second premise is she was not abusive or stupid so we have a moral premise and a factual premise. Both being suppressed in the argument that you ought to obey her, because she's your mother. Here's another. It's the Sabbath. So you ought go to the Synagogue. Well, that's clearly not valid. Once suppressed premises you're Jewish. The other suppressed premise is you haven't been to Synagogue already today on this Sabbath. And the third suppressed premise is a religious norm namely Jews ought to go to the Synagogue on the Sabbath and you need that whole bunch of suppressed premises in order to get. From the premise that is the Sabbath to the conclusion that you ought to go to Synagogue. Now of course all of those premises might be questionable, some people would question them, some people would deny them, but the point here is to figure out what's being assumed by somebody who gave the original argument. And anybody who says it's the Sabbath so you ought to go to Synagogue, seems to be assuming that you're Jewish, you haven't been already, and Jews ought to go to the Synagogue on the Sabbath. So what these suppressed premises do is they bring out the assumptions that somebody who gave that argument must have had in mind. The last case is a little bit trickier. It has to do with linguistics suppressed premises. Janet and Bob are first cousins, therefore they share a grandparent. Now, in order to understand that argument, we have to know that first cousins always share a grandparent. That just follows from the definition of what a first cousin is. But, it's not quite so obvious is that all biological sisters are female, and so there's even more need to bring out that linguistic suppressed premise in this case. But it's still not necessary to make the argument valid. It's just not possible that Janet and Bob. Are first cousins, and they don't share, a grand parent. Because the suppressed premise is purely linguistic, so it's necessarily true. So, you can't possibly, be first cousins without sharing a grandparent. Still, the point of bringing out linguistic suppressed premises is to show every little step along the way the argument might be valid without those suppressed linguistic premises but we won't understand why it's valid and why the reasoning goes through unless we add the linguistic suppressed premise. So it's worth doing that. Sh, here's a trick. Don't tell anybody. Okay? It's just between me and you. You could always make any argument valid just by adding a suppressed premise that says, if the premises are true then the conclusion is true. But don't tell anybody because. If people start doing that, and they make the argument valid that way, with that suppressed premise, we're never going to understand the pathway of reasoning. It makes the argument valid, but it doesn't serve the real purpose of the unending suppressed premises, which is to understand the pathway of reasoning. So you can do that, it's a trick. It makes the argument valid, but it doesn't achieve our goal because our goal is not just to make the argument valid, it's to make the argument valid so that we can understand the pathway of reasoning. So, it's important to know that trick, but don't use it. Unless you have to. The examples so far have been pretty trivial, I admit it. But the same points apply in very important context, such as political debates. Politicians can suppress premises in perfectly legitimate ways they're just trying to save time and make their arguments more efficient, maybe even sometimes clearer because you don't have to add all of those little details. But sometimes politicians abuse suppressed premises. They take things for granted that they shouldn't be taking for granted. And here's an example. A politician might argue, my opponent is soft on crime because he's opposed to the death penalty, well, that assumes as a suppressed premise that anyone who's opposed to the death penalty must be soft on crime. And if the politician were to come out and say that it would seem pretty questionable. And that's probably why he suppresses it. And then another politician might say, but my opponent is in favor of the death penalty so he must not have read all the recent studies that show that the death penalty doesn't deter. Well that argument assumes a suppressed premise that if you read those studies you would be convinced by them and that the only point of the death penalty is deterrence. But the point is that politicians talking about extremely important issues can take things for granted, that if they were brought into the light of day would be very questionable, and that is why they hide them. So when you're listening to people give arguments on important issues in your life, then you ought to be looking for these suppressed premises and asking yourself whether or not you really ought to be agreeing with them about that assumption. Finally, we've finished reconstruction. Yippee, right? Oh, no, not quite. because there's one more stage. And that stage is drawing a conclusion. Of course, if we've come up with a sound reconstruction then we know that the argument is sound, and we know that the conclusion is true, because every sound argument has a true conclusion. But if we don't come up with a sound reconstruction, then what do we say? Well we kind of ask whose fault is it. It might be the fault of the argument maybe we couldn't come up with a sound reconstruction because there just is no sound reconstruction. But maybe we didn't come up with a sound reconstruction because we just weren't imaginative enough or didn't try hard enough. Still if we try really long and hard. And charitably interpret the argument as best we can to make it look as good as we can and we still can't make it sound, then we've at least got reason to believe that the argument's not sound. Of course, that doesn't mean that the conclusion's not true because unsound arguments can still have true conclusions. But at least we know that this argument doesn't prove that the conclusion's true. And so this method of reconstruction can lead us either to the belief that the argument is sound because we found a sound reconstruction or to the conclusion that the argument's not sound. Because we tried long and hard to find a sound reconstruction and didn't. But that's still not going to show us that the conclusion of the argument is false. The point of reconstruction then is to reach a conclusion on this issue of whether the argument is sound or not. And if we try our best, and do it as well as we can, and charitably, then we can be justified in believing that the argument's sound or not.
