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Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:02.78,0:00:09.07,Default,,0000,0000,0000,,Great. We can do course analysis, we can\Nidentify the premises and conclusions, we
Dialogue: 0,0:00:09.07,0:00:14.96,Default,,0000,0000,0000,,can put them in standard form. What's\Nnext? Well, the next step is take those
Dialogue: 0,0:00:14.96,0:00:21.56,Default,,0000,0000,0000,,parts and put them in a certain order, and\Nfill in the missing gaps. We need to learn
Dialogue: 0,0:00:21.56,0:00:29.15,Default,,0000,0000,0000,,how to reconstruct arguments. Are you\Nready? Well, there are lots of ways to
Dialogue: 0,0:00:29.15,0:00:33.40,Default,,0000,0000,0000,,reconstruct. When you think about\Nconstructing a house, or a building. In
Dialogue: 0,0:00:33.40,0:00:38.19,Default,,0000,0000,0000,,order to construct a good building you've\Ngot know, what the goal is, what the
Dialogue: 0,0:00:38.19,0:00:43.35,Default,,0000,0000,0000,,standards of a good building are. The same\Nthing goes for reconstructing arguments.
Dialogue: 0,0:00:43.35,0:00:49.75,Default,,0000,0000,0000,,In order to reconstruct an argument\Nproperly, you need to know what the
Dialogue: 0,0:00:49.75,0:00:55.04,Default,,0000,0000,0000,,standards are for reconstruction. We're\Ntrying to reconstruct it so as to meet
Dialogue: 0,0:00:55.04,0:01:00.02,Default,,0000,0000,0000,,those standards. Because the goal is not\Nto reconstruct the argument in order to
Dialogue: 0,0:01:00.02,0:01:05.19,Default,,0000,0000,0000,,make it look bad. The point is going to be\Nreconstruct arguments so as to make them
Dialogue: 0,0:01:05.19,0:01:10.20,Default,,0000,0000,0000,,look good. Cuz by making your opponents\Nlook bad or silly, that doesn't do anybody
Dialogue: 0,0:01:10.20,0:01:15.21,Default,,0000,0000,0000,,any good. If you want to learn about their\Nperspective, and you want to learn from
Dialogue: 0,0:01:15.21,0:01:20.22,Default,,0000,0000,0000,,their views, then you need to reconstruct\Ntheir argument, so as to make it look as
Dialogue: 0,0:01:20.22,0:01:25.36,Default,,0000,0000,0000,,good as possible. And to do that, you need\Nto know about the standards for arguments.
Dialogue: 0,0:01:25.36,0:01:30.38,Default,,0000,0000,0000,,That is the standards that make arguments\Ngood or bad. So what we're going to do
Dialogue: 0,0:01:30.38,0:01:36.42,Default,,0000,0000,0000,,this week is we're going to look first at\Nsome standards for our arguments, validity
Dialogue: 0,0:01:36.42,0:01:41.24,Default,,0000,0000,0000,,and soundness in particular, and they\Nwe're going to use those standards to
Dialogue: 0,0:01:41.24,0:01:46.45,Default,,0000,0000,0000,,develop a method called reconstruction or\Ndeep analysis, I'll explain those terms
Dialogue: 0,0:01:46.45,0:01:51.59,Default,,0000,0000,0000,,later. And then we are going to apply that\Nmethods to a few concrete examples, in
Dialogue: 0,0:01:51.59,0:01:56.67,Default,,0000,0000,0000,,order to be able to take a passage and\Ntake those premises and conclusions and
Dialogue: 0,0:01:56.67,0:02:01.62,Default,,0000,0000,0000,,fill them out and get a full fledged\Nargument that if we've done it properly
Dialogue: 0,0:02:01.62,0:02:07.57,Default,,0000,0000,0000,,will be, be as good as it can be, and that\Nwe can learn from. That's the goal. Now,
Dialogue: 0,0:02:07.57,0:02:12.39,Default,,0000,0000,0000,,because an argument consists of premises\Nand a conclusion, and the premises are
Dialogue: 0,0:02:12.39,0:02:17.58,Default,,0000,0000,0000,,supposed to be related in the right way to\Nthe conclusion, there can be two main ways
Dialogue: 0,0:02:17.58,0:02:22.41,Default,,0000,0000,0000,,an argument can go wron g, two main vices\Nof argument, you might say. The first is
Dialogue: 0,0:02:22.41,0:02:27.11,Default,,0000,0000,0000,,there might be something wrong with the\Npremises. In particular, they might be
Dialogue: 0,0:02:27.11,0:02:32.02,Default,,0000,0000,0000,,false, or at least one of them might be\Nfalse. Second, there might be something
Dialogue: 0,0:02:32.02,0:02:37.14,Default,,0000,0000,0000,,bad about the relation between the\Npremises and the conclusion. The premises
Dialogue: 0,0:02:37.14,0:02:42.68,Default,,0000,0000,0000,,might fail to give a good reason for the\Nconclusion. Now each of these problems is
Dialogue: 0,0:02:42.68,0:02:48.28,Default,,0000,0000,0000,,something that we need to avoid and when\Nwe do avoid them, we get the corresponding
Dialogue: 0,0:02:48.28,0:02:53.94,Default,,0000,0000,0000,,virtues mainly validity and soundness. And\Nthose are the two notions that we want to
Dialogue: 0,0:02:53.94,0:02:59.27,Default,,0000,0000,0000,,discuss in this lecture and the next.\NLet's begin with the relation between the
Dialogue: 0,0:02:59.27,0:03:05.63,Default,,0000,0000,0000,,premises and the conclusion. What kind of\Nrelation between the premises and the
Dialogue: 0,0:03:05.63,0:03:10.83,Default,,0000,0000,0000,,conclusion is good for an argument or\Nmakes an argument good? Well, that
Dialogue: 0,0:03:10.83,0:03:16.46,Default,,0000,0000,0000,,depends. Some arguments are deductive and\Nothers are not. So, let's focus for a
Dialogue: 0,0:03:16.46,0:03:21.76,Default,,0000,0000,0000,,moment on deductive arguments. In\Ndeductive arguments, the conclusion is
Dialogue: 0,0:03:21.76,0:03:27.89,Default,,0000,0000,0000,,supposed to follow from the premises, but\Nwhat does that mean? I mean, what does it
Dialogue: 0,0:03:27.89,0:03:34.02,Default,,0000,0000,0000,,mean for a conclusion to follow from the\Npremises? That's a really hard notion to
Dialogue: 0,0:03:34.02,0:03:38.83,Default,,0000,0000,0000,,pin down. So what logicians usually do\Nand, and what we're going to do, is focus
Dialogue: 0,0:03:38.83,0:03:43.56,Default,,0000,0000,0000,,instead on the notion of validity. And the\Nidea is that a deductive argument is
Dialogue: 0,0:03:43.56,0:03:48.41,Default,,0000,0000,0000,,trying to structure itself so that it's\Nvalid. And we'll explain what validity is,
Dialogue: 0,0:03:48.41,0:03:52.73,Default,,0000,0000,0000,,but for now, I want to emphasize that\Nwe're only talking about deductive
Dialogue: 0,0:03:52.73,0:03:57.16,Default,,0000,0000,0000,,arguments. There's going to be another\Nclass of arguments called inductive
Dialogue: 0,0:03:57.16,0:04:02.07,Default,,0000,0000,0000,,arguments that we'll get to later in this\Ncourse, where they don't even pretend to
Dialogue: 0,0:04:02.07,0:04:07.10,Default,,0000,0000,0000,,be valid. They don't even pretend that the\Nconclusion follows from the premises. But
Dialogue: 0,0:04:07.10,0:04:12.77,Default,,0000,0000,0000,,just for simplicity, let's focus on\Ndeductive arguments now, and the idea is
Dialogue: 0,0:04:12.77,0:04:18.74,Default,,0000,0000,0000,,that the deductive argument should be\Nstructured in such a way that it's valid.
Dialogue: 0,0:04:19.18,0:04:25.78,Default,,0000,0000,0000,,Then the next question is what's validity?\NLet's start with a simple example. Suppose
Dialogue: 0,0:04:25.78,0:04:33.65,Default,,0000,0000,0000,,that you know Mary but you don't know her\Nchildren. However you do know that she has
Dialogue: 0,0:04:33.65,0:04:40.46,Default,,0000,0000,0000,,one child who is pregnant. And you also\Nknow that only daugh ters can become
Dialogue: 0,0:04:40.46,0:04:46.88,Default,,0000,0000,0000,,pregnant. So you have all that you need to\Nknow in order to draw a further
Dialogue: 0,0:04:46.88,0:04:55.18,Default,,0000,0000,0000,,conclusion, namely, Mary has at least one\Ndaughter. So here's the argument. Mary has
Dialogue: 0,0:04:55.18,0:05:02.46,Default,,0000,0000,0000,,a child who is pregnant. Only daughters\Ncan become pregnant, therefore, Mary has
Dialogue: 0,0:05:02.46,0:05:08.47,Default,,0000,0000,0000,,at least one daughter. Now, if you think\Nabout it, there's just no way, no
Dialogue: 0,0:05:08.47,0:05:15.90,Default,,0000,0000,0000,,possibility that both of those premises\Nare true and the conclusion is false. That
Dialogue: 0,0:05:15.90,0:05:22.15,Default,,0000,0000,0000,,is the feature that we're gonna call\Nvalidity. More generally, we can define
Dialogue: 0,0:05:22.15,0:05:28.83,Default,,0000,0000,0000,,validity in an argument so that an\Nargument is valid if and only if, it's not
Dialogue: 0,0:05:28.83,0:05:35.89,Default,,0000,0000,0000,,possible for the premises to be true and\Nthe conclusion false. That is, it's not
Dialogue: 0,0:05:35.89,0:05:40.94,Default,,0000,0000,0000,,possible for there to be a situation where\Nboth of those hold, that is a situation
Dialogue: 0,0:05:40.94,0:05:47.06,Default,,0000,0000,0000,,where the premises are true and the\Nconclusion is also false. Now that might
Dialogue: 0,0:05:47.06,0:05:52.57,Default,,0000,0000,0000,,strike you as a pretty simple notion. But\Nactually that little word possible is a
Dialogue: 0,0:05:52.57,0:05:57.94,Default,,0000,0000,0000,,problem. How do you tell what's possible\Nor what's not possible? Well, there's no
Dialogue: 0,0:05:57.94,0:06:03.44,Default,,0000,0000,0000,,mechanical solution to that and we'll\Nstruggle with that a little bit throughout
Dialogue: 0,0:06:03.44,0:06:08.73,Default,,0000,0000,0000,,this course. But for now, since we're\Nright at the start, let's think of it this
Dialogue: 0,0:06:08.73,0:06:13.94,Default,,0000,0000,0000,,way. Is there any way for you to tell a\Ncoherent story? Where the premises are
Dialogue: 0,0:06:13.94,0:06:19.58,Default,,0000,0000,0000,,true and the conclusion is false. Can you\Ndescribe a situation with that combination
Dialogue: 0,0:06:19.58,0:06:24.95,Default,,0000,0000,0000,,of truth values? That is, the premises\Nbeing true and the conclusion false in the
Dialogue: 0,0:06:24.95,0:06:30.33,Default,,0000,0000,0000,,same situation. If you can tell a coherent\Nstory with that combination then it's
Dialogue: 0,0:06:30.33,0:06:35.77,Default,,0000,0000,0000,,possible and the argument is not valid.\NBut if there is no way to tell a coherent
Dialogue: 0,0:06:35.77,0:06:41.08,Default,,0000,0000,0000,,story where the premises true and the\Nconclusion is false, then the argument is
Dialogue: 0,0:06:41.08,0:06:48.34,Default,,0000,0000,0000,,valid. Now let's try that test on our\Nexample. Mary has a child who is pregnant.
Dialogue: 0,0:06:48.34,0:06:56.32,Default,,0000,0000,0000,,Only daughters can be pregnant. Therefore,\NMary has a daughter. So is there any way
Dialogue: 0,0:06:56.32,0:07:02.75,Default,,0000,0000,0000,,to tell a coherent story where the two\Npremises are true? That is, where Mary has
Dialogue: 0,0:07:02.75,0:07:08.13,Default,,0000,0000,0000,,a child who is pregnant, and only\Ndaughters can be pregnant, but the
Dialogue: 0,0:07:08.13,0:07:14.63,Default,,0000,0000,0000,,conclusion is false. Mary does not have a\Ndaughter. Well, just try. Suppose Mary has
Dialogue: 0,0:07:14.63,0:07:20.52,Default,,0000,0000,0000,,only one child and i t's a son. There's\Nthe conclusion that's false. Good. What
Dialogue: 0,0:07:20.52,0:07:26.04,Default,,0000,0000,0000,,about that? But then, is that son\Npregnant? Well, if the son is not pregnant
Dialogue: 0,0:07:26.04,0:07:31.86,Default,,0000,0000,0000,,then the first premise's false. Mary\Ndoesn't have a child who is pregnant. But
Dialogue: 0,0:07:31.86,0:07:37.90,Default,,0000,0000,0000,,if the son is pregnant somehow, don't ask\Nme how, but if the son is pregnant then
Dialogue: 0,0:07:37.90,0:07:44.40,Default,,0000,0000,0000,,the second premise's not true. It can't be\Ntrue that only daughters can be pregnant
Dialogue: 0,0:07:44.40,0:07:51.57,Default,,0000,0000,0000,,because this child is a son. Okay, what if\NMary has two children? Try that. Try to
Dialogue: 0,0:07:51.57,0:07:56.98,Default,,0000,0000,0000,,tell the story that way. Mary has a\Ndaughter and a son. Now she's got a child
Dialogue: 0,0:07:56.98,0:08:02.05,Default,,0000,0000,0000,,who is pregnant, the daughter, and only\Ndaughters can be pregnant, but she has a
Dialogue: 0,0:08:02.05,0:08:07.11,Default,,0000,0000,0000,,son. Wait a minute, she's got a son and a\Ndaughter. So now the conclusion's true,
Dialogue: 0,0:08:07.11,0:08:12.51,Default,,0000,0000,0000,,because she does have a daughter even\Nthough she also has a son. Oh, oh, wait.
Dialogue: 0,0:08:12.51,0:08:21.43,Default,,0000,0000,0000,,How about this one? What if Mary has a\Nchild who is biologically female but sees
Dialogue: 0,0:08:21.43,0:08:29.66,Default,,0000,0000,0000,,himself as a male? And so she sees that\Nchild as a male, but that child is
Dialogue: 0,0:08:29.66,0:08:37.45,Default,,0000,0000,0000,,pregnant, cuz after all, they're\Nbiologically female. Now are the premises
Dialogue: 0,0:08:37.45,0:08:44.98,Default,,0000,0000,0000,,true and the conclusion false? Does that\Nstory make sense? Wait a minute. Either
Dialogue: 0,0:08:44.98,0:08:52.42,Default,,0000,0000,0000,,her child is a daughter or her child is a\Nson. Now if it's a daughter and its
Dialogue: 0,0:08:52.42,0:08:59.67,Default,,0000,0000,0000,,pregnant, no problem. The conclusion's\Ntrue. If it's a son, because that child
Dialogue: 0,0:08:59.67,0:09:05.80,Default,,0000,0000,0000,,sees himself as a male, then you've got a\Nchoice. Well, what about the first
Dialogue: 0,0:09:05.80,0:09:10.08,Default,,0000,0000,0000,,premise? The first premise is going to be\Ntrue. She does have a child, who is
Dialogue: 0,0:09:10.08,0:09:14.31,Default,,0000,0000,0000,,pregnant, but what about the second\Npremise, only daughters can be pregnant.
Dialogue: 0,0:09:14.31,0:09:19.06,Default,,0000,0000,0000,,Wait a minute. If that really is a son, if\Nwe're gonna call that a son, then it's not
Dialogue: 0,0:09:19.06,0:09:24.29,Default,,0000,0000,0000,,true that only daughters can be pregnant.\NSo now the second premise is false. So try
Dialogue: 0,0:09:24.29,0:09:30.07,Default,,0000,0000,0000,,it again. Try it with, you know, sex\Nchanges, and try it with Hermaphrodites
Dialogue: 0,0:09:30.07,0:09:36.25,Default,,0000,0000,0000,,tell the story any way you want about\NMary's children. And there's no way that
Dialogue: 0,0:09:36.25,0:09:42.74,Default,,0000,0000,0000,,both premises come out true when the\Nconclusion is false. That shows that the
Dialogue: 0,0:09:42.74,0:09:48.51,Default,,0000,0000,0000,,argument is valid. It might be just that\Nwe can't imagine the coherent story, which
Dialogue: 0,0:09:48.51,0:09:53.71,Default,,0000,0000,0000,,makes it invalid. But the fact that we've\Ntried hard and looked at all th e
Dialogue: 0,0:09:53.71,0:09:59.40,Default,,0000,0000,0000,,possibilities we can think of at least\Ngives us a good reason to think that this
Dialogue: 0,0:09:59.40,0:10:05.30,Default,,0000,0000,0000,,argument is valid. Now some people like to\Nthink of it in the reverse direction. They
Dialogue: 0,0:10:05.30,0:10:10.99,Default,,0000,0000,0000,,say, let's imagine that the conclusion is\Nfalse, and then, If it has to be the case,
Dialogue: 0,0:10:10.99,0:10:16.38,Default,,0000,0000,0000,,that at least one of the premises is\Nfalse, the argument is valid. Then you can
Dialogue: 0,0:10:16.38,0:10:22.18,Default,,0000,0000,0000,,define the validity as, is necessarily the\Ncase that if the conclusion is false one
Dialogue: 0,0:10:22.18,0:10:27.50,Default,,0000,0000,0000,,of the premises is false, or in every\Npossible situation, if the conclusion's
Dialogue: 0,0:10:27.50,0:10:32.82,Default,,0000,0000,0000,,false one of the premises is false. We can\Napply this new account of validity to the
Dialogue: 0,0:10:32.82,0:10:38.55,Default,,0000,0000,0000,,same old example. It's got to be the case\Nthat if Mary doesn't have a daughter, then
Dialogue: 0,0:10:38.55,0:10:42.98,Default,,0000,0000,0000,,she doesn't have a child who is a\Npregnant, or else there are at least some
Dialogue: 0,0:10:42.98,0:10:47.58,Default,,0000,0000,0000,,children who are pregnant who are not\Ndaughters. So notice in this case you're
Dialogue: 0,0:10:47.58,0:10:52.53,Default,,0000,0000,0000,,reasoning back from the falsehood of the\Nconclusion to at least one of the premises
Dialogue: 0,0:10:52.53,0:10:56.95,Default,,0000,0000,0000,,has to be false. whereas in the earlier\Ndefinition you were saying it's not
Dialogue: 0,0:10:56.95,0:11:01.67,Default,,0000,0000,0000,,possible in the situations where the\Npremises are true for the conclusion to be
Dialogue: 0,0:11:01.67,0:11:06.33,Default,,0000,0000,0000,,false. You can look at it either way,\Neither direction. Just pick the one that
Dialogue: 0,0:11:06.33,0:11:11.52,Default,,0000,0000,0000,,works for you and go with that definition,\Nbecause in the end, the two definitions
Dialogue: 0,0:11:11.52,0:11:16.34,Default,,0000,0000,0000,,are equivalent. It's just a matter of\Nwhat's going to help you understand which
Dialogue: 0,0:11:16.34,0:11:21.45,Default,,0000,0000,0000,,arguments are valid and which ones are\Nnot. In addition to understanding what
Dialogue: 0,0:11:21.45,0:11:27.13,Default,,0000,0000,0000,,validity is, it's also very important to\Nunderstand what validity is not. A lot of
Dialogue: 0,0:11:27.13,0:11:32.59,Default,,0000,0000,0000,,people get confused by the notion of\Nvalidity in this context, because they're
Dialogue: 0,0:11:32.59,0:11:38.27,Default,,0000,0000,0000,,thinking that to call an argument valid\Nmust be to call it good, right? You call a
Dialogue: 0,0:11:38.27,0:11:44.12,Default,,0000,0000,0000,,driver's license valid when it's good in\Nthe eyes of the law. But that's not what
Dialogue: 0,0:11:44.12,0:11:49.21,Default,,0000,0000,0000,,we're talking about here. The notion of\Nvalidity is getting used by logicians here
Dialogue: 0,0:11:49.21,0:11:54.42,Default,,0000,0000,0000,,as a technical notion and it's very, very,\Nvery important to remember that to call an
Dialogue: 0,0:11:54.42,0:11:59.77,Default,,0000,0000,0000,,argument valid is not to call it good. For\Nsome arguments, like deductive arguments
Dialogue: 0,0:11:59.77,0:12:05.54,Default,,0000,0000,0000,,the invalid might be necessary for them to\Nbe good. But it's not enough and we'll see
Dialogue: 0,0:12:05.54,0:12:11.11,Default,,0000,0000,0000,,a lot of examples of that later on. The\Nsecond point about what validity is not is
Dialogue: 0,0:12:11.11,0:12:16.34,Default,,0000,0000,0000,,that validity does not depend on whether\Nthe premises and the conclusion are
Dialogue: 0,0:12:16.34,0:12:21.78,Default,,0000,0000,0000,,actually true or false. Instead it depends\Non what's possible whether there is a
Dialogue: 0,0:12:21.78,0:12:27.89,Default,,0000,0000,0000,,certain combination, true premises and a\Nfalse conclusion, it's even possible. So,
Dialogue: 0,0:12:27.89,0:12:34.60,Default,,0000,0000,0000,,whether the premise is actually true in\Nthe actual world is not what's at issue.
Dialogue: 0,0:12:34.60,0:12:41.56,Default,,0000,0000,0000,,And we can see this, by seeing that some\Narguments with false premises can still be
Dialogue: 0,0:12:41.56,0:12:48.06,Default,,0000,0000,0000,,valid. And some arguments with true\Nconclusions can be invalid. So let's look
Dialogue: 0,0:12:48.06,0:12:54.96,Default,,0000,0000,0000,,at some examples of that. Indeed there\Nfour possibilities. Cuz remember, the
Dialogue: 0,0:12:54.96,0:13:02.88,Default,,0000,0000,0000,,conclusion could be true or false, and the\Npremises could be all true or at least one
Dialogue: 0,0:13:02.88,0:13:09.78,Default,,0000,0000,0000,,false. So we've got four possibilities.\NAnd all of those are possible except for
Dialogue: 0,0:13:09.78,0:13:14.63,Default,,0000,0000,0000,,one. The one combination that's not\Npossible for valid arguments is true
Dialogue: 0,0:13:14.63,0:13:19.68,Default,,0000,0000,0000,,premises and a false conclusion. But if\Nyou've got true premises and a true
Dialogue: 0,0:13:19.68,0:13:24.87,Default,,0000,0000,0000,,conclusion, it might be valid, it might\Nnot. If you've got false premises and a
Dialogue: 0,0:13:24.87,0:13:30.19,Default,,0000,0000,0000,,true conclusion it might be valid, it\Nmight not. If you got false premises and a
Dialogue: 0,0:13:30.19,0:13:35.62,Default,,0000,0000,0000,,false conclusion, it might be valid, it\Nmight not. So let's look at some examples
Dialogue: 0,0:13:35.62,0:13:41.22,Default,,0000,0000,0000,,each of those possibilities in order to\Nbetter understand the relation between
Dialogue: 0,0:13:41.22,0:13:46.89,Default,,0000,0000,0000,,premises and conclusion that exist when\Nthe argument is valid. It's hard to give
Dialogue: 0,0:13:46.89,0:13:51.64,Default,,0000,0000,0000,,examples with true premises or false\Nconclusion, or any these other
Dialogue: 0,0:13:51.64,0:13:56.60,Default,,0000,0000,0000,,combinations when the truth is\Ncontroversial. So we're going to have a
Dialogue: 0,0:13:56.60,0:14:02.42,Default,,0000,0000,0000,,really simple example, and we're going to\Nstart just by stipulating what the facts
Dialogue: 0,0:14:02.42,0:14:09.46,Default,,0000,0000,0000,,are. We're going to assume that all Ford\Ncars have four tires, but some Ford cards
Dialogue: 0,0:14:09.46,0:14:18.07,Default,,0000,0000,0000,,do not have four doors. We're also going\Nto assume that Henry's car is a Ford that
Dialogue: 0,0:14:18.07,0:14:25.20,Default,,0000,0000,0000,,has four doors. And Jane's car is a\NChrysler that has only two doors, not four
Dialogue: 0,0:14:25.20,0:14:30.34,Default,,0000,0000,0000,,doors. And we're just going to take those\Nfacts for granted and assume that that's
Dialogue: 0,0:14:30.34,0:14:35.04,Default,,0000,0000,0000,,the situation we're talking about, and\Nthen we can give examples of all the
Dialogue: 0,0:14:35.04,0:14:40.65,Default,,0000,0000,0000,,combinations that we discussed before.\NLet's begin with tr ue premises and a true
Dialogue: 0,0:14:40.65,0:14:46.72,Default,,0000,0000,0000,,conclusion. So, here's an example of that\Nsort. All Fords have four doors. Henry's
Dialogue: 0,0:14:46.72,0:14:52.64,Default,,0000,0000,0000,,car is a Ford, therefore, Henry's car has\Nfour doors. Is the first premise true?
Dialogue: 0,0:14:52.64,0:14:58.18,Default,,0000,0000,0000,,Yes, that's what we are assuming, that's\None of our assumptions. Is the second
Dialogue: 0,0:14:58.18,0:15:03.88,Default,,0000,0000,0000,,premise true? Yes. That's another one of\Nour assumptions. Is the conclusion true?
Dialogue: 0,0:15:03.88,0:15:09.57,Default,,0000,0000,0000,,Yes. So they're all true and now is the\Nargument valid? Is it possible that all
Dialogue: 0,0:15:09.57,0:15:15.41,Default,,0000,0000,0000,,Fords have four doors? Henry's car is a\NFord and yet it's not true that Henry's
Dialogue: 0,0:15:15.41,0:15:20.11,Default,,0000,0000,0000,,car has a four doors. I mean, just think\Nabout it. How would that happen? Well, for
Dialogue: 0,0:15:20.11,0:15:25.42,Default,,0000,0000,0000,,the conclusion to be false, it would have\Nto not have four doors. Suppose it has two
Dialogue: 0,0:15:25.42,0:15:30.55,Default,,0000,0000,0000,,doors. Well then, either it's not a Ford\Nor there's some Ford, namely Henry's Ford,
Dialogue: 0,0:15:30.55,0:15:35.48,Default,,0000,0000,0000,,that only has two doors and not four\Ndoors. So, there's just no coherent story
Dialogue: 0,0:15:35.48,0:15:40.54,Default,,0000,0000,0000,,you can tell where the premises of this\Nargument are true and the conclusion's
Dialogue: 0,0:15:40.54,0:15:45.60,Default,,0000,0000,0000,,false. Or in reverse, if you start off\Nwith the assumption that the conclusion's
Dialogue: 0,0:15:45.60,0:15:50.66,Default,,0000,0000,0000,,false. You can tell from that, that at\Nleast one of the premises has to be false
Dialogue: 0,0:15:50.66,0:15:58.47,Default,,0000,0000,0000,,as well. Nonetheless. There are other\Nexamples, where the premises are true, and
Dialogue: 0,0:15:58.47,0:16:04.41,Default,,0000,0000,0000,,the conclusion is true, but the argument\Nis not valid, instead it's invalid. Here's
Dialogue: 0,0:16:04.41,0:16:10.07,Default,,0000,0000,0000,,an example of that combination. All Ford\Ncars have four tires. Henry's car, has
Dialogue: 0,0:16:10.07,0:16:15.65,Default,,0000,0000,0000,,four tires. Therefore, Henry's car is a\NFord. Now, in this new argument, are all
Dialogue: 0,0:16:15.65,0:16:21.45,Default,,0000,0000,0000,,the premises true? Yes, the first premise\Nsays, all Ford cars have four tires. And
Dialogue: 0,0:16:21.45,0:16:27.46,Default,,0000,0000,0000,,that's true by our assumptions. Second\Npremises Henry's car has four tires and
Dialogue: 0,0:16:27.46,0:16:34.06,Default,,0000,0000,0000,,that's also true by our assumptions and is\Nthe conclusion true? Yes our assumptions
Dialogue: 0,0:16:34.06,0:16:40.73,Default,,0000,0000,0000,,also tells that Henry's car is a Ford. But\Nis it possible, is there any way to tell a
Dialogue: 0,0:16:40.73,0:16:46.69,Default,,0000,0000,0000,,coherent story where those premises are\Ntrue and the conclusion is false? Yes,
Dialogue: 0,0:16:46.69,0:16:53.39,Default,,0000,0000,0000,,absolutely. All that has to happen is that\NJane and Henry switch cars. Then the first
Dialogue: 0,0:16:53.39,0:17:00.29,Default,,0000,0000,0000,,premises can be true because all four cars\Nhave four tires, and the second premise is
Dialogue: 0,0:17:00.29,0:17:07.28,Default,,0000,0000,0000,,going to be true, because Henry's car has\Nfour times, of course now it's a Chrysler,
Dialogue: 0,0:17:06.22,0:17:12.03,Default,,0000,0000,0000,,cuz he got it from Jane, but the\Nconclusions can be false. Henry's car is
Dialogue: 0,0:17:12.03,0:17:16.49,Default,,0000,0000,0000,,not a Ford because Ford and Chrysler are\Ndifferent companies. So, if he switches
Dialogue: 0,0:17:16.49,0:17:21.12,Default,,0000,0000,0000,,cars with Jane and he has a Chrysler then\Nhe doesn't have a Ford. His car is not a
Dialogue: 0,0:17:21.12,0:17:27.47,Default,,0000,0000,0000,,Ford. Okay, so now you've got a situation\Nwhere the premises are true and conclusion
Dialogue: 0,0:17:27.47,0:17:33.25,Default,,0000,0000,0000,,false. It's not the actual situation but\Nits a possible situation. You can tell a
Dialogue: 0,0:17:33.25,0:17:39.40,Default,,0000,0000,0000,,coherent story with the premises true and\Nconclusions false and that tells you that
Dialogue: 0,0:17:39.40,0:17:44.89,Default,,0000,0000,0000,,the argument is invalid. Next, let's\Nconsider an example with false premises
Dialogue: 0,0:17:44.89,0:17:53.04,Default,,0000,0000,0000,,and a true conclusion. Premise one, all\NFords have four doors. Premise two,
Dialogue: 0,0:17:53.04,0:18:01.38,Default,,0000,0000,0000,,Henry's car is a Ford. Conclusion, Henry's\Ncar has four doors. Is the first premise
Dialogue: 0,0:18:01.38,0:18:07.85,Default,,0000,0000,0000,,true? No, it's not true that all Ford's\Nhave four doors. Our assumptions tell us
Dialogue: 0,0:18:07.85,0:18:14.10,Default,,0000,0000,0000,,that. Second, is Henry's car a Ford?\NThat's true. So one of the premises is
Dialogue: 0,0:18:14.10,0:18:20.44,Default,,0000,0000,0000,,false and the other one's true. That means\Nthey're not all true. And the conclusion,
Dialogue: 0,0:18:20.44,0:18:26.87,Default,,0000,0000,0000,,is that true? Yes, it is true that Henry's\Ncar has four doors. But remember, the fact
Dialogue: 0,0:18:26.87,0:18:32.09,Default,,0000,0000,0000,,that that's actually the case doesn't tell\Nus wether or not is valid. So, is it
Dialogue: 0,0:18:32.09,0:18:37.24,Default,,0000,0000,0000,,valid? That depends on wether it's\Npossible for the premises to be true and a
Dialogue: 0,0:18:37.24,0:18:42.97,Default,,0000,0000,0000,,conclusion false. Premises aren't actually\Ntrue, but is there a possible story that
Dialogue: 0,0:18:42.97,0:18:47.56,Default,,0000,0000,0000,,you could tell that would be coherent\Nwhere the premises are true and the
Dialogue: 0,0:18:47.56,0:18:52.34,Default,,0000,0000,0000,,conclusions false? That's the test of\Nvalidity. So let's apply it to this case.
Dialogue: 0,0:18:53.16,0:19:00.37,Default,,0000,0000,0000,,We'll just imagine, that, the conclusion's\Nfalse, that Henry's car does not have four
Dialogue: 0,0:19:00.37,0:19:06.34,Default,,0000,0000,0000,,doors. It's only got two doors. Then,\Nthere are really only two possibilities,
Dialogue: 0,0:19:06.34,0:19:12.57,Default,,0000,0000,0000,,either it's a ford or it's not a Ford. If\Nit is a Ford, then the first premise is
Dialogue: 0,0:19:12.57,0:19:18.95,Default,,0000,0000,0000,,false. It's not true that all Fords have\Nfour doors. But if Henry's car is not a
Dialogue: 0,0:19:18.95,0:19:24.15,Default,,0000,0000,0000,,Ford, then, the second premise is false,\Ncuz it says that Henry's car is a Ford.
Dialogue: 0,0:19:24.15,0:19:29.76,Default,,0000,0000,0000,,So, there's no coherent way in which it\Ncould possibly be true that both of these
Dialogue: 0,0:19:29.76,0:19:35.43,Default,,0000,0000,0000,,premises are true and the conclusion is\Nfalse so this argument's valid and not ice
Dialogue: 0,0:19:35.43,0:19:40.42,Default,,0000,0000,0000,,that, that shows that an argument can\Nvalid, even though it's got a false
Dialogue: 0,0:19:40.42,0:19:45.95,Default,,0000,0000,0000,,premise. Now, you might be thinking to\Nyourself this is crazy how can an argument
Dialogue: 0,0:19:45.95,0:19:51.28,Default,,0000,0000,0000,,be valid when one of it's premises are\Nfalse? An argument's no good when it's
Dialogue: 0,0:19:51.28,0:19:57.27,Default,,0000,0000,0000,,premises are false. Notice what that does.\NThat confuses the notion of valid. Like in
Dialogue: 0,0:19:57.27,0:20:02.63,Default,,0000,0000,0000,,a valid driver's license where to be vaild\Nis good. With the technical notion of
Dialogue: 0,0:20:02.63,0:20:07.65,Default,,0000,0000,0000,,validity that we're using here. The\Ntechnical notion of validity that we're
Dialogue: 0,0:20:07.65,0:20:12.95,Default,,0000,0000,0000,,using here has to do with the relation\Nbetween the premises and the conclusion.
Dialogue: 0,0:20:12.95,0:20:17.90,Default,,0000,0000,0000,,And in particular, it has to do with\Npossibilities, and not with the actual
Dialogue: 0,0:20:17.90,0:20:23.40,Default,,0000,0000,0000,,falsehood of the premise. So what we have\Nto ask ourselves is, what would happen if
Dialogue: 0,0:20:23.40,0:20:29.75,Default,,0000,0000,0000,,it really were true? That all Fords have\Nfour doors is not true in the actual
Dialogue: 0,0:20:29.75,0:20:35.82,Default,,0000,0000,0000,,world, but we're concerned with\Npossibility. And if all Fords did have
Dialogue: 0,0:20:35.82,0:20:43.02,Default,,0000,0000,0000,,four doors, and if Henry's car was a Ford,\Nthen it would have to have four doors. So,
Dialogue: 0,0:20:43.02,0:20:49.38,Default,,0000,0000,0000,,that possibility of the premise being\Ntrue, even though it's not, is what's
Dialogue: 0,0:20:49.38,0:20:55.39,Default,,0000,0000,0000,,crucial for determining validity. Because\Nit's not possible for the premises to be
Dialogue: 0,0:20:55.39,0:21:00.63,Default,,0000,0000,0000,,true, and the conclusion false. That makes\Nit valid in our technical sense. Even if
Dialogue: 0,0:21:00.63,0:21:06.01,Default,,0000,0000,0000,,it's not valid, in the common sense notion\Nof validity as goodness, we're not saying
Dialogue: 0,0:21:06.01,0:21:11.05,Default,,0000,0000,0000,,that the argument's a good argument. We're\Nsaying that it meets this technical
Dialogue: 0,0:21:11.05,0:21:15.97,Default,,0000,0000,0000,,definition of validity. That logicians\Nuse. Now the only combination of truth
Dialogue: 0,0:21:15.97,0:21:21.22,Default,,0000,0000,0000,,values in premise and conclusion, that you\Ncannot get with a valid argument is to
Dialogue: 0,0:21:21.22,0:21:27.02,Default,,0000,0000,0000,,have true premises, an a false conclusion.\NSo here's an example of that. Premise one,
Dialogue: 0,0:21:27.02,0:21:36.26,Default,,0000,0000,0000,,some Ford cars do not have four doors.\NPremise two, Henry's car is a Ford.
Dialogue: 0,0:21:36.68,0:21:44.33,Default,,0000,0000,0000,,Conclusion, Henry's car does not have four\Ndoors. The premises by our assumptions are
Dialogue: 0,0:21:44.33,0:21:49.81,Default,,0000,0000,0000,,both true and the conclusion is false and\Nit's not valid because it's easy to see
Dialogue: 0,0:21:49.81,0:21:55.42,Default,,0000,0000,0000,,how it might be possible for the premises\Nto be true and the conclusion false. It's
Dialogue: 0,0:21:55.42,0:22:00.49,Default,,0000,0000,0000,,simple. Even if some Ford's don't have\Nfour doors, Henry's car is one of the
Dialogue: 0,0:22:00.49,0:22:05.90,Default,,0000,0000,0000,,Ford's that does have four doors, and then\Nboth the premises can be true and the
Dialogue: 0,0:22:05.90,0:22:10.97,Default,,0000,0000,0000,,conclusions false. So that's how you can\Nget an invalid argument with true premises
Dialogue: 0,0:22:10.97,0:22:15.59,Default,,0000,0000,0000,,and a false conclusion. But you don't\Nreally even need that. Look. Every
Dialogue: 0,0:22:15.59,0:22:19.92,Default,,0000,0000,0000,,argument that has, true premises and a\Nfalse conclusion, has to be invalid.
Dialogue: 0,0:22:19.92,0:22:24.84,Default,,0000,0000,0000,,Because if it does in fact actually have\Ntrue premises and a false conclusion, then
Dialogue: 0,0:22:24.84,0:22:29.16,Default,,0000,0000,0000,,it's possible, for it to have true\Npremises and a false conclusion. So you
Dialogue: 0,0:22:29.16,0:22:34.10,Default,,0000,0000,0000,,can know right off the bat that every\Nargument with true premises and a false
Dialogue: 0,0:22:34.10,0:22:39.42,Default,,0000,0000,0000,,conclusion is invalid. What you can't know\Nis for the other combinations. Then you
Dialogue: 0,0:22:39.42,0:22:44.66,Default,,0000,0000,0000,,have to think of what is possible instead\Nof simply what is actual. So far we've
Dialogue: 0,0:22:44.66,0:22:50.04,Default,,0000,0000,0000,,only looked at arguments with all and some\Nand we've looked at Henry and Ford and
Dialogue: 0,0:22:50.04,0:22:54.70,Default,,0000,0000,0000,,Chrysler and so on. But the same points\Nare going to apply to lots of different
Dialogue: 0,0:22:54.70,0:23:01.50,Default,,0000,0000,0000,,arguments with very different forms. So\Nlets look at one example of that. Premise
Dialogue: 0,0:23:01.50,0:23:09.27,Default,,0000,0000,0000,,one, David, is either a swimmer or a\Ngolfer. Premise two, David, is a swimmer,
Dialogue: 0,0:23:09.27,0:23:16.72,Default,,0000,0000,0000,,therefore, conclusion, David is not a\Ngolfer. Okay, is it possible for the
Dialogue: 0,0:23:16.72,0:23:23.40,Default,,0000,0000,0000,,premises to be true and the conclusion\Nfalse? How could you tell a coherent story
Dialogue: 0,0:23:23.40,0:23:29.22,Default,,0000,0000,0000,,where both premises are true and the\Nconclusion is false? Just think about it.
Dialogue: 0,0:23:29.22,0:23:35.17,Default,,0000,0000,0000,,How could that happen? Oh I've got it! He\Ncould be both a swimmer and a golfer, like
Dialogue: 0,0:23:35.17,0:23:40.72,Default,,0000,0000,0000,,me. I play golf, and I also swim, and lots\Nof people do. Now of course, if you have
Dialogue: 0,0:23:40.72,0:23:46.55,Default,,0000,0000,0000,,or, and you say something like he's either\Nmale or female, maybe you can't have both.
Dialogue: 0,0:23:46.55,0:23:52.38,Default,,0000,0000,0000,,But with swimming and golfing you can just\Nbe both a swimmer and also a golfer. And
Dialogue: 0,0:23:52.38,0:23:57.72,Default,,0000,0000,0000,,then the premises can be true when the\Nconclusion is false, which shows that this
Dialogue: 0,0:23:57.72,0:24:03.99,Default,,0000,0000,0000,,argument is not valid. Now let's try this\Nother example which is a lot like the last
Dialogue: 0,0:24:03.99,0:24:09.56,Default,,0000,0000,0000,,one, but it's different in an important\Nway. Premise one, David is either a
Dialogue: 0,0:24:09.56,0:24:15.80,Default,,0000,0000,0000,,swimmer or a golfer. Premise two, David is\Nnot a swimmer, therefore conclusion, David
Dialogue: 0,0:24:15.80,0:24:21.92,Default,,0000,0000,0000,,is a golfer. Is there any way? Is it\Npossible? Is there anyway to tell a
Dialogue: 0,0:24:21.92,0:24:29.50,Default,,0000,0000,0000,,coherent story where, the premises are\Ntrue and the conclusion is false? We know.
Dialogue: 0,0:24:29.94,0:24:34.43,Default,,0000,0000,0000,,Well just think about it, the four\Npossibilities. Suppose that David is both
Dialogue: 0,0:24:34.43,0:24:39.15,Default,,0000,0000,0000,,a swimmer and also a golfer. Well then the\Nconclusion's true, right? So you can't
Dialogue: 0,0:24:39.15,0:24:43.16,Default,,0000,0000,0000,,have two premises and a false conclusion\Nbecause then in that case then the
Dialogue: 0,0:24:43.40,0:24:50.18,Default,,0000,0000,0000,,conclusion is true. Now, suppose that\NDavid is a golfer, but he's not a swimmer.
Dialogue: 0,0:24:50.18,0:24:55.66,Default,,0000,0000,0000,,Well again, the conclusion's true. So\Nthat's not a case where the premise's is
Dialogue: 0,0:24:55.66,0:25:00.14,Default,,0000,0000,0000,,true and the conclusion's false. but\Nsuppose he's not a golfer but he is a
Dialogue: 0,0:25:00.14,0:25:04.74,Default,,0000,0000,0000,,swimmer Well wait a minute. In that case\Nthe second premise is wrong, because it
Dialogue: 0,0:25:04.74,0:25:08.87,Default,,0000,0000,0000,,says, he's not a swimmer and we're, in\Nthis story, imagining that he is a
Dialogue: 0,0:25:08.87,0:25:13.24,Default,,0000,0000,0000,,swimmer. Now suppose that he's neither a\Nswimmer nor a golfer. Well then the
Dialogue: 0,0:25:13.24,0:25:17.54,Default,,0000,0000,0000,,conclusion is false, and that second\Npremise is true. But wait a minute, now
Dialogue: 0,0:25:17.54,0:25:22.26,Default,,0000,0000,0000,,the first premise is false, because the\Nfirst premise says, he either a swimmer or
Dialogue: 0,0:25:22.26,0:25:27.16,Default,,0000,0000,0000,,a golfer. In this story it's saying that\Nhe's neither. So, those are the four
Dialogue: 0,0:25:27.16,0:25:32.15,Default,,0000,0000,0000,,possibilities and there's none of them\Nwhere the premises are true and the
Dialogue: 0,0:25:32.15,0:25:36.87,Default,,0000,0000,0000,,conclusions false. So it's not possible\Nfor the premises to be true and
Dialogue: 0,0:25:36.87,0:25:42.78,Default,,0000,0000,0000,,conclusions to be false in this case, so\Nthis argument is valid. And did you notice
Dialogue: 0,0:25:42.78,0:25:48.09,Default,,0000,0000,0000,,something? I didn't make assumptions like\Nin Henry, and the Ford, and the Chrysler,
Dialogue: 0,0:25:48.09,0:25:53.59,Default,,0000,0000,0000,,cuz we don't need to know whether David\Nreally is a swimmer or a golfer. We don't
Dialogue: 0,0:25:53.59,0:25:59.10,Default,,0000,0000,0000,,need to know the actual facts of the world\Nat all. We could tell that this argument
Dialogue: 0,0:25:59.10,0:26:04.38,Default,,0000,0000,0000,,is valid without knowing what kinds of\Nsports David does. And that shows you that
Dialogue: 0,0:26:04.38,0:26:09.17,Default,,0000,0000,0000,,whether an argument is valid or not\Ndepends on what's possible, not on what's
Dialogue: 0,0:26:09.17,0:26:13.72,Default,,0000,0000,0000,,actual. Cuz you can know that the\Nargument's valid, even if you don't know
Dialogue: 0,0:26:13.72,0:26:18.90,Default,,0000,0000,0000,,whether in the actual world he's a swimmer\Nor golfer or neither or both or one but
Dialogue: 0,0:26:18.90,0:26:23.87,Default,,0000,0000,0000,,not the other. We haven't been through all\Nof the possibilities, but we have seen
Dialogue: 0,0:26:23.87,0:26:28.84,Default,,0000,0000,0000,,that you can have invalid arguments with\Ntrue premises and true conclusions, and
Dialogue: 0,0:26:28.84,0:26:34.05,Default,,0000,0000,0000,,you can have valid arguments with false\Npremises and true conclusions, and we've
Dialogue: 0,0:26:34.05,0:26:37.85,Default,,0000,0000,0000,,got a little table that shows us the other\Nposs ibilities.
Dialogue: 0,0:26:37.86,0:26:43.07,Default,,0000,0000,0000,,Instead of going through all of those\Nother possibilities myself, I think it'd
Dialogue: 0,0:26:43.07,0:26:48.28,Default,,0000,0000,0000,,be better, if. You did a few exercises,\Nand that'll, make sure that you understand
Dialogue: 0,0:26:48.28,0:26:53.83,Default,,0000,0000,0000,,this notion of validity before we go on\Nand try to show how validity is related to