[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:04.64,0:00:11.45,Default,,0000,0000,0000,,In the last lecture, I said that, we were\Ngoing to spend this unit learning the
Dialogue: 0,0:00:11.45,0:00:18.15,Default,,0000,0000,0000,,rules for evaluating deductive arguments.\NNow this week, we're gonna learn the rules
Dialogue: 0,0:00:18.15,0:00:24.25,Default,,0000,0000,0000,,for evaluating deductive arguments that\Ninvolve, what I'm gonna call propositional
Dialogue: 0,0:00:24.25,0:00:30.82,Default,,0000,0000,0000,,connectives. Now, what are propositional\Nconnectives? Well, in order to explain
Dialogue: 0,0:00:30.82,0:00:36.98,Default,,0000,0000,0000,,what propositional connectives are. I\Nfirst have to tell you what propositions
Dialogue: 0,0:00:36.98,0:00:42.74,Default,,0000,0000,0000,,are and then I can talk about connectives.\NSo first, propositions. What's a
Dialogue: 0,0:00:42.74,0:00:49.14,Default,,0000,0000,0000,,proposition? A proposition, is the kind of\Nthing that can be true, or false and that
Dialogue: 0,0:00:49.14,0:00:54.74,Default,,0000,0000,0000,,can serve as the premise, or the\Nconclusion of an argument. Here let me
Dialogue: 0,0:00:54.74,0:01:07.24,Default,,0000,0000,0000,,give you an example. See this book this\Nbook is not a proposition. It can't be
Dialogue: 0,0:01:07.24,0:01:13.42,Default,,0000,0000,0000,,true or false, and it can't serve as the\Npremise or the conclusion of an argument.
Dialogue: 0,0:01:13.70,0:01:21.71,Default,,0000,0000,0000,,See this hand, this hand is not a\Nproposition it can be true or false, and
Dialogue: 0,0:01:21.71,0:01:30.04,Default,,0000,0000,0000,,it can serve as the premise or the\Nconclusion of a argument. But now suppose
Dialogue: 0,0:01:30.04,0:01:40.56,Default,,0000,0000,0000,,I say, the book is in my hand. Now what I\Njust said, that the book is in my hand is
Dialogue: 0,0:01:40.56,0:01:47.72,Default,,0000,0000,0000,,a proposition, it can be true in fact, it\Nis true, or it can be false and right now
Dialogue: 0,0:01:47.72,0:01:54.45,Default,,0000,0000,0000,,it is false. It can also serve as the\Npremise of an argument. I could say, the
Dialogue: 0,0:01:54.45,0:02:01.26,Default,,0000,0000,0000,,book is in my hand, therefore, my hand is\Nnot free to shake yours. And it could
Dialogue: 0,0:02:01.26,0:02:08.60,Default,,0000,0000,0000,,serve as the conclusion of an argument. I\Ncould say, you just gave me the book and I
Dialogue: 0,0:02:08.60,0:02:15.03,Default,,0000,0000,0000,,haven't let go of it, therefore, the book\Nis in my hand. I just told you what
Dialogue: 0,0:02:15.03,0:02:20.61,Default,,0000,0000,0000,,propositions are. But what's a\Npropositional connective? A propositional
Dialogue: 0,0:02:20.61,0:02:26.50,Default,,0000,0000,0000,,connective is something that takes\Npropositions and makes new propositions
Dialogue: 0,0:02:26.50,0:02:32.63,Default,,0000,0000,0000,,out of it. Let me give you an example to\Nillustrate. Consider a proposition, the
Dialogue: 0,0:02:32.63,0:02:39.99,Default,,0000,0000,0000,,book is under my hand. Now consider the\Nproposition, my foot is under the book. We
Dialogue: 0,0:02:39.99,0:02:47.47,Default,,0000,0000,0000,,can combine those two propositions using\Nthe propositional connective end to make
Dialogue: 0,0:02:47.47,0:02:55.06,Default,,0000,0000,0000,,the new proposition. The book is under my\Nhand, and by foot is under the book. Now
Dialogue: 0,0:02:55.06,0:03:00.73,Default,,0000,0000,0000,,what I've just said that the book is under\Nmy hand and my foot is under the book,
Dialogue: 0,0:03:00.73,0:03:06.05,Default,,0000,0000,0000,,that's a proposition. It's the kind of\Nthing that could be true or false. For
Dialogue: 0,0:03:06.05,0:03:11.37,Default,,0000,0000,0000,,instance, right now it's true and right\Nnow it's false. It's also the kind of
Dialogue: 0,0:03:11.37,0:03:16.48,Default,,0000,0000,0000,,thing that can be premise or the\Nconclusion of the argument. For instance,
Dialogue: 0,0:03:16.48,0:03:22.08,Default,,0000,0000,0000,,I could say, what you're seeing right now\Nis really happening, therefore, the book
Dialogue: 0,0:03:22.08,0:03:29.28,Default,,0000,0000,0000,,is under my hand and my foot is under the\Nbook. Or I could say, the book is under my
Dialogue: 0,0:03:29.28,0:03:37.70,Default,,0000,0000,0000,,hand, and my foot is under the book.\NTherefore, my foot is under my hand. So
Dialogue: 0,0:03:37.42,0:03:41.46,Default,,0000,0000,0000,,you see that the book is under my hand,\Nand my foot is under the book. That's the
Dialogue: 0,0:03:41.46,0:03:46.02,Default,,0000,0000,0000,,kinda thing that can be true or false and\Nit's the kind of thing that can be the
Dialogue: 0,0:03:46.02,0:03:51.30,Default,,0000,0000,0000,,premise, or the conclusion of an argument.\NSo it's a proposition, but it's a
Dialogue: 0,0:03:51.30,0:03:58.16,Default,,0000,0000,0000,,proposition that we made by combining two\Nother propositions. See how propositional
Dialogue: 0,0:03:58.16,0:04:04.74,Default,,0000,0000,0000,,connectives work? They're beautiful,\Naren't they? I just gave you an example of
Dialogue: 0,0:04:04.74,0:04:10.86,Default,,0000,0000,0000,,a propositional connective. I called it\Nthe proposition connective and. But in
Dialogue: 0,0:04:10.86,0:04:16.98,Default,,0000,0000,0000,,English, the word and can be used in\Ndifferent ways. It's not always used as a
Dialogue: 0,0:04:16.98,0:04:23.42,Default,,0000,0000,0000,,proposition connective. Let me give you\Ndifferent examples of how and can be used.
Dialogue: 0,0:04:23.42,0:04:29.74,Default,,0000,0000,0000,,Think about the sentence, Jack and Jill\Nfinally talked. Okay now, there are three
Dialogue: 0,0:04:29.74,0:04:36.32,Default,,0000,0000,0000,,different ways to understand what that\Nsentence is saying. Jack and Jill could be
Dialogue: 0,0:04:36.32,0:04:42.74,Default,,0000,0000,0000,,the name of a fast food company that\Nserves a special stew that's very popular
Dialogue: 0,0:04:42.74,0:04:49.48,Default,,0000,0000,0000,,with its patrons. Now, maybe lawyers have\Nbeen wondering what the ingredients are in
Dialogue: 0,0:04:49.48,0:04:55.90,Default,,0000,0000,0000,,Jack and Jill's special stew because many\Nof Jack and Jill's patrons have been
Dialogue: 0,0:04:55.90,0:05:02.25,Default,,0000,0000,0000,,coming down with an unusual disease. So,\Nlawyers have been asking Jack and Jill to
Dialogue: 0,0:05:02.25,0:05:07.97,Default,,0000,0000,0000,,disclose what's in their stew. Jack and\NJill has been refusing to do so. But
Dialogue: 0,0:05:07.97,0:05:13.99,Default,,0000,0000,0000,,finally, the spokesman for Jack and Jill\Ndiscloses what's in their stew. I might
Dialogue: 0,0:05:13.99,0:05:20.01,Default,,0000,0000,0000,,tell you about that situation by saying\NJack and Jill finally talked. There, I'm
Dialogue: 0,0:05:20.01,0:05:26.19,Default,,0000,0000,0000,,telling you there's a particular company,\Na company called Jack and Jill, and that
Dialogue: 0,0:05:26.19,0:05:32.72,Default,,0000,0000,0000,,company finally talked through their\Nspokesperson. Here's a second way to
Dialogue: 0,0:05:32.72,0:05:38.16,Default,,0000,0000,0000,,understand the sentence, Jack and Jill\Nfinally talked. Suppose that Jack and Jill
Dialogue: 0,0:05:38.16,0:05:43.52,Default,,0000,0000,0000,,ar e a couple, and recently they've been\Ngoing through a tough time. They've been
Dialogue: 0,0:05:43.52,0:05:49.02,Default,,0000,0000,0000,,angry and resentful towards each other.\NAnd they haven't talked about what's been
Dialogue: 0,0:05:49.02,0:05:54.53,Default,,0000,0000,0000,,bothering them. Now, I might tell you,\NJack and Jill finally talked. And what I
Dialogue: 0,0:05:54.53,0:06:00.65,Default,,0000,0000,0000,,mean by that is, that they finally talked\Nto each other about what's bothering them.
Dialogue: 0,0:06:00.65,0:06:07.38,Default,,0000,0000,0000,,Now that's different, from the first\Nexample in which I said, Jack and Jill
Dialogue: 0,0:06:07.38,0:06:14.55,Default,,0000,0000,0000,,finally talked. There, I was saying that a\Nparticular thing the company, Jack and
Dialogue: 0,0:06:14.55,0:06:21.69,Default,,0000,0000,0000,,Jill. Finally talked about the ingredients\Nin its special stew. But in this second
Dialogue: 0,0:06:21.69,0:06:27.78,Default,,0000,0000,0000,,example, I'm saying that two things, Jack\Nand Jill finally talked to each other. Let
Dialogue: 0,0:06:27.78,0:06:33.72,Default,,0000,0000,0000,,me give you a third way to understand the\Nsentence Jack and Jill finally talked.
Dialogue: 0,0:06:33.72,0:06:39.59,Default,,0000,0000,0000,,Imagine that Jack, Jill, and Roger are\Nhaving a silence contest. They're having a
Dialogue: 0,0:06:39.59,0:06:45.61,Default,,0000,0000,0000,,contest to see who can go for the longest\Nperiod of time without talking. And I'm
Dialogue: 0,0:06:45.61,0:06:53.13,Default,,0000,0000,0000,,watching them to see who wins. Well, you\Ncall be periodically and ask me as anyone
Dialogue: 0,0:06:53.13,0:06:59.62,Default,,0000,0000,0000,,of them talked? And for the first few\Nhours I might say to you nope, none of
Dialogue: 0,0:06:59.62,0:07:07.39,Default,,0000,0000,0000,,them has talked yet. And then at one point\Nyou call me and you ask me, has anyone of
Dialogue: 0,0:07:07.39,0:07:14.55,Default,,0000,0000,0000,,them talked? And I say well Jack and Jill\Nfinally talked. Now here I'm not saying
Dialogue: 0,0:07:14.55,0:07:23.37,Default,,0000,0000,0000,,that Jack or Jill talked to each other.\NI'm saying that Jack finally talked, and
Dialogue: 0,0:07:23.37,0:07:32.71,Default,,0000,0000,0000,,Jill finally talked. So, when I say Jack\Nand Jill finally talked. I'm expressing a
Dialogue: 0,0:07:32.71,0:07:40.40,Default,,0000,0000,0000,,proposition that's made up of two other\Npropositions. The proposition that Jack
Dialogue: 0,0:07:40.40,0:07:48.17,Default,,0000,0000,0000,,finally talked, and the proposition that\NJill finally talked. When I say Jack and
Dialogue: 0,0:07:48.17,0:07:55.45,Default,,0000,0000,0000,,Jill finally talked, I'm using the word\Nand, as a propositional connective. It
Dialogue: 0,0:07:55.45,0:08:02.09,Default,,0000,0000,0000,,takes two propositions. First, that Jack\Nfinally talked, adn second that Jill
Dialogue: 0,0:08:02.09,0:08:09.15,Default,,0000,0000,0000,,finally talked. And it combines those two\Npropositions into a third proposition. The
Dialogue: 0,0:08:09.15,0:08:14.80,Default,,0000,0000,0000,,proposition that, Jack and Jill. Finally\Ntalked. Now that's a third way to
Dialogue: 0,0:08:14.80,0:08:20.20,Default,,0000,0000,0000,,understand the sentence Jack and Jill\Nfinally talked and it's different from the
Dialogue: 0,0:08:20.20,0:08:25.47,Default,,0000,0000,0000,,first two. But that's the only way of\Nunderstanding the word and, so that it's a
Dialogue: 0,0:08:25.47,0:08:30.27,Default,,0000,0000,0000,,propositional conn ective in that\Nsentence. So I've just explained to you
Dialogue: 0,0:08:30.27,0:08:35.34,Default,,0000,0000,0000,,what propositional connectives are. I gave\Nyou an example of a propositional
Dialogue: 0,0:08:35.34,0:08:40.54,Default,,0000,0000,0000,,connective and, and I showed how the\NEnglish word and, can sometimes be used as
Dialogue: 0,0:08:40.54,0:08:46.18,Default,,0000,0000,0000,,a propositional connective but sometimes\Nnot. Now the English language like every
Dialogue: 0,0:08:46.18,0:08:52.33,Default,,0000,0000,0000,,other natural language, contains lots and\Nlots of different phrases that can be used
Dialogue: 0,0:08:52.33,0:08:57.60,Default,,0000,0000,0000,,as propositional connectives. For\Ninstance, consider the phrase, I believe
Dialogue: 0,0:08:57.60,0:09:03.87,Default,,0000,0000,0000,,that. You tell me Jack and Jill finally\Ntalked. Well, I might say I believe that
Dialogue: 0,0:09:03.87,0:09:10.01,Default,,0000,0000,0000,,Jack and Jill finally talked. There, I'm\Ntaking one proposition Jack and Jill
Dialogue: 0,0:09:10.01,0:09:16.23,Default,,0000,0000,0000,,finally talked, and attaching the phrase\Nto it, I believe that to make another
Dialogue: 0,0:09:16.23,0:09:22.61,Default,,0000,0000,0000,,proposition namely, I believe that Jack\Nand Jill finally talked. Or consider the
Dialogue: 0,0:09:22.61,0:09:28.96,Default,,0000,0000,0000,,phrase, I hate it when. You might tell me,\Nit's raining, and I might say, I hate it
Dialogue: 0,0:09:28.96,0:09:35.31,Default,,0000,0000,0000,,when it's raining. See there, I take the\Nproposition it's raining, and I attach a
Dialogue: 0,0:09:35.31,0:09:41.42,Default,,0000,0000,0000,,phrase to it, I hate it when, to make\Nanother proposition, I hate it when it's
Dialogue: 0,0:09:41.42,0:09:47.48,Default,,0000,0000,0000,,raining. So these are other examples of\Nhow phrases in English, I believe that, or
Dialogue: 0,0:09:47.48,0:09:52.75,Default,,0000,0000,0000,,I hate it when, can be used as\Npropositional connectives. They can take
Dialogue: 0,0:09:52.75,0:09:58.23,Default,,0000,0000,0000,,other propositions and make new\Npropositions out of them. But and is a
Dialogue: 0,0:09:58.23,0:10:03.70,Default,,0000,0000,0000,,very different kind of propositional\Nconnective from I believe that or I hate
Dialogue: 0,0:10:03.70,0:10:09.38,Default,,0000,0000,0000,,it when. And it's different in two ways.\NOne way it's different is that it makes a
Dialogue: 0,0:10:09.38,0:10:13.94,Default,,0000,0000,0000,,new proposition out of two other\Npropositions, not just one other
Dialogue: 0,0:10:13.94,0:10:19.42,Default,,0000,0000,0000,,proposition. So when you make a new\Nproposition by attaching I hate it when to
Dialogue: 0,0:10:19.42,0:10:24.89,Default,,0000,0000,0000,,another proposition, what you're doing is\Nturning one proposition into another
Dialogue: 0,0:10:24.89,0:10:30.08,Default,,0000,0000,0000,,proposition. But when you make a new\Nproposition by combining two other
Dialogue: 0,0:10:30.08,0:10:36.06,Default,,0000,0000,0000,,propositions using the word and, you're\Nmaking a new proposition out of two other
Dialogue: 0,0:10:36.06,0:10:41.53,Default,,0000,0000,0000,,propositions. Jack finally talked, and\NJill finally talked. You make the new
Dialogue: 0,0:10:41.53,0:10:47.66,Default,,0000,0000,0000,,proposition, Jack and Jill finally talked.\NThat's one way in which the propositional
Dialogue: 0,0:10:47.66,0:10:53.34,Default,,0000,0000,0000,,connective and is different from the\Npropositional connective, I hate it when.
Dialogue: 0,0:10:53.88,0:10:59.30,Default,,0000,0000,0000,,But there's a second wa y, in which the\Npropositional connective, and, differs
Dialogue: 0,0:10:59.30,0:11:04.100,Default,,0000,0000,0000,,from the propositional connective, I hate\Nit when. And that is, that when you use
Dialogue: 0,0:11:04.100,0:11:10.63,Default,,0000,0000,0000,,the propositional connective and, to\Ncombine two other propositions into a new
Dialogue: 0,0:11:10.63,0:11:16.62,Default,,0000,0000,0000,,proposition. Whether that proposition is\Ntrue or false doesn't depend upon anything
Dialogue: 0,0:11:16.62,0:11:22.04,Default,,0000,0000,0000,,other than whether the two original\Npropositions that you used to build it
Dialogue: 0,0:11:22.04,0:11:28.71,Default,,0000,0000,0000,,were true or false, that's all it depends\Nupon. Let me illustrate this point using
Dialogue: 0,0:11:28.71,0:11:35.36,Default,,0000,0000,0000,,something we call a truth table. A truth\Ntable is a way of representing various
Dialogue: 0,0:11:35.36,0:11:42.35,Default,,0000,0000,0000,,possible situations, and how the truth of\Na proposition depends upon which of those
Dialogue: 0,0:11:42.35,0:11:49.09,Default,,0000,0000,0000,,various possible situations is real. For\Ninstance, consider the two possibilities
Dialogue: 0,0:11:49.09,0:11:55.83,Default,,0000,0000,0000,,there are with Jack finally talked. The\Nproposition Jack finally taught, could be
Dialogue: 0,0:11:55.83,0:12:01.91,Default,,0000,0000,0000,,true. Or it could be false. The\Nproposition Jill finally talked could be
Dialogue: 0,0:12:01.91,0:12:08.50,Default,,0000,0000,0000,,true or it could be false. So, there are\Nfour possibilities we have to consider.
Dialogue: 0,0:12:08.50,0:12:14.86,Default,,0000,0000,0000,,Either Jack finally talked is true and\NJill finally talked is true. Or Jack
Dialogue: 0,0:12:14.86,0:12:21.81,Default,,0000,0000,0000,,finally talked is true and Jill finally\Ntalked is false. Or Jack finally talked is
Dialogue: 0,0:12:21.81,0:12:28.76,Default,,0000,0000,0000,,false and Jill finally talked is true. Or\Nfinally, Jack finally talked is false and
Dialogue: 0,0:12:28.76,0:12:35.33,Default,,0000,0000,0000,,Jill finally talked is false. Those are\Nthe four possible situations. Now, if the
Dialogue: 0,0:12:35.33,0:12:40.91,Default,,0000,0000,0000,,first of those four situations is the real\Nsituation, so it's true that Jack finally
Dialogue: 0,0:12:40.91,0:12:45.82,Default,,0000,0000,0000,,talked and it's true that Jill finally\Ntalked, then is it going to be true or
Dialogue: 0,0:12:45.82,0:12:52.78,Default,,0000,0000,0000,,false that Jack and Jill finally talked?\NIt's going to be true. All right, cuz Jack
Dialogue: 0,0:12:52.78,0:13:00.37,Default,,0000,0000,0000,,finally talked, and Jill finally talked,\Nso Jack and Jill finally talked. Now
Dialogue: 0,0:13:00.37,0:13:05.90,Default,,0000,0000,0000,,suppose it's true that Jack finally\Ntalked, but it's false that Jill finally
Dialogue: 0,0:13:05.90,0:13:11.35,Default,,0000,0000,0000,,talked. Then is it going to be true or\Nfalse that Jack and Jill finally talked?
Dialogue: 0,0:13:11.35,0:13:18.15,Default,,0000,0000,0000,,It'll be false, and suppose it's false\Nthat Jack finally talked, but it's true
Dialogue: 0,0:13:18.15,0:13:23.84,Default,,0000,0000,0000,,that Jill finally talked. Then, is it\Ngoing to be true or false that Jack and
Dialogue: 0,0:13:23.84,0:13:29.81,Default,,0000,0000,0000,,Jill finally talked, again it's going to\Nbe false. And finally, suppose it's false
Dialogue: 0,0:13:29.81,0:13:35.22,Default,,0000,0000,0000,,that Jack finally talked and it's also\Nfalse that Jill final ly talked. Then is
Dialogue: 0,0:13:35.22,0:13:40.13,Default,,0000,0000,0000,,it going to be true or false that Jack and\NJill finally talked? Well obviously in
Dialogue: 0,0:13:40.13,0:13:45.68,Default,,0000,0000,0000,,that situation, it's going to be false\Nthat Jack and Jill finally talked. So what
Dialogue: 0,0:13:45.68,0:13:52.84,Default,,0000,0000,0000,,this truth table demonstrates is that the\Ntruth of the proposition Jack and Jill
Dialogue: 0,0:13:52.84,0:13:58.52,Default,,0000,0000,0000,,finally talked. Just depends, it depends\Non nothing other than the truth of the
Dialogue: 0,0:13:58.52,0:14:03.84,Default,,0000,0000,0000,,proposition Jack finally talked, and the\Ntruth of the proposition Jill finally
Dialogue: 0,0:14:03.84,0:14:08.67,Default,,0000,0000,0000,,talked. In other words, the truth of the\Nproposition that we've use the
Dialogue: 0,0:14:08.67,0:14:14.20,Default,,0000,0000,0000,,propositional connective and to build.\NDepends on nothing other than the truth of
Dialogue: 0,0:14:14.20,0:14:19.50,Default,,0000,0000,0000,,the two ingredient propositions that we\Nconnected by means of the propositional
Dialogue: 0,0:14:19.50,0:14:24.92,Default,,0000,0000,0000,,connective and. Because the propositional\Nconnective and, works that way because it
Dialogue: 0,0:14:24.92,0:14:30.14,Default,,0000,0000,0000,,builds new propositions whose truth\Ndepends on nothing other than the truth of
Dialogue: 0,0:14:30.14,0:14:35.57,Default,,0000,0000,0000,,the ingredient propositions that go into\Nbuilding them. That kind of propositional
Dialogue: 0,0:14:35.57,0:14:41.11,Default,,0000,0000,0000,,connective is one that we're going to call\Na truth functional connective. Now and,
Dialogue: 0,0:14:41.11,0:14:47.26,Default,,0000,0000,0000,,the propositional connective and, is a\Ntruth-functional connective. But not all
Dialogue: 0,0:14:47.26,0:14:52.23,Default,,0000,0000,0000,,propositional connectives are\Ntruth-functional connectives. For
Dialogue: 0,0:14:52.23,0:14:58.06,Default,,0000,0000,0000,,instance, suppose we try to construct a\Ntruth table for I hate it when, the
Dialogue: 0,0:14:58.06,0:15:04.73,Default,,0000,0000,0000,,propositional connective I hate it when.\NWell, so consider the proposition, it's
Dialogue: 0,0:15:04.73,0:15:11.36,Default,,0000,0000,0000,,raining. Now that proposition could be\Ntrue or it could be false. Sometimes its
Dialogue: 0,0:15:11.36,0:15:17.75,Default,,0000,0000,0000,,true, sometimes its false. So lets\Nconsider these two possible situations. So
Dialogue: 0,0:15:17.75,0:15:24.56,Default,,0000,0000,0000,,suppose the proposition Its raining is\Ntrue. In that situation is it going to be
Dialogue: 0,0:15:24.56,0:15:31.80,Default,,0000,0000,0000,,true or false that I hated when its\Nraining. Could be either one, it could be
Dialogue: 0,0:15:31.80,0:15:38.77,Default,,0000,0000,0000,,raining even though I enjoyed the rain or\Nit could be raining even though I hate the
Dialogue: 0,0:15:38.77,0:15:45.04,Default,,0000,0000,0000,,rain. Or it could be raining even though\NI'm indifferent to the rain. So the truth,
Dialogue: 0,0:15:45.04,0:15:53.60,Default,,0000,0000,0000,,of I hate it when it's raining isn't\Ndetermined by its raining. So, if it's
Dialogue: 0,0:15:53.60,0:16:00.01,Default,,0000,0000,0000,,true that it's raining. It's unclear\Nwhether, I hate it when it's raining.
Dialogue: 0,0:16:00.01,0:16:06.47,Default,,0000,0000,0000,,Could be true, could be false. Suppose\Nit's false, that it's raining. Then, is it
Dialogue: 0,0:16:06.47,0:16:12.33,Default,,0000,0000,0000,,going to be true or false that I hate it\Nwhen it's raining. Again, could be either
Dialogue: 0,0:16:12.33,0:16:18.26,Default,,0000,0000,0000,,one. The truth of I hate it when it's\Nraining isn't determined by the falsehood
Dialogue: 0,0:16:18.26,0:16:23.90,Default,,0000,0000,0000,,of it's raining. So, even if it's not\Nraining, that doesn't mean anything one
Dialogue: 0,0:16:23.90,0:16:29.84,Default,,0000,0000,0000,,way or the other for whether I hate it\Nwhen it's raining. So once again, if it's
Dialogue: 0,0:16:29.84,0:16:37.38,Default,,0000,0000,0000,,false that it's raining, I hate it when\Nit's raining, could be true or could be
Dialogue: 0,0:16:37.38,0:16:44.21,Default,,0000,0000,0000,,false. So the proposition, I hated when\Nit's raining. Whether that proposition is
Dialogue: 0,0:16:44.21,0:16:51.39,Default,,0000,0000,0000,,true or false doesn't just depend on the\Ntruth or the falsehood of the proposition
Dialogue: 0,0:16:51.39,0:16:57.96,Default,,0000,0000,0000,,it's raining, that you built this\Nproposition out of using the propositional
Dialogue: 0,0:16:57.96,0:17:04.69,Default,,0000,0000,0000,,connective, I hate it when. Because of\Nthat, the propositional connective I hate
Dialogue: 0,0:17:04.69,0:17:10.30,Default,,0000,0000,0000,,it when is not a truth-functional\Nconnective. It's different from the
Dialogue: 0,0:17:10.30,0:17:16.89,Default,,0000,0000,0000,,propositional connective and which is a\Ntruth-functional connective. A moment ago,
Dialogue: 0,0:17:16.89,0:17:23.48,Default,,0000,0000,0000,,we built a truth table for a proposition\Nthat was built using a truth-functional
Dialogue: 0,0:17:23.48,0:17:29.01,Default,,0000,0000,0000,,connective, specifically the\Ntruth-functional connective and. But I'd
Dialogue: 0,0:17:29.01,0:17:35.58,Default,,0000,0000,0000,,like us to notice something about that\Ntruth table. Notice that if we replace the
Dialogue: 0,0:17:35.58,0:17:40.63,Default,,0000,0000,0000,,particular propositions that we are\Nputting together using the
Dialogue: 0,0:17:40.63,0:17:47.21,Default,,0000,0000,0000,,truth-functional connective and, to make a\Ndifferent resultant proposition. Even if
Dialogue: 0,0:17:47.21,0:17:53.62,Default,,0000,0000,0000,,we change the ingredient propositions the\Ntruth table looks the same. Let me show
Dialogue: 0,0:17:53.62,0:17:59.76,Default,,0000,0000,0000,,you what I mean. Suppose instead of having\NJack and Jill finally talked. We have Jack
Dialogue: 0,0:17:59.76,0:18:05.39,Default,,0000,0000,0000,,finally walked and Jill finally talked. So\Nnow, we're connecting two different
Dialogue: 0,0:18:05.39,0:18:10.94,Default,,0000,0000,0000,,propositions using the truth-functional\Nconnective and. There's Jack finally
Dialogue: 0,0:18:10.94,0:18:16.86,Default,,0000,0000,0000,,walked, there's Jill finally talked. And\Nthen we connect them up into Jack finally
Dialogue: 0,0:18:16.86,0:18:22.71,Default,,0000,0000,0000,,walked and Jill finally talked. Okay, now\Nthe truth of that resultant proposition,
Dialogue: 0,0:18:22.71,0:18:28.26,Default,,0000,0000,0000,,Jack finally walked and Jill finally\Ntalked. How does that depend on the truth
Dialogue: 0,0:18:28.26,0:18:32.94,Default,,0000,0000,0000,,or false sort of the ingredient\Npropositions?Jack Jack finally walked and
Dialogue: 0,0:18:32.94,0:18:38.63,Default,,0000,0000,0000,,Jill finally talked. Well it's the same\Npatent we saw earlier. If it's true that
Dialogue: 0,0:18:38.63,0:18:44.52,Default,,0000,0000,0000,,Jack finally walked, and it's also true\Nthat Jill finally talked. and it's also
Dialogue: 0,0:18:44.52,0:18:49.39,Default,,0000,0000,0000,,true that Jill finally tal ked.\NThen it's going to be true that Jack
Dialogue: 0,0:18:49.39,0:18:55.01,Default,,0000,0000,0000,,finally walked and Jill finally talked. If\Nit's true that Jack finally walked, but
Dialogue: 0,0:18:55.01,0:19:00.23,Default,,0000,0000,0000,,it's false that Jill finally talked, then\Nit's going to be false that Jack finally
Dialogue: 0,0:19:00.23,0:19:05.45,Default,,0000,0000,0000,,walked and Jill finally talked. If it's\Nfalse that Jack finally walked but it's
Dialogue: 0,0:19:05.45,0:19:10.74,Default,,0000,0000,0000,,true that Jill finally talked, then it's\Ngoing to be false that Jack finally walked
Dialogue: 0,0:19:10.74,0:19:16.16,Default,,0000,0000,0000,,and Jill finally talked. And if it's false\Nthat Jack finally walked and it's false
Dialogue: 0,0:19:16.16,0:19:21.38,Default,,0000,0000,0000,,that Jill finally talked, then it's going\Nto be false that Jack finally walked and
Dialogue: 0,0:19:21.38,0:19:28.18,Default,,0000,0000,0000,,Jill finally talked. So even if we change\None of the ingredient propositions as long
Dialogue: 0,0:19:28.18,0:19:33.88,Default,,0000,0000,0000,,as we're combining propositions using the\Ntruth functional connective and, the
Dialogue: 0,0:19:33.88,0:19:41.61,Default,,0000,0000,0000,,overall truth table looks the same. We\Ncould change them some more to illustrate
Dialogue: 0,0:19:41.61,0:19:47.52,Default,,0000,0000,0000,,this point. I suppose if we changed Jill\Nfinally talked to the zebra escaped.
Dialogue: 0,0:19:59.69,0:20:10.32,Default,,0000,0000,0000,,Change it here, so notice what we have\Nhere. We take two propositions, the
Dialogue: 0,0:20:11.95,0:20:20.19,Default,,0000,0000,0000,,proposition Jack finally walked, and the\Nproposition the zebra escaped. And we put
Dialogue: 0,0:20:20.19,0:20:28.02,Default,,0000,0000,0000,,them together with the truth functional\Nconnective, and to create a resultant
Dialogue: 0,0:20:28.02,0:20:35.25,Default,,0000,0000,0000,,proposition Jack finally walked and the\Nzebra escaped. Now, when is that
Dialogue: 0,0:20:35.25,0:20:43.01,Default,,0000,0000,0000,,proposition gonna be true? Well, again it\Ndepends just on, when these propositions
Dialogue: 0,0:20:43.01,0:20:48.24,Default,,0000,0000,0000,,are true. So if it's true, that Jack\Nfinally walked, and it's also true that
Dialogue: 0,0:20:48.24,0:20:53.76,Default,,0000,0000,0000,,the zebra escaped, then it's going to be\Ntrue that Jack finally walked and the
Dialogue: 0,0:20:53.76,0:20:58.52,Default,,0000,0000,0000,,zebra escaped. If it's true that Jack\Nfinally walked, but it's false that the
Dialogue: 0,0:20:58.52,0:21:03.27,Default,,0000,0000,0000,,zebra escaped, then it's going to be false\Nthat Jack finally walked and the zebra
Dialogue: 0,0:21:03.27,0:21:07.90,Default,,0000,0000,0000,,escaped. If it's false that Jack finally\Nwalked and it's true that the zebra
Dialogue: 0,0:21:07.90,0:21:12.76,Default,,0000,0000,0000,,escaped, then it's going to be false that\NJack finally walked and the zebra escaped.
Dialogue: 0,0:21:12.76,0:21:17.33,Default,,0000,0000,0000,,And finally, if it's false that Jack\Nfinally walked and it's false that the
Dialogue: 0,0:21:17.33,0:21:22.07,Default,,0000,0000,0000,,zebra escaped, then of course it's going\Nto be false that Jack finally walked and
Dialogue: 0,0:21:22.07,0:21:27.05,Default,,0000,0000,0000,,the zebra escaped. So once again, same\Ntruth table even if we change the
Dialogue: 0,0:21:27.05,0:21:33.41,Default,,0000,0000,0000,,ingredient propositions that we're putting\Ntogether with the functional connective an
Dialogue: 0,0:21:33.41,0:21:40.46,Default,,0000,0000,0000,,d to make the resultive proposition. Now,\Nsince the truth table stays the same even
Dialogue: 0,0:21:40.46,0:21:47.53,Default,,0000,0000,0000,,when we change these propositions up on\Ntop. We could represent that fact, by
Dialogue: 0,0:21:47.53,0:21:55.24,Default,,0000,0000,0000,,replacing these propositions altogether\Nwith variables that can range over any
Dialogue: 0,0:21:55.24,0:22:03.05,Default,,0000,0000,0000,,proposition. So, for instance, instead of\Nsaying Jack finally walked, we could just
Dialogue: 0,0:22:03.05,0:22:11.06,Default,,0000,0000,0000,,have a variable here call it P1 Our first\Nproposition. Instead of saying the zebra
Dialogue: 0,0:22:11.06,0:22:17.99,Default,,0000,0000,0000,,escaped we can have a variable there, call\Nit P2 our second proposition. And finally,
Dialogue: 0,0:22:17.99,0:22:26.85,Default,,0000,0000,0000,,when we put those two propositions\Ntogether using the truth functional
Dialogue: 0,0:22:26.85,0:22:36.02,Default,,0000,0000,0000,,connective and. We'll have P1 one and. P2.\NSo that's going to be our resultant
Dialogue: 0,0:22:36.02,0:22:43.26,Default,,0000,0000,0000,,proposition, P1 and P2. And whatever\Nexactly that is, is going to depend of
Dialogue: 0,0:22:43.26,0:22:51.26,Default,,0000,0000,0000,,course on what P1 is and what P2 is. But\Nwhether this third proposition is true or
Dialogue: 0,0:22:51.26,0:22:59.28,Default,,0000,0000,0000,,false again is only going to depend on the\Ntruth or falsehood of P1 and of P2, when
Dialogue: 0,0:22:59.28,0:23:07.51,Default,,0000,0000,0000,,P1 whatever exactly that is, is true and\NP2 is true then. The proposition p1 and p2
Dialogue: 0,0:23:07.51,0:23:15.73,Default,,0000,0000,0000,,is going to be true. Whatever proposition\Nthat is, is going to be true. And in every
Dialogue: 0,0:23:15.73,0:23:23.85,Default,,0000,0000,0000,,other possible situation, that proposition\Nis going to be false. So no matter what
Dialogue: 0,0:23:23.85,0:23:32.08,Default,,0000,0000,0000,,proposition we have for P1 and P2 their\Nconjunction P1 and P2 is going to be true,
Dialogue: 0,0:23:32.08,0:23:39.62,Default,,0000,0000,0000,,just in those situations when P1 and P2\Nare both true. That's the truth table for
Dialogue: 0,0:23:39.62,0:23:46.05,Default,,0000,0000,0000,,the truth functional connective and, which\Nwe'll also call conjunction. In the next
Dialogue: 0,0:23:46.05,0:23:52.14,Default,,0000,0000,0000,,lecture, we're going to see how we can use\Nthe truth table for the truth functional
Dialogue: 0,0:23:52.14,0:23:58.16,Default,,0000,0000,0000,,connective and. To figure out the rules\Nfor evaluating deductive arguments that
Dialogue: 0,0:23:58.16,0:24:04.25,Default,,0000,0000,0000,,rely on the truth functional connected\Nand. And in the following three lectures,
Dialogue: 0,0:24:04.25,0:24:10.64,Default,,0000,0000,0000,,we'll see how we can use the truth tables\Nfor other truth functional connectives, to
Dialogue: 0,0:24:10.64,0:24:16.50,Default,,0000,0000,0000,,figure out the rules for evaluating\Ndeductive arguments that use those other
Dialogue: 0,0:24:16.50,0:24:18.94,Default,,0000,0000,0000,,connectives. See you in next lecture.