[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:04.44,0:00:09.65,Default,,0000,0000,0000,,In the last lecture. We talked about the\Ntruth functional connective, conjunction.
Dialogue: 0,0:00:09.65,0:00:14.93,Default,,0000,0000,0000,,We gave the truth table for conjunction.\NAnd we showed how we could use the truth
Dialogue: 0,0:00:14.93,0:00:20.41,Default,,0000,0000,0000,,table for conjunction to figure out which\Ninferences that use conjunction are valid
Dialogue: 0,0:00:20.41,0:00:25.88,Default,,0000,0000,0000,,and which inferences are not. Today, we're\Ngoing to talk about the truth functional
Dialogue: 0,0:00:25.88,0:00:31.16,Default,,0000,0000,0000,,connective, disjunction. We're going to\Ngive the truth table for dis-junction, and
Dialogue: 0,0:00:31.16,0:00:36.63,Default,,0000,0000,0000,,we're going to show how we can use that\Ntruth table to figure out which inferences
Dialogue: 0,0:00:36.63,0:00:41.86,Default,,0000,0000,0000,,that use dis-junction are valid and which\Nare not. Now in English, we usually
Dialogue: 0,0:00:41.86,0:00:47.99,Default,,0000,0000,0000,,express disjunction by using the word or\Nbut the word or can be used in a couple
Dialogue: 0,0:00:47.99,0:00:53.59,Default,,0000,0000,0000,,different ways in English. For instance,\Nsuppose that Manchester is playing
Dialogue: 0,0:00:53.59,0:00:59.19,Default,,0000,0000,0000,,Barcelona tonight and you ask me, who's\Ngoing to win? And I say, well, I have no
Dialogue: 0,0:00:59.19,0:01:04.71,Default,,0000,0000,0000,,idea who's going to win but I can tell you\Nthis, it's going to be Manchester or
Dialogue: 0,0:01:04.71,0:01:10.47,Default,,0000,0000,0000,,Barcelona. Now, what I'm suggesting when I\Nsay, it's going to be Manchester or
Dialogue: 0,0:01:10.47,0:01:16.19,Default,,0000,0000,0000,,Barcelona, is that it's not going to be\Nboth. Manchester might win, Barcelona
Dialogue: 0,0:01:16.19,0:01:21.74,Default,,0000,0000,0000,,might win. But there's no possible way\Nthat both of them are going to win.
Dialogue: 0,0:01:21.74,0:01:27.70,Default,,0000,0000,0000,,Sometimes, in English, when you want to\Nsay that it's going to be one thing or the
Dialogue: 0,0:01:27.70,0:01:33.33,Default,,0000,0000,0000,,other, but not both, you say, either or\Neither Manchester is going to win, or
Dialogue: 0,0:01:33.33,0:01:40.47,Default,,0000,0000,0000,,Barcelona is going to win. But sometimes\Nwhen we use the word or, we mean it could
Dialogue: 0,0:01:40.47,0:01:46.78,Default,,0000,0000,0000,,be one, or the other, or both. So for\Ninstance, suppose you ask me what we
Dialogue: 0,0:01:46.78,0:01:54.00,Default,,0000,0000,0000,,should have for dinner tonight and I say\Nwell we could have chicken or fish. Well
Dialogue: 0,0:01:54.00,0:02:01.09,Default,,0000,0000,0000,,there's no suggestion that we couldn't\Nhave both maybe we could have a little bit
Dialogue: 0,0:02:01.09,0:02:08.93,Default,,0000,0000,0000,,of chicken and a little of fish. So it has\Nto be chicken or fish or both. When I say
Dialogue: 0,0:02:08.93,0:02:16.49,Default,,0000,0000,0000,,chicken or fish, I'm not suggesting it\Ncan't be both. Sometimes in English we use
Dialogue: 0,0:02:16.49,0:02:23.84,Default,,0000,0000,0000,,the phrase and, or to express that it\Ncould be one or the other or both. I'll
Dialogue: 0,0:02:23.84,0:02:31.35,Default,,0000,0000,0000,,say, we could have the chicken and, or the\Nfish. The truth functional connective
Dialogue: 0,0:02:31.35,0:02:37.56,Default,,0000,0000,0000,,disjunction is expressed by the second\Nmeaning of or. It's expressed by the
Dialogue: 0,0:02:37.56,0:02:44.27,Default,,0000,0000,0000,,English phrase and, or where you me an it\Ncould be one or the other or both. That's
Dialogue: 0,0:02:44.27,0:02:50.57,Default,,0000,0000,0000,,what we're going to call disjunction in\Nthis class. Now let's look at the truth
Dialogue: 0,0:02:50.57,0:02:58.41,Default,,0000,0000,0000,,table for disjunction. So lets look at the\Ntruth table for dis-junction. Suppose
Dialogue: 0,0:02:58.41,0:03:06.87,Default,,0000,0000,0000,,you're using disjunction to combine the\Npropositions We eat chicken and we eat
Dialogue: 0,0:03:06.87,0:03:15.21,Default,,0000,0000,0000,,fish into the disjunctive proposition We\Neat chicken or fish. Well when is that
Dialogue: 0,0:03:15.21,0:03:23.35,Default,,0000,0000,0000,,disjunctive proposition going to be true?\NIf it's true that we eat chicken, and it's
Dialogue: 0,0:03:23.35,0:03:30.99,Default,,0000,0000,0000,,true that we eat fish, then it's going to\Nbe true that we eat chicken or fish cuz
Dialogue: 0,0:03:30.99,0:03:38.64,Default,,0000,0000,0000,,remember, when we use or here, we don't\Nmean either or, but not both. We mean and
Dialogue: 0,0:03:38.64,0:03:45.62,Default,,0000,0000,0000,,or. Could be one, could be the other, or\Ncould be both. So if it's true that we eat
Dialogue: 0,0:03:45.62,0:03:50.87,Default,,0000,0000,0000,,chicken and it's true that we eat fish,\Nit's going to be true that we eat chicken
Dialogue: 0,0:03:50.87,0:03:56.04,Default,,0000,0000,0000,,or fish. Now supposed it's true that we\Neat chicken, but its false that we eat
Dialogue: 0,0:03:56.04,0:04:03.23,Default,,0000,0000,0000,,fish. Well. Then, it's still going to be\Ntrue that we eat chicken or fish. Suppose
Dialogue: 0,0:04:03.23,0:04:10.30,Default,,0000,0000,0000,,it's false that we eat chicken, but true\Nthat we eat fish. Then, it's still going
Dialogue: 0,0:04:09.76,0:04:17.37,Default,,0000,0000,0000,,to be true that we eat chicken or fish.\NBut suppose it's false that we eat chicken
Dialogue: 0,0:04:17.37,0:04:24.68,Default,,0000,0000,0000,,and it's also false that we eat fish.\NThen, is it going to be true that we eat
Dialogue: 0,0:04:24.68,0:04:31.63,Default,,0000,0000,0000,,chicken or fish? No! Because we won't be\Neating either. So then it'll be false that
Dialogue: 0,0:04:31.63,0:04:38.36,Default,,0000,0000,0000,,we eat chicken or fish. This is the truth\Ntable for disjunction. And, like the truth
Dialogue: 0,0:04:38.36,0:04:44.66,Default,,0000,0000,0000,,table that we saw for conjunction, it's\Ngoing to work no matter what propositions
Dialogue: 0,0:04:44.66,0:04:50.95,Default,,0000,0000,0000,,we put into here, or here, or here. So, no\Nmatter what proposition you have right
Dialogue: 0,0:04:50.95,0:04:57.01,Default,,0000,0000,0000,,here, call it P1. And, no matter what\Nproposition you have right here, call it
Dialogue: 0,0:04:57.01,0:05:03.48,Default,,0000,0000,0000,,P2. When you use the truth functional\Nconnective disjunction. To create a new
Dialogue: 0,0:05:03.48,0:05:09.59,Default,,0000,0000,0000,,proposition out of those two\Nproposition's, so you got a new
Dialogue: 0,0:05:09.59,0:05:16.93,Default,,0000,0000,0000,,proposition P one or P two. That new\Ndisjunctive proposition is going to be
Dialogue: 0,0:05:16.93,0:05:23.55,Default,,0000,0000,0000,,true. Whenever P1 is true, and it's also\Ngoing to be true whenever P2 is true. So
Dialogue: 0,0:05:23.55,0:05:31.02,Default,,0000,0000,0000,,unlike conjunction. Where you need both of\Nthe two ingredient propositions to be true
Dialogue: 0,0:05:31.02,0:05:36.83,Default,,0000,0000,0000,,in order for the conjunctive proposition\Nto be true. In disjunc tion, you only need
Dialogue: 0,0:05:36.83,0:05:42.43,Default,,0000,0000,0000,,for one of the of the two ingredient\Npropositions to be true in order for the
Dialogue: 0,0:05:42.43,0:05:47.95,Default,,0000,0000,0000,,disjunctive proposition to be true. The\Ndisjunctive proposition is false only
Dialogue: 0,0:05:47.95,0:05:53.19,Default,,0000,0000,0000,,when. Both of the two ingredient\Npropositions are false. That's the only
Dialogue: 0,0:05:53.19,0:05:59.18,Default,,0000,0000,0000,,time a disjunction is false. So now, let\Nme give you an example, of how you can use
Dialogue: 0,0:05:59.18,0:06:04.97,Default,,0000,0000,0000,,the truth table for disjunction. Just show\Nthat a particular kind of argument is
Dialogue: 0,0:06:04.97,0:06:10.10,Default,,0000,0000,0000,,valid. We're going to discuss, a kind of\Nargument that is sometimes known. As
Dialogue: 0,0:06:10.10,0:06:17.24,Default,,0000,0000,0000,,process of elimination. Here's how it\Ngoes. Suppose, that you have to solve. A
Dialogue: 0,0:06:17.24,0:06:24.01,Default,,0000,0000,0000,,murder mystery. Mister Jones, has been\Nstabbed in his living room. With a knife
Dialogue: 0,0:06:24.01,0:06:30.49,Default,,0000,0000,0000,,in the back. Now, you figured out that\Nthere were only two people in the house at
Dialogue: 0,0:06:30.49,0:06:35.96,Default,,0000,0000,0000,,the time of his stabbing, the butler and\Nthe accountant. You also know that the
Dialogue: 0,0:06:35.96,0:06:41.64,Default,,0000,0000,0000,,knife is positioned in Mr. Johnson's back\Nin such a way that he couldn't possibly
Dialogue: 0,0:06:41.64,0:06:47.03,Default,,0000,0000,0000,,have stabbed himself. So it had to be\Nsomeone else. And whoever else it was it
Dialogue: 0,0:06:47.03,0:06:52.78,Default,,0000,0000,0000,,had to be someone who's in the house at\Nthe time of the stabbing. So it could only
Dialogue: 0,0:06:52.78,0:06:59.79,Default,,0000,0000,0000,,have been, the butler or the accountant,\Nor maybe both. So you know that the butler
Dialogue: 0,0:06:59.79,0:07:06.29,Default,,0000,0000,0000,,did it, or the accountant did it. Now you\Nfind out that the accountant is a
Dialogue: 0,0:07:06.29,0:07:13.25,Default,,0000,0000,0000,,quadriplegic, so the accountant couldn't\Nhave stabbed Mr. Jones in the back. So now
Dialogue: 0,0:07:13.25,0:07:20.41,Default,,0000,0000,0000,,you know that the account didn't do it.\NAnd so, from the two premises, the butler
Dialogue: 0,0:07:20.41,0:07:27.52,Default,,0000,0000,0000,,did it, or the accountant did it. And the\Naccountant didn't do it. You can conclude,
Dialogue: 0,0:07:27.52,0:07:33.66,Default,,0000,0000,0000,,the butler did it. Now, why is that\Nargument valid? Here's why. Think about
Dialogue: 0,0:07:33.66,0:07:39.78,Default,,0000,0000,0000,,the truth table for disjunction again. So\Nremember the first premise, the butler did
Dialogue: 0,0:07:39.78,0:07:44.50,Default,,0000,0000,0000,,it or the accountant did it is a\Ndisjunction. It's going to be true
Dialogue: 0,0:07:44.50,0:07:50.24,Default,,0000,0000,0000,,whenever one of it's disjuncts is true,\None of it's ingredient propositions is
Dialogue: 0,0:07:50.24,0:07:55.55,Default,,0000,0000,0000,,true. So it's going to be true whenever\Nthe butler did it, and it's going to be
Dialogue: 0,0:07:55.55,0:08:00.71,Default,,0000,0000,0000,,true whenever the butler did it. The\Nsecond premise tells you that the
Dialogue: 0,0:08:00.71,0:08:06.86,Default,,0000,0000,0000,,accountant didn't do it. So the only way\Nfor the first premise to be true, given
Dialogue: 0,0:08:06.86,0:08:12.83,Default,,0000,0000,0000,,that the accountant didn't do it, is fo r\Nthe butler to have done it. And so you
Dialogue: 0,0:08:12.83,0:08:18.00,Default,,0000,0000,0000,,know, since the accountant couldn't have\Ndone it. That the only way for the
Dialogue: 0,0:08:18.00,0:08:23.45,Default,,0000,0000,0000,,dis-junction, the butler did it or the\Naccountant did it to be true, is for the
Dialogue: 0,0:08:23.45,0:08:29.18,Default,,0000,0000,0000,,butler to have done it and that's why you\Ncan conclude the butler did it and your
Dialogue: 0,0:08:29.18,0:08:35.23,Default,,0000,0000,0000,,argument is valid. That's one example of a\Nprocess of elimination argument. Of course
Dialogue: 0,0:08:35.23,0:08:40.65,Default,,0000,0000,0000,,there are lots of others, but with all of\Nthose others you can see why they are
Dialogue: 0,0:08:40.65,0:08:46.28,Default,,0000,0000,0000,,valid by looking at the truth table for\Ndis-junction. Remember how you can use the
Dialogue: 0,0:08:46.28,0:08:51.97,Default,,0000,0000,0000,,truth functional connective conjunction to\Nbuild a new proposition out of not just
Dialogue: 0,0:08:51.97,0:08:57.60,Default,,0000,0000,0000,,two other propositions but sometimes three\Nother propositions. You can conjoin one
Dialogue: 0,0:08:57.60,0:09:03.48,Default,,0000,0000,0000,,proposition with a second and with a\Nthird. Well, you can do the same thing
Dialogue: 0,0:09:03.48,0:09:10.84,Default,,0000,0000,0000,,with disjunction. You can disjoin one\Nproposition with a second and a third, to
Dialogue: 0,0:09:10.84,0:09:19.19,Default,,0000,0000,0000,,create the proposition. Either this, or\Nthat or the other or any combination of
Dialogue: 0,0:09:19.19,0:09:27.76,Default,,0000,0000,0000,,the three. What does the truth table for\Nthat look like? Here it is. The
Dialogue: 0,0:09:27.76,0:09:36.85,Default,,0000,0000,0000,,disjunctive proposition, P1 or P2 or P3,\Nis going to be true. Whenever P1 is true,
Dialogue: 0,0:09:36.85,0:09:43.12,Default,,0000,0000,0000,,it's also going to be true whenever P2 is\Ntrue. And it's also going to be true
Dialogue: 0,0:09:43.12,0:09:49.74,Default,,0000,0000,0000,,whenever P3 is true. In fact, the only\Ntime that P1 or P2 or P3, the only time
Dialogue: 0,0:09:49.74,0:09:55.93,Default,,0000,0000,0000,,that, that disjunctive proposition is\Ngoing to be false is when all these
Dialogue: 0,0:09:55.93,0:10:03.40,Default,,0000,0000,0000,,ingredient propositions are false. So\Nhere's what the truth table for P1, or P2,
Dialogue: 0,0:10:03.40,0:10:10.58,Default,,0000,0000,0000,,or P3 looks. Now let's use the truth table\Nfor our triple disjunction to show how a
Dialogue: 0,0:10:10.58,0:10:16.34,Default,,0000,0000,0000,,particular process of elimination argument\Ncan be valid. Let's go back to our murder
Dialogue: 0,0:10:16.34,0:10:21.47,Default,,0000,0000,0000,,mystery in order to do that. Now suppose\Nthat you find out contrary to what you had
Dialogue: 0,0:10:21.88,0:10:27.56,Default,,0000,0000,0000,,previously believed, that Butler and the\Naccountant were not the only people in the
Dialogue: 0,0:10:27.56,0:10:33.38,Default,,0000,0000,0000,,house, at the time of Mr. Jonathan's\Ndeath. In addition, the maid was in the
Dialogue: 0,0:10:33.38,0:10:38.26,Default,,0000,0000,0000,,house and the cook was in the house.\NAlright. Well, now, you know, that the
Dialogue: 0,0:10:38.26,0:10:44.04,Default,,0000,0000,0000,,butler or the maid or the cook did it. We\Ndon't yet know which of them did it, but
Dialogue: 0,0:10:44.04,0:10:49.59,Default,,0000,0000,0000,,we know that the butler or the maid or the\Ncook did it. Now suppose that yo u find
Dialogue: 0,0:10:49.59,0:10:54.35,Default,,0000,0000,0000,,out that the maid and the cook, at the\Ntime of the stabbing we're off in the
Dialogue: 0,0:10:54.35,0:10:58.87,Default,,0000,0000,0000,,opposite corner of the house doing\Nsomething else together. Well now you
Dialogue: 0,0:10:58.87,0:11:03.97,Default,,0000,0000,0000,,know, that the maid didn't do it. And you\Nknow that the cook didn't do it. So what
Dialogue: 0,0:11:03.97,0:11:09.35,Default,,0000,0000,0000,,can you conclude from those three\Npremises? Premise one, the butler or the
Dialogue: 0,0:11:09.35,0:11:15.24,Default,,0000,0000,0000,,maid or the cook did it. Premise two, the\Nmaid didn't do it. And premise three: the
Dialogue: 0,0:11:15.24,0:11:21.46,Default,,0000,0000,0000,,cook didn't do it. Well, lets use the\Ntruth table to figure this out. Premise
Dialogue: 0,0:11:21.46,0:11:28.46,Default,,0000,0000,0000,,one of the truth table tells you that the\Nbutler or the maid or the cook did it. So
Dialogue: 0,0:11:28.46,0:11:35.56,Default,,0000,0000,0000,,the situation in which it falls that the\Nbutler or the maid or the cook did it that
Dialogue: 0,0:11:35.56,0:11:42.65,Default,,0000,0000,0000,,situation is ruled out by premise one. So\Npremise one tells you at that situation is
Dialogue: 0,0:11:42.65,0:11:51.51,Default,,0000,0000,0000,,not the actual situation. Premise two\Ntells you that the maid did not do it. So
Dialogue: 0,0:11:51.51,0:11:56.77,Default,,0000,0000,0000,,any situation in which its true that the\Nmaid did it is also not the actual
Dialogue: 0,0:11:56.77,0:12:02.10,Default,,0000,0000,0000,,situation. So this situation is one in\Nwhich its true that the maid did it so
Dialogue: 0,0:12:02.10,0:12:07.77,Default,,0000,0000,0000,,that's not the actual situation according\Nto premise two. This situation is one in
Dialogue: 0,0:12:07.77,0:12:13.38,Default,,0000,0000,0000,,which its true that the maid did it. So\Nthat's not the actual situation according
Dialogue: 0,0:12:13.38,0:12:18.54,Default,,0000,0000,0000,,to premise two. This situation is one in\Nwhich its true that the maid did it. So
Dialogue: 0,0:12:18.54,0:12:23.87,Default,,0000,0000,0000,,that's not the actual situation according\Nto premise two, and this situation is one
Dialogue: 0,0:12:23.87,0:12:28.63,Default,,0000,0000,0000,,in which it is true that the maid did it.\NSo that's not the actual situation
Dialogue: 0,0:12:28.63,0:12:35.02,Default,,0000,0000,0000,,according to premise two. Premise three\Ntells you that the cook didn't do it. So,
Dialogue: 0,0:12:35.02,0:12:40.89,Default,,0000,0000,0000,,that rules out any situation in which it's\Ntrue that the cook did it. Well, here's a
Dialogue: 0,0:12:40.89,0:12:46.82,Default,,0000,0000,0000,,situation in which it's true that the cook\Ndid it. So, that situation is ruled out by
Dialogue: 0,0:12:46.82,0:12:52.47,Default,,0000,0000,0000,,premise three. And, here's a situation in\Nwhich it's true that the cook did it. So,
Dialogue: 0,0:12:52.47,0:12:57.77,Default,,0000,0000,0000,,that situation is ruled out by premise\Nthree. So, premise one rules out this
Dialogue: 0,0:12:57.77,0:13:05.38,Default,,0000,0000,0000,,situation. Premise two, rules out this,\Nthis, this and this situation. And premise
Dialogue: 0,0:13:05.38,0:13:14.79,Default,,0000,0000,0000,,three, rules out this, this, this and this\Nsituation. Well, whats left? The only
Dialogue: 0,0:13:14.79,0:13:25.02,Default,,0000,0000,0000,,situation left that could be the actual\Nsituation is this one. See cause in this
Dialogue: 0,0:13:25.02,0:13:30.60,Default,,0000,0000,0000,,situation, it's t rue that the butler or\Nthe maid or the cook did it just as
Dialogue: 0,0:13:30.60,0:13:36.69,Default,,0000,0000,0000,,premise one tells us. Its false that the\Nmaid did just as premise two tells us, and
Dialogue: 0,0:13:36.69,0:13:43.03,Default,,0000,0000,0000,,its false that the cook did just as\Npremise three tells us. But, that's the
Dialogue: 0,0:13:43.03,0:13:48.81,Default,,0000,0000,0000,,situation in which it's true that the\Nbutler did it. So, the conclusion that we
Dialogue: 0,0:13:48.81,0:13:54.89,Default,,0000,0000,0000,,can draw, based on the situations that are\Nruled out by premises one, two, and three,
Dialogue: 0,0:13:54.89,0:14:00.82,Default,,0000,0000,0000,,is that the actual situation is this one,\Nand in that actual situation, it's true
Dialogue: 0,0:14:00.82,0:14:08.58,Default,,0000,0000,0000,,that the butler did it. So, the butler did\Nit That's why the process of elimination
Dialogue: 0,0:14:08.58,0:14:15.17,Default,,0000,0000,0000,,reasoning that we just considered is\Nvalid. If premise one says, the butler or
Dialogue: 0,0:14:15.17,0:14:20.88,Default,,0000,0000,0000,,the maid or the cook did it. Premise two\Nsays the maid didn't do it, and premise
Dialogue: 0,0:14:20.88,0:14:26.73,Default,,0000,0000,0000,,three says that the cook didn't do it.\NThen by process of elimination we can draw
Dialogue: 0,0:14:26.73,0:14:32.29,Default,,0000,0000,0000,,the valid conclusion that the butler did\Nit and this is why. Let me give you
Dialogue: 0,0:14:32.29,0:14:38.36,Default,,0000,0000,0000,,another example of how you can use the\Ntruth table for disjunction in order to
Dialogue: 0,0:14:38.36,0:14:44.20,Default,,0000,0000,0000,,show whether or not the process of\Nelimination argument is valid. Suppose we
Dialogue: 0,0:14:44.20,0:14:49.97,Default,,0000,0000,0000,,know that Walter is a professional\Nfootball player. Well, that means that he
Dialogue: 0,0:14:49.97,0:14:55.42,Default,,0000,0000,0000,,plays either American football, U.S.\NFootball, or European football, which
Dialogue: 0,0:14:55.42,0:15:01.88,Default,,0000,0000,0000,,Americans call soccer, or Australian rules\Nfootball. But now suppose we find out that
Dialogue: 0,0:15:01.88,0:15:08.62,Default,,0000,0000,0000,,Walter does not play American football.\NAnd you conclude from that, that he must
Dialogue: 0,0:15:08.62,0:15:14.100,Default,,0000,0000,0000,,play European football. So you argue as\Nfollows. Premise 1- Walter plays either
Dialogue: 0,0:15:14.100,0:15:21.02,Default,,0000,0000,0000,,American football or European football or\NAustralian Rules football, premise 2- he
Dialogue: 0,0:15:21.02,0:15:26.67,Default,,0000,0000,0000,,does not play American football and\Ntherefore you conclude he plays European
Dialogue: 0,0:15:26.67,0:15:32.11,Default,,0000,0000,0000,,football. Well, that argument is invalid\Nand we can use the truth table for
Dialogue: 0,0:15:32.11,0:15:38.24,Default,,0000,0000,0000,,disjunction to show why it's invalid. Look\Nat this truth table. Premise one, recall,
Dialogue: 0,0:15:38.24,0:15:45.07,Default,,0000,0000,0000,,is that Walter plays American or European\Nor Australian rules football. So premise
Dialogue: 0,0:15:45.07,0:15:51.56,Default,,0000,0000,0000,,one rules out the situation in which it's\Nfalse that Walter plays American or
Dialogue: 0,0:15:51.56,0:15:58.56,Default,,0000,0000,0000,,European or Australian rules football. And\Nthat's all it rules out. It just rules out
Dialogue: 0,0:15:58.56,0:16:05.94,Default,,0000,0000,0000,,the situation in which it's false that\NWalter plays an y of those. Premise two,
Dialogue: 0,0:16:05.94,0:16:12.55,Default,,0000,0000,0000,,Walter doesn't play American Football.\NThat rules out the situation in which it's
Dialogue: 0,0:16:12.55,0:16:21.19,Default,,0000,0000,0000,,true that Walter plays American football.\NSo it rules out this situation. And rules
Dialogue: 0,0:16:21.19,0:16:33.06,Default,,0000,0000,0000,,out this situation. And it rules out this\Nsituation. And it rules out this
Dialogue: 0,0:16:33.06,0:16:41.39,Default,,0000,0000,0000,,situation. So, premise one rules out the\Nsituation represented at the bottom.
Dialogue: 0,0:16:41.39,0:16:48.17,Default,,0000,0000,0000,,Premise two rules out the situations\Nrepresented by these four columns at the
Dialogue: 0,0:16:48.17,0:16:57.49,Default,,0000,0000,0000,,top. So, can we conclude that Walter plays\NEuropean football? No. He might play
Dialogue: 0,0:16:57.49,0:17:04.52,Default,,0000,0000,0000,,European football but he might also play\NAustralian Rules football. He's looked all
Dialogue: 0,0:17:04.52,0:17:11.21,Default,,0000,0000,0000,,the premise one and premise two together\Nrule out is these five situations. But
Dialogue: 0,0:17:11.21,0:17:17.99,Default,,0000,0000,0000,,there is no three situations that are\Npossible. In one of them Walter plays both
Dialogue: 0,0:17:17.99,0:17:24.42,Default,,0000,0000,0000,,European football and Australian rules\Nfootball. In another one of them, Walter
Dialogue: 0,0:17:24.42,0:17:29.85,Default,,0000,0000,0000,,plays European football, but not\NAustralian rules football, and in the
Dialogue: 0,0:17:29.85,0:17:35.44,Default,,0000,0000,0000,,third situation, this left open by\Npremises one and two, it's false that
Dialogue: 0,0:17:35.44,0:17:41.73,Default,,0000,0000,0000,,Walter plays European football but true\Nthat he plays Australian rules football.
Dialogue: 0,0:17:41.73,0:17:48.11,Default,,0000,0000,0000,,So based on the information that premises\None and two give us, we cannot conclude
Dialogue: 0,0:17:48.11,0:17:54.09,Default,,0000,0000,0000,,that Walter plays European football. He\Nmight play Australian rules football
Dialogue: 0,0:17:54.09,0:17:59.99,Default,,0000,0000,0000,,instead. So the argument that you made is\Ninvalid. In the next lecture, we're going
Dialogue: 0,0:17:59.56,0:18:05.55,Default,,0000,0000,0000,,to consider a truth functional connective\Nthat's different from conjunction and
Dialogue: 0,0:18:05.55,0:18:10.76,Default,,0000,0000,0000,,disjunction in the following way. While\Nconjunction and disjunction are
Dialogue: 0,0:18:10.76,0:18:16.41,Default,,0000,0000,0000,,connectives that can be used to build\Npropositions out of two or more other
Dialogue: 0,0:18:16.41,0:18:22.07,Default,,0000,0000,0000,,propositions. Negation, the connective\Nthat we'll talk about next time, is the
Dialogue: 0,0:18:22.07,0:18:27.95,Default,,0000,0000,0000,,connective that is used to build new\Npropositions out of just one single other
Dialogue: 0,0:18:27.95,0:18:33.82,Default,,0000,0000,0000,,proposition. Negation, in other words, is\Na connective that you apply to one
Dialogue: 0,0:18:33.82,0:18:39.78,Default,,0000,0000,0000,,proposition to build a second proposition.\NAnd that's what we'll talk about next
Dialogue: 0,0:18:39.78,0:18:44.75,Default,,0000,0000,0000,,time. Now, there's some exercise's for you\Nto do. These exercises test your
Dialogue: 0,0:18:44.75,0:18:50.15,Default,,0000,0000,0000,,understanding of the truth table for\Ndisjunction and of how the truth table for
Dialogue: 0,0:18:50.15,0:18:55.35,Default,,0000,0000,0000,,dis-junction can be used to determine\Nwhether a part icular argument that uses
Dialogue: 0,0:18:55.35,0:18:58.02,Default,,0000,0000,0000,,disjunction is a valid argument or not.