WEBVTT 00:00:00.000 --> 00:00:10.942 align:middle line:90% 00:00:10.942 --> 00:00:12.400 align:middle line:84% NORVIN RICHARDS: So we have already 00:00:12.400 --> 00:00:16.353 align:middle line:84% talked for a while about various kinds of ambiguity. 00:00:16.353 --> 00:00:18.520 align:middle line:84% And today, we're going to talk about ambiguity more. 00:00:18.520 --> 00:00:20.978 align:middle line:84% This is, if anything, the best time to talk about ambiguity 00:00:20.978 --> 00:00:23.497 align:middle line:84% because we're now actually into semantics. 00:00:23.497 --> 00:00:25.330 align:middle line:84% The kinds of ambiguity we were talking about 00:00:25.330 --> 00:00:29.350 align:middle line:84% before were kinds of what's sometimes 00:00:29.350 --> 00:00:31.810 align:middle line:84% called structural ambiguity-- that is, 00:00:31.810 --> 00:00:34.630 align:middle line:84% sentences that had more than one meaning. 00:00:34.630 --> 00:00:37.895 align:middle line:84% The way we were talking about it was had more than one 00:00:37.895 --> 00:00:39.520 align:middle line:84% meaning because it was possible to draw 00:00:39.520 --> 00:00:41.240 align:middle line:90% more than one tree for them. 00:00:41.240 --> 00:00:43.870 align:middle line:84% So the sentence that we spend a lot of time talking about 00:00:43.870 --> 00:00:46.120 align:middle line:84% was I once shot an elephant in my pajamas, 00:00:46.120 --> 00:00:52.390 align:middle line:84% where the whole joke there was that "in my pajamas" could 00:00:52.390 --> 00:00:54.628 align:middle line:84% be attached in a couple of different places. 00:00:54.628 --> 00:00:56.170 align:middle line:84% It could either modify "the elephant" 00:00:56.170 --> 00:00:58.540 align:middle line:84% or it could modify the verb phrase "shot an elephant." 00:00:58.540 --> 00:01:02.290 align:middle line:84% And the upshot of that was, well, the pajamas 00:01:02.290 --> 00:01:04.209 align:middle line:84% could be on either of you, and yeah-- 00:01:04.209 --> 00:01:04.959 align:middle line:90% ambiguity. 00:01:04.959 --> 00:01:08.278 align:middle line:84% Similar kinds of ambiguities in these other examples. 00:01:08.278 --> 00:01:09.820 align:middle line:84% But there's another kind of ambiguity 00:01:09.820 --> 00:01:11.890 align:middle line:84% that's the one I want to talk about today. 00:01:11.890 --> 00:01:14.650 align:middle line:90% 00:01:14.650 --> 00:01:17.830 align:middle line:84% People have claimed that this sentence is ambiguous-- 00:01:17.830 --> 00:01:19.690 align:middle line:90% "someone loves everyone." 00:01:19.690 --> 00:01:22.100 align:middle line:84% The claim is this can mean at least two things. 00:01:22.100 --> 00:01:25.930 align:middle line:84% It can mean-- let's get some lights on up here in the front. 00:01:25.930 --> 00:01:28.750 align:middle line:90% 00:01:28.750 --> 00:01:31.450 align:middle line:90% Oh dear, so many options. 00:01:31.450 --> 00:01:36.290 align:middle line:90% 00:01:36.290 --> 00:01:38.510 align:middle line:90% Stage left, stage right-- 00:01:38.510 --> 00:01:40.480 align:middle line:90% sure. 00:01:40.480 --> 00:01:41.230 align:middle line:90% Oh, I see. 00:01:41.230 --> 00:01:44.110 align:middle line:90% 00:01:44.110 --> 00:01:44.950 align:middle line:90% That's what I want. 00:01:44.950 --> 00:01:49.000 align:middle line:90% 00:01:49.000 --> 00:01:51.520 align:middle line:84% Two kinds of meanings for this that people have posited-- 00:01:51.520 --> 00:01:59.620 align:middle line:84% one meaning in which it means the following situation holds 00:01:59.620 --> 00:02:01.390 align:middle line:90% everyone is loved. 00:02:01.390 --> 00:02:07.390 align:middle line:84% That is, for each person, there is someone that loves them. 00:02:07.390 --> 00:02:11.380 align:middle line:84% That's what's diagrammed in that first diagram 00:02:11.380 --> 00:02:16.375 align:middle line:84% up there, where the love relation holds between X and A 00:02:16.375 --> 00:02:16.900 align:middle line:90% and B-- 00:02:16.900 --> 00:02:19.840 align:middle line:84% X loves both A and B, and between Y and C, 00:02:19.840 --> 00:02:23.020 align:middle line:84% and between Z and both D and E. So that's 00:02:23.020 --> 00:02:24.972 align:middle line:84% a possible reading for the sentence. 00:02:24.972 --> 00:02:26.680 align:middle line:84% And then there's another possible reading 00:02:26.680 --> 00:02:29.380 align:middle line:84% for the sentence, and then there are 00:02:29.380 --> 00:02:33.160 align:middle line:84% arguments about whether this is a different reading or not, 00:02:33.160 --> 00:02:35.320 align:middle line:84% in which it means someone loves everyone 00:02:35.320 --> 00:02:38.350 align:middle line:84% what that means is there is a person who loves everyone. 00:02:38.350 --> 00:02:39.760 align:middle line:90% Maybe it's my grandma-- 00:02:39.760 --> 00:02:40.880 align:middle line:90% very loving person. 00:02:40.880 --> 00:02:43.700 align:middle line:90% She loves absolutely everyone. 00:02:43.700 --> 00:02:46.300 align:middle line:84% And so the love relation holds between X and absolutely 00:02:46.300 --> 00:02:49.010 align:middle line:90% everyone, including herself. 00:02:49.010 --> 00:02:51.890 align:middle line:84% So that's a kind of ambiguity people have claimed to exist. 00:02:51.890 --> 00:02:54.730 align:middle line:84% I don't want us to get too hung up on whether it does. 00:02:54.730 --> 00:02:57.640 align:middle line:84% There are clearer examples maybe. 00:02:57.640 --> 00:03:00.400 align:middle line:84% Think about a sentence like "Everyone in this room 00:03:00.400 --> 00:03:01.810 align:middle line:90% speaks two languages." 00:03:01.810 --> 00:03:04.215 align:middle line:90% 00:03:04.215 --> 00:03:06.340 align:middle line:84% This is going to be a clearer example because we'll 00:03:06.340 --> 00:03:09.550 align:middle line:84% see that the availability of the two meanings 00:03:09.550 --> 00:03:12.160 align:middle line:84% can be affected by things that we can do. 00:03:12.160 --> 00:03:14.900 align:middle line:90% What's something this can mean? 00:03:14.900 --> 00:03:16.200 align:middle line:90% Yeah? 00:03:16.200 --> 00:03:18.270 align:middle line:84% AUDIENCE: For every individual, it's 00:03:18.270 --> 00:03:21.150 align:middle line:84% true that that individual speaks two different languages. 00:03:21.150 --> 00:03:22.775 align:middle line:84% NORVIN RICHARDS: Yeah, so it's possible 00:03:22.775 --> 00:03:25.380 align:middle line:84% that it means everyone in this room is bilingual. 00:03:25.380 --> 00:03:28.420 align:middle line:84% So maybe I speak English and Spanish, 00:03:28.420 --> 00:03:31.530 align:middle line:84% and you speak Ukrainian and Polish, 00:03:31.530 --> 00:03:34.170 align:middle line:84% and you speak Mandarin and Japanese. 00:03:34.170 --> 00:03:35.930 align:middle line:84% So everybody in this room is bilingual. 00:03:35.930 --> 00:03:38.700 align:middle line:90% It could mean that. 00:03:38.700 --> 00:03:40.470 align:middle line:84% What's another thing it can mean? 00:03:40.470 --> 00:03:41.092 align:middle line:90% Yeah? 00:03:41.092 --> 00:03:43.050 align:middle line:84% AUDIENCE: If you put together all the languages 00:03:43.050 --> 00:03:45.300 align:middle line:84% that everyone in this room knew, it would only be two. 00:03:45.300 --> 00:03:46.633 align:middle line:90% NORVIN RICHARDS: Right, exactly. 00:03:46.633 --> 00:03:48.780 align:middle line:84% So if you took a survey of everybody in this room 00:03:48.780 --> 00:03:50.780 align:middle line:84% and found out all the languages that they speak, 00:03:50.780 --> 00:03:52.980 align:middle line:84% there would be two things, two languages that we all 00:03:52.980 --> 00:03:53.920 align:middle line:90% have in common. 00:03:53.920 --> 00:03:57.360 align:middle line:84% Maybe we all speak English and we all speak Tagalog. 00:03:57.360 --> 00:04:00.060 align:middle line:84% Maybe some of you speak 12 languages, but two of them 00:04:00.060 --> 00:04:01.590 align:middle line:90% are English and Tagalog. 00:04:01.590 --> 00:04:03.260 align:middle line:84% That's another thing that it could mean. 00:04:03.260 --> 00:04:03.760 align:middle line:90% Yeah? 00:04:03.760 --> 00:04:09.030 align:middle line:84% AUDIENCE: I don't actually read the sentence that second way. 00:04:09.030 --> 00:04:11.700 align:middle line:84% If everyone in this room speaks two languages, 00:04:11.700 --> 00:04:15.190 align:middle line:84% as in collectively, everyone in this room speaks two languages. 00:04:15.190 --> 00:04:16.720 align:middle line:90% That just doesn't-- 00:04:16.720 --> 00:04:17.980 align:middle line:90% I don't read it like that. 00:04:17.980 --> 00:04:20.522 align:middle line:84% NORVIN RICHARDS: That's not the first reading you get for it. 00:04:20.522 --> 00:04:21.920 align:middle line:84% Yeah, I agree with you, actually. 00:04:21.920 --> 00:04:24.250 align:middle line:84% So what you're claiming is that if I 00:04:24.250 --> 00:04:26.200 align:middle line:84% were to say "Everyone in this room 00:04:26.200 --> 00:04:28.948 align:middle line:84% speaks two languages, namely English and Tagalog," 00:04:28.948 --> 00:04:31.240 align:middle line:84% your interpretation would be that everyone in this room 00:04:31.240 --> 00:04:32.740 align:middle line:84% is bilingual in English and Tagalog. 00:04:32.740 --> 00:04:35.957 align:middle line:84% (Tagalog is a language from the Philippines.) 00:04:35.957 --> 00:04:37.540 align:middle line:84% It's a lot easier to get that reading, 00:04:37.540 --> 00:04:39.790 align:middle line:84% I agree with you, than it is to get the other reading, 00:04:39.790 --> 00:04:42.340 align:middle line:84% where it just means everyone in this room is bilingual. 00:04:42.340 --> 00:04:42.970 align:middle line:90% Yeah? 00:04:42.970 --> 00:04:46.960 align:middle line:84% AUDIENCE: I think I would have [INAUDIBLE] 00:04:46.960 --> 00:04:50.357 align:middle line:90% something to me in total. 00:04:50.357 --> 00:04:51.940 align:middle line:84% NORVIN RICHARDS: Everyone in this room 00:04:51.940 --> 00:04:54.460 align:middle line:90% speaks two languages between us. 00:04:54.460 --> 00:04:56.918 align:middle line:84% Yeah, you feel as though there could be modifications 00:04:56.918 --> 00:04:58.960 align:middle line:84% that you could make that would make that reading. 00:04:58.960 --> 00:05:00.550 align:middle line:84% Here's one modification you can make that makes 00:05:00.550 --> 00:05:01.467 align:middle line:90% that reading come out. 00:05:01.467 --> 00:05:03.160 align:middle line:90% You can passivize the sentence. 00:05:03.160 --> 00:05:08.410 align:middle line:84% So "Two languages are spoken by everyone in this room," 00:05:08.410 --> 00:05:10.690 align:middle line:84% I think has that reading really clear. 00:05:10.690 --> 00:05:13.750 align:middle line:84% There are two languages that we all have in common. 00:05:13.750 --> 00:05:16.098 align:middle line:84% It's possible that it can also mean the other thing, 00:05:16.098 --> 00:05:17.890 align:middle line:84% that it can also mean everyone in this room 00:05:17.890 --> 00:05:21.880 align:middle line:84% is bilingual, but at least can mean that. 00:05:21.880 --> 00:05:26.140 align:middle line:84% The fact that we can have this sensation that these two 00:05:26.140 --> 00:05:29.860 align:middle line:84% imaginable readings are maybe both available for both 00:05:29.860 --> 00:05:32.350 align:middle line:84% of these sentences, maybe not, but certainly one 00:05:32.350 --> 00:05:35.530 align:middle line:84% is more available than the other depending 00:05:35.530 --> 00:05:37.697 align:middle line:84% on whether the sentence is active or passive-- 00:05:37.697 --> 00:05:39.280 align:middle line:84% it suggests we want to be able to talk 00:05:39.280 --> 00:05:41.830 align:middle line:84% about this kind of difference in meaning 00:05:41.830 --> 00:05:42.970 align:middle line:90% between these sentences. 00:05:42.970 --> 00:05:45.430 align:middle line:84% So we're going to develop the tools to do that today. 00:05:45.430 --> 00:05:50.030 align:middle line:90% 00:05:50.030 --> 00:05:52.250 align:middle line:84% So in order to do that, we're going 00:05:52.250 --> 00:05:54.980 align:middle line:84% to need to develop a theory of a certain special kind of noun 00:05:54.980 --> 00:05:57.320 align:middle line:84% phrase-- what's called a quantifier. 00:05:57.320 --> 00:05:58.820 align:middle line:84% And to do that, we're going to start 00:05:58.820 --> 00:06:01.230 align:middle line:84% by talking about what noun phrases mean more generally. 00:06:01.230 --> 00:06:03.140 align:middle line:90% So here's a noun phrase-- 00:06:03.140 --> 00:06:07.730 align:middle line:84% refers to a person who's the TA for some of you. 00:06:07.730 --> 00:06:11.643 align:middle line:84% And if you were to ask, what does that noun phrase mean? 00:06:11.643 --> 00:06:13.310 align:middle line:84% Well, we talked about this a little bit. 00:06:13.310 --> 00:06:16.550 align:middle line:84% I had the example of there are various things that you 00:06:16.550 --> 00:06:18.785 align:middle line:90% could use to refer to me. 00:06:18.785 --> 00:06:20.660 align:middle line:84% You could refer to me as "Professor Richards" 00:06:20.660 --> 00:06:23.630 align:middle line:84% or as "Norvin" or "that so-and-so who gave me a C"-- 00:06:23.630 --> 00:06:25.500 align:middle line:90% and we're talking about that. 00:06:25.500 --> 00:06:29.270 align:middle line:84% So similarly, here's a phrase that if you ask what it means, 00:06:29.270 --> 00:06:32.570 align:middle line:84% you might expect that if we look this up in your mental lexicon, 00:06:32.570 --> 00:06:35.810 align:middle line:84% what we would find is a picture of this guy-- 00:06:35.810 --> 00:06:38.390 align:middle line:84% those of you who have him as your TA, at least. 00:06:38.390 --> 00:06:39.890 align:middle line:84% So if you don't have him as your TA, 00:06:39.890 --> 00:06:42.223 align:middle line:84% maybe you don't know who he is, but he's one of the TAs. 00:06:42.223 --> 00:06:44.450 align:middle line:90% 00:06:44.450 --> 00:06:48.560 align:middle line:84% And to say, for example, "Enrico Flor is an avid hangglider" 00:06:48.560 --> 00:06:51.030 align:middle line:90% is to say something like-- 00:06:51.030 --> 00:06:54.290 align:middle line:84% we ask what that means, it's going to mean something like-- 00:06:54.290 --> 00:06:57.092 align:middle line:84% we'll have to figure out the meaning of avid hangglider. 00:06:57.092 --> 00:06:59.300 align:middle line:84% What is it to say that someone is an avid hangglider? 00:06:59.300 --> 00:07:01.160 align:middle line:84% But when we figure out what that is, 00:07:01.160 --> 00:07:02.780 align:middle line:84% we'll have a list of all of the people 00:07:02.780 --> 00:07:04.070 align:middle line:90% who are avid hanggliders. 00:07:04.070 --> 00:07:08.360 align:middle line:84% And this claim is that list will have Enrico Flor's name on it. 00:07:08.360 --> 00:07:11.310 align:middle line:90% That's what that means. 00:07:11.310 --> 00:07:15.350 align:middle line:84% So that's a comparatively simple meaning for a noun phrase. 00:07:15.350 --> 00:07:18.350 align:middle line:84% Enrico Flor-- that noun phrase refers to that guy. 00:07:18.350 --> 00:07:20.960 align:middle line:90% 00:07:20.960 --> 00:07:24.380 align:middle line:84% What if I wanted to tell you, the 24.900 TAs are avid 00:07:24.380 --> 00:07:25.760 align:middle line:90% hanggliders. 00:07:25.760 --> 00:07:29.150 align:middle line:84% So again, we're going to have a list of the avid hanggliders. 00:07:29.150 --> 00:07:32.780 align:middle line:90% What does this sentence say? 00:07:32.780 --> 00:07:34.640 align:middle line:90% What does it mean? 00:07:34.640 --> 00:07:38.270 align:middle line:84% AUDIENCE: You first have to parse what the 24.900 TAs are 00:07:38.270 --> 00:07:42.260 align:middle line:84% and decompose that into a list of people and match them up 00:07:42.260 --> 00:07:44.898 align:middle line:90% with who are the [INAUDIBLE]. 00:07:44.898 --> 00:07:46.190 align:middle line:90% NORVIN RICHARDS: Yeah, exactly. 00:07:46.190 --> 00:07:47.450 align:middle line:90% That's a nice way to say it. 00:07:47.450 --> 00:07:49.700 align:middle line:84% So we're going to have a list of the avid hanggliders, 00:07:49.700 --> 00:07:52.057 align:middle line:84% and we're going to have a list of the 24.900 TAs. 00:07:52.057 --> 00:07:54.140 align:middle line:84% It'll have Enrico Flor, and it'll have Yash Sinha, 00:07:54.140 --> 00:07:58.010 align:middle line:84% and it'll have all four of the TAs. 00:07:58.010 --> 00:07:59.875 align:middle line:84% And what this says is if you look 00:07:59.875 --> 00:08:01.250 align:middle line:84% at that list of avid hanggliders, 00:08:01.250 --> 00:08:02.958 align:middle line:84% it'll have all four of those names on it. 00:08:02.958 --> 00:08:07.320 align:middle line:90% 00:08:07.320 --> 00:08:09.960 align:middle line:84% I'm trying to lure you into a false sense of security here. 00:08:09.960 --> 00:08:13.250 align:middle line:84% So far, this should seem pretty simple. 00:08:13.250 --> 00:08:14.890 align:middle line:90% So yeah, there's a list-- 00:08:14.890 --> 00:08:15.430 align:middle line:90% set. 00:08:15.430 --> 00:08:16.630 align:middle line:90% I've made it a set here. 00:08:16.630 --> 00:08:20.380 align:middle line:84% It's a set that contains Enrico and Peter and Yash and Anton. 00:08:20.380 --> 00:08:23.890 align:middle line:84% And what we're saying is that set 00:08:23.890 --> 00:08:26.535 align:middle line:84% is a subset of the set of avid hanggliders. 00:08:26.535 --> 00:08:31.630 align:middle line:90% 00:08:31.630 --> 00:08:36.320 align:middle line:90% What set does "every Italian"-- 00:08:36.320 --> 00:08:38.289 align:middle line:90% Enrico Flor is Italian-- 00:08:38.289 --> 00:08:43.200 align:middle line:84% what set does "every Italian" refer to, 00:08:43.200 --> 00:08:45.780 align:middle line:84% if we're going to let noun phrases refer to sets? 00:08:45.780 --> 00:08:47.560 align:middle line:90% Yeah? 00:08:47.560 --> 00:08:50.680 align:middle line:84% AUDIENCE: Either every person such that that person 00:08:50.680 --> 00:08:55.573 align:middle line:84% has Italian citizenship or Italian ancestry? 00:08:55.573 --> 00:08:57.740 align:middle line:84% NORVIN RICHARDS: Yeah, so you're being very careful. 00:08:57.740 --> 00:08:59.520 align:middle line:84% But yes, so somehow we'll have to define 00:08:59.520 --> 00:09:00.520 align:middle line:90% what we mean by Italian. 00:09:00.520 --> 00:09:01.062 align:middle line:90% You're right. 00:09:01.062 --> 00:09:01.960 align:middle line:90% That's right. 00:09:01.960 --> 00:09:05.020 align:middle line:84% And then we'll end up with a list of Italians. 00:09:05.020 --> 00:09:07.510 align:middle line:90% And then that'll be the set. 00:09:07.510 --> 00:09:10.570 align:middle line:84% So similarly, if you say "Every Italian is an avid hangglider," 00:09:10.570 --> 00:09:13.670 align:middle line:84% what we mean is it's kind of like "The 24.900 TAs are avid 00:09:13.670 --> 00:09:14.350 align:middle line:90% hanggliders." 00:09:14.350 --> 00:09:16.150 align:middle line:84% Everyone in this list is also in this list. 00:09:16.150 --> 00:09:17.920 align:middle line:84% Everyone in this set is also in this set. 00:09:17.920 --> 00:09:20.020 align:middle line:90% That's what that means. 00:09:20.020 --> 00:09:22.587 align:middle line:84% So "every Italian" will have a list of Italians-- 00:09:22.587 --> 00:09:23.920 align:middle line:90% that's how the list could start. 00:09:23.920 --> 00:09:29.050 align:middle line:84% And you're saying everybody in that 00:09:29.050 --> 00:09:32.120 align:middle line:90% list is an avid hangglider. 00:09:32.120 --> 00:09:35.282 align:middle line:90% OK, so far, so good. 00:09:35.282 --> 00:09:36.240 align:middle line:90% How about "No Italian?" 00:09:36.240 --> 00:09:36.990 align:middle line:90% What set is that? 00:09:36.990 --> 00:09:39.790 align:middle line:90% 00:09:39.790 --> 00:09:40.960 align:middle line:90% Yeah? 00:09:40.960 --> 00:09:43.210 align:middle line:84% AUDIENCE: It's like if you took the set of all people, 00:09:43.210 --> 00:09:45.280 align:middle line:84% but you took out all of the Italians. 00:09:45.280 --> 00:09:46.988 align:middle line:84% NORVIN RICHARDS: Subtracted the Italians. 00:09:46.988 --> 00:09:49.568 align:middle line:90% 00:09:49.568 --> 00:09:51.860 align:middle line:84% AUDIENCE: It would be the partition of all people who's 00:09:51.860 --> 00:09:53.135 align:middle line:90% not Italian. 00:09:53.135 --> 00:09:54.760 align:middle line:84% NORVIN RICHARDS: But if it means that-- 00:09:54.760 --> 00:09:56.500 align:middle line:90% no, that's a nice idea. 00:09:56.500 --> 00:09:59.553 align:middle line:84% So we'll take the set of people, and we'll subtract from it 00:09:59.553 --> 00:10:00.970 align:middle line:84% all of the Italians, everybody who 00:10:00.970 --> 00:10:02.410 align:middle line:90% was on the list of Italians. 00:10:02.410 --> 00:10:05.170 align:middle line:84% But then what is "No Italian is an avid hangglider" 00:10:05.170 --> 00:10:05.890 align:middle line:90% going to mean? 00:10:05.890 --> 00:10:08.610 align:middle line:90% 00:10:08.610 --> 00:10:09.352 align:middle line:90% Yeah? 00:10:09.352 --> 00:10:11.310 align:middle line:84% AUDIENCE: Just means that of the list of people 00:10:11.310 --> 00:10:13.560 align:middle line:84% that you identify as Italians, none of them 00:10:13.560 --> 00:10:15.997 align:middle line:84% will be found in the list of avid hanggliders. 00:10:15.997 --> 00:10:17.830 align:middle line:84% NORVIN RICHARDS: So we want it to mean that. 00:10:17.830 --> 00:10:19.260 align:middle line:90% But if it meant what Raquel-- 00:10:19.260 --> 00:10:21.498 align:middle line:84% if no Italian meant what Raquel wanted it to make-- 00:10:21.498 --> 00:10:23.040 align:middle line:84% I'm sorry, Raquel, I'm picking on you 00:10:23.040 --> 00:10:25.410 align:middle line:84% because you were smart enough to make a suggestion-- it 00:10:25.410 --> 00:10:29.858 align:middle line:84% would mean everyone who is not Italian is an avid hangglider. 00:10:29.858 --> 00:10:32.400 align:middle line:84% And that's not what "No Italian is an avid hangglider" means, 00:10:32.400 --> 00:10:33.270 align:middle line:90% I think. 00:10:33.270 --> 00:10:34.785 align:middle line:84% Sorry, what were you going to say? 00:10:34.785 --> 00:10:35.190 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:10:35.190 --> 00:10:36.482 align:middle line:90% NORVIN RICHARDS: Say that, yes. 00:10:36.482 --> 00:10:39.000 align:middle line:84% Yeah, I'm sorry, I should start calling on you 00:10:39.000 --> 00:10:40.922 align:middle line:90% guys instead of-- yes, Raquel? 00:10:40.922 --> 00:10:42.630 align:middle line:84% AUDIENCE: If there is an avid hangglider, 00:10:42.630 --> 00:10:46.230 align:middle line:84% it has to be part of the subtracted-- 00:10:46.230 --> 00:10:48.450 align:middle line:84% like the set that doesn't have Italian-- 00:10:48.450 --> 00:10:51.210 align:middle line:84% like every single one must, but if there is going to be one, 00:10:51.210 --> 00:10:52.410 align:middle line:90% it better be in that. 00:10:52.410 --> 00:10:54.202 align:middle line:84% NORVIN RICHARDS: All the other hang gliders 00:10:54.202 --> 00:10:57.030 align:middle line:84% have to be in the complement set of the set of Italians, 00:10:57.030 --> 00:10:58.800 align:middle line:90% something like that. 00:10:58.800 --> 00:10:59.630 align:middle line:90% Yeah? 00:10:59.630 --> 00:11:00.930 align:middle line:90% Yeah, Joseph? 00:11:00.930 --> 00:11:03.180 align:middle line:84% AUDIENCE: Instead of Italians, instead of hanggliders, 00:11:03.180 --> 00:11:04.523 align:middle line:90% the intersection is a null set. 00:11:04.523 --> 00:11:06.690 align:middle line:84% NORVIN RICHARDS: Yeah, so I think what we're saying, 00:11:06.690 --> 00:11:09.330 align:middle line:84% what we're getting to and I think you said this more 00:11:09.330 --> 00:11:13.260 align:middle line:84% or less the same way, every other set that we've talked 00:11:13.260 --> 00:11:16.590 align:middle line:84% about, when we said "The 24.900 TAs are avid hanggliders," 00:11:16.590 --> 00:11:19.110 align:middle line:84% we said, yeah, there's a set of 24.900 TAs and there's a set 00:11:19.110 --> 00:11:21.930 align:middle line:84% of avid hanggliders, and the first set is contained 00:11:21.930 --> 00:11:23.130 align:middle line:90% in the second set. 00:11:23.130 --> 00:11:24.210 align:middle line:90% That's what that means. 00:11:24.210 --> 00:11:26.677 align:middle line:84% And every Italian is an avid hangglider-- 00:11:26.677 --> 00:11:29.010 align:middle line:84% there's a set of Italians and a set of avid hanggliders, 00:11:29.010 --> 00:11:31.410 align:middle line:84% and the first set is contained in the second set. 00:11:31.410 --> 00:11:35.280 align:middle line:84% But "no," as in "no Italian," makes 00:11:35.280 --> 00:11:38.280 align:middle line:84% you have the sets interact with each other in a different way. 00:11:38.280 --> 00:11:42.420 align:middle line:84% It says this first set is not contained. 00:11:42.420 --> 00:11:45.520 align:middle line:84% Nothing in this first set is contained in the second set. 00:11:45.520 --> 00:11:47.665 align:middle line:84% So this is a popular way of talking 00:11:47.665 --> 00:11:50.040 align:middle line:84% about the meanings of what are called quantifiers-- words 00:11:50.040 --> 00:11:52.140 align:middle line:90% like "every" and "no." 00:11:52.140 --> 00:11:53.250 align:middle line:90% So it's not the null set. 00:11:53.250 --> 00:11:54.990 align:middle line:84% It's not a set containing no Italian. 00:11:54.990 --> 00:11:58.570 align:middle line:90% 00:11:58.570 --> 00:12:01.653 align:middle line:84% A popular way of talking about the meanings of these kinds 00:12:01.653 --> 00:12:03.570 align:middle line:84% of expressions-- these are called quantifiers, 00:12:03.570 --> 00:12:07.620 align:middle line:84% these expressions which do fancier things with sets than 00:12:07.620 --> 00:12:11.172 align:middle line:84% just say, oh yeah, this set is inside this set-- 00:12:11.172 --> 00:12:12.630 align:middle line:84% a popular way of talking about them 00:12:12.630 --> 00:12:16.020 align:middle line:84% is to say they do fancier things with sets. 00:12:16.020 --> 00:12:18.660 align:middle line:84% They allow you to do more interesting things 00:12:18.660 --> 00:12:20.970 align:middle line:84% with set interaction than just say this set is 00:12:20.970 --> 00:12:22.380 align:middle line:90% a subset of that set. 00:12:22.380 --> 00:12:23.380 align:middle line:90% That's what they do. 00:12:23.380 --> 00:12:25.680 align:middle line:90% That's what they're for. 00:12:25.680 --> 00:12:28.847 align:middle line:84% Quantifiers have a bunch of interesting properties. 00:12:28.847 --> 00:12:30.180 align:middle line:90% They're weird in other ways too. 00:12:30.180 --> 00:12:33.060 align:middle line:84% So, for example, there is something called 00:12:33.060 --> 00:12:35.760 align:middle line:90% the Law of Contradiction. 00:12:35.760 --> 00:12:39.180 align:middle line:84% If-- the Law of Contradiction says if you take two predicates 00:12:39.180 --> 00:12:43.660 align:middle line:84% that are contradictory, like "be inside" and "be outside," 00:12:43.660 --> 00:12:47.910 align:middle line:84% if you join me in imagining that it's not possible to be both 00:12:47.910 --> 00:12:51.000 align:middle line:90% inside and outside-- 00:12:51.000 --> 00:12:52.553 align:middle line:84% and I can see some of you thinking 00:12:52.553 --> 00:12:54.970 align:middle line:84% of alternative ways of thinking about the world in which-- 00:12:54.970 --> 00:12:58.000 align:middle line:84% but suppose I'm halfway inside and halfway outside. 00:12:58.000 --> 00:12:59.760 align:middle line:90% Which am I? 00:12:59.760 --> 00:13:02.035 align:middle line:84% I'm in the Department of Linguistics and Philosophy, 00:13:02.035 --> 00:13:03.910 align:middle line:84% so I'm used to hearing people talk like that. 00:13:03.910 --> 00:13:06.480 align:middle line:90% But please stop. 00:13:06.480 --> 00:13:09.095 align:middle line:84% Just imagine that you're either inside or you are outside 00:13:09.095 --> 00:13:09.720 align:middle line:90% and that's all. 00:13:09.720 --> 00:13:12.000 align:middle line:84% And imagine that Paul is a single person. 00:13:12.000 --> 00:13:14.700 align:middle line:84% There's only one person on Earth named Paul. 00:13:14.700 --> 00:13:21.930 align:middle line:84% So then "Paul is inside and Paul is outside" cannot be true. 00:13:21.930 --> 00:13:23.560 align:middle line:90% That's the Law of Contradiction. 00:13:23.560 --> 00:13:27.150 align:middle line:84% So if you have two predicates that are opposites of each 00:13:27.150 --> 00:13:29.760 align:middle line:84% other, cannot both be true of a single person, 00:13:29.760 --> 00:13:33.360 align:middle line:84% then if you apply them to a single person, 00:13:33.360 --> 00:13:35.080 align:middle line:84% then the sentence has to be false. 00:13:35.080 --> 00:13:36.960 align:middle line:84% That's what that first example is. 00:13:36.960 --> 00:13:39.600 align:middle line:84% It's an example of the Law of Contradiction. 00:13:39.600 --> 00:13:42.390 align:middle line:84% But there are quantifiers like "several Americans," 00:13:42.390 --> 00:13:45.120 align:middle line:84% which just flagrantly violate the Law of Contradiction. 00:13:45.120 --> 00:13:47.370 align:middle line:84% So "Several Americans are inside and several Americans 00:13:47.370 --> 00:13:48.660 align:middle line:90% are outside"-- 00:13:48.660 --> 00:13:49.800 align:middle line:90% fine. 00:13:49.800 --> 00:13:50.970 align:middle line:90% No problem. 00:13:50.970 --> 00:13:52.680 align:middle line:84% And you don't have to play games with 00:13:52.680 --> 00:13:55.110 align:middle line:84% whether if you're halfway inside or halfway outside 00:13:55.110 --> 00:13:59.488 align:middle line:84% or you're inside the building but you're outside the campus 00:13:59.488 --> 00:14:00.030 align:middle line:90% or something. 00:14:00.030 --> 00:14:01.320 align:middle line:90% Just forget about all that. 00:14:01.320 --> 00:14:06.320 align:middle line:90% 00:14:06.320 --> 00:14:08.540 align:middle line:84% There are also quantifiers that fail 00:14:08.540 --> 00:14:11.990 align:middle line:84% what's called the Law of the Excluded Middle. 00:14:11.990 --> 00:14:13.880 align:middle line:84% The Law of the Excluded Middle says 00:14:13.880 --> 00:14:17.930 align:middle line:84% if you have two predicates like "be under 6 feet tall" 00:14:17.930 --> 00:14:22.260 align:middle line:84% and "be over 5 feet tall," then a sentence 00:14:22.260 --> 00:14:24.240 align:middle line:84% like "Takashi is under 6 feet tall 00:14:24.240 --> 00:14:29.230 align:middle line:84% or Takashi is over 5 feet tall" has to be true. 00:14:29.230 --> 00:14:32.700 align:middle line:84% We don't have to measure Takashi to find out whether that's true 00:14:32.700 --> 00:14:34.530 align:middle line:84% because the set of people who are 00:14:34.530 --> 00:14:38.790 align:middle line:84% under 6 feet tall and the set of people who are over 5 feet tall 00:14:38.790 --> 00:14:40.240 align:middle line:90% overlap. 00:14:40.240 --> 00:14:42.030 align:middle line:84% If you have both of those sets together, 00:14:42.030 --> 00:14:44.070 align:middle line:90% they cover all people. 00:14:44.070 --> 00:14:47.730 align:middle line:84% Any height that someone is, they are at least one 00:14:47.730 --> 00:14:49.980 align:middle line:84% of those two things, possibly both. 00:14:49.980 --> 00:14:53.320 align:middle line:84% Someone who's between 5 feet tall and 6 feet tall is both. 00:14:53.320 --> 00:14:56.410 align:middle line:84% And someone who's under 5 is under 6, 00:14:56.410 --> 00:15:00.590 align:middle line:84% and someone who's over 6 is, well, over 5. 00:15:00.590 --> 00:15:01.760 align:middle line:90% That sound right? 00:15:01.760 --> 00:15:06.290 align:middle line:84% These are two predicates such that here's 5 feet tall. 00:15:06.290 --> 00:15:07.800 align:middle line:90% Here's 6 feet tall. 00:15:07.800 --> 00:15:10.670 align:middle line:84% We're talking about people who are under 6 feet tall 00:15:10.670 --> 00:15:13.190 align:middle line:84% and also the people who are over 5 feet tall. 00:15:13.190 --> 00:15:15.500 align:middle line:90% Well, we've covered everybody. 00:15:15.500 --> 00:15:17.360 align:middle line:84% So we don't have to look at Takashi. 00:15:17.360 --> 00:15:20.592 align:middle line:84% We don't have to know who Takashi is. 00:15:20.592 --> 00:15:21.800 align:middle line:90% That first sentence is true-- 00:15:21.800 --> 00:15:27.290 align:middle line:84% Takashi is under 6 feet tall or Takashi is over 5 feet tall. 00:15:27.290 --> 00:15:30.590 align:middle line:84% But the second sentence is false, or at least 00:15:30.590 --> 00:15:32.100 align:middle line:90% doesn't have to be true. 00:15:32.100 --> 00:15:34.760 align:middle line:84% So "All Japanese men are under 6 feet tall 00:15:34.760 --> 00:15:39.440 align:middle line:84% or all Japanese men are over 5 feet tall." 00:15:39.440 --> 00:15:41.090 align:middle line:90% That could be false. 00:15:41.090 --> 00:15:43.805 align:middle line:84% Can somebody name a context in which that would be false? 00:15:43.805 --> 00:15:47.655 align:middle line:90% 00:15:47.655 --> 00:15:49.280 align:middle line:84% I'm asking you to do it because I can't 00:15:49.280 --> 00:15:50.630 align:middle line:90% do math while standing up here. 00:15:50.630 --> 00:15:51.950 align:middle line:90% Yeah, Joseph. 00:15:51.950 --> 00:15:55.483 align:middle line:84% AUDIENCE: There happened to be a particularly tall-- 00:15:55.483 --> 00:15:58.360 align:middle line:84% someone who's over 6 feet, or particularly short 00:15:58.360 --> 00:16:01.677 align:middle line:84% under 5 feet [INAUDIBLE],, and the population of Japanese men 00:16:01.677 --> 00:16:02.710 align:middle line:90% are [INAUDIBLE]. 00:16:02.710 --> 00:16:04.822 align:middle line:90% 00:16:04.822 --> 00:16:06.530 align:middle line:84% NORVIN RICHARDS: Yeah, there we go, good. 00:16:06.530 --> 00:16:08.810 align:middle line:84% So as long as you have at least one Japanese man who's 00:16:08.810 --> 00:16:10.910 align:middle line:84% over 6 feet tall and at least one Japanese man who 00:16:10.910 --> 00:16:13.160 align:middle line:84% is under 5 feet tall, the rest of the Japanese men 00:16:13.160 --> 00:16:14.580 align:middle line:90% can all do whatever they want. 00:16:14.580 --> 00:16:16.970 align:middle line:90% The sentence will be false. 00:16:16.970 --> 00:16:18.110 align:middle line:90% Good. 00:16:18.110 --> 00:16:21.080 align:middle line:84% So quantifier phrases, quantifiers, 00:16:21.080 --> 00:16:23.690 align:middle line:84% quantification expressions, like "all Japanese men" 00:16:23.690 --> 00:16:28.610 align:middle line:84% or "some Italians" or "no Italians," 00:16:28.610 --> 00:16:36.410 align:middle line:84% fail these otherwise reliable generalizations 00:16:36.410 --> 00:16:40.100 align:middle line:90% about sentences. 00:16:40.100 --> 00:16:43.070 align:middle line:84% So expressions like "no Turks" or "several Americans" 00:16:43.070 --> 00:16:44.810 align:middle line:84% or "all Italians" or "most Ukrainians" 00:16:44.810 --> 00:16:46.380 align:middle line:90% don't refer to sets of people. 00:16:46.380 --> 00:16:47.130 align:middle line:90% What do they mean? 00:16:47.130 --> 00:16:50.970 align:middle line:90% Well, what they do is they-- 00:16:50.970 --> 00:16:53.960 align:middle line:84% already said this-- these words at the beginning, like "no" 00:16:53.960 --> 00:16:59.540 align:middle line:84% or "several" or "all" or "most," are doing cool set 00:16:59.540 --> 00:17:03.440 align:middle line:84% theoretic things with the set that they are combining with. 00:17:03.440 --> 00:17:07.190 align:middle line:84% So the set of Turks or Americans or Italians or Ukrainians, 00:17:07.190 --> 00:17:09.829 align:middle line:84% they're causing that set to interact in interesting ways 00:17:09.829 --> 00:17:12.387 align:middle line:84% with a set that's determined by the rest of the sentence. 00:17:12.387 --> 00:17:13.970 align:middle line:84% In order to talk about this, let me do 00:17:13.970 --> 00:17:18.488 align:middle line:90% a quick review of set theory. 00:17:18.488 --> 00:17:20.530 align:middle line:84% You're not going to need to very much that theory 00:17:20.530 --> 00:17:21.859 align:middle line:90% in order to do this. 00:17:21.859 --> 00:17:24.069 align:middle line:84% I tell you this because I don't very much set theory, 00:17:24.069 --> 00:17:27.970 align:middle line:84% and I can do this, so I'll just show you what 00:17:27.970 --> 00:17:30.980 align:middle line:90% I'm going to show you here. 00:17:30.980 --> 00:17:34.270 align:middle line:90% Here are two sets, pi and phi-- 00:17:34.270 --> 00:17:35.470 align:middle line:90% a Venn diagram. 00:17:35.470 --> 00:17:37.750 align:middle line:84% It's hopefully not too unfamiliar. 00:17:37.750 --> 00:17:41.590 align:middle line:84% Two sets, pi and phi, which have an overlap 00:17:41.590 --> 00:17:44.290 align:middle line:84% that contains D and F, and then there are also 00:17:44.290 --> 00:17:47.178 align:middle line:84% things that are only in pi and not in phi, like A and B. 00:17:47.178 --> 00:17:49.720 align:middle line:84% And there are some things that are only in phi and not in pi, 00:17:49.720 --> 00:17:51.520 align:middle line:90% like C and E. That sound right? 00:17:51.520 --> 00:17:55.020 align:middle line:84% People are all familiar with Venn diagrams. 00:17:55.020 --> 00:17:59.970 align:middle line:84% We say that D and F is the intersection of pi and phi, 00:17:59.970 --> 00:18:04.140 align:middle line:84% and that little hoop is the thing that you 00:18:04.140 --> 00:18:07.380 align:middle line:90% use to express intersection. 00:18:07.380 --> 00:18:12.997 align:middle line:84% And we say that A, B, C, D, and F is the union of pi and phi, 00:18:12.997 --> 00:18:15.330 align:middle line:84% where I have, for some reason, used the word "of" twice. 00:18:15.330 --> 00:18:18.900 align:middle line:84% I'll try to fix that before I put up the slides. 00:18:18.900 --> 00:18:21.450 align:middle line:84% And the little thing that looks more or less like a U 00:18:21.450 --> 00:18:24.510 align:middle line:90% is the expression for union. 00:18:24.510 --> 00:18:28.410 align:middle line:84% We also say that A, B, and D is a subset of pi, 00:18:28.410 --> 00:18:31.515 align:middle line:84% and there's a symbol that's used sometimes for subsets. 00:18:31.515 --> 00:18:34.560 align:middle line:90% 00:18:34.560 --> 00:18:39.970 align:middle line:84% None of this seems alarming-- subsets, union, intersection? 00:18:39.970 --> 00:18:42.285 align:middle line:84% OK, so here's the popular answer-- 00:18:42.285 --> 00:18:44.410 align:middle line:84% which we've now already gone through for quantifier 00:18:44.410 --> 00:18:47.590 align:middle line:84% meaning-- what we say is when you're saying something 00:18:47.590 --> 00:18:52.120 align:middle line:84% like "All Americans eat junk food" is you are asserting 00:18:52.120 --> 00:18:54.040 align:middle line:84% a relation between the set of Americans 00:18:54.040 --> 00:18:56.882 align:middle line:90% and the set of junk food eaters. 00:18:56.882 --> 00:18:58.840 align:middle line:84% You're saying something about what happens when 00:18:58.840 --> 00:19:02.590 align:middle line:90% you intersect those two sets. 00:19:02.590 --> 00:19:05.530 align:middle line:84% And depending on what quantifier you're using, 00:19:05.530 --> 00:19:07.080 align:middle line:84% you're making different assertions 00:19:07.080 --> 00:19:08.830 align:middle line:84% about the relation between these two sets. 00:19:08.830 --> 00:19:14.206 align:middle line:84% So "all" says set number one is a subset of set number two-- 00:19:14.206 --> 00:19:15.395 align:middle line:90% what some say. 00:19:15.395 --> 00:19:18.125 align:middle line:90% 00:19:18.125 --> 00:19:19.085 align:middle line:90% Yeah, [INAUDIBLE]? 00:19:19.085 --> 00:19:20.960 align:middle line:84% AUDIENCE: The intersection is not a null set. 00:19:20.960 --> 00:19:23.180 align:middle line:84% NORVIN RICHARDS: Yeah, the intersection is nonempty. 00:19:23.180 --> 00:19:24.930 align:middle line:84% So there are things that are in both sets. 00:19:24.930 --> 00:19:28.070 align:middle line:90% 00:19:28.070 --> 00:19:31.730 align:middle line:84% "No" says the intersection of set one and set two is empty-- 00:19:31.730 --> 00:19:33.410 align:middle line:90% "No Americans eat nattoo"-- 00:19:33.410 --> 00:19:35.110 align:middle line:90% are people familiar with nattoo? 00:19:35.110 --> 00:19:36.860 align:middle line:84% Have we talked about nattoo in this class? 00:19:36.860 --> 00:19:39.560 align:middle line:84% Yes, some of us are from nattoo cultures. 00:19:39.560 --> 00:19:43.670 align:middle line:90% Nattoo is a Japanese food. 00:19:43.670 --> 00:19:46.460 align:middle line:84% It's very good, and it's good for you. 00:19:46.460 --> 00:19:48.985 align:middle line:84% It's high in protein, but it's one of those kinds of food-- 00:19:48.985 --> 00:19:51.110 align:middle line:84% I think a lot of cultures have something like this. 00:19:51.110 --> 00:19:54.050 align:middle line:84% It's a kind of food one of the points of which 00:19:54.050 --> 00:19:56.180 align:middle line:84% is to feed it to outsiders so that you 00:19:56.180 --> 00:19:59.010 align:middle line:90% can watch and be amused. 00:19:59.010 --> 00:20:01.790 align:middle line:84% So this happened to me when I was living in Japan. 00:20:01.790 --> 00:20:05.330 align:middle line:84% We were visiting some the family of a Japanese friend of mine, 00:20:05.330 --> 00:20:07.622 align:middle line:84% and the mother made me up a big dish of nattoo 00:20:07.622 --> 00:20:09.830 align:middle line:84% and they put it in front of me, and the entire family 00:20:09.830 --> 00:20:11.720 align:middle line:90% gathered around to watch. 00:20:11.720 --> 00:20:13.430 align:middle line:84% So you see what is he going to do?-- 00:20:13.430 --> 00:20:17.010 align:middle line:90% Nattoo is fermented soybeans. 00:20:17.010 --> 00:20:23.660 align:middle line:84% So the soybeans are covered in a thin layer of slime, 00:20:23.660 --> 00:20:27.680 align:middle line:84% and then you mix this up with rice and often mustard 00:20:27.680 --> 00:20:29.000 align:middle line:90% and soy sauce. 00:20:29.000 --> 00:20:29.750 align:middle line:90% It's really tasty. 00:20:29.750 --> 00:20:31.542 align:middle line:84% It's really good, but it's also very messy. 00:20:31.542 --> 00:20:34.042 align:middle line:84% So if you're like me and you have facial hair, 00:20:34.042 --> 00:20:35.750 align:middle line:84% by the time you're done, your entire face 00:20:35.750 --> 00:20:38.180 align:middle line:84% is covered in nattoo slime, so you 00:20:38.180 --> 00:20:39.960 align:middle line:84% have to go take a shower after you eat. 00:20:39.960 --> 00:20:42.110 align:middle line:90% But it's good for you. 00:20:42.110 --> 00:20:43.460 align:middle line:90% Tasty stuff. 00:20:43.460 --> 00:20:45.380 align:middle line:84% So it's not true that no Americans eat nattoo, 00:20:45.380 --> 00:20:46.255 align:middle line:90% but it's grammatical. 00:20:46.255 --> 00:20:48.147 align:middle line:84% And what it means is the set of Americans-- 00:20:48.147 --> 00:20:49.730 align:middle line:84% you're looking at the set of Americans 00:20:49.730 --> 00:20:51.397 align:middle line:84% and the set of nattoo eaters, and you're 00:20:51.397 --> 00:20:53.940 align:middle line:84% saying the intersection of those sets is empty. 00:20:53.940 --> 00:20:57.770 align:middle line:84% There's nothing that's in both of these sets. 00:20:57.770 --> 00:21:00.740 align:middle line:84% OK, I don't know whether we have a food like that 00:21:00.740 --> 00:21:03.427 align:middle line:84% in our culture, a food that you feed to people 00:21:03.427 --> 00:21:05.510 align:middle line:84% in order to be amused by their attempts to eat it. 00:21:05.510 --> 00:21:07.310 align:middle line:84% This is something to think about. 00:21:07.310 --> 00:21:08.780 align:middle line:84% I can tell you that the Tagalog version of it though. 00:21:08.780 --> 00:21:11.238 align:middle line:84% I'm sorry, I'll start talking about sets again in a second. 00:21:11.238 --> 00:21:13.910 align:middle line:84% The Tagalog version of this is something called balut. 00:21:13.910 --> 00:21:15.800 align:middle line:84% Have I talked about it in this class? 00:21:15.800 --> 00:21:16.730 align:middle line:90% You've had balut too? 00:21:16.730 --> 00:21:18.020 align:middle line:90% You're an adventurous person. 00:21:18.020 --> 00:21:21.485 align:middle line:84% AUDIENCE: I have not had [INAUDIBLE].. 00:21:21.485 --> 00:21:22.897 align:middle line:90% NORVIN RICHARDS: Not balut, OK. 00:21:22.897 --> 00:21:24.230 align:middle line:90% AUDIENCE: --a whole other level. 00:21:24.230 --> 00:21:27.860 align:middle line:84% NORVIN RICHARDS: Yeah, balut is a duck's egg 00:21:27.860 --> 00:21:29.720 align:middle line:84% that has been allowed to be fertilized. 00:21:29.720 --> 00:21:31.345 align:middle line:84% It's a popular food in the Philippines, 00:21:31.345 --> 00:21:32.813 align:middle line:90% so people sell it in the street. 00:21:32.813 --> 00:21:34.730 align:middle line:84% You have balut sellers who walk around saying, 00:21:34.730 --> 00:21:39.170 align:middle line:84% balut [NON-ENGLISH],, which means "Balut strengthens your knees." 00:21:39.170 --> 00:21:42.590 align:middle line:84% That's apparently the standard thing you say. 00:21:42.590 --> 00:21:46.100 align:middle line:84% And balut is a duck's egg that's been fertilized and then 00:21:46.100 --> 00:21:47.738 align:middle line:90% hardboiled before it hatches. 00:21:47.738 --> 00:21:49.280 align:middle line:84% So you've got a hardboiled duck's egg 00:21:49.280 --> 00:21:53.148 align:middle line:84% with a duck embryo inside, which you're supposed to eat. 00:21:53.148 --> 00:21:54.690 align:middle line:84% When I was living in the Philippines, 00:21:54.690 --> 00:21:56.810 align:middle line:84% my host brother got me got me a balut. 00:21:56.810 --> 00:21:58.993 align:middle line:90% And we were in a dark room. 00:21:58.993 --> 00:22:00.410 align:middle line:84% He handed me the balut, and I went 00:22:00.410 --> 00:22:05.270 align:middle line:84% to turn on the light he was like, no, just eat it. 00:22:05.270 --> 00:22:08.280 align:middle line:84% And I unfortunately turned on the light, so I chickened out. 00:22:08.280 --> 00:22:12.380 align:middle line:84% I looked at it, and there's a little duck looking up at me. 00:22:12.380 --> 00:22:14.160 align:middle line:90% Pretty weird. 00:22:14.160 --> 00:22:17.270 align:middle line:84% So quantifiers-- so that's their version of that. 00:22:17.270 --> 00:22:23.300 align:middle line:84% Quantifiers then-- quantifiers like all or no or three-- 00:22:23.300 --> 00:22:27.470 align:middle line:84% are saying things about the interactions of the two sets. 00:22:27.470 --> 00:22:30.230 align:middle line:90% So "all" says the first set. 00:22:30.230 --> 00:22:34.280 align:middle line:84% So in a sentence like "All Americans eat nattoo," 00:22:34.280 --> 00:22:35.900 align:middle line:84% the first set is the set of Americans 00:22:35.900 --> 00:22:38.780 align:middle line:84% and the second set is the set of nattoo eaters, 00:22:38.780 --> 00:22:41.540 align:middle line:84% "all" says the first set is a subset of the second set. 00:22:41.540 --> 00:22:44.390 align:middle line:84% "Some" says the intersection of these sets is nonempty. 00:22:44.390 --> 00:22:47.350 align:middle line:84% "No" says the intersection of these sets is empty. 00:22:47.350 --> 00:22:49.850 align:middle line:84% "Three" says, if you look at the intersection of these sets, 00:22:49.850 --> 00:22:51.050 align:middle line:90% you will find three things. 00:22:51.050 --> 00:22:53.403 align:middle line:90% That has cardinality three. 00:22:53.403 --> 00:22:55.445 align:middle line:84% That's the kind of meaning that a quantifier has. 00:22:55.445 --> 00:23:01.120 align:middle line:90% 00:23:01.120 --> 00:23:04.120 align:middle line:84% If you're already familiar with set theory, 00:23:04.120 --> 00:23:06.610 align:middle line:84% it's obviously interesting to try 00:23:06.610 --> 00:23:10.630 align:middle line:84% to think about what kinds of intersections between sets 00:23:10.630 --> 00:23:14.200 align:middle line:90% quantifiers can state. 00:23:14.200 --> 00:23:18.610 align:middle line:84% So mathematicians can get sets to tangle 00:23:18.610 --> 00:23:20.980 align:middle line:84% with each other in all kinds of entertaining ways. 00:23:20.980 --> 00:23:23.860 align:middle line:84% I mean, there are all kinds of things you can get sets to do. 00:23:23.860 --> 00:23:26.920 align:middle line:84% It turns out that natural language quantifiers 00:23:26.920 --> 00:23:31.180 align:middle line:84% are what's called conservative, which means that you can always 00:23:31.180 --> 00:23:35.410 align:middle line:84% replace set number two with the intersection of set number one 00:23:35.410 --> 00:23:37.630 align:middle line:84% and set number two and get the same meaning. 00:23:37.630 --> 00:23:38.297 align:middle line:90% That is to say-- 00:23:38.297 --> 00:23:40.380 align:middle line:84% maybe I'm about to do this on the slide, but here, 00:23:40.380 --> 00:23:41.800 align:middle line:90% we'll do it on the board-- 00:23:41.800 --> 00:23:46.672 align:middle line:84% if this is set number one and this is set number two, 00:23:46.672 --> 00:23:48.130 align:middle line:84% I've been talking about quantifiers 00:23:48.130 --> 00:23:49.505 align:middle line:84% as though they tell you something 00:23:49.505 --> 00:23:51.470 align:middle line:90% about this set and this set. 00:23:51.470 --> 00:23:56.125 align:middle line:84% But all of the quantifiers can be stated in terms of this set, 00:23:56.125 --> 00:24:00.550 align:middle line:84% set number one, and this area here, the intersection of set 00:24:00.550 --> 00:24:01.960 align:middle line:90% number one and set number two. 00:24:01.960 --> 00:24:06.880 align:middle line:84% This part of set number two is always 00:24:06.880 --> 00:24:09.280 align:middle line:84% irrelevant to the meaning of a quantifier. 00:24:09.280 --> 00:24:14.110 align:middle line:84% That's a fact about natural language quantifiers. 00:24:14.110 --> 00:24:16.790 align:middle line:90% And it's not a necessary fact. 00:24:16.790 --> 00:24:19.900 align:middle line:84% So here's an example, if I say "All opera singers 00:24:19.900 --> 00:24:22.090 align:middle line:84% smoke," which I believe to be false, 00:24:22.090 --> 00:24:25.600 align:middle line:84% but anyway, I'm making a claim about the relationship 00:24:25.600 --> 00:24:28.943 align:middle line:84% between the set of opera singers and the set of smokers. 00:24:28.943 --> 00:24:30.610 align:middle line:84% I'm saying that the set of opera singers 00:24:30.610 --> 00:24:34.320 align:middle line:84% is completely contained in the set of smokers. 00:24:34.320 --> 00:24:37.230 align:middle line:84% But that's essentially the same thing. 00:24:37.230 --> 00:24:40.320 align:middle line:84% It is the same thing as saying that all opera singers are 00:24:40.320 --> 00:24:41.460 align:middle line:90% opera singers who smoke. 00:24:41.460 --> 00:24:44.370 align:middle line:84% That is, opera singers are all in the set of smoking opera 00:24:44.370 --> 00:24:46.020 align:middle line:90% singers. 00:24:46.020 --> 00:24:50.790 align:middle line:84% We don't care about smokers who are not opera singers when 00:24:50.790 --> 00:24:54.210 align:middle line:84% we are thinking about the meaning of "All opera singers 00:24:54.210 --> 00:24:55.390 align:middle line:90% smoke." 00:24:55.390 --> 00:24:57.450 align:middle line:84% So if I tell you "All opera singers smoke" 00:24:57.450 --> 00:25:00.570 align:middle line:84% and you begin to talk to me about someone who smokes and is 00:25:00.570 --> 00:25:04.270 align:middle line:84% not an opera singer, which may be fun to talk about that, 00:25:04.270 --> 00:25:06.760 align:middle line:84% but it's not relevant to the truth of my claim. 00:25:06.760 --> 00:25:10.230 align:middle line:84% The truth of my claim is only about the set of opera singers 00:25:10.230 --> 00:25:12.258 align:middle line:84% and the set of smoking opera singers. 00:25:12.258 --> 00:25:13.800 align:middle line:84% It says that the set of opera singers 00:25:13.800 --> 00:25:16.950 align:middle line:84% is completely contained in the set of smoking opera singers. 00:25:16.950 --> 00:25:18.760 align:middle line:90% Does that make sense? 00:25:18.760 --> 00:25:21.060 align:middle line:84% So if I say "All opera singers smoke" and you tell me, 00:25:21.060 --> 00:25:23.550 align:middle line:84% "Oh no, Arnold Schwarzenegger smokes, 00:25:23.550 --> 00:25:27.210 align:middle line:84% and he's not an opera singer," you haven't contradicted me. 00:25:27.210 --> 00:25:28.080 align:middle line:90% It doesn't matter. 00:25:28.080 --> 00:25:31.860 align:middle line:90% 00:25:31.860 --> 00:25:33.350 align:middle line:84% You can imagine quantifiers which 00:25:33.350 --> 00:25:34.438 align:middle line:90% would not be conservative. 00:25:34.438 --> 00:25:35.480 align:middle line:90% So I've just made one up. 00:25:35.480 --> 00:25:37.310 align:middle line:90% Here's a quantifier, "glorp." 00:25:37.310 --> 00:25:41.480 align:middle line:84% It says, if you add up all of the things in set number one 00:25:41.480 --> 00:25:44.030 align:middle line:84% and set number two, so the union of set number one 00:25:44.030 --> 00:25:46.490 align:middle line:84% and set number two has cardinality three. 00:25:46.490 --> 00:25:48.050 align:middle line:90% I just made up glorp. 00:25:48.050 --> 00:25:49.670 align:middle line:90% I'll give you an example. 00:25:49.670 --> 00:25:52.910 align:middle line:84% It would be true, in this picture, that glorp circles are 00:25:52.910 --> 00:25:57.900 align:middle line:84% red because if you add up the number of circles 00:25:57.900 --> 00:26:02.690 align:middle line:84% and the number of red things, the total is three. 00:26:02.690 --> 00:26:06.150 align:middle line:84% There are two circles and one red thing. 00:26:06.150 --> 00:26:09.740 align:middle line:84% So if there were a quantifier glorp, 00:26:09.740 --> 00:26:11.900 align:middle line:84% then you could say that glorp circles 00:26:11.900 --> 00:26:14.600 align:middle line:90% are red in this picture. 00:26:14.600 --> 00:26:17.720 align:middle line:84% There is no quantifier glorp, not in English and not 00:26:17.720 --> 00:26:19.820 align:middle line:84% in any language on Earth as far as we can tell. 00:26:19.820 --> 00:26:22.910 align:middle line:84% So quantifiers don't ever do this kind of thing. 00:26:22.910 --> 00:26:24.890 align:middle line:84% And this would be a nonconservative quantifier 00:26:24.890 --> 00:26:27.650 align:middle line:84% because in order to evaluate glorp, 00:26:27.650 --> 00:26:30.350 align:middle line:84% you would have to look not just at the part of set number two 00:26:30.350 --> 00:26:33.440 align:middle line:84% that's intersecting with set number one, 00:26:33.440 --> 00:26:36.020 align:middle line:84% but also at the part of set number two 00:26:36.020 --> 00:26:38.330 align:middle line:84% that I've hatched out here, the part that's 00:26:38.330 --> 00:26:39.860 align:middle line:90% not part of set number one. 00:26:39.860 --> 00:26:42.170 align:middle line:84% So this is a nonconservative quantifier, 00:26:42.170 --> 00:26:44.000 align:middle line:90% and there aren't any. 00:26:44.000 --> 00:26:44.780 align:middle line:90% That's the point. 00:26:44.780 --> 00:26:49.360 align:middle line:90% 00:26:49.360 --> 00:26:51.870 align:middle line:90% OK, good. 00:26:51.870 --> 00:26:55.500 align:middle line:90% So just practice some more-- 00:26:55.500 --> 00:26:59.130 align:middle line:90% so "all Brazilians love soccer." 00:26:59.130 --> 00:27:01.890 align:middle line:84% There's this danger when you do simple sentences 00:27:01.890 --> 00:27:04.740 align:middle line:84% with qualifiers in them that you will find yourself trafficking 00:27:04.740 --> 00:27:05.850 align:middle line:90% in stereotypes. 00:27:05.850 --> 00:27:08.127 align:middle line:84% This is why I like to use examples 00:27:08.127 --> 00:27:10.710 align:middle line:84% like "All opera singers smoke," which there isn't a stereotype 00:27:10.710 --> 00:27:14.290 align:middle line:90% about as far as I know. 00:27:14.290 --> 00:27:16.590 align:middle line:84% So, of course, it's not true that all Brazilians 00:27:16.590 --> 00:27:17.100 align:middle line:90% love soccer. 00:27:17.100 --> 00:27:19.050 align:middle line:90% It might almost be true. 00:27:19.050 --> 00:27:23.010 align:middle line:84% It says there's a relation between the set of Brazilians 00:27:23.010 --> 00:27:25.140 align:middle line:84% and the set of people who love soccer-- 00:27:25.140 --> 00:27:27.930 align:middle line:84% namely, the first set is a subset of the second set. 00:27:27.930 --> 00:27:30.660 align:middle line:84% If you look at the set of people who love soccer, 00:27:30.660 --> 00:27:32.820 align:middle line:84% inside that set, you will find all 00:27:32.820 --> 00:27:35.190 align:middle line:84% of the Brazilians, the people in the Brazilian set. 00:27:35.190 --> 00:27:38.770 align:middle line:90% 00:27:38.770 --> 00:27:42.100 align:middle line:84% Let's talk a little more about how we get these sets, 00:27:42.100 --> 00:27:44.390 align:middle line:84% just to be slightly more formal about it. 00:27:44.390 --> 00:27:47.230 align:middle line:84% So what we'll say is the set of Brazilians-- maybe 00:27:47.230 --> 00:27:48.430 align:middle line:90% that's not such a mystery. 00:27:48.430 --> 00:27:50.050 align:middle line:90% So all Brazilians love soccer-- 00:27:50.050 --> 00:27:54.110 align:middle line:84% you're taking the set from the rest of the noun phrase. 00:27:54.110 --> 00:27:57.457 align:middle line:84% So "All Brazilians love soccer"-- 00:27:57.457 --> 00:27:59.290 align:middle line:84% the first set is just the set of Brazilians, 00:27:59.290 --> 00:28:02.110 align:middle line:84% the thing that comes after all that's part of the noun phrase 00:28:02.110 --> 00:28:03.640 align:middle line:90% there. 00:28:03.640 --> 00:28:07.120 align:middle line:84% If it were more extensive than just Brazilians, then 00:28:07.120 --> 00:28:08.210 align:middle line:90% that set might change. 00:28:08.210 --> 00:28:11.410 align:middle line:84% So if I said something like "All female Brazilians love soccer," 00:28:11.410 --> 00:28:15.010 align:middle line:84% "All Brazilians from São Paulo" love soccer, 00:28:15.010 --> 00:28:18.200 align:middle line:84% we'd have a different set, Brazilians from São Paulo. 00:28:18.200 --> 00:28:19.630 align:middle line:90% And then the second set-- 00:28:19.630 --> 00:28:23.680 align:middle line:84% what we're doing is we're taking the set of things x such 00:28:23.680 --> 00:28:25.390 align:middle line:90% that x loves soccer. 00:28:25.390 --> 00:28:28.270 align:middle line:84% We're getting that set by replacing 00:28:28.270 --> 00:28:31.370 align:middle line:84% the quantifier "all Brazilians" with a variable. 00:28:31.370 --> 00:28:33.490 align:middle line:84% So we start off with "All Brazilians love soccer." 00:28:33.490 --> 00:28:35.115 align:middle line:84% We're going to replace "All Brazilians" 00:28:35.115 --> 00:28:36.940 align:middle line:90% with a variable called x. 00:28:36.940 --> 00:28:38.110 align:middle line:90% So x loves soccer. 00:28:38.110 --> 00:28:40.000 align:middle line:84% So the second set is the set of x. 00:28:40.000 --> 00:28:43.090 align:middle line:84% We have this property x loves soccer. 00:28:43.090 --> 00:28:46.385 align:middle line:84% This is just an attempt to do very slightly more formally 00:28:46.385 --> 00:28:48.010 align:middle line:84% what I've been kind of breezing through 00:28:48.010 --> 00:28:49.180 align:middle line:90% in the preceding slides. 00:28:49.180 --> 00:28:52.630 align:middle line:84% But does any of this seem alarming or disturbing? 00:28:52.630 --> 00:28:54.430 align:middle line:90% Is it causing unhappiness? 00:28:54.430 --> 00:28:56.972 align:middle line:84% Have you all had your nattoo this morning? 00:28:56.972 --> 00:28:58.930 align:middle line:84% This is good-- maybe I should bring some nattoo 00:28:58.930 --> 00:29:00.990 align:middle line:84% and I can stand around and watch. 00:29:00.990 --> 00:29:04.240 align:middle line:90% It would be revenge. 00:29:04.240 --> 00:29:06.338 align:middle line:84% I will not bring a balut to class. 00:29:06.338 --> 00:29:07.630 align:middle line:90% Not sure where I would get one. 00:29:07.630 --> 00:29:10.710 align:middle line:90% 00:29:10.710 --> 00:29:15.720 align:middle line:84% So it's worth doing this because doing this slight formalization 00:29:15.720 --> 00:29:18.030 align:middle line:84% of what we've been doing because, well, I've 00:29:18.030 --> 00:29:20.088 align:middle line:84% have been carefully giving you examples 00:29:20.088 --> 00:29:21.630 align:middle line:84% in which the quantifier is a subject, 00:29:21.630 --> 00:29:23.880 align:middle line:84% but, of course, quantifiers don't have to be subjects. 00:29:23.880 --> 00:29:28.260 align:middle line:84% You can say things like "Soccer bores all Americans." 00:29:28.260 --> 00:29:31.840 align:middle line:84% Here, the first set is going to be the set of Americans. 00:29:31.840 --> 00:29:34.100 align:middle line:90% What's the second set? 00:29:34.100 --> 00:29:35.870 align:middle line:84% So "Americans" as a subset of what set? 00:29:35.870 --> 00:29:38.890 align:middle line:90% 00:29:38.890 --> 00:29:41.700 align:middle line:90% Again, what we do is-- 00:29:41.700 --> 00:29:42.780 align:middle line:90% sorry, go ahead. 00:29:42.780 --> 00:29:44.657 align:middle line:84% AUDIENCE: X such that soccer bores x? 00:29:44.657 --> 00:29:46.740 align:middle line:84% NORVIN RICHARDS: Yeah, x such that soccer bores x. 00:29:46.740 --> 00:29:49.890 align:middle line:84% So we take this sentence, we replace "all Americans" with x, 00:29:49.890 --> 00:29:53.532 align:middle line:84% and now we have the set of x such that soccer bores x. 00:29:53.532 --> 00:29:55.240 align:middle line:84% X doesn't have to be in subject position. 00:29:55.240 --> 00:29:56.760 align:middle line:90% That's the only point here. 00:29:56.760 --> 00:29:59.022 align:middle line:90% That can be anywhere. 00:29:59.022 --> 00:30:03.090 align:middle line:84% So that's how we'll do the meaning of qualifiers. 00:30:03.090 --> 00:30:05.490 align:middle line:84% So it says "Americans" is a subset 00:30:05.490 --> 00:30:09.060 align:middle line:84% of the people whom soccer bores, the x such that soccer bores x. 00:30:09.060 --> 00:30:11.310 align:middle line:84% So the quantifier has been replaced with the variable. 00:30:11.310 --> 00:30:15.540 align:middle line:90% 00:30:15.540 --> 00:30:19.020 align:middle line:84% So now we can get back to the ambiguity 00:30:19.020 --> 00:30:21.900 align:middle line:84% that I started us off with, and I 00:30:21.900 --> 00:30:26.188 align:middle line:84% will try to do this slowly and carefully. 00:30:26.188 --> 00:30:28.230 align:middle line:84% What we're going to see is that a way of thinking 00:30:28.230 --> 00:30:30.660 align:middle line:84% about the ambiguity that I started this off with 00:30:30.660 --> 00:30:33.990 align:middle line:84% is to think, yeah, you have these two qualifiers 00:30:33.990 --> 00:30:36.060 align:middle line:84% that are doing these operations involving 00:30:36.060 --> 00:30:38.518 align:middle line:90% the formation of sets. 00:30:38.518 --> 00:30:40.560 align:middle line:84% So in all of the sentences I've given you before, 00:30:40.560 --> 00:30:42.120 align:middle line:84% there's only been one quantifier, 00:30:42.120 --> 00:30:43.890 align:middle line:84% so it forms these sets and asserts 00:30:43.890 --> 00:30:45.170 align:middle line:90% a relation between them. 00:30:45.170 --> 00:30:47.670 align:middle line:84% But in a sentence like this, where there are two qualifiers, 00:30:47.670 --> 00:30:50.850 align:middle line:84% well, you're going to need to perform that kind of operation 00:30:50.850 --> 00:30:53.070 align:middle line:90% twice. 00:30:53.070 --> 00:30:55.770 align:middle line:84% And the ambiguity just has to do with the order in which you 00:30:55.770 --> 00:30:57.370 align:middle line:90% perform the operations. 00:30:57.370 --> 00:30:59.640 align:middle line:84% So do you do the operations for "some child" 00:30:59.640 --> 00:31:02.670 align:middle line:84% first and then the operations for "every puppy," 00:31:02.670 --> 00:31:04.740 align:middle line:84% or do you do the operations for "every puppy" 00:31:04.740 --> 00:31:08.230 align:middle line:84% first and then the operations for "some child"? 00:31:08.230 --> 00:31:11.220 align:middle line:84% So if I remember my own slides correctly, 00:31:11.220 --> 00:31:13.620 align:middle line:84% I think what we're going to do now is work fairly slowly 00:31:13.620 --> 00:31:15.787 align:middle line:84% and painfully through what happens if you do the two 00:31:15.787 --> 00:31:17.050 align:middle line:90% things in that order. 00:31:17.050 --> 00:31:19.290 align:middle line:84% But I'm telling you this now in advance 00:31:19.290 --> 00:31:21.240 align:middle line:84% to give you some hope that you will 00:31:21.240 --> 00:31:24.450 align:middle line:84% have an understanding by the time we're done of what 00:31:24.450 --> 00:31:25.540 align:middle line:90% the heck is going on here. 00:31:25.540 --> 00:31:29.490 align:middle line:84% It's just what order do you do the operations in. 00:31:29.490 --> 00:31:31.410 align:middle line:84% That's why there's ambiguity here. 00:31:31.410 --> 00:31:33.920 align:middle line:84% You have these two qualifiers and you 00:31:33.920 --> 00:31:35.920 align:middle line:84% have options about which one to interpret first. 00:31:35.920 --> 00:31:38.490 align:middle line:84% So if you interpret "every" first, then you're 00:31:38.490 --> 00:31:42.540 align:middle line:84% saying the set of puppies is a subset of the set of things 00:31:42.540 --> 00:31:43.620 align:middle line:90% that some child loves. 00:31:43.620 --> 00:31:46.730 align:middle line:90% 00:31:46.730 --> 00:31:51.020 align:middle line:84% And then, if you interpret that part, 00:31:51.020 --> 00:31:54.590 align:middle line:84% you're going to say, what's the set of things 00:31:54.590 --> 00:31:55.640 align:middle line:90% that some child loves? 00:31:55.640 --> 00:31:58.190 align:middle line:84% Well, it's the set such that the intersection 00:31:58.190 --> 00:32:00.680 align:middle line:84% of the set of children with the set of things 00:32:00.680 --> 00:32:03.525 align:middle line:90% that loves them is nonempty. 00:32:03.525 --> 00:32:05.900 align:middle line:84% So if we interpret "every" first, then the sentence means 00:32:05.900 --> 00:32:08.750 align:middle line:84% the set of puppies is a subset of the set 00:32:08.750 --> 00:32:11.870 align:middle line:84% of things such that the intersection 00:32:11.870 --> 00:32:14.300 align:middle line:84% of the set of children with the set of things 00:32:14.300 --> 00:32:18.590 align:middle line:84% that love those things is nonempty-- whew. 00:32:18.590 --> 00:32:22.430 align:middle line:84% If we do the operations in that order we get that reading. 00:32:22.430 --> 00:32:26.120 align:middle line:84% That is, we get the reading the set of puppies 00:32:26.120 --> 00:32:29.150 align:middle line:84% is a subset of the things that some child loves. 00:32:29.150 --> 00:32:32.003 align:middle line:84% Some child loves many things, possibly, 00:32:32.003 --> 00:32:33.920 align:middle line:84% and among those things is the set of puppies-- 00:32:33.920 --> 00:32:35.570 align:middle line:84% so every member of the set of puppies 00:32:35.570 --> 00:32:39.350 align:middle line:84% is such that the intersection of children such 00:32:39.350 --> 00:32:41.450 align:middle line:84% that there is some child that loves it. 00:32:41.450 --> 00:32:43.790 align:middle line:84% And I think I have a picture of that now-- yeah, there. 00:32:43.790 --> 00:32:47.473 align:middle line:84% So doing the operations in that order, we get this reading. 00:32:47.473 --> 00:32:48.890 align:middle line:84% Every member of the set of puppies 00:32:48.890 --> 00:32:52.640 align:middle line:84% has this property-- there is some child that loves it. 00:32:52.640 --> 00:32:54.590 align:middle line:84% That's a reading the sentence can have, 00:32:54.590 --> 00:32:58.160 align:middle line:84% and we can get this reading by doing the interpretation 00:32:58.160 --> 00:33:00.920 align:middle line:90% of every puppy first. 00:33:00.920 --> 00:33:04.060 align:middle line:84% That's one reading the sentence can have. 00:33:04.060 --> 00:33:06.272 align:middle line:84% So that's the reading that's pictured here, 00:33:06.272 --> 00:33:08.230 align:middle line:84% where there are many puppies and many children, 00:33:08.230 --> 00:33:11.710 align:middle line:84% and every puppy is loved by at least one child, possibly 00:33:11.710 --> 00:33:13.130 align:middle line:90% more than one. 00:33:13.130 --> 00:33:15.610 align:middle line:84% There are also children who love more than one puppy. 00:33:15.610 --> 00:33:18.220 align:middle line:84% Children are not monogamous when it comes to puppies. 00:33:18.220 --> 00:33:22.440 align:middle line:90% 00:33:22.440 --> 00:33:25.050 align:middle line:84% What if you interpreted "some child" first? 00:33:25.050 --> 00:33:27.810 align:middle line:84% Well, then you'd be saying take the set of children 00:33:27.810 --> 00:33:31.290 align:middle line:84% and the set of things that love every puppy. 00:33:31.290 --> 00:33:34.870 align:middle line:90% That intersection is nonempty. 00:33:34.870 --> 00:33:36.490 align:middle line:84% So take a deep breath because we're 00:33:36.490 --> 00:33:37.840 align:middle line:84% about to interpret the second part of that, 00:33:37.840 --> 00:33:40.090 align:middle line:84% but even before we interpret the second part of that, 00:33:40.090 --> 00:33:41.715 align:middle line:84% maybe this is the point at which things 00:33:41.715 --> 00:33:43.720 align:middle line:84% are as coherent as they're ever going to get. 00:33:43.720 --> 00:33:47.620 align:middle line:84% What this means is there is at least one child 00:33:47.620 --> 00:33:49.390 align:middle line:90% that loves every puppy. 00:33:49.390 --> 00:33:51.922 align:middle line:84% There's at least one child who's very fond of puppies. 00:33:51.922 --> 00:33:53.380 align:middle line:84% That's the other kind of reading we 00:33:53.380 --> 00:33:56.560 align:middle line:84% were saying this kind of sentence could have. 00:33:56.560 --> 00:33:58.570 align:middle line:90% So we next interpret that. 00:33:58.570 --> 00:34:00.370 align:middle line:84% So the intersection of the set of children 00:34:00.370 --> 00:34:03.130 align:middle line:84% and the set of things such that the set of puppies 00:34:03.130 --> 00:34:07.542 align:middle line:84% is a subset of the things that that thing loves is nonempty. 00:34:07.542 --> 00:34:09.000 align:middle line:84% And to put that back in English, it 00:34:09.000 --> 00:34:11.370 align:middle line:84% means there is at least one child such 00:34:11.370 --> 00:34:13.469 align:middle line:84% that the set of puppies is a subset of the things 00:34:13.469 --> 00:34:14.472 align:middle line:90% that x loves. 00:34:14.472 --> 00:34:16.889 align:middle line:84% Or to put it another way, there is at least one child such 00:34:16.889 --> 00:34:18.347 align:middle line:84% that all puppies are loved by them. 00:34:18.347 --> 00:34:20.820 align:middle line:90% 00:34:20.820 --> 00:34:25.080 align:middle line:84% So early in this-- maybe one of the first things I said today 00:34:25.080 --> 00:34:28.590 align:middle line:84% was a sentence like "Some child loves every puppy"-- 00:34:28.590 --> 00:34:31.590 align:middle line:84% or I think the example back then was "Someone loves everyone"-- 00:34:31.590 --> 00:34:33.330 align:middle line:84% people have argued that it's ambiguous, 00:34:33.330 --> 00:34:35.760 align:middle line:84% that it can mean either there is one person who 00:34:35.760 --> 00:34:40.398 align:middle line:84% loves everyone or everyone has someone that loves them. 00:34:40.398 --> 00:34:42.690 align:middle line:84% And these are both meanings that the sentence can have. 00:34:42.690 --> 00:34:44.491 align:middle line:84% And I switched over to people and languages 00:34:44.491 --> 00:34:46.949 align:middle line:84% because our intuitions about the difference between the two 00:34:46.949 --> 00:34:50.870 align:middle line:84% meanings are a little sharper for that kind of example. 00:34:50.870 --> 00:34:52.370 align:middle line:84% Here, I'm showing you some mechanics 00:34:52.370 --> 00:34:55.730 align:middle line:84% that we can use to get this ambiguity, 00:34:55.730 --> 00:35:01.100 align:middle line:84% and the mechanics involve allowing yourself 00:35:01.100 --> 00:35:03.638 align:middle line:84% to do the operations for interpreting 00:35:03.638 --> 00:35:05.930 align:middle line:84% the quantifier-- when you have more than one quantifier 00:35:05.930 --> 00:35:08.790 align:middle line:84% in a sentence, you're allowed to interpret them in either order. 00:35:08.790 --> 00:35:11.900 align:middle line:84% So you're allowed to do the operations for the subject 00:35:11.900 --> 00:35:13.793 align:middle line:84% first or the operations for the object first, 00:35:13.793 --> 00:35:15.710 align:middle line:84% and depending on which of those things you do, 00:35:15.710 --> 00:35:19.160 align:middle line:84% you get these two different readings for the sentence. 00:35:19.160 --> 00:35:21.980 align:middle line:90% So far so good? 00:35:21.980 --> 00:35:25.700 align:middle line:84% Sorry, this is a lot to deal with on a Tuesday morning 00:35:25.700 --> 00:35:26.545 align:middle line:90% through a mask. 00:35:26.545 --> 00:35:35.230 align:middle line:90% 00:35:35.230 --> 00:35:38.310 align:middle line:84% So here's the tree for that sentence 00:35:38.310 --> 00:35:40.050 align:middle line:90% "some child loves every puppy." 00:35:40.050 --> 00:35:43.320 align:middle line:84% And we've said that's an ambiguous tree. 00:35:43.320 --> 00:35:46.320 align:middle line:90% So why is the tree ambiguous? 00:35:46.320 --> 00:35:48.790 align:middle line:84% What I've now said a couple of times-- and who knows, 00:35:48.790 --> 00:35:50.010 align:middle line:90% this could be true-- 00:35:50.010 --> 00:35:53.100 align:middle line:84% is yeah, you've got these two qualifiers. 00:35:53.100 --> 00:35:58.507 align:middle line:84% You've got to perform operations that form these sets. 00:35:58.507 --> 00:36:00.840 align:middle line:84% The part of the process of interpreting these qualifiers 00:36:00.840 --> 00:36:04.440 align:middle line:84% involves forming these sets and there's nothing in particular 00:36:04.440 --> 00:36:07.290 align:middle line:84% telling you what order to perform those operations in. 00:36:07.290 --> 00:36:10.440 align:middle line:84% And so you can interpret them in either order, 00:36:10.440 --> 00:36:12.120 align:middle line:90% and so you get ambiguities. 00:36:12.120 --> 00:36:13.920 align:middle line:84% That's the way I've been talking. 00:36:13.920 --> 00:36:17.410 align:middle line:84% That turns out to be a lie, which is kind of interesting. 00:36:17.410 --> 00:36:22.550 align:middle line:84% We have lots of good evidence, and I'll show you some of it, 00:36:22.550 --> 00:36:25.580 align:middle line:84% that we don't just get to freely choose the order in which we 00:36:25.580 --> 00:36:27.020 align:middle line:90% interpret qualifiers. 00:36:27.020 --> 00:36:31.640 align:middle line:84% But what really happens is that there is another kind 00:36:31.640 --> 00:36:33.600 align:middle line:90% of movement operation. 00:36:33.600 --> 00:36:36.860 align:middle line:84% So we've left syntax behind, and maybe some of you 00:36:36.860 --> 00:36:40.190 align:middle line:84% were hoping we wouldn't have to see things move anymore, 00:36:40.190 --> 00:36:43.130 align:middle line:84% but actually, in semantics, there's also movement going on, 00:36:43.130 --> 00:36:46.588 align:middle line:84% possibly movement of an even sneakier and weirder kind. 00:36:46.588 --> 00:36:49.130 align:middle line:84% There's lots of evidence that the reason that the sentence is 00:36:49.130 --> 00:36:52.070 align:middle line:84% ambiguous is that there's an operation which 00:36:52.070 --> 00:36:55.490 align:middle line:84% is optional that takes the object "every puppy" 00:36:55.490 --> 00:37:01.420 align:middle line:84% and moves it to a position above "some child" in the process 00:37:01.420 --> 00:37:04.280 align:middle line:90% of interpreting the sentence. 00:37:04.280 --> 00:37:07.670 align:middle line:84% Now there are several alarming things about this movement. 00:37:07.670 --> 00:37:10.730 align:middle line:84% All of the movements that I've shown you up until now-- 00:37:10.730 --> 00:37:13.040 align:middle line:84% so when I first tried introducing you to movement, 00:37:13.040 --> 00:37:21.110 align:middle line:84% I think I was showing you things like "Mary devoured a pizza." 00:37:21.110 --> 00:37:23.060 align:middle line:84% I was saying yeah, look, the pizza 00:37:23.060 --> 00:37:24.500 align:middle line:90% absolutely has to be here. 00:37:24.500 --> 00:37:27.800 align:middle line:90% You can't say "Mary devoured." 00:37:27.800 --> 00:37:30.290 align:middle line:90% That's out. 00:37:30.290 --> 00:37:34.820 align:middle line:84% So "devour" selects for a sister-- it absolutely 00:37:34.820 --> 00:37:35.870 align:middle line:90% has to have a sister. 00:37:35.870 --> 00:37:37.515 align:middle line:84% And moreover, its sister absolutely 00:37:37.515 --> 00:37:38.640 align:middle line:90% has to be right next to it. 00:37:38.640 --> 00:37:42.870 align:middle line:84% So if I put an adverb here, it gets bad. 00:37:42.870 --> 00:37:45.513 align:middle line:84% So Mary devoured quickly a pizza-- that's no good. 00:37:45.513 --> 00:37:47.930 align:middle line:84% So we know something about the properties of the "devour." 00:37:47.930 --> 00:37:49.740 align:middle line:84% It absolutely has to have an object, 00:37:49.740 --> 00:37:51.740 align:middle line:84% and the object absolutely has to be right after. 00:37:51.740 --> 00:37:53.250 align:middle line:90% It cannot be anywhere else. 00:37:53.250 --> 00:37:55.625 align:middle line:84% And then I said, wait, what about "what did Mary devour?" 00:37:55.625 --> 00:37:58.750 align:middle line:90% 00:37:58.750 --> 00:38:05.830 align:middle line:84% And we ended up deciding that "what" is starting off here 00:38:05.830 --> 00:38:08.080 align:middle line:90% and it's moving up to here. 00:38:08.080 --> 00:38:09.830 align:middle line:90% And that's why it's over there. 00:38:09.830 --> 00:38:13.690 align:middle line:84% So we said the process of producing a sentence like "what 00:38:13.690 --> 00:38:16.300 align:middle line:84% did Mary devour" involves "what" starting off 00:38:16.300 --> 00:38:17.530 align:middle line:90% exactly where it should-- 00:38:17.530 --> 00:38:20.590 align:middle line:84% as the sister of "devour" right next to "devour"-- 00:38:20.590 --> 00:38:22.180 align:middle line:84% and then there's this other process 00:38:22.180 --> 00:38:24.130 align:middle line:84% that doesn't care about what "devour" wants. 00:38:24.130 --> 00:38:25.572 align:middle line:84% This process of wh- movement that 00:38:25.572 --> 00:38:28.030 align:middle line:84% takes "what" and moves it to the beginning of the sentence, 00:38:28.030 --> 00:38:28.530 align:middle line:90% we saw. 00:38:28.530 --> 00:38:31.210 align:middle line:84% Some languages have this and others don't. 00:38:31.210 --> 00:38:32.710 align:middle line:84% I was looking at WALS the other day. 00:38:32.710 --> 00:38:34.918 align:middle line:84% It turns out roughly a third of the world's languages 00:38:34.918 --> 00:38:36.338 align:middle line:90% have this, and English does. 00:38:36.338 --> 00:38:38.380 align:middle line:84% So you take what and you move it to the beginning 00:38:38.380 --> 00:38:40.960 align:middle line:90% of the sentence. 00:38:40.960 --> 00:38:43.210 align:middle line:84% So every kind of movement that we've seen up until now 00:38:43.210 --> 00:38:44.170 align:middle line:90% has been like this. 00:38:44.170 --> 00:38:46.060 align:middle line:84% It's been part of an explanation for why 00:38:46.060 --> 00:38:48.220 align:middle line:84% you pronounce things in different places 00:38:48.220 --> 00:38:50.088 align:middle line:90% than you would expect. 00:38:50.088 --> 00:38:51.880 align:middle line:84% You would expect "devour" to have a sister, 00:38:51.880 --> 00:38:53.838 align:middle line:84% to have an object that would be right after it. 00:38:53.838 --> 00:38:56.350 align:middle line:84% And "what" isn't there, and it's because of a movement 00:38:56.350 --> 00:38:58.122 align:middle line:90% operation. 00:38:58.122 --> 00:38:59.580 align:middle line:84% I'm going to give you some evidence 00:38:59.580 --> 00:39:02.100 align:middle line:84% now that this ambiguity shows up because you have 00:39:02.100 --> 00:39:04.920 align:middle line:84% the option of moving "every puppy" to a position 00:39:04.920 --> 00:39:06.570 align:middle line:84% to the left of "some child," higher 00:39:06.570 --> 00:39:08.910 align:middle line:90% than "some child" in the tree. 00:39:08.910 --> 00:39:11.640 align:middle line:84% But this had better be a different kind of movement 00:39:11.640 --> 00:39:13.890 align:middle line:84% because the sentence is ambiguous 00:39:13.890 --> 00:39:18.970 align:middle line:84% even if you don't see the noun phrases going anywhere else. 00:39:18.970 --> 00:39:25.800 align:middle line:84% This is a type of movement called covert movement, 00:39:25.800 --> 00:39:29.100 align:middle line:84% and you should all be very suspicious of this 00:39:29.100 --> 00:39:34.200 align:middle line:84% because basically, it's like the-- 00:39:34.200 --> 00:39:35.070 align:middle line:90% what's it like? 00:39:35.070 --> 00:39:37.200 align:middle line:84% It's like the dark matter that physicists 00:39:37.200 --> 00:39:38.700 align:middle line:84% have to posit in order to explain 00:39:38.700 --> 00:39:41.130 align:middle line:84% why most of the matter in the universe 00:39:41.130 --> 00:39:42.660 align:middle line:90% doesn't seem to be there. 00:39:42.660 --> 00:39:45.540 align:middle line:84% So there's all this undetectable matter that's out there. 00:39:45.540 --> 00:39:47.553 align:middle line:90% We just haven't detected it yet. 00:39:47.553 --> 00:39:49.470 align:middle line:84% Somehow, when physicists say things like this, 00:39:49.470 --> 00:39:52.390 align:middle line:84% we believe them because they can build bombs and things. 00:39:52.390 --> 00:39:55.190 align:middle line:84% But I'm about to say something kind of similar to that. 00:39:55.190 --> 00:39:56.940 align:middle line:84% We have some arguments, really good ones-- 00:39:56.940 --> 00:39:58.920 align:middle line:84% I'll try to show you some of them, anyway-- 00:39:58.920 --> 00:40:01.140 align:middle line:90% that this thing can move. 00:40:01.140 --> 00:40:04.290 align:middle line:84% And the fact that when it moves, you still pronounce it 00:40:04.290 --> 00:40:07.710 align:middle line:84% as though it hadn't moved, this is really interesting, 00:40:07.710 --> 00:40:10.990 align:middle line:84% but what it shows is that this is dark matter. 00:40:10.990 --> 00:40:11.700 align:middle line:90% It is moving. 00:40:11.700 --> 00:40:13.117 align:middle line:84% It's just not moving in a way that 00:40:13.117 --> 00:40:16.778 align:middle line:84% changes the order of the sentence, order of the words. 00:40:16.778 --> 00:40:18.570 align:middle line:84% All of you are making the appropriate face, 00:40:18.570 --> 00:40:19.770 align:middle line:90% which is a very skeptical one. 00:40:19.770 --> 00:40:21.160 align:middle line:84% I mean, some of you are wearing masks, 00:40:21.160 --> 00:40:23.285 align:middle line:84% so I can only see your skeptical eyebrows and eyes, 00:40:23.285 --> 00:40:26.098 align:middle line:90% but I appreciate that. 00:40:26.098 --> 00:40:27.390 align:middle line:90% Let me show you some arguments. 00:40:27.390 --> 00:40:32.210 align:middle line:84% First, there are some languages-- 00:40:32.210 --> 00:40:34.410 align:middle line:84% yeah, so here's another ambiguous example. 00:40:34.410 --> 00:40:37.640 align:middle line:90% "Most people ate two cakes." 00:40:37.640 --> 00:40:40.160 align:middle line:90% That can mean two things. 00:40:40.160 --> 00:40:42.500 align:middle line:84% It can mean either-- what's one thing it can mean? 00:40:42.500 --> 00:40:47.370 align:middle line:90% 00:40:47.370 --> 00:40:49.770 align:middle line:84% Softening you up for the next set of slides. 00:40:49.770 --> 00:40:52.200 align:middle line:84% You don't have to use x's and y's and things. 00:40:52.200 --> 00:40:54.090 align:middle line:84% Just tell me what it seems to mean. 00:40:54.090 --> 00:40:57.270 align:middle line:90% 00:40:57.270 --> 00:40:57.770 align:middle line:90% Yeah? 00:40:57.770 --> 00:40:59.102 align:middle line:84% AUDIENCE: Most of the people in the room 00:40:59.102 --> 00:41:00.620 align:middle line:90% ate two cakes for each person. 00:41:00.620 --> 00:41:01.320 align:middle line:84% NORVIN RICHARDS: For each person. 00:41:01.320 --> 00:41:03.080 align:middle line:84% So there were a whole bunch of cakes, 00:41:03.080 --> 00:41:04.692 align:middle line:90% and there was a free for all. 00:41:04.692 --> 00:41:06.650 align:middle line:84% People could have as many cakes as they wanted, 00:41:06.650 --> 00:41:09.067 align:middle line:84% and we were keeping track of how many cakes people wanted, 00:41:09.067 --> 00:41:10.550 align:middle line:90% and most people ate two cakes. 00:41:10.550 --> 00:41:12.170 align:middle line:90% Some people ate three. 00:41:12.170 --> 00:41:15.440 align:middle line:84% There was this Richards guy who ate 12. 00:41:15.440 --> 00:41:17.180 align:middle line:84% And then some people didn't eat any. 00:41:17.180 --> 00:41:18.290 align:middle line:90% But most people ate two. 00:41:18.290 --> 00:41:19.940 align:middle line:90% That's one thing it can mean. 00:41:19.940 --> 00:41:22.110 align:middle line:84% What's another thing it can mean? 00:41:22.110 --> 00:41:22.865 align:middle line:90% Yeah? 00:41:22.865 --> 00:41:24.990 align:middle line:84% AUDIENCE: There are a total of two cakes from which 00:41:24.990 --> 00:41:26.100 align:middle line:90% most people have eaten. 00:41:26.100 --> 00:41:28.950 align:middle line:84% NORVIN RICHARDS: Yeah, so there were various cakes 00:41:28.950 --> 00:41:30.600 align:middle line:84% out there, maybe really big cakes 00:41:30.600 --> 00:41:33.360 align:middle line:84% that you could eat a slice of, and we were finding out 00:41:33.360 --> 00:41:34.830 align:middle line:84% what the most popular cakes were, 00:41:34.830 --> 00:41:38.220 align:middle line:84% and most people ate two cakes, the vanilla 00:41:38.220 --> 00:41:40.110 align:middle line:84% frosted and the chocolate frosted, 00:41:40.110 --> 00:41:41.918 align:middle line:84% and then there were a couple of other cakes 00:41:41.918 --> 00:41:42.960 align:middle line:90% that were not as popular. 00:41:42.960 --> 00:41:44.250 align:middle line:90% So concentrate on those. 00:41:44.250 --> 00:41:46.050 align:middle line:90% It can kind of mean that. 00:41:46.050 --> 00:41:48.780 align:middle line:84% Some of you were raising your eyebrows at that. 00:41:48.780 --> 00:41:51.360 align:middle line:90% But it can sort of mean that. 00:41:51.360 --> 00:41:53.460 align:middle line:84% So one reason to take seriously the idea 00:41:53.460 --> 00:41:55.890 align:middle line:84% that this ambiguity comes from an optional movement 00:41:55.890 --> 00:42:00.270 align:middle line:84% operation which you can't see is that there are languages 00:42:00.270 --> 00:42:02.410 align:middle line:90% in which you can see it. 00:42:02.410 --> 00:42:05.290 align:middle line:84% So you remember how I said English has wh- movement 00:42:05.290 --> 00:42:08.230 align:middle line:84% and there are languages out there that don't, languages 00:42:08.230 --> 00:42:12.010 align:middle line:84% like Mandarin or Japanese or Chaha or whatever? 00:42:12.010 --> 00:42:14.440 align:middle line:84% Similarly, this operation that takes one 00:42:14.440 --> 00:42:17.140 align:middle line:84% quantifier and moves it past another quantifier-- 00:42:17.140 --> 00:42:18.640 align:middle line:84% you don't get to see it in English, 00:42:18.640 --> 00:42:21.610 align:middle line:84% but you do get to see it, for example, in Hungarian. 00:42:21.610 --> 00:42:27.350 align:middle line:84% So in Hungarian, the Hungarian translations for "Most people 00:42:27.350 --> 00:42:34.030 align:middle line:84% ate two cakes" have two word orders, each of which 00:42:34.030 --> 00:42:36.400 align:middle line:90% means only a single thing. 00:42:36.400 --> 00:42:38.242 align:middle line:84% So you either say, in Hungarian-- 00:42:38.242 --> 00:42:39.700 align:middle line:84% I don't speak Hungarian and I won't 00:42:39.700 --> 00:42:40.825 align:middle line:90% try to say these sentences. 00:42:40.825 --> 00:42:42.980 align:middle line:84% Does anyone here speak Hungarian? 00:42:42.980 --> 00:42:45.055 align:middle line:90% OK, that's very freeing. 00:42:45.055 --> 00:42:47.555 align:middle line:84% I almost feel as though I should try to say these sentences. 00:42:47.555 --> 00:42:49.930 align:middle line:84% I know you don't know what Hungarian is supposed to sound 00:42:49.930 --> 00:42:52.530 align:middle line:90% like, but I won't. 00:42:52.530 --> 00:42:55.700 align:middle line:84% The first sentence only has one meaning, 00:42:55.700 --> 00:42:58.200 align:middle line:84% and the second sentence also has only one meaning. 00:42:58.200 --> 00:43:00.320 align:middle line:84% So you can take these expressions "most people" 00:43:00.320 --> 00:43:02.960 align:middle line:84% and "from two cakes" and put them in either order, 00:43:02.960 --> 00:43:05.540 align:middle line:84% and depending on what order you're in, 00:43:05.540 --> 00:43:06.780 align:middle line:90% you only get one reading. 00:43:06.780 --> 00:43:11.720 align:middle line:84% So the first sentence means the first reading that was offered, 00:43:11.720 --> 00:43:16.520 align:middle line:84% the most reasonable reading, most of the people 00:43:16.520 --> 00:43:18.590 align:middle line:90% ate two kinds of cake. 00:43:18.590 --> 00:43:22.160 align:middle line:84% The second meaning means there were two particular cakes that 00:43:22.160 --> 00:43:24.480 align:middle line:90% were the most popular ones. 00:43:24.480 --> 00:43:26.930 align:middle line:84% So in Hungarian, the order in which 00:43:26.930 --> 00:43:29.480 align:middle line:84% you apply the operations to interpret the qualifiers 00:43:29.480 --> 00:43:31.050 align:middle line:90% is not optional. 00:43:31.050 --> 00:43:32.090 align:middle line:90% It's completely fixed. 00:43:32.090 --> 00:43:34.785 align:middle line:84% It's determined by the order of the phrases. 00:43:34.785 --> 00:43:36.410 align:middle line:84% That's what determines what's going on. 00:43:36.410 --> 00:43:38.840 align:middle line:84% And the claim is that all languages 00:43:38.840 --> 00:43:42.560 align:middle line:90% are Hungarian deep down. 00:43:42.560 --> 00:43:47.040 align:middle line:84% It's just that some languages are better at this than others. 00:43:47.040 --> 00:43:49.820 align:middle line:84% So there are languages like Hungarian, 00:43:49.820 --> 00:43:52.250 align:middle line:84% for example, that are really good at being Hungarian. 00:43:52.250 --> 00:43:53.850 align:middle line:90% You can just see it right there. 00:43:53.850 --> 00:43:55.308 align:middle line:84% And then there are other languages, 00:43:55.308 --> 00:43:58.410 align:middle line:84% like English, that are Hungarian but they're shy about it. 00:43:58.410 --> 00:44:01.070 align:middle line:84% And so you don't get to see the relevant kinds of movement. 00:44:01.070 --> 00:44:06.200 align:middle line:90% 00:44:06.200 --> 00:44:08.930 align:middle line:90% OK, what are we doing? 00:44:08.930 --> 00:44:13.760 align:middle line:84% So I'm going to show you some more reasons 00:44:13.760 --> 00:44:19.400 align:middle line:84% to take this idea seriously that this operation, which is called 00:44:19.400 --> 00:44:26.778 align:middle line:84% quantifier raising, or QR, that it exists. 00:44:26.778 --> 00:44:28.820 align:middle line:84% So we'll talk about some of the properties of it. 00:44:28.820 --> 00:44:33.045 align:middle line:90% 00:44:33.045 --> 00:44:34.920 align:middle line:84% We'll talk about some of the properties of it 00:44:34.920 --> 00:44:37.080 align:middle line:90% in the next little while. 00:44:37.080 --> 00:44:39.630 align:middle line:84% Here's another sentence with two qualifiers in it. 00:44:39.630 --> 00:44:43.410 align:middle line:84% This is work that I'm taking from my colleague Danny 00:44:43.410 --> 00:44:45.270 align:middle line:84% Fox, who's done a lot of fantastic work 00:44:45.270 --> 00:44:48.330 align:middle line:84% on the properties of quantifiers. 00:44:48.330 --> 00:44:50.310 align:middle line:84% So here's an ambiguous sentence, "A guard 00:44:50.310 --> 00:44:52.530 align:middle line:84% is standing in front of every building." 00:44:52.530 --> 00:44:56.130 align:middle line:90% What does this sentence mean? 00:44:56.130 --> 00:44:57.120 align:middle line:90% Yes? 00:44:57.120 --> 00:44:59.850 align:middle line:84% AUDIENCE: Either that every building has a different guard 00:44:59.850 --> 00:45:01.225 align:middle line:84% standing in front of it, or there 00:45:01.225 --> 00:45:03.000 align:middle line:84% is one guard that is continuously standing 00:45:03.000 --> 00:45:03.810 align:middle line:90% in front of every building. 00:45:03.810 --> 00:45:04.660 align:middle line:84% NORVIN RICHARDS: Yeah, there we go. 00:45:04.660 --> 00:45:07.350 align:middle line:84% So it has a sensible reading-- every building is guarded. 00:45:07.350 --> 00:45:12.210 align:middle line:84% And it has a reading involving a very large guard, 00:45:12.210 --> 00:45:15.480 align:middle line:84% or maybe lots of really small buildings or something 00:45:15.480 --> 00:45:17.955 align:middle line:90% like that. 00:45:17.955 --> 00:45:20.580 align:middle line:84% Oh yeah, no, let's imagine that there's more than one building. 00:45:20.580 --> 00:45:23.410 align:middle line:90% 00:45:23.410 --> 00:45:25.410 align:middle line:84% So those are two things the sentence could mean. 00:45:25.410 --> 00:45:28.590 align:middle line:84% So yeah, here are a bunch of buildings, a bunch of guards, 00:45:28.590 --> 00:45:32.900 align:middle line:84% one guard per building, or a bunch of buildings and one 00:45:32.900 --> 00:45:35.090 align:middle line:90% guard who is kind of wide. 00:45:35.090 --> 00:45:37.460 align:middle line:84% So it could mean either of those things that's it. 00:45:37.460 --> 00:45:40.300 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:45:40.300 --> 00:45:42.500 align:middle line:84% NORVIN RICHARDS: Ah, yes, so if the buildings are 00:45:42.500 --> 00:45:44.000 align:middle line:84% all in a circle and they're all facing each other, 00:45:44.000 --> 00:45:45.890 align:middle line:84% there could be one guard in the middle. 00:45:45.890 --> 00:45:48.050 align:middle line:84% A guard is standing-- he managed to stand 00:45:48.050 --> 00:45:50.720 align:middle line:84% in front of every building by standing right 00:45:50.720 --> 00:45:51.673 align:middle line:90% in the center spot. 00:45:51.673 --> 00:45:53.090 align:middle line:84% Yes, I suppose it could mean that. 00:45:53.090 --> 00:45:55.010 align:middle line:90% I think that's right. 00:45:55.010 --> 00:45:58.820 align:middle line:90% Let's discount that reading. 00:45:58.820 --> 00:46:01.228 align:middle line:84% So here's an ambiguity, the kind of ambiguity 00:46:01.228 --> 00:46:02.270 align:middle line:90% we've been talking about. 00:46:02.270 --> 00:46:05.330 align:middle line:84% You've got these two qualifiers and you 00:46:05.330 --> 00:46:08.240 align:middle line:84% can interpret-- so the first pass on why 00:46:08.240 --> 00:46:10.190 align:middle line:84% we got this kind of ambiguity was there's 00:46:10.190 --> 00:46:14.480 align:middle line:84% this process of interpreting qualifiers where you figure out 00:46:14.480 --> 00:46:16.670 align:middle line:84% what the sets are that the quantifier is relating, 00:46:16.670 --> 00:46:18.795 align:middle line:84% and you relate them to each other. 00:46:18.795 --> 00:46:21.170 align:middle line:84% And if you have a sentence that has two qualifiers in it, 00:46:21.170 --> 00:46:22.970 align:middle line:90% you get to do that process-- 00:46:22.970 --> 00:46:25.250 align:middle line:84% either you've got to quantifier, quantifier number one 00:46:25.250 --> 00:46:26.420 align:middle line:90% and quantifier number two. 00:46:26.420 --> 00:46:29.360 align:middle line:84% You either apply that process to quantifier number one first 00:46:29.360 --> 00:46:31.760 align:middle line:90% or quantifier number two first. 00:46:31.760 --> 00:46:35.930 align:middle line:84% And then I asserted and offered you, so far, 00:46:35.930 --> 00:46:38.810 align:middle line:90% only evidence from Hungarian. 00:46:38.810 --> 00:46:40.310 align:middle line:84% I asserted that there is actually 00:46:40.310 --> 00:46:42.590 align:middle line:84% this operation of quantifier raising 00:46:42.590 --> 00:46:46.550 align:middle line:84% that has the option of moving one quantifier to a higher 00:46:46.550 --> 00:46:48.170 align:middle line:84% position than the other quantifier, 00:46:48.170 --> 00:46:52.190 align:middle line:84% and that the order in which you perform the operations 00:46:52.190 --> 00:46:53.060 align:middle line:90% is actually fixed. 00:46:53.060 --> 00:46:55.477 align:middle line:84% It's completely determined by the structure 00:46:55.477 --> 00:46:57.560 align:middle line:84% that you get after you've done quantifier raising, 00:46:57.560 --> 00:46:59.060 align:middle line:90% if you have. 00:46:59.060 --> 00:47:01.070 align:middle line:84% So what I'm going to do in the next few slides 00:47:01.070 --> 00:47:04.580 align:middle line:84% is show you some reasons to take that seriously, even 00:47:04.580 --> 00:47:06.650 align:middle line:90% for English. 00:47:06.650 --> 00:47:08.840 align:middle line:84% So here's a sentence that has ambiguity 00:47:08.840 --> 00:47:12.110 align:middle line:84% and the story was going to be it's ambiguous because you have 00:47:12.110 --> 00:47:15.200 align:middle line:84% the option of leaving "every building" where it is 00:47:15.200 --> 00:47:17.810 align:middle line:84% or the option of moving "every building" so that it's 00:47:17.810 --> 00:47:19.760 align:middle line:90% higher than "a guard." 00:47:19.760 --> 00:47:24.510 align:middle line:84% And if you take the option of moving "every building" 00:47:24.510 --> 00:47:27.740 align:middle line:84% so that it's higher than "a guard," invisibly, 00:47:27.740 --> 00:47:29.390 align:middle line:84% without changing the word order-- 00:47:29.390 --> 00:47:32.420 align:middle line:84% very weird to try to understand what's going on-- 00:47:32.420 --> 00:47:35.630 align:middle line:84% then what you do so the generalization is 00:47:35.630 --> 00:47:38.670 align:middle line:84% that you must interpret the highest quantifier first. 00:47:38.670 --> 00:47:40.280 align:middle line:84% So if you do QR of "every building" 00:47:40.280 --> 00:47:43.130 align:middle line:84% higher than "a guard," what you're saying is you're 00:47:43.130 --> 00:47:46.100 align:middle line:84% going to start by relating the set of buildings 00:47:46.100 --> 00:47:49.310 align:middle line:84% to the set of things that a guard is standing in front of. 00:47:49.310 --> 00:47:51.590 align:middle line:84% And you're going to say that first set is completely 00:47:51.590 --> 00:47:53.660 align:middle line:90% contained in the second set. 00:47:53.660 --> 00:47:57.860 align:middle line:84% And then you will interpret the quantifier of "guard." 00:47:57.860 --> 00:48:01.730 align:middle line:84% So you have this optional operation of QR, 00:48:01.730 --> 00:48:08.252 align:middle line:84% and there isn't actually any optionality in the order 00:48:08.252 --> 00:48:09.710 align:middle line:84% in which you interpret quantifiers. 00:48:09.710 --> 00:48:12.110 align:middle line:84% You always interpret the highest quantifier first. 00:48:12.110 --> 00:48:13.670 align:middle line:90% That's going to be the story. 00:48:13.670 --> 00:48:15.590 align:middle line:84% The optionality has to do with the optionality 00:48:15.590 --> 00:48:19.042 align:middle line:90% of the application of QR. 00:48:19.042 --> 00:48:21.000 align:middle line:84% So here's a sentence with two qualifiers in it, 00:48:21.000 --> 00:48:21.840 align:middle line:90% and it's ambiguous. 00:48:21.840 --> 00:48:24.390 align:middle line:84% And I'm asserting it's ambiguous because you can do QR. 00:48:24.390 --> 00:48:26.610 align:middle line:84% Here's another sentence with two quantifiers in it: 00:48:26.610 --> 00:48:27.990 align:middle line:84% "A guard said that I should stand 00:48:27.990 --> 00:48:31.380 align:middle line:90% in front of every building." 00:48:31.380 --> 00:48:34.250 align:middle line:84% Now is this ambiguous in the same way? 00:48:34.250 --> 00:48:34.750 align:middle line:90% No. 00:48:34.750 --> 00:48:37.400 align:middle line:90% 00:48:37.400 --> 00:48:41.080 align:middle line:84% It doesn't mean-- so what does it mean? 00:48:41.080 --> 00:48:43.380 align:middle line:90% 00:48:43.380 --> 00:48:43.880 align:middle line:90% Joseph? 00:48:43.880 --> 00:48:47.812 align:middle line:84% AUDIENCE: The guard thinks that I have to be particularly-- 00:48:47.812 --> 00:48:48.770 align:middle line:90% NORVIN RICHARDS: Large. 00:48:48.770 --> 00:48:51.690 align:middle line:84% AUDIENCE: --to be able to stand in front of all [INAUDIBLE].. 00:48:51.690 --> 00:48:52.982 align:middle line:90% NORVIN RICHARDS: Yeah, exactly. 00:48:52.982 --> 00:48:57.090 align:middle line:84% There is one guard who demands that I gain weight-- 00:48:57.090 --> 00:48:58.605 align:middle line:84% wants me to be wide enough to stand 00:48:58.605 --> 00:48:59.730 align:middle line:90% in front of every building. 00:48:59.730 --> 00:49:00.230 align:middle line:90% Yeah, Faith? 00:49:00.230 --> 00:49:04.500 align:middle line:84% AUDIENCE: I interpreted it instead as move from one 00:49:04.500 --> 00:49:06.180 align:middle line:90% building to the next one. 00:49:06.180 --> 00:49:08.460 align:middle line:84% NORVIN RICHARDS: Yeah, that's a more reasonable thing 00:49:08.460 --> 00:49:10.860 align:middle line:84% for the guard to ask me to do, isn't it? 00:49:10.860 --> 00:49:14.040 align:middle line:84% And I guess it helps that we've switched here 00:49:14.040 --> 00:49:18.510 align:middle line:84% to "That I should stand in front of every building" 00:49:18.510 --> 00:49:19.650 align:middle line:90% rather than-- 00:49:19.650 --> 00:49:21.150 align:middle line:84% so what we had before was a guard 00:49:21.150 --> 00:49:23.340 align:middle line:84% is standing in front of every building. 00:49:23.340 --> 00:49:25.020 align:middle line:84% I guess we could interpret that as meaning that there's 00:49:25.020 --> 00:49:27.210 align:middle line:84% a single guard who is walking from building to building 00:49:27.210 --> 00:49:28.500 align:middle line:84% and standing briefly in front of them. 00:49:28.500 --> 00:49:30.270 align:middle line:84% These are all ways of getting a single guard 00:49:30.270 --> 00:49:31.110 align:middle line:90% to do all the work. 00:49:31.110 --> 00:49:32.068 align:middle line:90% There's only one guard. 00:49:32.068 --> 00:49:35.297 align:middle line:90% Yeah, you're absolutely right. 00:49:35.297 --> 00:49:36.880 align:middle line:84% But it doesn't have the other reading. 00:49:36.880 --> 00:49:40.112 align:middle line:84% It doesn't mean there was one guard who 00:49:40.112 --> 00:49:42.070 align:middle line:84% wanted me to stand in front of the Stata Center 00:49:42.070 --> 00:49:43.600 align:middle line:84% and another guard who wanted me to stand in front 00:49:43.600 --> 00:49:45.433 align:middle line:84% of the Student Center, and another guard who 00:49:45.433 --> 00:49:47.410 align:middle line:84% wanted me to stand in front of the MIT Museum. 00:49:47.410 --> 00:49:48.285 align:middle line:90% It doesn't mean that. 00:49:48.285 --> 00:49:50.910 align:middle line:90% 00:49:50.910 --> 00:49:52.260 align:middle line:90% All right, why not? 00:49:52.260 --> 00:49:55.290 align:middle line:84% Because we've got two qualifiers. 00:49:55.290 --> 00:49:57.510 align:middle line:84% Why can't we interpret these qualifiers 00:49:57.510 --> 00:49:59.582 align:middle line:90% in any order we want? 00:49:59.582 --> 00:50:02.070 align:middle line:84% Well, if we believe in QR, we have an answer to that. 00:50:02.070 --> 00:50:04.340 align:middle line:84% We get to say what's special about this example 00:50:04.340 --> 00:50:05.930 align:middle line:84% and distinguishes it from the examples 00:50:05.930 --> 00:50:10.070 align:middle line:84% we had before is that "a guard" is in the matrix clause, 00:50:10.070 --> 00:50:12.650 align:middle line:84% and there's an embedded clause, an embedded CP, 00:50:12.650 --> 00:50:14.900 align:middle line:84% that I should stand in front of every building. 00:50:14.900 --> 00:50:17.150 align:middle line:90% Yeah, that's an embedded clause. 00:50:17.150 --> 00:50:17.900 align:middle line:90% Is that clear? 00:50:17.900 --> 00:50:19.670 align:middle line:90% Should I draw a tree? 00:50:19.670 --> 00:50:22.820 align:middle line:84% So say it's taking, as its sister, 00:50:22.820 --> 00:50:25.220 align:middle line:84% a CP that I should stand in front of every building. 00:50:25.220 --> 00:50:27.137 align:middle line:84% And what we're learning is that although there 00:50:27.137 --> 00:50:28.820 align:middle line:84% is this optional operation, QR, that 00:50:28.820 --> 00:50:30.680 align:middle line:84% can get one quantifier passed to another, 00:50:30.680 --> 00:50:33.215 align:middle line:84% it can't get you out of a clause. 00:50:33.215 --> 00:50:35.660 align:middle line:84% We're going to have to figure out what counts as a clause, 00:50:35.660 --> 00:50:37.550 align:middle line:84% but apparently this counts as a clause. 00:50:37.550 --> 00:50:40.670 align:middle line:84% There's some limitation on how far you can QR. 00:50:40.670 --> 00:50:44.920 align:middle line:90% 00:50:44.920 --> 00:50:45.790 align:middle line:90% How about this one? 00:50:45.790 --> 00:50:49.330 align:middle line:84% "A guard seems to be standing in front of every building." 00:50:49.330 --> 00:50:50.320 align:middle line:90% Is that ambiguous? 00:50:50.320 --> 00:51:01.970 align:middle line:90% 00:51:01.970 --> 00:51:03.940 align:middle line:90% I think so. 00:51:03.940 --> 00:51:09.350 align:middle line:84% So it means either "Looks like every building is guarded" 00:51:09.350 --> 00:51:14.540 align:middle line:90% or "Man, that guard is wide!" 00:51:14.540 --> 00:51:16.550 align:middle line:84% or "Man, that guard is running hard 00:51:16.550 --> 00:51:18.440 align:middle line:84% to be in front of every building at once!" 00:51:18.440 --> 00:51:21.110 align:middle line:84% or "Look how clever that guard is at geometry. 00:51:21.110 --> 00:51:23.930 align:middle line:84% He's managed to stand in front of every building at once!" 00:51:23.930 --> 00:51:28.050 align:middle line:84% (Lucky thing for him, they all face each other.) 00:51:28.050 --> 00:51:33.710 align:middle line:84% So it has two meanings, one with a very wide 00:51:33.710 --> 00:51:35.912 align:middle line:84% or clever or fast-moving guard, and then 00:51:35.912 --> 00:51:37.370 align:middle line:84% the other more normal reading where 00:51:37.370 --> 00:51:38.915 align:middle line:84% it's like every building has a guard. 00:51:38.915 --> 00:51:40.790 align:middle line:84% So either every building is such that there's 00:51:40.790 --> 00:51:42.290 align:middle line:84% a guard standing in front of it, or there 00:51:42.290 --> 00:51:43.707 align:middle line:84% is a guard who is somehow standing 00:51:43.707 --> 00:51:45.890 align:middle line:90% in front of every building. 00:51:45.890 --> 00:51:47.360 align:middle line:90% So yes, this is ambiguous. 00:51:47.360 --> 00:51:50.740 align:middle line:90% 00:51:50.740 --> 00:51:52.030 align:middle line:90% How about this one? 00:51:52.030 --> 00:51:53.473 align:middle line:84% "I seem to a guard to be standing 00:51:53.473 --> 00:51:54.640 align:middle line:90% in front of every building." 00:51:54.640 --> 00:51:57.640 align:middle line:90% 00:51:57.640 --> 00:52:00.010 align:middle line:90% Is that ambiguous? 00:52:00.010 --> 00:52:01.510 align:middle line:90% No. 00:52:01.510 --> 00:52:03.340 align:middle line:84% This is a sentence about one guard 00:52:03.340 --> 00:52:06.640 align:middle line:84% who needs rest, who needs to be taken 00:52:06.640 --> 00:52:10.270 align:middle line:84% off-duty and convinced to get some rest. 00:52:10.270 --> 00:52:12.460 align:middle line:84% This is a guard who thinks that, I don't know, 00:52:12.460 --> 00:52:14.320 align:middle line:84% maybe he goes to one building and I'm there 00:52:14.320 --> 00:52:16.778 align:middle line:84% and he goes to another building and I seem to be there too, 00:52:16.778 --> 00:52:19.810 align:middle line:84% and he's seeing me everywhere and this guard has problems. 00:52:19.810 --> 00:52:21.180 align:middle line:90% And besides-- yes? 00:52:21.180 --> 00:52:23.140 align:middle line:84% AUDIENCE: Is it just because "a guard" could 00:52:23.140 --> 00:52:26.410 align:middle line:84% be referring to multiple guards whereas I-- you can't 00:52:26.410 --> 00:52:29.765 align:middle line:90% have more than one I? 00:52:29.765 --> 00:52:31.390 align:middle line:84% NORVIN RICHARDS: But the question still 00:52:31.390 --> 00:52:33.430 align:middle line:90% remains, the other reading-- 00:52:33.430 --> 00:52:34.510 align:middle line:90% you're absolutely right. 00:52:34.510 --> 00:52:36.052 align:middle line:84% But the other reading that this could 00:52:36.052 --> 00:52:39.520 align:middle line:84% have would be one with something like every building 00:52:39.520 --> 00:52:42.310 align:middle line:84% has this property: I seem to a guard 00:52:42.310 --> 00:52:44.467 align:middle line:90% to be standing in front of it. 00:52:44.467 --> 00:52:46.050 align:middle line:84% That would be a reading that would be, 00:52:46.050 --> 00:52:48.303 align:middle line:84% like, "For this building, there's 00:52:48.303 --> 00:52:50.470 align:middle line:84% a guard who thinks that I'm standing in front of it. 00:52:50.470 --> 00:52:51.750 align:middle line:84% And for this other building, there's 00:52:51.750 --> 00:52:53.375 align:middle line:84% another guard, maybe a different guard, 00:52:53.375 --> 00:52:55.260 align:middle line:84% who thinks that I'm standing in front of it." 00:52:55.260 --> 00:52:58.740 align:middle line:84% That's a story where there are lots 00:52:58.740 --> 00:53:03.300 align:middle line:84% of guards who don't necessarily believe 00:53:03.300 --> 00:53:04.830 align:middle line:84% that I am simultaneously standing 00:53:04.830 --> 00:53:06.080 align:middle line:90% in front of lots of buildings. 00:53:06.080 --> 00:53:08.007 align:middle line:84% They just all-- their hallucinations 00:53:08.007 --> 00:53:09.090 align:middle line:90% are more simple than that. 00:53:09.090 --> 00:53:11.007 align:middle line:84% They just all see me in front of one building, 00:53:11.007 --> 00:53:13.132 align:middle line:84% one particular building, maybe the building they're 00:53:13.132 --> 00:53:14.250 align:middle line:90% supposed to be guarding. 00:53:14.250 --> 00:53:15.667 align:middle line:84% All of them are taking the day off 00:53:15.667 --> 00:53:17.970 align:middle line:84% because they're like, oh yeah, that Richards guy, he's 00:53:17.970 --> 00:53:20.300 align:middle line:90% guarding that building. 00:53:20.300 --> 00:53:20.930 align:middle line:90% Yeah? 00:53:20.930 --> 00:53:23.303 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:53:23.303 --> 00:53:24.220 align:middle line:90% NORVIN RICHARDS: Yeah? 00:53:24.220 --> 00:53:26.020 align:middle line:84% AUDIENCE: Somehow it didn't register to me 00:53:26.020 --> 00:53:27.560 align:middle line:90% that you were the one-- 00:53:27.560 --> 00:53:30.173 align:middle line:90% not the guard. 00:53:30.173 --> 00:53:32.840 align:middle line:84% NORVIN RICHARDS: Yeah, so that's what the second sentence means. 00:53:32.840 --> 00:53:34.757 align:middle line:84% But the point is that it only means one thing. 00:53:34.757 --> 00:53:37.120 align:middle line:84% It means there is one guard who thinks that I'm standing 00:53:37.120 --> 00:53:38.245 align:middle line:90% in front of every building. 00:53:38.245 --> 00:53:40.822 align:middle line:84% It doesn't mean every building is such 00:53:40.822 --> 00:53:42.280 align:middle line:84% that there is some guard who thinks 00:53:42.280 --> 00:53:43.700 align:middle line:90% I'm standing in front of it. 00:53:43.700 --> 00:53:44.470 align:middle line:90% Doesn't mean that. 00:53:44.470 --> 00:53:45.690 align:middle line:90% Yeah? 00:53:45.690 --> 00:53:51.420 align:middle line:84% AUDIENCE: Could it be that a guard [INAUDIBLE]?? 00:53:51.420 --> 00:53:53.760 align:middle line:84% It's a singular phrase, but it could 00:53:53.760 --> 00:54:00.560 align:middle line:84% refer to any number of people, whereas "I seem to a guard" 00:54:00.560 --> 00:54:04.010 align:middle line:84% means that there is one entity that "a guard" refers to 00:54:04.010 --> 00:54:05.180 align:middle line:90% and it can't be anyone else. 00:54:05.180 --> 00:54:09.253 align:middle line:84% There is a person who has this quality that saw you. 00:54:09.253 --> 00:54:10.670 align:middle line:84% NORVIN RICHARDS: Yeah, so that's-- 00:54:10.670 --> 00:54:13.190 align:middle line:84% I think there was a related comment earlier, 00:54:13.190 --> 00:54:14.810 align:middle line:84% and I think that's onto something, 00:54:14.810 --> 00:54:18.890 align:middle line:84% but it's describing the problem that we have. 00:54:18.890 --> 00:54:21.748 align:middle line:84% If it's "A guard is standing in front of every building," 00:54:21.748 --> 00:54:24.290 align:middle line:84% or "A guard seems to be standing in front of every building," 00:54:24.290 --> 00:54:27.020 align:middle line:84% then yeah, "a guard" can either be one guard that's 00:54:27.020 --> 00:54:29.720 align:middle line:84% in many places at once or it can be many guards, 00:54:29.720 --> 00:54:30.710 align:middle line:90% one for each building. 00:54:30.710 --> 00:54:33.410 align:middle line:90% That's the original ambiguity. 00:54:33.410 --> 00:54:36.080 align:middle line:84% "A guard" has that power that it can do that. 00:54:36.080 --> 00:54:38.690 align:middle line:84% But why can't it do it in the second sentence 00:54:38.690 --> 00:54:39.590 align:middle line:90% is the question? 00:54:39.590 --> 00:54:43.970 align:middle line:84% Why can't the second sentence mean 00:54:43.970 --> 00:54:47.060 align:middle line:84% there are three guards-- let's call them A, B, and C, 00:54:47.060 --> 00:54:49.520 align:middle line:84% and guard A thinks that I'm standing in front of building 00:54:49.520 --> 00:54:52.090 align:middle line:84% number one, and guard B thinks that I'm standing in front 00:54:52.090 --> 00:54:53.840 align:middle line:84% of building number two, and guard C thinks 00:54:53.840 --> 00:54:57.760 align:middle line:84% that I'm standing in front of building number three. 00:54:57.760 --> 00:55:00.670 align:middle line:84% Why can't it mean that when the first sentence can 00:55:00.670 --> 00:55:03.080 align:middle line:84% mean A seems to be standing in front of building one, 00:55:03.080 --> 00:55:05.080 align:middle line:84% B seems to be standing in front of building two, 00:55:05.080 --> 00:55:07.163 align:middle line:84% C seems to be standing in front of building three. 00:55:07.163 --> 00:55:09.640 align:middle line:84% We can play that game, the alphabet and number game, 00:55:09.640 --> 00:55:12.500 align:middle line:84% with the first example, but not with the second example. 00:55:12.500 --> 00:55:15.420 align:middle line:90% We're trying to figure out why. 00:55:15.420 --> 00:55:19.030 align:middle line:84% Yep, I'm trying to figure out why. 00:55:19.030 --> 00:55:22.940 align:middle line:84% Here's a plausible story about why. 00:55:22.940 --> 00:55:25.970 align:middle line:84% We went through this very fast, so I don't blame anybody 00:55:25.970 --> 00:55:27.620 align:middle line:90% if you don't remember this. 00:55:27.620 --> 00:55:29.848 align:middle line:84% But when we were doing "A guard seems 00:55:29.848 --> 00:55:31.640 align:middle line:84% to be standing in front of every building," 00:55:31.640 --> 00:55:32.750 align:middle line:90% sentences like that-- 00:55:32.750 --> 00:55:40.770 align:middle line:90% 00:55:40.770 --> 00:55:45.390 align:middle line:84% what we said was that there is a movement operation going 00:55:45.390 --> 00:55:48.720 align:middle line:84% on in sentences involving "seems," this kind of sentence 00:55:48.720 --> 00:55:52.590 align:middle line:84% involving "seems," where "seem" is followed by an infinitive. 00:55:52.590 --> 00:55:57.060 align:middle line:84% What's going on is that "the guard," the thing that 00:55:57.060 --> 00:55:59.850 align:middle line:84% ends up in subject position, starts out 00:55:59.850 --> 00:56:00.990 align:middle line:90% in the embedded clause. 00:56:00.990 --> 00:56:06.060 align:middle line:84% Here is a guard, and it's raising, moving up to here. 00:56:06.060 --> 00:56:09.570 align:middle line:84% There's NP movement-- so a movement. 00:56:09.570 --> 00:56:12.810 align:middle line:84% I'm sorry, I know it's dangerous taking 24.900 from 00:56:12.810 --> 00:56:15.390 align:middle line:84% a syntactician, because I keep trying to change the subject 00:56:15.390 --> 00:56:16.877 align:middle line:90% back to syntax. 00:56:16.877 --> 00:56:18.960 align:middle line:84% So now we're going to talk about syntax some more. 00:56:18.960 --> 00:56:20.835 align:middle line:84% This is a bit of syntax that we talked about. 00:56:20.835 --> 00:56:23.977 align:middle line:84% I tried to convince you that sentences like this, sentences 00:56:23.977 --> 00:56:25.560 align:middle line:84% with "seem" and an infinitive in them, 00:56:25.560 --> 00:56:27.870 align:middle line:84% the subject of the whole thing started out 00:56:27.870 --> 00:56:28.890 align:middle line:90% in the embedded clause. 00:56:28.890 --> 00:56:30.270 align:middle line:84% One of the kinds of arguments had 00:56:30.270 --> 00:56:32.820 align:middle line:84% to do with properties of idioms, that you could say things 00:56:32.820 --> 00:56:41.350 align:middle line:84% like "The shit seems to have hit the fan," 00:56:41.350 --> 00:56:44.080 align:middle line:84% where we think that the idiom is "The shit hit 00:56:44.080 --> 00:56:48.730 align:middle line:84% the fan," that "the shit" needs to be somewhere near 00:56:48.730 --> 00:56:51.293 align:middle line:84% "hit the fan," but it's way over there, and the story was, 00:56:51.293 --> 00:56:53.710 align:middle line:84% yeah, that's because it starts out in the embedded clause, 00:56:53.710 --> 00:56:57.700 align:middle line:84% and it undergoes NP movement into the matrix clause. 00:56:57.700 --> 00:56:59.560 align:middle line:90% So it moves, it raises. 00:56:59.560 --> 00:57:01.000 align:middle line:90% That sound familiar at all? 00:57:01.000 --> 00:57:05.297 align:middle line:84% Have you all expunged the terrible memory of syntax? 00:57:05.297 --> 00:57:06.880 align:middle line:84% That's the way we were talking before. 00:57:06.880 --> 00:57:09.420 align:middle line:90% 00:57:09.420 --> 00:57:14.480 align:middle line:84% So we said a bit ago that QR is clause-bound. 00:57:14.480 --> 00:57:15.080 align:middle line:90% There we go. 00:57:15.080 --> 00:57:16.610 align:middle line:84% That's us saying the QR is clause-bound. 00:57:16.610 --> 00:57:17.690 align:middle line:84% "The guard said that I should stand 00:57:17.690 --> 00:57:18.620 align:middle line:90% in front of every building." 00:57:18.620 --> 00:57:19.280 align:middle line:90% I said yeah. 00:57:19.280 --> 00:57:20.690 align:middle line:90% Why isn't that ambiguous? 00:57:20.690 --> 00:57:23.930 align:middle line:84% Well, it's not ambiguous because "every building" is inside 00:57:23.930 --> 00:57:26.480 align:middle line:84% an embedded clause that doesn't contain "a guard." 00:57:26.480 --> 00:57:29.255 align:middle line:90% 00:57:29.255 --> 00:57:31.850 align:middle line:84% So QR can't take "every building" 00:57:31.850 --> 00:57:34.790 align:middle line:90% and move it past "a guard." 00:57:34.790 --> 00:57:37.950 align:middle line:84% And then I think I also said, if we're saying things like that, 00:57:37.950 --> 00:57:39.440 align:middle line:84% we eventually will have to explain 00:57:39.440 --> 00:57:42.500 align:middle line:84% what kinds of things-- what we mean by clauses, exactly. 00:57:42.500 --> 00:57:44.660 align:middle line:84% So clause has to include things like that-- 00:57:44.660 --> 00:57:47.940 align:middle line:84% I should stand in front of every building. 00:57:47.940 --> 00:57:53.608 align:middle line:84% What about a sentence like "A guard 00:57:53.608 --> 00:57:55.650 align:middle line:84% seems to be standing in front of every building"? 00:57:55.650 --> 00:57:57.193 align:middle line:90% Well, here we get ambiguity. 00:57:57.193 --> 00:57:59.610 align:middle line:84% And it could be that we're getting ambiguity here because, 00:57:59.610 --> 00:58:13.575 align:middle line:84% well, "every building" has the option of undergoing QR here. 00:58:13.575 --> 00:58:17.150 align:middle line:90% 00:58:17.150 --> 00:58:19.430 align:middle line:84% The chalk I'm using is very small. 00:58:19.430 --> 00:58:21.920 align:middle line:84% I'm blaming my illegible handwriting 00:58:21.920 --> 00:58:24.955 align:middle line:90% on the poor quality of my chalk. 00:58:24.955 --> 00:58:27.080 align:middle line:84% It's foolish of me to pick up a new piece of chalk, 00:58:27.080 --> 00:58:28.400 align:middle line:84% because that will blow that excuse out 00:58:28.400 --> 00:58:29.650 align:middle line:90% of the water in just a second. 00:58:29.650 --> 00:58:32.610 align:middle line:90% 00:58:32.610 --> 00:58:35.840 align:middle line:90% So here's "a guard" in the end. 00:58:35.840 --> 00:58:37.370 align:middle line:84% It could be that there's ambiguity 00:58:37.370 --> 00:58:39.440 align:middle line:84% in "a guard seems to be standing in front of every building" 00:58:39.440 --> 00:58:41.270 align:middle line:84% because "every building" can undergo QR up 00:58:41.270 --> 00:58:45.570 align:middle line:84% to here to a position above "every guard." 00:58:45.570 --> 00:58:47.850 align:middle line:84% If that's possible, then that would be telling us 00:58:47.850 --> 00:58:50.910 align:middle line:84% that well this TP down here, "to be standing in 00:58:50.910 --> 00:58:53.490 align:middle line:84% front of every building" doesn't count as a clause 00:58:53.490 --> 00:58:55.420 align:middle line:90% that you can QR out of that. 00:58:55.420 --> 00:58:57.120 align:middle line:84% So when we say that QR is clause-bound, 00:58:57.120 --> 00:58:59.010 align:middle line:84% we don't mean this kind of thing. 00:58:59.010 --> 00:59:01.460 align:middle line:90% We mean tensed clauses. 00:59:01.460 --> 00:59:04.760 align:middle line:84% But another possibility is that we do actually 00:59:04.760 --> 00:59:08.180 align:middle line:84% mean tensed clauses and that the reason we do actually 00:59:08.180 --> 00:59:12.530 align:middle line:84% need every TP, that QR out of this TP is impossible, 00:59:12.530 --> 00:59:15.020 align:middle line:84% and that it's not possible to QR up to here, 00:59:15.020 --> 00:59:16.820 align:middle line:90% it's only possible to QR here. 00:59:16.820 --> 00:59:26.870 align:middle line:90% 00:59:26.870 --> 00:59:28.970 align:middle line:84% And that the reason that you get ambiguity 00:59:28.970 --> 00:59:31.550 align:middle line:84% in "A guard seems to be standing in front of every building" 00:59:31.550 --> 00:59:32.540 align:middle line:90% goes like this-- 00:59:32.540 --> 00:59:34.790 align:middle line:84% "every building" can QR to a position 00:59:34.790 --> 00:59:37.070 align:middle line:84% in the periphery of that embedded clause, 00:59:37.070 --> 00:59:40.750 align:middle line:84% and "a guard" started out in that embedded clause. 00:59:40.750 --> 00:59:43.290 align:middle line:90% And that's enough. 00:59:43.290 --> 00:59:46.545 align:middle line:84% This would be a story where we're already-- 00:59:46.545 --> 00:59:49.897 align:middle line:84% if we're doing QR at all, we're slowly, hopefully, 00:59:49.897 --> 00:59:52.230 align:middle line:84% getting accustomed to the idea that part of interpreting 00:59:52.230 --> 00:59:55.350 align:middle line:84% sentences will be interpreting things in places where we 00:59:55.350 --> 00:59:58.090 align:middle line:90% cannot necessarily see them. 00:59:58.090 --> 01:00:00.720 align:middle line:84% So we can take things and move them invisibly to other places 01:00:00.720 --> 01:00:02.950 align:middle line:90% and interpret them there. 01:00:02.950 --> 01:00:04.500 align:middle line:84% So in "A guard seems to be standing 01:00:04.500 --> 01:00:05.940 align:middle line:84% in front of every building," there 01:00:05.940 --> 01:00:08.590 align:middle line:84% are two invisible movements going on. 01:00:08.590 --> 01:00:10.640 align:middle line:84% One is we are invisibly moving "every building," 01:00:10.640 --> 01:00:12.390 align:middle line:84% maybe not all the way up to here, but just 01:00:12.390 --> 01:00:15.210 align:middle line:84% to the edge of the embedded clause, the embedded TP. 01:00:15.210 --> 01:00:19.020 align:middle line:84% And we are invisibly taking "a guard," which started out 01:00:19.020 --> 01:00:21.370 align:middle line:84% in the embedded subject position and moved up to here 01:00:21.370 --> 01:00:25.010 align:middle line:84% and underwent NP movement, and we're putting it back. 01:00:25.010 --> 01:00:27.135 align:middle line:84% So we end up with "every building" above "a guard." 01:00:27.135 --> 01:00:30.050 align:middle line:90% 01:00:30.050 --> 01:00:32.000 align:middle line:90% And the reason to take that-- 01:00:32.000 --> 01:00:32.750 align:middle line:90% you're stunned. 01:00:32.750 --> 01:00:34.250 align:middle line:84% I don't blame you for being stunned. 01:00:34.250 --> 01:00:37.070 align:middle line:84% So there are these two invisible things happening. 01:00:37.070 --> 01:00:40.070 align:middle line:84% A reason to take that idea seriously 01:00:40.070 --> 01:00:42.140 align:middle line:84% is the fact at the bottom of this. 01:00:42.140 --> 01:00:43.850 align:middle line:84% So "I seem to a guard to be standing 01:00:43.850 --> 01:00:46.490 align:middle line:84% in front of every building--" we can get a story 01:00:46.490 --> 01:00:48.650 align:middle line:84% about why we're not getting ambiguity here if we're 01:00:48.650 --> 01:00:51.530 align:middle line:84% willing to say no, QR can't, in fact, get out 01:00:51.530 --> 01:00:53.783 align:middle line:84% of an infinitival clause like "to be standing 01:00:53.783 --> 01:00:54.950 align:middle line:90% in front of every building." 01:00:54.950 --> 01:00:57.410 align:middle line:84% It can only get to the edge of such a clause. 01:00:57.410 --> 01:00:58.970 align:middle line:84% And what's special about this example 01:00:58.970 --> 01:01:02.717 align:middle line:84% is that "a guard" is not inside the embedded clause 01:01:02.717 --> 01:01:04.550 align:middle line:84% "to be standing in front of every building." 01:01:04.550 --> 01:01:07.520 align:middle line:90% It's an argument of "seem." 01:01:07.520 --> 01:01:10.563 align:middle line:90% So it's in the higher clause. 01:01:10.563 --> 01:01:12.480 align:middle line:84% I don't know why I did this with a blackboard. 01:01:12.480 --> 01:01:13.770 align:middle line:90% I think I have slides here. 01:01:13.770 --> 01:01:14.710 align:middle line:90% So let me show you the slides. 01:01:14.710 --> 01:01:15.585 align:middle line:90% Maybe they will help. 01:01:15.585 --> 01:01:18.750 align:middle line:90% 01:01:18.750 --> 01:01:21.860 align:middle line:84% So we think that "a guard seems to be 01:01:21.860 --> 01:01:23.360 align:middle line:84% standing in front of every building" 01:01:23.360 --> 01:01:24.990 align:middle line:90% involves a step of movement. 01:01:24.990 --> 01:01:27.480 align:middle line:84% "A guard" is moving out of the embedded clause 01:01:27.480 --> 01:01:29.415 align:middle line:84% and into the matrix subject position. 01:01:29.415 --> 01:01:32.390 align:middle line:90% 01:01:32.390 --> 01:01:35.175 align:middle line:84% And I see now I don't actually have slides 01:01:35.175 --> 01:01:36.300 align:middle line:90% that help with any of this. 01:01:36.300 --> 01:01:38.990 align:middle line:84% So the reason we're getting this ambiguity 01:01:38.990 --> 01:01:41.840 align:middle line:84% is not that "every building" can QR past the higher 01:01:41.840 --> 01:01:42.980 align:middle line:90% position of "a guard." 01:01:42.980 --> 01:01:45.500 align:middle line:84% It can only QR past the lower position of "a guard," 01:01:45.500 --> 01:01:47.100 align:middle line:90% and that's good enough. 01:01:47.100 --> 01:01:49.460 align:middle line:84% So we get to interpret the lower position of "a guard" 01:01:49.460 --> 01:01:53.150 align:middle line:84% as well as the higher invisible position of "every building." 01:01:53.150 --> 01:01:55.405 align:middle line:84% So we get a handle on all of these facts 01:01:55.405 --> 01:01:56.780 align:middle line:84% as long as we're willing to posit 01:01:56.780 --> 01:02:00.470 align:middle line:84% these particular invisible kinds of movements. 01:02:00.470 --> 01:02:02.990 align:middle line:84% Learning something about QR-- when we say it's clause-bound, 01:02:02.990 --> 01:02:06.350 align:middle line:84% we mean it can't get any further than TP, any kind of TP, 01:02:06.350 --> 01:02:07.645 align:middle line:90% tensed or nontensed. 01:02:07.645 --> 01:02:10.900 align:middle line:90% 01:02:10.900 --> 01:02:12.940 align:middle line:84% Now Danny Fox also discovered something else 01:02:12.940 --> 01:02:14.890 align:middle line:90% that's cool about QR. 01:02:14.890 --> 01:02:17.300 align:middle line:84% He's discovered many cool things. 01:02:17.300 --> 01:02:20.570 align:middle line:84% And the next thing is quite long and complicated, 01:02:20.570 --> 01:02:23.980 align:middle line:84% so maybe I will pause here and take questions. 01:02:23.980 --> 01:02:25.480 align:middle line:84% Do people have questions about this? 01:02:25.480 --> 01:02:29.900 align:middle line:84% Would you like me to go through it more slowly or carefully? 01:02:29.900 --> 01:02:34.437 align:middle line:84% I've been talking so far as QR is always optional. 01:02:34.437 --> 01:02:36.520 align:middle line:84% Danny Fox has discovered-- it was one of his early 01:02:36.520 --> 01:02:37.902 align:middle line:90% discoveries-- 01:02:37.902 --> 01:02:39.610 align:middle line:84% it's actually more complicated than that. 01:02:39.610 --> 01:02:41.860 align:middle line:84% What we'll see, and we'll start doing this next time, 01:02:41.860 --> 01:02:45.790 align:middle line:84% is that you can only do QR if it's 01:02:45.790 --> 01:02:49.160 align:middle line:84% going to change the meaning of the sentence. 01:02:49.160 --> 01:02:51.550 align:middle line:84% So if you have two qualifiers, you 01:02:51.550 --> 01:02:54.740 align:middle line:84% can QR the lower quantifier past the higher quantifier 01:02:54.740 --> 01:02:56.740 align:middle line:84% if that's going to give you a different meaning, 01:02:56.740 --> 01:03:00.910 align:middle line:84% a meaning you wouldn't have had if the QR hadn't happened. 01:03:00.910 --> 01:03:03.580 align:middle line:84% If you have a sentence where QR wouldn't affect the meaning, 01:03:03.580 --> 01:03:04.510 align:middle line:90% it can't happen. 01:03:04.510 --> 01:03:08.000 align:middle line:90% 01:03:08.000 --> 01:03:09.560 align:middle line:84% And what we'll do next time-- we'll 01:03:09.560 --> 01:03:10.970 align:middle line:84% start with this next time-- we'll 01:03:10.970 --> 01:03:12.815 align:middle line:84% develop the tools to discover that, 01:03:12.815 --> 01:03:15.140 align:middle line:84% the tools that Danny Fox discovered, 01:03:15.140 --> 01:03:18.540 align:middle line:84% and then I'll show you that that's true. 01:03:18.540 --> 01:03:20.810 align:middle line:84% So any further questions about any of this? 01:03:20.810 --> 01:03:24.530 align:middle line:84% At this point, you should all be weirded out. 01:03:24.530 --> 01:03:26.780 align:middle line:84% Suddenly things are moving around in an invisible way, 01:03:26.780 --> 01:03:28.363 align:middle line:84% and this is part of interpreting them. 01:03:28.363 --> 01:03:29.840 align:middle line:90% Yeah? 01:03:29.840 --> 01:03:31.610 align:middle line:84% AUDIENCE: If QR are can only happen 01:03:31.610 --> 01:03:39.330 align:middle line:84% if it will change the meaning of the sentence, that indicates 01:03:39.330 --> 01:03:42.450 align:middle line:84% that the English language, and I imagine other languages that 01:03:42.450 --> 01:03:49.440 align:middle line:84% allow this, they build in the ambiguity as opposed 01:03:49.440 --> 01:03:51.272 align:middle line:84% to trying to mitigate the ambiguity? 01:03:51.272 --> 01:03:52.980 align:middle line:84% NORVIN RICHARDS: Oh, I see what you mean. 01:03:52.980 --> 01:03:55.320 align:middle line:90% I think I see what you mean. 01:03:55.320 --> 01:03:57.600 align:middle line:84% I mean, the claim in the end is that the structures 01:03:57.600 --> 01:04:01.020 align:middle line:84% that are interpreted are never ambiguous. 01:04:01.020 --> 01:04:03.870 align:middle line:90% You either do QR or you don't. 01:04:03.870 --> 01:04:05.880 align:middle line:84% And if you do QR, then you get one reading. 01:04:05.880 --> 01:04:08.310 align:middle line:84% And if you don't do QR, then you get another reading. 01:04:08.310 --> 01:04:10.560 align:middle line:84% And English is one of the languages in which you don't 01:04:10.560 --> 01:04:13.800 align:middle line:84% get to see QR, and the result is that the sentence is ambiguous 01:04:13.800 --> 01:04:16.503 align:middle line:84% because you can't tell whether QR has happened or not. 01:04:16.503 --> 01:04:18.420 align:middle line:84% There are languages out there, like Hungarian, 01:04:18.420 --> 01:04:22.303 align:middle line:84% where you can see QR, and so the sentences are not ambiguous. 01:04:22.303 --> 01:04:24.720 align:middle line:84% But yes, that means there are certain kinds of ambiguities 01:04:24.720 --> 01:04:27.720 align:middle line:84% in English that don't exist in some other languages, 01:04:27.720 --> 01:04:28.560 align:middle line:90% like Hungarian. 01:04:28.560 --> 01:04:29.610 align:middle line:84% There are other languages where it's 01:04:29.610 --> 01:04:30.735 align:middle line:90% more complicated than that. 01:04:30.735 --> 01:04:35.760 align:middle line:84% So there are languages like Japanese, 01:04:35.760 --> 01:04:37.760 align:middle line:84% and German, actually, has a version of this too. 01:04:37.760 --> 01:04:41.840 align:middle line:84% But in Japanese, if you have two qualifiers, 01:04:41.840 --> 01:04:43.460 align:middle line:84% their scope with respect to each other 01:04:43.460 --> 01:04:47.270 align:middle line:84% is unambiguous unless you move one of them past the other, 01:04:47.270 --> 01:04:49.100 align:middle line:90% and then it becomes ambiguous. 01:04:49.100 --> 01:04:53.120 align:middle line:84% So basically, it's as though the movement operation that 01:04:53.120 --> 01:04:56.270 align:middle line:84% moves one quantifier past the other could be QR 01:04:56.270 --> 01:04:58.170 align:middle line:90% or it could be something else. 01:04:58.170 --> 01:05:01.130 align:middle line:84% And so you can't tell whether you have done QR of that thing 01:05:01.130 --> 01:05:01.740 align:middle line:90% or not. 01:05:01.740 --> 01:05:04.400 align:middle line:84% But there is no invisible QR in Japanese-- 01:05:04.400 --> 01:05:06.030 align:middle line:90% something like that. 01:05:06.030 --> 01:05:07.610 align:middle line:90% Cool. 01:05:07.610 --> 01:05:08.300 align:middle line:90% All right, good. 01:05:08.300 --> 01:05:11.568 align:middle line:84% Thank you for coming in braving my possible cold viruses. 01:05:11.568 --> 01:05:13.110 align:middle line:84% I apologize for exposing you to them. 01:05:13.110 --> 01:05:16.900 align:middle line:90% And I will see you on Thursday. 01:05:16.900 --> 01:05:24.000 align:middle line:90%