WEBVTT 00:37.510 --> 00:37.891 The End 01:04.099 --> 01:05.440 Good afternoon, it's 1313. 01:05.600 --> 01:10.762 I think I'm online and I think we're back here for Uncertainty 101. 01:10.823 --> 01:12.924 We're just going to get started right away. 01:12.984 --> 01:19.387 This is the second half of understanding life as a pattern, integrity, and understanding how science is broken. 01:20.768 --> 01:26.851 As I said earlier this morning, I'm going to use the work of William Briggs, 01:27.822 --> 01:45.058 that is posted on Substack and Rumble and YouTube and elsewhere, a friend of mine who I met over the last couple of years through the Broken Science Initiative, who I think has an excellent take on David Stove's work and this excellent take on the rationality of induction. 01:45.098 --> 01:52.245 And so I think that's what we're really gonna be focused on on the afternoons and Tuesdays and Thursdays for the coming few weeks. 01:53.524 --> 02:16.128 I'm very excited to see what I can contribute to sort of distilling these ideas down in parallel with this, again, understanding life as a pattern integrity and how that changes the way that we think about that, about how we teach biology and then how we teach science to our kids, I think is going to be reflected in this combination as well. 02:17.309 --> 02:18.110 So thanks very much. 02:18.411 --> 02:35.648 I don't see anybody here, but I'm just gonna keep going and and switch over here See if I can put my that's the wrong one this one and See what we've got here Now I need my head out of the way anyway 02:41.496 --> 02:43.516 All right, here we go, my friends. 02:43.797 --> 02:53.399 We're finally going to do this class, which I'm titling Uncertainty, or Uncertainty and Probability Theory. 02:53.859 --> 03:00.220 The uncertainty comes from my book, and also the probability theory comes from Jane's. 03:00.900 --> 03:05.421 It's a very heavy book, thick, solid paper. 03:05.561 --> 03:06.802 You know you're really going to get something. 03:09.549 --> 03:13.111 We're also going to use the works of David Stove and the Rationality of Induction. 03:13.491 --> 03:15.352 I'll flash that book up when we come to it. 03:15.993 --> 03:18.054 Now, how to best do this class, I haven't a clue. 03:18.094 --> 03:21.616 I thought about it a long time, and I figured out I have no idea. 03:22.817 --> 03:24.277 So I'm going to run these lectures. 03:24.297 --> 03:25.538 I'm going to run these videos. 03:26.519 --> 03:37.605 And it's, you know, I'm talking to a screen, and I don't do as good when I'm not talking to an audience, because when I see the audience, I can see the mystification and the puzzlement 03:38.718 --> 04:07.610 their faces and I know when I'm saying something too fast too slow or too complex or I'm not making making sense something like this I don't have that ability to do that here so we're gonna have to rely on me guessing what you like you can leave comments to these videos wherever you see the video and I'll look at those comments I'll read them all and I will answer the best ones next week's blog 04:08.539 --> 04:13.303 And in next week's video, not the best ones, the ones I think are the most compelling or something like this. 04:14.364 --> 04:15.886 I don't know how else to do it. 04:15.906 --> 04:19.188 I mean, you can also email me comments, that kind of a thing. 04:20.089 --> 04:25.894 I simply won't have time to answer every comment individually if there turn out to be a lot of them. 04:25.914 --> 04:27.716 If there's only one or two, then it's no problem. 04:31.167 --> 04:35.929 As far as signing up goes to the class, that kind of thing, we'll figure it out. 04:36.249 --> 04:37.750 There's going to be some homeworks. 04:37.950 --> 04:40.952 I'm going to give you one at the end of this particular lecture. 04:42.172 --> 04:45.033 And you have your go at it, see how you do. 04:45.234 --> 04:48.115 And I'll answer it in the next video. 04:48.495 --> 04:50.676 Unless it's so easy, I don't think it's worth answering. 04:50.736 --> 04:51.997 I think that's the case today. 04:52.077 --> 04:52.477 We'll see. 04:54.175 --> 04:54.936 And we'll go from there. 04:55.736 --> 04:59.038 Whether or not there'll be projects and so forth, we'll just have to figure out. 04:59.078 --> 05:06.223 Whether there can be a sign-up, maybe I can make a sign-up database or something like this, just for your own sake, to make sure you stay on track. 05:06.243 --> 05:07.684 Well, we'll see. 05:08.045 --> 05:08.265 All right. 05:08.865 --> 05:09.846 So we're going to start trivially. 05:09.926 --> 05:11.967 This is uncertainty. 05:12.027 --> 05:15.230 If there's uncertainty, well, we must also have certainty, in which there is. 05:15.790 --> 05:17.952 And that involves matters of truth and all that. 05:18.232 --> 05:19.953 And we're not going to get into that today. 05:20.013 --> 05:20.754 We will get into it. 05:21.876 --> 05:23.717 We're going to let all that kind of stuff float today. 05:23.777 --> 05:25.357 Today is kind of like a teaser course. 05:25.377 --> 05:28.558 We're going to start with something very simple, even trivial. 05:29.959 --> 05:30.359 Logic. 05:31.139 --> 05:37.681 And because most people think that logic is the epitome of rational thought, but it's not true. 05:38.641 --> 05:39.302 It's not so. 05:39.402 --> 05:40.762 Logic is not the epitome. 05:41.082 --> 05:49.365 In fact, logic, and I'm going to give you some teasers to this today, logic is based on even more fundamental thought. 05:50.393 --> 05:56.859 which is our intuitions, our inductions, our faith even. 05:56.879 --> 06:05.647 And it's going to turn out there's at least five different kinds of induction that we use that provide these basic truths. 06:05.687 --> 06:08.890 And I'm going to prove that to you a little bit today, not entirely, but a little bit. 06:10.211 --> 06:11.913 Also, we're going to use math eventually. 06:11.993 --> 06:15.656 I try to keep away from that on the blog, but there's no getting away from it here. 06:15.736 --> 06:16.537 I'll try to still 06:18.309 --> 06:21.231 de-emphasize it as I'll explain why in this lecture. 06:21.791 --> 06:23.393 So today is just to give you a taste. 06:23.693 --> 06:25.354 Now I want to orient this towards science. 06:25.955 --> 06:31.720 Our primary interest is in the kind of like a philosophy of science, although the techniques here of course apply anywhere. 06:32.781 --> 06:34.422 We're primarily interested in science. 06:34.942 --> 06:36.884 I'm not going to do any science for you. 06:36.924 --> 06:41.748 You're going to do it on your own in whatever fields or applications that you're interested in. 06:41.928 --> 06:43.870 I'm going to do these apparatus 06:44.831 --> 06:53.240 that allow us to think about what we know, about what we're uncertain of, and how to quantify, if we can, that uncertainty, which leads to probability. 06:53.800 --> 06:58.605 And then the practice of probability models is usually called statistics. 06:59.426 --> 07:01.208 So we're going to go through all that kind of a thing. 07:03.356 --> 07:04.297 And let's start simple. 07:04.357 --> 07:05.958 So I'm gonna start with James. 07:06.638 --> 07:13.222 I'm gonna start with James We're gonna start in his chapter one and next week or something like this We'll probably move to my book and back and forth. 07:13.262 --> 07:19.766 We'll jump around and I'll take stuff in order but Which I hope you could follow. 07:20.146 --> 07:28.030 James you can find online at least some of the chapters because this book was published posthumously by a student of James, E.T. 07:28.091 --> 07:28.351 James 07:29.862 --> 07:33.384 He passed these around back in the old Usenet days. 07:34.145 --> 07:41.731 We used to have postscript files of individual chapters that we passed around back in grad school and so forth. 07:42.431 --> 07:43.973 But they were never assigned as a course. 07:44.013 --> 07:48.276 And I don't know how many courses in actual statistics departments. 07:49.892 --> 07:52.073 Now this damn computer keeps falling asleep on me. 07:52.333 --> 07:54.353 I've tried every setting there is to keep it awake. 07:54.793 --> 07:55.353 It won't do it. 07:55.413 --> 08:00.415 So if I have to dodge over there every five minutes or so, forgive me. 08:00.515 --> 08:03.456 And I'm not going to edit me dodging out there because I'm too lazy. 08:04.516 --> 08:05.116 And I don't know how. 08:05.756 --> 08:06.837 So let's start very simple. 08:07.237 --> 08:08.177 Let's start very simple. 08:08.477 --> 08:14.439 In my book, too, you can kind of find online in places, but I'll give you what you need and post excerpts and all that kind of thing. 08:17.657 --> 08:18.599 Let's start very simply. 08:18.639 --> 08:19.561 We have a proposition. 08:20.202 --> 08:21.405 A, I'm going to call it a proposition. 08:21.425 --> 08:25.052 This is just some sentence in whichever language you prefer. 08:25.072 --> 08:27.497 You know, this A can be 08:28.322 --> 08:33.244 the proposition that this chalk is yellow, or it could be that this chalk is black. 08:33.344 --> 08:35.465 That's a false proposition. 08:35.625 --> 08:37.886 This one is going to be out of sync, but the rest of them are. 08:37.926 --> 08:40.647 Remember, he just started and did it just like he described. 08:40.687 --> 08:41.867 So give him a little credit. 08:41.887 --> 08:44.028 He gets much better as the videos go on. 08:44.108 --> 08:47.469 So I'm really thankful that he started. 08:47.509 --> 08:49.090 I think he's on episode 18 now. 08:49.130 --> 08:55.292 I just put the link in there so you can get the book and you can find where all these classes are if you want to get ahead or you want to repeat it or whatever. 08:55.852 --> 08:57.274 You don't have to do it with me. 08:57.334 --> 09:00.777 You can do it directly on his website or on his sub stack. 09:15.558 --> 09:24.321 the proposition that this chalk is yellow, or it could be that this chalk is black, and that's a false proposition based on the observation that it's yellow. 09:25.682 --> 09:31.504 You know, anything we like as a proposition here, that's what we're going to first assume. 09:32.245 --> 09:34.866 We're going to subjectively choose this proposition. 09:35.406 --> 09:38.647 Aha, so there's subjectivity coming involved right now. 09:39.207 --> 09:43.209 Now, what can we conclude from taking this proposition A is true? 09:45.265 --> 09:53.732 We're going to use this form of logical notation, which means, therefore, we're going to conclude A is true. 09:54.213 --> 09:55.794 OK, wow, what have we done? 09:56.194 --> 09:57.496 Well, we've said that A is true. 09:57.516 --> 09:58.436 And what can we conclude? 09:58.537 --> 09:59.477 Well, that A is true. 10:00.078 --> 10:02.460 And we think, how wonderful this is, how simple. 10:02.980 --> 10:05.082 But how can you prove this? 10:06.123 --> 10:07.024 You can't prove it. 10:07.244 --> 10:08.065 You have to assume it. 10:09.422 --> 10:16.050 It's one of these things that is an axiom of logic we're going to base it on. 10:16.391 --> 10:28.565 And axioms themselves are based on deeper modes of thought, these inductions, these intellections, these intuitions, these faiths that we have. 10:29.437 --> 10:33.259 So this very simple thing right here has already proven at least two things. 10:33.619 --> 10:37.260 That it's partly subjective logic, because we picked this proposition. 10:37.941 --> 10:42.723 We can use rational thought to conclude that A is itself true because A is true. 10:44.724 --> 10:53.747 And the reason we know it's true is not based on any proofs other than proofs based on our intuition, which we'll come to again. 10:53.988 --> 10:57.189 Now also, there's one more thing I forgot to say. 10:58.649 --> 11:03.874 that A is true, given we assume A is true, is objectively rigorous. 11:04.615 --> 11:05.916 It's objectively rigorous. 11:06.216 --> 11:07.878 It is in no way subjective. 11:08.459 --> 11:15.706 Once we have set this equation up, that's what this is, is an equation, we are forced to conclude that A is true. 11:16.086 --> 11:22.192 We cannot conclude subjectively that C is true, where C does not equal A. 11:24.056 --> 11:26.738 All right, so there's subjectivity in the initial parts. 11:27.178 --> 11:39.006 There's rigorous objectivity in the moves that we make, the logical moves that we make, because logic is only the science of connections of propositions. 11:39.506 --> 11:41.648 The propositions themselves are subjective. 11:41.688 --> 11:43.709 The connections are objective. 11:44.349 --> 11:49.133 And the reason we can work these simple proofs is because of our intuitions. 11:49.453 --> 11:50.714 So right there, we've done a lot. 11:51.533 --> 11:57.118 That's kind of a teaser about what we're going to see and we're going to be able to draw a probability from this today. 11:57.378 --> 12:01.982 So now let's move, this isn't in Janes, I'm going to now move to the simplest one which is in Janes. 12:03.663 --> 12:07.707 Here is a logical equation if you like. 12:15.233 --> 12:16.775 Well this is where we'll start with a premise here. 12:21.337 --> 12:22.938 A premise, I made it up. 12:25.019 --> 12:26.500 A condition, an assumption. 12:28.241 --> 12:32.983 It says if the proposition A is true, then the proposition B is true. 12:33.003 --> 12:37.426 And this is a shorthand way of writing it, so I don't have to write out is true, is true. 12:38.406 --> 12:40.047 It's just a pain to keep writing out. 12:40.087 --> 12:45.230 So you, as the watcher and the listener to this, have to keep this in mind. 12:45.811 --> 12:47.311 If A is true, then B is true. 12:48.112 --> 12:49.593 Why is this important? 12:49.633 --> 12:50.153 I made it up. 12:51.240 --> 12:52.961 That's all I'm saying is I made it up. 12:53.001 --> 12:55.081 Here's the subjective part of logic right here. 12:55.822 --> 12:57.682 So I can say one other thing. 12:57.722 --> 12:59.903 Let's say A is true. 13:01.284 --> 13:02.204 What can we conclude? 13:03.445 --> 13:08.827 Well, since Aristotle, we all know we can conclude that B is true. 13:09.187 --> 13:11.408 Because we said if A is true, then B is true. 13:13.228 --> 13:16.069 And we assumed, subjectively, that A is true. 13:16.669 --> 13:20.491 Therefore, we can rigorously, objectively conclude that B is true. 13:21.141 --> 13:24.904 So we have our subjectivity and our objectivity mixed in here again. 13:26.385 --> 13:27.666 Now, you could prove this. 13:28.407 --> 13:33.051 This is something that can be proved based on those initial assumptions that come from our intuition. 13:33.171 --> 13:36.793 Using rules of logic, we can use things called truth tables. 13:37.314 --> 13:38.515 Maybe I'll get into those. 13:40.168 --> 13:41.189 dumb computer anyway. 13:41.709 --> 13:52.255 Maybe I'll show you some truth tables and there's also this kind of line by line you write all this stuff out in a very formal way and you prove these kind of things and that's all fine. 13:52.475 --> 13:54.036 There's nothing wrong with those things. 13:54.056 --> 13:57.778 There's nothing wrong with those methods whatsoever and they can be very useful and in fact are. 13:58.902 --> 14:04.926 But they can lead to the reification of the symbols themselves. 14:05.166 --> 14:09.088 This happens all the time, especially in math, and James goes into this later. 14:09.148 --> 14:10.509 I go into it a little bit too. 14:12.310 --> 14:20.115 The symbols, because they're so great, become realer than the underlying entities that we originally had an interest in. 14:21.238 --> 14:24.681 Our original interest was in these propositions A and B. That's it. 14:25.181 --> 14:27.783 And we wanted to know what relations they had with one another. 14:28.264 --> 14:30.746 We didn't care about the actual logic itself. 14:30.786 --> 14:33.068 We wanted to know what they said about the propositions. 14:33.428 --> 14:35.229 But if we're not careful, we could forget things. 14:35.870 --> 14:39.113 And I'm going to show you exactly how now. 14:40.013 --> 14:41.394 So there's other ways we could prove this. 14:41.655 --> 14:44.877 And I'm going to use a really simple graphical way here. 14:45.198 --> 14:48.100 And this symbol is also used formally in logic. 14:48.140 --> 14:50.622 I'm going to expropriate it and show you. 14:51.189 --> 15:07.204 So we're going to say A, draw this little arrow here, which has a meaning in logic, but I'm going to steal it and overload it, as they say, by writing this little always underneath right there. 15:08.746 --> 15:12.449 So it's always the case that if A is true, then B is true. 15:13.350 --> 15:14.271 We're just going to assume that. 15:15.993 --> 15:17.798 So if A is true, then B is true. 15:17.839 --> 15:18.641 That's our assumption. 15:18.721 --> 15:19.604 And then A is true. 15:19.644 --> 15:21.048 Well, it's always true that B is true. 15:21.248 --> 15:23.214 So here is our simple graphical proof. 15:24.599 --> 15:25.219 It's trivial. 15:25.680 --> 15:26.881 It's nothing. 15:27.181 --> 15:43.832 We haven't gained much by doing this, except for learning again that there's subjectivity in picking these things, objectivity in the way we formally make our proofs, and the initial proofs are based on axiom which we get from our intuitions. 15:44.473 --> 15:44.793 Okay. 15:45.093 --> 15:47.575 And we can use these alternate ways of looking at things. 15:48.755 --> 15:49.056 Okay. 15:49.376 --> 15:50.397 Let's look at the second one. 15:50.417 --> 15:53.759 I'm looking for my eraser, which I stuck here. 15:54.395 --> 15:54.595 All right. 16:10.059 --> 16:12.740 We have a sophisticated operation here, only the best. 16:13.140 --> 16:18.082 I got this sidewalk chalk for the grandkids and I find it works out pretty well for this board. 16:18.122 --> 16:19.282 I hope you can see it anyway. 16:19.302 --> 16:21.243 Okay. 16:23.240 --> 16:27.221 Well, we have our old friendly initial premise that we assumed. 16:27.281 --> 16:28.441 If A is true, then B is true. 16:28.481 --> 16:29.322 We haven't changed that. 16:29.902 --> 16:31.482 Now we're going to assume that B is false. 16:32.883 --> 16:33.483 What can we say? 16:34.903 --> 16:37.044 Well, we're going to say that A is false. 16:39.424 --> 16:43.065 But we've done something else here, even in the first one. 16:43.125 --> 16:44.265 I didn't show it in the first one. 16:44.626 --> 16:48.066 But we have all kind of tacit premises that are going on in here. 16:48.467 --> 16:50.067 There are tacit, implicit premises. 16:53.789 --> 16:57.151 That's the premises, like, let me write them down here. 16:57.751 --> 17:01.273 The grammar, the definitions. 17:01.813 --> 17:03.214 You know what the word if means. 17:03.634 --> 17:05.074 You know what the word than means. 17:05.094 --> 17:06.435 You know what the word false means. 17:06.755 --> 17:08.116 You know what the word therefore means. 17:08.156 --> 17:10.737 You know what they mean in the order that they're given. 17:11.137 --> 17:14.079 So we have the definitions of the words, we have the grammar. 17:15.099 --> 17:16.500 All of that is in this equation. 17:17.625 --> 17:19.286 although we don't write it in this equation. 17:19.506 --> 17:25.208 And we can even write it in more compact form by using, you know, there's more compact symbology we could use. 17:25.648 --> 17:29.090 And all that tacit stuff gets blown away, we forget it's there. 17:29.730 --> 17:37.733 But when we write it out in full English form, which I didn't here, I wrote a shorthand, James writes it even longer, we forget that those tacit premises are there. 17:38.154 --> 17:38.814 These are here. 17:40.034 --> 17:43.836 And these premises are just as important as the ones we wrote here. 17:45.126 --> 17:47.528 that can't be emphasized too strongly. 17:47.628 --> 17:51.590 Even though it seems trivial, this is going to play a very huge role. 17:52.310 --> 17:52.691 All right? 17:52.711 --> 17:53.551 So all that's there. 17:55.112 --> 18:05.658 And the reason is, which we're going to learn in just a second, or emphasize again in a second, is because we've made a tacit assumption here that maybe you don't see. 18:06.799 --> 18:09.461 This is a well-known syllogism. 18:09.521 --> 18:11.542 I'm not going to bore us with it too much. 18:11.602 --> 18:13.863 But if A is true, then B is true. 18:13.963 --> 18:14.584 B is false. 18:14.984 --> 18:15.825 Therefore a is false. 18:15.865 --> 18:16.945 Everybody will nod their head. 18:16.985 --> 18:17.205 Yeah. 18:17.245 --> 18:17.806 Yeah, that's right. 18:17.826 --> 18:18.186 That's right. 18:18.406 --> 18:41.839 But why well, we could go to a truth table But that's not getting us to the reason why that's not getting us to the reason why so pause the video and think about it For a moment without thinking about the formal proofs and everything and then i'll get to it in the next example Okay, so i'm pausing it for you because I don't know the answer to this um, I don't know what the tacit assumption is that b 18:43.300 --> 18:53.602 is dependent on A. I mean, I guess if A, there might be some interdependency there that's assumed that isn't implied or whatever by the original assumption, something like that. 18:53.662 --> 18:53.962 I don't know. 18:54.282 --> 18:54.382 OK. 18:55.862 --> 18:56.462 I didn't pause. 18:56.522 --> 18:59.323 I just made it slow motion, stopped it, and make it look like it paused. 18:59.343 --> 18:59.963 Very dramatic. 19:00.423 --> 19:02.323 I got only the best special effects here. 19:04.284 --> 19:05.344 I actually paused here. 19:05.564 --> 19:06.944 Freeze up every five minutes. 19:07.044 --> 19:08.044 Piece of junk anyway. 19:08.685 --> 19:08.985 All right. 19:13.698 --> 19:20.343 I want to make sure I stick with Jane's because in case you are reading the book, I don't want to jump around too much. 19:21.163 --> 19:21.904 Okay. 19:28.748 --> 19:30.349 I wrote an A over there for a purpose. 19:31.470 --> 19:37.834 Now, if A is true, then B, our friendly premise that we start with, and we're going to assume B is true. 19:39.093 --> 19:42.336 And we're going to try to conclude that A is true. 19:43.017 --> 19:47.041 And everybody will say, without any familiarity with this, no, we can't say that. 19:47.061 --> 19:48.883 And it's true, you can't. 19:49.063 --> 19:49.924 This is a fallacy. 19:50.625 --> 19:51.126 But why? 19:51.986 --> 19:58.153 Well, you'll read some books and everything, and they'll give you an example why A is true, then if B is true, that A 20:00.385 --> 20:02.247 is true does not follow. 20:02.747 --> 20:11.055 It may be true in some way or another that A is in fact a true premise, but we can't conclude it using logic from these premises. 20:11.255 --> 20:14.418 We cannot draw this conclusion from these premises. 20:15.739 --> 20:16.220 But why? 20:17.120 --> 20:19.663 Well, we could use a truth table, but that's not going to give us anything. 20:20.672 --> 20:27.658 It's because we think to ourselves, and when we give an example, or examples are given of this, we think, well, you know what? 20:28.259 --> 20:30.621 A is not the only way that B can be true. 20:30.961 --> 20:36.085 It is true that if A, then B, that's our assumption. 20:36.446 --> 20:48.296 This just means if A, then B. But it also could be that some C is true, and therefore B, or some D is true, or some 20:50.259 --> 20:57.907 B is true and then B. We reason this way without writing down these tacit. 20:58.487 --> 21:02.051 These are more tacit premises right here. 21:02.932 --> 21:03.772 We don't write them down. 21:03.953 --> 21:04.433 They're there. 21:04.513 --> 21:09.198 That's how we come up with counter examples to this particular thing to prove it's a fallacy. 21:11.400 --> 21:12.141 Perfectly fine. 21:13.294 --> 21:16.317 Except when we get lost, we forget we have some power here. 21:16.657 --> 21:22.342 We've just given ourselves a lot of boost by writing it down formally like this. 21:24.043 --> 21:30.689 For one thing, we can say it can't be that A is true, because it could be that C is true, or D is true, or E is true, or one of these other propositions. 21:31.509 --> 21:37.795 But we could turn this fallacy into a logical syllogism with a true conclusion by doing this. 21:48.092 --> 21:49.113 A is more plausible. 21:51.394 --> 21:52.715 So if A is true, B is true. 21:53.556 --> 21:56.017 We know B is true, now A is not true. 21:56.918 --> 22:00.200 Can't conclude it, but we can conclude A is more plausible. 22:00.460 --> 22:00.861 And how? 22:00.941 --> 22:02.222 What proof can we use for that? 22:02.582 --> 22:04.123 Well, we just had it right here. 22:05.504 --> 22:08.706 We know that A is one of the ways that B can be true. 22:09.286 --> 22:11.007 C is one of the ways that D can be true. 22:11.248 --> 22:15.971 D or E, whatever the set we have that we're imagining, it's there. 22:16.829 --> 22:17.949 Now, A is among them. 22:19.270 --> 22:25.531 So therefore, if B is true, then A is more plausible. 22:27.971 --> 22:33.492 There's also, if I can write this symbol if you don't mind, there's a whole world of propositions out there. 22:33.512 --> 22:38.033 There's an infinite number of propositions, which I'll just label W1, W2, W3, YW, words. 22:42.602 --> 22:47.904 There's all these other propositions that are not in this set that we can apply B from. 22:49.204 --> 22:53.926 So A is in this set we can apply B from, and that we know B is true. 22:54.466 --> 22:57.507 Therefore, A is indeed more plausible. 22:58.327 --> 23:02.268 We have just proved, well, what have we proved? 23:03.029 --> 23:05.149 What's a synonym for plausible? 23:07.930 --> 23:09.931 Likely, A is more likely. 23:11.055 --> 23:11.816 More likely than what? 23:11.876 --> 23:16.681 More likely than any of these propositions here, this infinite set of propositions here. 23:17.062 --> 23:18.323 And what's a synonym for likely? 23:19.104 --> 23:20.486 Well, probability. 23:21.334 --> 23:22.434 A is more probable. 23:23.035 --> 23:33.339 In other words, we have just made a probabilistic conclusion, a probabilistic syllogism right here, so probability is a matter of logic. 23:33.699 --> 23:35.020 Probability is logical. 23:35.560 --> 23:38.461 It's no different than regular logic at all. 23:39.101 --> 23:44.904 It's just yet, it's the expansion of logic until we're to conclusions where we're not certain. 23:45.124 --> 23:46.724 We are uncertain about this. 23:47.505 --> 23:50.266 We're certain about this conclusion, we're not certain about 23:51.633 --> 23:53.395 the conclusion A by itself. 23:55.178 --> 23:55.778 So there we go. 23:56.339 --> 23:56.700 That's it. 23:57.420 --> 24:00.364 We've just proved that probability is a matter of logic. 24:00.484 --> 24:01.866 And of course, it's not a complete proof. 24:01.906 --> 24:03.408 I'm just teasing this right today. 24:04.369 --> 24:05.551 Before we get too far into this. 24:06.260 --> 24:09.861 I want to make sure we understand that this is not causality. 24:09.921 --> 24:11.022 Logic is not cause. 24:11.482 --> 24:14.743 Although, when we know cause, we also have logic. 24:14.843 --> 24:16.304 It doesn't go the other way around, though. 24:16.624 --> 24:21.606 So, for instance, assume that A is rain. 24:21.726 --> 24:23.186 This is the example James used. 24:25.907 --> 24:29.669 Rain, and B is clouds. 24:32.432 --> 24:39.277 If it's raining, then it's cloudy, lest the devil's beating his wife, if you understand that bit of humor. 24:40.037 --> 24:41.859 You can laugh, feel free, I can't hear you. 24:43.420 --> 24:44.200 Rain and clouds. 24:44.721 --> 24:55.288 Well, obviously, the clouds are part of the causal reason that it's raining, because you get the moisture, the precipitation comes out of the clouds, cloud condensation, nuclei, and all this kind of stuff. 24:56.829 --> 24:59.631 So, we can get logically true, 25:00.521 --> 25:05.243 If it's raining and it's cloudy, that's perfectly logically true, but the causality is backwards. 25:05.723 --> 25:11.064 And we're going to keep this in mind because we've just shown that logic is probability. 25:11.345 --> 25:22.508 So when we come to conclusions that we're making, probabilistic conclusions, particularly in statistics, and we're making claims of causality, we can get the cause completely backwards or just completely wrong. 25:23.549 --> 25:23.909 All right. 25:24.169 --> 25:27.730 So we're not doing causality when we're doing logic. 25:28.604 --> 25:28.884 At all. 25:29.404 --> 25:29.704 All right. 25:30.285 --> 25:32.545 Causes, causes the other way around. 25:32.605 --> 25:35.146 We think of cause and then we can build logic on top of that. 25:35.746 --> 25:36.146 All right. 25:37.187 --> 25:37.767 Ah, okay. 25:38.347 --> 25:40.708 So we have only a couple of more real brief ones. 25:41.328 --> 25:42.488 I want to stick with James. 25:42.528 --> 25:43.349 Where's my eraser? 25:45.709 --> 25:45.989 Okay. 25:46.029 --> 25:50.631 So just to expand on that. 25:52.585 --> 26:04.869 What James kind of expands on that, or the way that it doesn't seem like Matt's going to do it here, is the idea that if you have dark clouds at 945, 26:11.536 --> 26:19.959 it doesn't give you a logical certainty that rain will follow, but it could increase the probability in your mind, decrease the plausibility that rain will follow. 26:20.600 --> 26:29.003 And if you obey that weak syllogism, then you might not, you might cancel your plans because you see dark clouds. 26:29.563 --> 26:37.587 And now the inverse of that would be, of course, not, of course, to me, it's not obvious, but this is why we're doing this together. 26:39.367 --> 26:40.568 The logical connection 26:41.266 --> 26:48.891 that he's implying here the other way around is dark clouds, sorry, rain at 10 a.m. 26:49.752 --> 26:54.395 is the cause of the dark clouds at 9.45, and that's not true. 26:55.215 --> 26:57.757 It can be the logical consequence in one direction. 26:57.777 --> 27:05.722 It cannot be the cause of it, and in science, the logical part 27:07.130 --> 27:09.331 can be confused with the causal part. 27:09.391 --> 27:13.452 And I'm not sure that I'm getting it exactly right yet. 27:13.492 --> 27:14.713 And that's why we're auditing it. 27:14.773 --> 27:15.873 That's why we're doing this. 27:16.233 --> 27:36.021 But I think we're getting closer to understanding how this logic, if applied willy-nilly incorrectly with null hypotheses and p-values, can very quickly become an illusion of knowledge creation and an illusion of progression and understanding that is really mythology creating. 27:39.124 --> 27:44.669 We're going to keep our friendly premise up here. 27:50.074 --> 27:51.476 Now we're going to say A is false. 27:52.276 --> 27:54.238 And therefore, what can we conclude? 27:55.019 --> 28:03.327 Well, we can't conclude B by itself. 28:03.867 --> 28:04.208 And why? 28:05.953 --> 28:07.974 This is a fallacy by itself, right? 28:08.034 --> 28:11.495 Without this verbiage I've set up here. 28:11.915 --> 28:13.255 If A is true, then B is true. 28:13.275 --> 28:14.276 A is false. 28:14.296 --> 28:19.037 And then we try to conclude something about B being, whoops, I didn't mean to say B itself. 28:19.097 --> 28:25.059 I meant to say B false. 28:25.179 --> 28:29.601 I'll just put that in parentheses there to try to separate this off right there. 28:30.905 --> 28:39.649 Because why well in counter examples we give and everything because we know there's other ways for B to be true It could be that C is true that therefore B is true. 28:40.109 --> 28:55.076 There could be one of these other propositions out there that That make B true is true and so B could be true or false We don't know we can't conclude from this but we can we can change it 28:59.056 --> 29:00.816 I make this conclusion logically. 29:01.237 --> 29:02.457 B is less plausible. 29:02.617 --> 29:03.097 And why? 29:03.717 --> 29:19.821 Because in this world of propositions that say nothing about B, that doesn't mean anything to us, but we've eliminated one reason, one way that we know B can be true from this list of other premises or propositions. 29:20.081 --> 29:24.002 And so there are many ways that dark clouds can be present at 945 and 29:27.234 --> 29:29.779 One of them might be that it's going to rain at 10 o'clock. 29:31.522 --> 29:38.314 But the fact that it doesn't rain at 10 o'clock doesn't mean that there aren't other reasons why there would be clouds at 945. 29:40.154 --> 29:43.295 And so I think we're getting, I think we're getting there. 29:43.836 --> 29:54.980 And again, this logic and applying it correctly is not the same as taking those intuitions upon which this logic is being applied and working through them correctly. 29:55.040 --> 30:02.544 So again, I really think we're going to get to the, to a good explanation, a good way of understanding how science has been broken. 30:02.884 --> 30:03.384 That we have. 30:04.366 --> 30:15.231 We've eliminated that, therefore now B, if we take B, we take C, D, E, and all these, along with the world of premises, it's less plausible now that B can be true. 30:15.271 --> 30:22.994 We've removed one of the logical reasons that B can be true, that rather, not B can be true, not in a causal sense, that we could know B is true. 30:23.634 --> 30:24.595 Sometimes I slip up. 30:25.964 --> 30:26.644 It's very bad. 30:26.704 --> 30:30.246 I'm the one, above all people, who should know better than this. 30:30.766 --> 30:32.567 Not that causes B to be true. 30:32.907 --> 30:34.987 That causes us to know that B is true. 30:35.007 --> 30:39.909 It's a difference between what is and what we know about what is. 30:39.989 --> 30:45.051 And we make that mistake in probability all the time. 30:45.111 --> 30:47.672 And I should know better than anybody, so I kick myself for that. 30:47.692 --> 30:49.013 All right. 30:50.460 --> 30:51.980 I actually would have to watch that again. 30:52.020 --> 30:55.761 I'm not really sure what semantic mistake he made there. 30:55.781 --> 30:59.342 No, or the certainty with which we know something. 30:59.362 --> 31:00.902 Consider all of that again. 31:01.443 --> 31:03.643 Consider all of these examples I've just given you. 31:03.663 --> 31:06.024 I'm going to give you, this is your homework right now, okay? 31:06.364 --> 31:07.064 This is your homework. 31:07.144 --> 31:09.744 I'm going to write, what am I going to do? 31:09.784 --> 31:12.805 I'm going to erase this bits here just so I can write out the homework a little bit. 31:15.766 --> 31:16.506 Let's see here. 31:22.110 --> 31:23.391 This is also from James. 31:25.552 --> 31:26.193 Let's see here. 31:38.861 --> 31:47.847 We're changing our first premise from if A is true, then B is true, to if A is true, then B is not necessarily true, but more plausible. 31:50.309 --> 31:51.810 And then we're going to also assume 31:54.551 --> 31:55.472 B is true. 32:02.136 --> 32:02.397 Whoops. 32:07.740 --> 32:09.922 No use cursing the microphone off for hitting me, I guess. 32:10.762 --> 32:10.963 All right. 32:11.043 --> 32:14.065 If A is true, then B is more plausible. 32:14.325 --> 32:16.326 That's something we're going to assume. 32:17.107 --> 32:18.548 We're also going to assume B is true. 32:19.048 --> 32:22.391 And then we're going to conclude that A is more plausible. 32:22.411 --> 32:24.012 This proposition A is more plausible. 32:25.014 --> 32:26.895 Now, I'm not going to show you how to do this. 32:26.935 --> 32:28.396 You're going to figure it out on your own. 32:28.436 --> 32:33.199 I've given you the tools to do that already using the previous two examples. 32:33.920 --> 32:40.524 This forms the bulk of a lot of uncertain reasoning. 32:41.545 --> 32:49.530 James gives the example of a cop walking the beat and seeing a man crawling out of a jewelry store window with a bag. 32:50.630 --> 32:52.392 The cop arrests the man with the bag. 32:52.412 --> 32:52.572 Why? 32:53.749 --> 32:55.109 Well, you fill in that yourself. 32:55.849 --> 32:56.870 You fill in that yourself. 32:56.890 --> 32:57.990 That's part of your homework. 32:58.330 --> 33:01.030 Is it absolutely true that the man is a thief? 33:01.490 --> 33:01.651 No. 33:02.171 --> 33:04.491 I mean, the guy could be, it could be the owner of the thing. 33:04.691 --> 33:07.252 He's blocked himself out of the store for whatever reason. 33:07.312 --> 33:07.692 Who knows? 33:07.732 --> 33:14.413 There could be all kinds of reasons that the man is not a thief, but the cop arrested him anyway. 33:14.493 --> 33:14.953 So why? 33:15.013 --> 33:16.013 So we got to figure that out. 33:16.533 --> 33:19.754 If we can figure out this form of reasoning, then we're going to move into probability. 33:21.030 --> 33:21.991 That's it for today. 33:22.732 --> 33:24.193 Let me know what you think in the comments. 33:24.273 --> 33:27.796 We did very little, but teased a lot. 33:28.817 --> 33:31.259 And I was supposed to go 10 minutes. 33:31.279 --> 33:32.640 I think this is a bit longer. 33:33.100 --> 33:33.741 So there you have it. 33:34.081 --> 33:34.822 Thanks for watching. 33:35.943 --> 33:39.285 Okay, so that was the first episode. 33:40.506 --> 33:41.787 He's gonna probably disappear. 33:41.828 --> 33:42.268 There we go. 33:43.809 --> 33:47.953 What I think we could do now is just very quickly look over this 33:49.508 --> 33:56.935 this chapter here and see if we can get a little bit more out of this text where he was deriving this first lecture from. 33:57.835 --> 34:13.309 So we emphasize at the outset that we are concerned here with logical connections because some discussions and applications of inference have fallen into serious error through failure to see the distinction between logical implication and physical causation. 34:14.209 --> 34:35.796 The distinction is analyzed in some depth by Simon and Rescher in 1966, who note that all attempts to interpret implication as expressing physical causation founder on the lack of contraposition expressed in the second syllogism. 34:36.936 --> 34:39.757 So the syllogism is this thing down here. 34:43.049 --> 34:45.894 two-week assumptions, the reverse, that kind of thing. 34:45.974 --> 34:53.626 All the things that Matt was talking about are what are gonna come up in this reading as well. 34:53.686 --> 34:55.249 Again, remember you can download this. 34:56.658 --> 35:06.043 So in this case, another weak syllogism still using the major premise is, and so the major premise is the initial premise. 35:06.644 --> 35:08.465 If A is true, then B is true. 35:08.685 --> 35:11.946 A is false, therefore B becomes less plausible. 35:12.026 --> 35:18.190 This is a weak syllogism that still uses the major premise. 35:19.372 --> 35:40.864 In this case, the evidence does not prove that B is false, but one of the possible reasons for it being true has been eliminated, so we feel less confident about B. The reasonings of a scientist by which he accepts or rejects his theories consist almost entirely of syllogisms of the second and third kind. 35:42.478 --> 36:04.757 And so it is really dovetailing nicely with the stuff that we discussed in the Biology 101 lecture, where the way of doing biology in a reductionist manner allows people to build assumptions based on assumptions that they themselves are accepting. 36:05.734 --> 36:15.658 And if you get more than one of those on top of one another, the logical arguments that you make with those assumptions can seem very powerful. 36:15.698 --> 36:27.222 But in the end, you're standing on such a wobbly base that nothing that you're doing here at the moving parts end is solving or answering any reasonable questions. 36:28.243 --> 36:32.945 And so I think that's actually quite cool. 36:34.554 --> 36:37.015 I think it's actually a pretty nice little way to put it. 36:37.035 --> 36:37.836 I'm going to leave it there. 36:37.916 --> 36:43.278 I'm going to watch what we see and watch where we got and how these things combine. 36:43.318 --> 36:53.584 Again, he's going to do another, we're going to do number two on Thursday, right after we do the biology 101 underscore number two. 36:54.144 --> 37:00.447 And I think this is going to work out really well for us because we have a little skeleton of a plan for Tuesday and Thursday. 37:00.467 --> 37:03.989 And then in the middle, I just have to fill it in with some journal clubs and some, 37:04.609 --> 37:14.260 Study halls and some commentaries and whatever and I think this is gonna be a lot of fun So because everybody was so so upset And I apologize. 37:14.300 --> 37:26.273 I didn't know it was such an important thing So upset that I have not managed to get this up that we will bring you out and 37:29.215 --> 37:30.916 Try to get that up to speed there. 37:31.896 --> 37:33.417 Thanks very much for joining me. 37:33.877 --> 37:39.140 If you liked what you saw, please go to gigaohmbiological.com and try to find a way to support the work. 37:40.000 --> 37:43.882 And these should also be up on stream.gigaohm.bio. 37:45.744 --> 37:48.867 And yeah, I'm going to see you again tomorrow at 10.10. 37:48.927 --> 37:52.131 I'm not sure exactly what I'm going to be doing, but it'll probably be a study hall. 37:52.612 --> 37:55.395 I got a whole huge list of things that I need to watch. 37:55.936 --> 37:58.059 And so we'll just probably choose at random from that. 37:58.079 --> 38:00.361 And then Thursday, I'll see you back here again. 38:01.002 --> 38:13.571 I'm going to drop a interview that occurred last night with Jason Levine that you can find on Rumble, but I'm going to put a copy of it on stream.gigaohm.bio as well. 38:14.331 --> 38:20.716 And Mark Housatonic at Mark at Housatonic ITS has been working real hard. 38:20.796 --> 38:27.381 And so make sure if you haven't been paying attention to what he's up to on Twitch and posting on stream.gigaohm.bio, please 38:27.962 --> 38:28.907 Check that out as well. 38:28.928 --> 38:30.416 See you guys again tomorrow. 38:30.457 --> 38:31.302 Thanks a lot for joining me.