You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.

1485 lines
42 KiB

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.