0:00

listeners. This is the eighty thousand hours podcast

0:02

where we haven't usually end up conversations about the world's

0:04

most pressing problems, what I can do to solve them.

0:06

And whether if I were at least as handsome as Ryan

0:08

goes I'd be exactly as handsome as Ryan Gosling.

0:10

I'm Rob Woodland, head of research at

0:12

eighty thousand hours. Many people have asked

0:14

me to interview Allen Hayek over the years and this year

0:16

I finally got to do it when I went home for effective

0:19

autism global Australia back in July.

0:21

Alan is one of the most prominent philosophers

0:23

focused on resolving puzzles in probability and expected

0:25

value issues that, it turns out crop up

0:27

shockingly often when you try doing research

0:29

to figure out how to do the most good. We

0:31

did the first hour on at the conference, then another

0:34

few hours of recording back in Allan's office.

0:36

The first hour is very accessible, but I won't lie.

0:38

The later part of the conversation is among the

0:40

more advanced content that we've had on the show, so far.

0:43

To help you out, I've recorded a number of cut

0:45

ins to quickly define terms like Epicycle's

0:47

or Dutch books, which are familiar to

0:49

philosophers but not so familiar to the rest of

0:51

us. Katie Moore has also gone

0:53

through the transcript and added a lot of links that will

0:55

take you to articles that elaborate on concepts

0:58

and arguments as they come up, if you don't mind reading

1:00

interviews rather than listening to them. People

1:02

familiar with these topics should find this interview

1:04

super informative, while I hope those who aren't so

1:06

familiar will learn a lot even if they don't follow

1:08

every single point that's being made. Some of

1:10

the things we cover are simple tricks for doing philosophy

1:13

well, why fruquintism is misguided, what

1:15

probability fundamentally is, problems

1:17

with using expected value and whether we should use it

1:19

anyway, a fundamental problem with Pascal's

1:22

wager and why the dominant theory of kind of factual's

1:24

philosophy is unworkable. One

1:26

quick notice is that eighty thousand hours is

1:28

currently hiring a recruiter to help

1:30

grow our team with applications for that role closing

1:32

soon on November the second. I'll

1:35

say little more about that in the outro, but if

1:37

you'd like to know more about that recruiter role, you

1:39

can get a full job description on our job board

1:41

at eighty thousand hours dot org slash jobs.

1:43

Alright. With that further ado, I bring you. Alan Hayek.

1:48

Today, I'm speaking with Alan Hayek.

1:50

Alan is a professor of philosophy at the Australian

1:52

National University. Years ago, he

1:54

did his PhD at Princeton where he won

1:56

a fellowship for displaying in the judgment of the university

1:59

the highest scholarly excellence of all

2:01

graduate students across all of their disciplines.

2:03

These days, he has a broad ranging interest across

2:05

epistemology, philosophy of language and

2:07

philosophical methodology. His work

2:10

is of great interest to me and the effective

2:12

autism because he is one of the world's

2:14

top experts on the philosophy of probability,

2:16

bayesianism, decision theory, expected value

2:18

and counterfactuals. Some of his

2:21

more memorably titled papers include

2:23

fifteen arguments against frequentism, waging

2:25

war on Pascal's wager, vexing

2:27

expectations, most counterfactors are

2:29

false, and a follow-up paper titled, most manufacturers

2:31

are still false. He's currently working on

2:34

a book on Canifactual's title would work.

2:36

This is our first ever live recording of the show.

2:38

So for once, I should also welcome all of you

2:40

in the audience as well. And before we button

2:43

down for the recording, let's have a random applause

2:45

for Alan.

2:50

Thank you. Great to be here, Rob. Thanks so much

2:52

for having me on the show. Okay.

2:55

I hope we're gonna get to talk about whether

2:57

Besianism is the final big evolution

2:59

and probability. and why you think objective

3:01

consequentialism is even wronger than many people

3:03

can even imagine. But first, you started

3:05

out studying maths and which

3:07

are kinda practical fields in which you could have

3:09

been gainfully employed doing something of obvious

3:11

now you. Yes. What made you switch into philosophy

3:13

after you finished your undergrad degree? Yeah. I

3:16

was studying, as you say, math and statistics,

3:18

and I went to lots of courses on

3:20

probability. And my professors

3:23

would write equations on the board, p of

3:25

this equals p of that.

3:27

And I was wondering, what is this p? What does

3:30

probability mean, and I asked one of them,

3:32

what does probability mean? And he

3:34

looked at me like I needed medication. And

3:37

he said, well, that's a philosophical question.

3:40

And I began a master's in

3:42

statistics, and I got as far as photocopying

3:45

the article that my supervisor wanted

3:47

me to read and I sat down,

3:50

started reading it and I went, and

3:53

I don't know if you've seen pulp fiction, but there's

3:55

a moment where Jules the hitman

3:58

has a moment of clarity. Right. I

4:00

had a moment of clarity. I realized I didn't

4:02

want to go on with statistics -- Yeah. -- but

4:04

what to do instead traveled the world

4:06

hoping to find myself on the road.

4:09

And I did it happened in Western Ontario,

4:12

and a friend of mine who'd

4:14

had his moment of clarity was studying

4:16

philosophy there. He showed me

4:18

the courses that he was studying he

4:20

was looking at. And I

4:22

thought, wow. how cool is that? And

4:24

you could hear that Penny dropped several provinces

4:27

away. That was my second moment of

4:29

clarity. Yeah. That's what I wanna do,

4:31

philosophy. What what was it that bug I mean,

4:33

obviously, most statisticians kinda don't care

4:35

about these, deeper questions about what probability

4:37

is given that they can just, like, do operations on it.

4:39

And what what like, why couldn't you let it go?

4:42

Yeah. In a way, I was

4:44

less interested in the the sort of practical

4:46

payoffs. I I was just wondering,

4:49

where does probability fit into my of

4:51

conceptual scheme, you know -- Yeah. --

4:53

how does it relate to other things? What

4:55

does it really mean? When I say something

4:57

like the probability of rain

4:59

tomorrow is point three. What

5:01

have I said? I understand the stuff about rain,

5:04

but the probability stuff, I didn't understand.

5:06

And here I am, I'm still asking that question. What

5:08

does p mean? Yeah. Okay. Well, we'll

5:10

get to what p means later on.

5:12

But, like, what what are your main focuses at the

5:14

moment? I guess, so you're working on kind of actuals

5:16

primarily. Right? Yeah. That's right. And the

5:18

book would work. Thanks for the advertising.

5:21

And as always, I'm working on

5:23

probability. I still ask what

5:25

is pee. And that's

5:27

related to decision theory, something that I

5:29

think quite a lot about. That got me into

5:31

things like Pascale's wager, still

5:34

thinking about that. We'll probably

5:36

talk about my heuristics and

5:38

some of that comes up as well.

5:40

Yeah. Makes sense. So we're gonna

5:42

get into the details of probability and can affect

5:44

us later on. But first, I wanted to dive

5:46

into this, yeah, other passion of yours, which is

5:48

philosophical methodology. Mhmm.

5:50

Yeah. How did you first get into that topic?

5:52

Yeah. It began when I was a graduate

5:54

student at Princeton. I was

5:56

surrounded by these really good philosophers.

5:59

I wanted one day to be a good philosopher

6:01

or as good as I could be. And I

6:03

noticed there were these recurring patterns

6:05

of thought, sometimes in their work,

6:07

sometimes in conversations, sometimes

6:10

in Q and A. For example,

6:12

I would hear a really good question at

6:14

Q and A. Three weeks later, the same

6:16

person would ask a similar question.

6:18

I thought it worked last time. It

6:20

worked again. There's a recurring

6:22

pattern here. Yeah. I'll internalize

6:24

this. So I started to make a list of these

6:26

recurring patterns of thought, philosophical techniques

6:29

that seem to be fertile. And now

6:31

my list is hundreds long. Why

6:33

isn't this just really an obvious thing. You would think you would

6:35

kind of start of philosophy PhD just before,

6:37

like, here's all the tools in the toolkit.

6:39

Just like go and do this. Yeah. Yeah. It's

6:41

funny. I think that these are strangely

6:43

underexplored. We

6:46

teach our students logic, for example,

6:48

that's certainly one tool in the toolbox. Yeah.

6:50

I think we have all these other techniques and

6:52

we don't nearly discuss them

6:54

enough, think about them. And then I went on

6:56

to teaching at Celtic And

6:59

I had these very smart students for ten

7:01

weeks. How do I convey to them? How

7:03

philosophy is done? Of course, I had

7:05

them read the classics. They

7:07

cart and Hume and so on. But

7:09

along the way, I'd occasionally drop in these

7:11

philosophical heuristics, these

7:13

techniques,

7:14

the partly

7:15

just to show them how philosophy is done, but

7:17

also just it helps You

7:19

do philosophy. And, yeah,

7:21

philosophy is hard. Yeah. I think we we

7:23

could use all the help that we can get,

7:26

especially when you've just written

7:28

some philosophical paper,

7:30

some view of your own. It's curiously

7:32

hard to be your own critic, and

7:34

other people are lining up to

7:36

point out the problems with your view. Mhmm.

7:38

But these heuristics, I think, help

7:40

guide your mind to finding the problems before

7:43

others -- Others -- -- gleefully. -- before you point

7:45

them out. Yeah. That's right. Yeah. What are

7:47

your papers on on this topic? Well,

7:49

you sound extremely defensive in

7:51

a sense that you're you're like, worry

7:53

that other philosophers are gonna judge you daring

7:55

to write down a bunch of heuristics. Yeah. Yeah. Do

7:57

you wanna explain what what of what's going on with

7:59

that? Yes. It's as if I'm

8:01

like the magician who gives away the

8:03

the tricks of the trade.

8:05

And I find this a very strange

8:08

attitude. I mean, think of some other

8:10

area where there are heuristics like

8:12

chess. Mhmm. there's

8:14

no problem with the chess book actually giving

8:16

you some advice, Castle early

8:19

and often avoid isolated pawns

8:21

or in that there are various

8:23

fertile heuristics. But I

8:25

don't know, somehow in philosophy, some

8:27

people view it with a bit of suspicion

8:29

that this isn't really depth

8:32

this isn't really getting to the

8:34

profundity of philosophy. Mhmm.

8:36

And I'm not saying you should just

8:38

follow these heuristics mindlessly

8:41

just like when you're playing chess, you shouldn't

8:43

just mindlessly play

8:45

the things. Yeah. But I

8:48

think they help I think they get you

8:50

closer to your targets. And

8:53

I think they actually help

8:55

creativity too, that somehow, as

8:57

I say, philosophy is hard. So

8:59

These are just techniques to breaking down

9:01

a hard problem into easier sub

9:03

problems, and then you can make progress

9:06

on those. Okay. So, yeah, let's hear one

9:08

of these heuristics. What's what's one that really stands out

9:10

as as a special use one? Yeah. I I

9:12

like the one I call check

9:14

extreme cases. Okay? You're in

9:16

some domain. Extreme cases

9:18

are things like the first case or

9:20

the last case or the biggest or

9:22

the smallest or the

9:24

best or the worst or the smelliest

9:26

to or what have you. Yeah. Okay?

9:29

Now you've got this huge

9:31

search space. Someone gives a big

9:33

philosophical thesis. Suppose

9:35

you want to test it. You

9:37

know, stress test it. Are they counter

9:39

examples? Hard

9:40

problem. Somewhere

9:41

in the search space find

9:44

trouble. Find counter examples. Easier

9:46

subproblem. go to

9:48

the corner cases, go to the

9:50

extreme cases. Mhmm. And often the trouble

9:52

lurks there, if it looks

9:54

anywhere, and it's a smaller

9:57

search space. So that's the technique. I could

9:59

give you some examples. That looks like Yeah. Good

10:01

example to you. All right. Brandi

10:03

O's philosophical thesis every

10:06

event has a cause. Okay? Yeah.

10:08

Okay. And at first, you

10:10

might think, gee, I don't know. Is that

10:12

true or false? Is it it's kind of hard to

10:14

to tell? Alright.

10:15

Hard problem come up with

10:17

a counter example to every event has

10:19

a cause. Easier subproblem

10:22

consider extreme cases of

10:24

events. For example, the first

10:27

event. Call it the big bang.

10:29

Yeah. The big bang didn't have

10:31

a cause counter example, or

10:33

philosophers sometimes say that you should only

10:35

believe in entities that have

10:37

causal efficacy. they have

10:39

some poof. Yeah.

10:41

Like, that's maybe a reason to be suspicious

10:43

of numbers. Maybe numbers don't exist,

10:45

because they don't cause

10:47

anything. And then Lewis has

10:49

us imagine, well, what about the

10:52

entity which is the whole of history

10:54

There's causation. We never. But that

10:56

doesn't cause anything. Right. So according to this

10:58

principle, you shouldn't believe in

11:00

the whole of history. Okay. So

11:02

there the heuristics doing, I suppose,

11:04

negative work. It's -- Yeah. -- destructive

11:07

shooting down some position. But

11:09

I think it could also be constructive.

11:12

Right. Maybe just worth explaining a little bit

11:14

of, I guess, one of your theories of what philosophy

11:16

is. Yeah. Yeah. You want it? Oh, well,

11:18

I think you're thinking of that a lot

11:20

of philosophies, the demolition of common

11:22

sense, followed by damage control.

11:25

Yeah. I love that I love that question. Yeah.

11:27

And philosophy often comes up with

11:29

some radical claim like,

11:31

you know, we don't know anything.

11:33

Mhmm. And but then

11:35

we try to soften the blow a bit and we we

11:37

find some way. Maybe we know a little

11:39

bit. We know a little bit or we have to

11:41

understand knowledge the right way.

11:44

Anyway, so far the heuristics

11:46

have been this extreme cases heuristic

11:48

was somewhat negative. It

11:50

was pointing out a counter example to

11:52

some big thesis. I think

11:54

it could also be constructive.

11:56

I guess maybe long

11:58

termism could be thought of in this

12:00

way. Maybe

12:02

the thing that comes naturally really to us is to

12:04

focus on the short term consequences

12:06

of what we do and we think that's what

12:08

matters. Then you push that out a

12:10

bit And then that extreme case

12:12

would be, well, gosh, our actions

12:14

have consequences until the

12:16

end of time, you know, for the rest of history. So

12:19

maybe we should be more focused on

12:21

that. Yeah. And that's now the beginning of a

12:23

more positive movement.

12:26

Yeah. I guess, so a

12:28

simple question there might be like, for how long

12:30

should we consider the consequences of, like, what should be the

12:32

scope of our moral consideration? And here, say, well,

12:34

let's consider the extreme possibility. We should consider

12:36

all space and all time forever. That's

12:38

right. And then a related heuristic, so

12:40

I started with check extreme

12:43

cases. And sometimes you might just check near

12:45

extreme cases. So you back off a bit

12:47

and they're a little bit more plausible.

12:49

So maybe we don't need to look until the

12:51

end of time, but still look far

12:54

ahead and that

12:56

is still at some odds with

12:58

initial common sense. Yes, I

13:00

guess, people might often come back and say, sure and

13:02

they stream situation doesn't work. Like, lots of things

13:04

don't work in extremes. Like, it's it's more sensible

13:06

to focus on the on the middle cases. Yeah.

13:08

And so this isn't, like, actually, such a powerful

13:11

objection. What do you what do you think of that? I think for

13:13

that very reason that this is a fertile

13:15

heuristic because we spend our lives

13:17

mostly living among the normal cases.

13:19

So extreme cases don't come

13:21

so naturally do is even though they may

13:23

well be troubled for

13:25

some philosophical position. In fact, maybe

13:27

especially because they're extreme.

13:29

They're more troubled than

13:31

the middle cases. Yeah. I guess it I guess it

13:33

depends on whether the claim is like a more

13:35

pragmatic one about like how you ought to do things every day

13:37

or whether you're trying to claim that I've discovered

13:39

some like transcended fundamental truth, and you'll

13:41

be like, well, it doesn't work in this, like, one case.

13:43

That's it. You you said it. You you were claiming that this

13:45

was like something that should cover everything, and now

13:47

it doesn't. and philosophers often do that. They have

13:49

these grandiose claims. Every

13:51

event has a cause or what have you. Yeah.

13:53

And this is a good way of stress testing

13:55

such claims. Okay. Yeah. What's what's

13:57

another heuristic? Yeah. I

13:59

like to focus on the word

14:03

and I say see the word

14:05

in neon lights because

14:07

it typically comes with a presupposition.

14:09

VX typically

14:11

presupposes there's exactly one x.

14:14

There are two ways that could go

14:16

wrong. There could be multiple x's

14:18

or there could be none at

14:20

all. Right? So an example

14:22

of that. do the right thing.

14:25

Just rolls

14:27

off the tongue. Yeah. Rolls off the tongue.

14:30

Alright. The right thing.

14:33

Now that like there's exactly one right

14:36

thing to do. Well,

14:38

two ways we could challenge that. There could

14:40

be multiple right things.

14:42

Yeah. And maybe it's okay if you do any

14:44

one of them, but still that we're challenging

14:46

the pre supposition. There's exactly one.

14:48

This comes up by the way. I don't know if we'll get to

14:50

talk about Pascal's wager at

14:52

some point, but it turns out that there are

14:54

many ways to follow Pascal's

14:57

advice. Going in the other

14:59

direction, maybe there's no

15:01

right thing. Think of a moral

15:03

dilemma like Sophie's choice

15:05

you know, there's no right thing to do

15:07

or Sartre's case of the

15:09

student who's torn between

15:11

fighting in the war or

15:13

staying home with his mother. Yeah.

15:15

What's the right thing to do in this moral

15:17

dilemma? It's not clear that there is one.

15:19

Or at least if you if you start saying that

15:21

there is one thing, then you're making a claim, maybe,

15:23

without even realizing that you're making a claim, you feel

15:25

like you've slipped in an assumption -- Yeah. -- by

15:27

using the That that's right. Yeah. Any

15:29

other examples of that one? Of a of

15:31

a v or, like, people just assuming that there's one

15:34

answer. Yeah. Yes. I

15:36

I think

15:37

Yes, maximizing expected utility. We'll

15:39

probably talk about expected

15:41

utility later on and there is

15:43

– here we're being told do

15:46

the thing that maximizes expected

15:48

utility. If you hear it that way, then there are

15:50

problems on each side. There could be ties.

15:52

for expected utility. Yeah. Or there could be

15:55

nothing that maximizes it. Things just

15:57

get better and better without

15:59

end. It's slightly I guess it's not the same,

16:01

but it reminds me of this saying that in

16:03

philosophy, you can have, like, two two problems.

16:05

One is have, like, no answer to a question. Yeah.

16:07

And the other is to have like so many explanations.

16:09

You can't tell which one's the right one. That's right.

16:11

And this corresponds to the two

16:13

ways. And again, it's breaking down, so

16:15

to speak, harder problem into easier sub

16:17

problems. So you look on each

16:19

side, are there too many of these

16:21

things or are there not enough?

16:23

Yeah. Okay. Yeah. What's what's another

16:25

one? Yep. philosophers love to

16:27

talk about what's possible. They

16:29

love to say x is possible.

16:31

Yeah. I guess a classic case of that like,

16:33

the the zombie thing If I'm

16:35

a zombie yeah. That's right. Our zombie's

16:38

possible. Okay. But that is like a beings that would act

16:40

like people but have no conscious experience. That's

16:42

exactly right. Yeah. And

16:44

philosophers love to distinguish different

16:46

senses of possibility, logical,

16:49

metaphysical, no make what's

16:51

consistent with the laws of nature,

16:53

dogmatic, what's consistent with

16:55

one's beliefs, epistemic and so

16:57

on dontic. And

16:59

there are various techniques for

17:02

generating possibilities or

17:04

for for arguing that something

17:06

called an x is possible.

17:08

Yeah. And when you think about

17:10

it, there are two moving parts to that.

17:12

There's x and is

17:14

possible. possible

17:15

So focus on is possible first.

17:18

One kind of technique says,

17:21

look at some other property of

17:23

x. and it follows from x having this other property

17:25

that x is possible. Let

17:27

let's just do a few of those. Yeah. x

17:31

is actual Okay. So

17:33

suppose x is actual. So for a lot of

17:35

the modalities I just talked about, the

17:37

possibilities, that's a good way

17:39

to establish that x

17:41

is possible Hi, listeners. Rob here

17:43

with a definition to help you out.

17:45

Epistemic refers to

17:47

epistemology, which is the sub

17:49

field of philosophy that's studies,

17:51

the nature of knowledge, how do we know things, what

17:53

things do we know? Then we talked

17:55

about actual. Actual here refers

17:57

to things actually existing. So

17:59

actual is kind of a a

17:59

definite philosophy is used to mean something that's real in

18:02

this world. Okay. Back

18:03

to the show. Well, you gave a

18:04

good one. x is conceivable. That's

18:07

David Dave Charmers appeals to that one in

18:09

the zombie argument -- Yeah. -- x is

18:12

conceivable so it's possible so that it's

18:14

possible to imagine it. And therefore -- Yeah. --

18:16

you, like, start thing from that. Yeah. right.

18:18

Yeah. Yeah. Yeah. What so what what

18:20

are some examples of cases where people where philosophers make

18:22

this argument, I guess, we've got the zombie one. But

18:24

-- Yes. -- it seems like

18:26

like, it's maybe a slightly dubious style

18:29

of argument where you're saying, well, something can be imagined.

18:31

Therefore, like, I'm gonna conclude things from that.

18:33

Yeah. Yeah. That's right. And of course,

18:35

philosophers love thought experiments. And

18:37

I guess soon we'll be talking about some pretty

18:40

ricochet thought experiments. And even

18:42

if these things aren't actual,

18:44

like the Saint Petersburg game or something, still

18:46

we might say, look, we can conceive

18:48

of this. In that sense, it's possible and

18:50

we should take it seriously and

18:53

test our theories against it. And

18:55

that was, by the way, one just one way

18:57

to show the next is possible. Okay. Yeah. And

18:59

remember, is the other moving

19:01

part x as How about we look

19:03

at some other object, let's

19:05

call it, y, some other

19:08

thing, And why is

19:10

possible? We could all agree on

19:12

that. And X is appropriately related

19:15

to why and we

19:17

conclude that X must be possible too. So you're

19:19

related in what in what way.

19:21

So here are some ways. If y

19:24

is possible and y

19:26

entails x. Okay.

19:28

Then it seems pretty safe that x is

19:30

possible too. Yeah. If they're

19:32

compatible, then it seems that x is

19:34

possible too. We just use the term entail

19:36

or entailment. Intailment in

19:38

philosophy is a kind of a fancy

19:40

way of saying that something necessarily

19:42

implies something else So

19:44

if a and tails b, then

19:46

if a is true, then b is also

19:48

true. Okay. Back

19:49

to the show. Here's one

19:50

of my favorite ones. almost

19:54

x is possible. So let

19:56

y be almost x.

19:58

It's very similar to x in

20:00

some appropriate sense. Yeah.

20:02

And then you say, well, the small

20:04

difference between y,

20:06

which is almost x and x

20:08

won't make a difference. to possibility. An

20:10

example of that, according

20:12

to behaviorism, it's not

20:14

possible to have a

20:16

mental life and no

20:18

behavioral

20:19

manifestation of it whatsoever. Reply?

20:22

Yes, it is

20:23

possible because it's possible to

20:26

have almost no

20:28

behavioral manifestation of your mental life.

20:30

Think of Stephen Hawking, sadly

20:32

no longer with us. And

20:35

towards the end, I guess he had just very

20:38

minimal behavior movement of his

20:40

finger, not much more. Obviously,

20:42

he had a rich mental

20:44

life. And now imagine just just

20:46

that finger movement stopping, so he loses that

20:48

last bit of behavior. Yeah. It's

20:50

not like the lights suddenly go out

20:52

for Steven Hawkins. So it is possible.

20:54

Yeah. This is reminding me of another line of argument that

20:56

some people might have heard, which is, you know, some

20:59

people say, oh, you couldn't create a mechanical

21:01

mind or you couldn't out of machines. And you

21:03

say, well, let's take a human brain and let's just

21:05

replace one neuron with a mechanism that that

21:07

does what just what that neuron does. It'll be like, are

21:09

you not a person now? Are you not conscious? And I'll

21:11

be like, No. No. No. No. Really? So they're like,

21:13

what if we place another one? And then the other

21:15

person is either just forced to say, like, you're

21:17

becoming gradually, gradually less conscious. order

21:19

can see or or that there's some sharp cut

21:21

off, which also seems plausible. Excellent.

21:23

So this is another of the heuristics

21:25

of this kind. Let's call it extrapolation.

21:27

Mhmm. So you have a sequence of things and

21:29

you think that each of them is possible.

21:31

Well, now let's just go to the

21:34

next step. That should be possible too. Or

21:36

interpolation. Mhmm. Start with two

21:38

things that you know are possible, maybe

21:40

because they're actual. And now

21:42

interpolate on some whatever gradeable

21:45

scale, Hume's missing shade

21:47

of blue is like this. Okay?

21:49

Take two shades of

21:51

blue that are actual, therefore

21:54

possible. And now imagine a

21:56

missing shade of blue. It's not

21:58

actual, but it's

22:00

somehow between those two on some natural

22:02

scale. Yeah. Well, that seems to be possible

22:04

too. Okay. Yeah. I mean,

22:06

couldn't someone respond that it's not possible,

22:08

but actually too close. There's no shade in between.

22:10

They could say that. And you got to be careful

22:12

with your scales too, and

22:15

sometimes extrapolating or

22:17

interpolating will give you wrong

22:19

answers. Like think

22:21

of the sequence one over n,

22:23

you know, one half

22:25

third quarter, etcetera. Is it

22:28

possible for that sequence

22:30

to reach zero Well,

22:32

no. It gets as close as you like. So

22:35

almost reaching zero is possible, but

22:37

it never actually hits

22:40

zero. That's not possible for that sequence.

22:42

Well, what's an example of the thing we kind of repeat

22:44

the thing with the the sequence again and again and again. I

22:46

guess that's an example we are kind of strapolating. Are

22:48

there examples where you take some principal and then you

22:50

just like keep operating it and then you get some absurd conclusion?

22:53

How about maybe the

22:55

lottery paradox is I guess, you should think

22:57

about -- Yeah. -- or even better maybe the Preface

23:00

Paradox. Oh, I don't know that one. Yeah. Let's do

23:02

the Preface Paradox. This

23:04

puts pressure on the idea that

23:07

Belief is closed under

23:10

conjunction. Okay? You've just

23:12

written

23:12

a long book

23:13

and then you write the following

23:16

preface. I

23:16

believe everything

23:17

I say in this book, but

23:20

I'm confident that there's a

23:22

mistake somewhere in the book.

23:24

Yeah. Okay. So

23:27

I I did my best

23:29

to get sentence number one

23:31

right. I believe sentence number one.

23:33

I believe sentence number two. I

23:36

believe the final sentence of the book,

23:39

but I don't believe the conjunction of

23:41

the book on the contrary. I know that

23:43

in long books like this there's

23:45

always a mistake somewhere. Okay. So

23:47

this puts pressure on the idea that belief, even

23:49

rational belief is closed under

23:52

conjunction. Yeah. A different approach that

23:54

sometimes I apply is, like, trying to subdivide things,

23:56

like, super closely. Yeah. So so

23:58

every so often people say to me, batch

24:01

not possible to put a probability on, like,

24:03

things that have never happened before. So it's, like, fine

24:05

to say that the probability of a coin

24:07

flipping heads is fifty percent.

24:09

But if you say something like the probability of a

24:11

nuclear war in twenty twenty seven is

24:13

one point five percent, then this is just a bunch

24:15

of silliness and like because this never happened before.

24:17

then, of course, you can say, well, if you define

24:19

all events like sufficiently closely, then none of them

24:21

have ever happened before. Like, all events are unprecedented

24:24

once you, like, specify exactly what they are. That

24:27

that's right. If you specify the events too

24:29

precisely, then they're all unique. If

24:31

you specify them too

24:33

loosely, then, of course,

24:35

anything can be described as

24:37

something happens. Yeah. Okay. We have many

24:39

instances of that. Alright? And

24:41

now you want to find the right level of

24:43

grain that describes this

24:46

event in an informative way and

24:48

such that susceptible, let's go to

24:50

some probability. Now that I think about it, I mean, that

24:52

that potentially creates trouble for the, like, coin

24:54

being fifty percent. because you say, well, like,

24:56

each coin flip is unique in its own way. I mean,

24:58

like, exactly like whether in any

25:01

specific case, like, it depends on how they flipped it. And

25:03

so if you define and and if you like specify that, then

25:05

it's a hundred percent and zero percent. Yeah.

25:07

Maybe we'll soon be talking about frequentism,

25:09

but this is related to a famous problem

25:12

for the frequentist account of probability, the

25:14

problem of the single case. Right.

25:16

At some level of specification, every event

25:18

only happens once And then in

25:20

some events, that is quite a natural thing to

25:23

do. Like, this year's

25:25

NFL grand final That's

25:27

Australian rules football for the non Australian.

25:30

Okay. That seems to be a unique

25:33

event. And there may

25:35

be an issue, but how we assign probabilities

25:37

to it. But it seems as

25:39

far as frequencies go, it's a

25:41

one off thing. It's either one or zero for

25:43

say calling would my team winning. Yeah.

25:46

Yeah. Alright. Yeah. Are there any other any other

25:48

heuristics that people should keep in mind if they wanna kinda out

25:50

with their friends in conversation before we

25:52

move on? Yeah. 0II

25:53

like to think about

25:56

putting

25:56

contrastive stress on different

25:59

words in a claim and that that

26:01

makes you realize there's a there's a

26:03

contrast class this as opposed to

26:05

that. Let's take for

26:07

example, smoking a pack

26:09

a day causes lung

26:11

cancer. That's that seems

26:13

reasonable when you just say it like

26:15

that. Well, smoking as

26:17

opposed to other things you could do

26:19

with a cigarette like stroking it. Okay?

26:22

Yes. It seems like the smoking is relevant.

26:25

Yeah.

26:25

Smoking a pack

26:26

a day. Smoking one pack

26:29

a day Now as opposed to

26:31

none, yes, that seems

26:33

to cause lung cancer.

26:35

But what

26:35

about smoking one pack

26:38

a day as

26:38

opposed to three packs a

26:41

day. Now it's not so clear that

26:43

it's the one pack a day

26:45

that causes the

26:47

lung cancer as opposed to

26:49

three. And this now makes you

26:51

think that explanation must

26:53

be a contrastive matter.

26:55

Yeah. Isn't that and yeah. This thing

26:57

is opposed to lip band counterfactuals or like

27:00

an alternative. They're saying one is opposed to zero,

27:02

but we don't we don't say that most of the time. And

27:04

so we could eventually end up having a kind of

27:06

factual that you haven't really, like, properly thought through?

27:08

Yeah. Yeah. And, yes, this

27:10

makes you be honest. What am I

27:12

contrasting this thing with

27:14

maybe that was implicit and not

27:16

obvious. And this this technique where

27:18

you, I mentally, italicize different

27:20

words in a claim, and

27:22

and say, okay. In each case, this as opposed

27:24

to what. And then I realized, oh, okay.

27:26

I was making a presupposition or

27:28

something like that. Yeah. Okay. So

27:31

I suppose, like, all of these heuristics can

27:33

potentially provide kinda stress cases

27:35

or, like, I guess, considerations against

27:37

conclusions that people are putting forward. Yeah. In

27:39

general, do you think that there's very often, like,

27:41

decisive arguments against the position? Or or is it more

27:43

often that all of these weaknesses kind of

27:45

accumulate? And then you end up with kind of view that,

27:47

like, this many like little pro there's too many problems

27:49

here for this to be quite the right theory.

27:51

Yeah. This thing, like, most most theories you can throw

27:53

something at them and be like, it doesn't feel quite right in this

27:55

case. Yeah. Lewis famously

27:57

said, philosophical positions are

27:59

rarely refuted. Get

28:01

here may have done it. That's the justified

28:03

true belief, analysis of knowledge, Girdle

28:05

might have done it, but it's it's about

28:07

it. It's rare. Hey, listeners. We just

28:09

mentioned getier problems, which We

28:11

don't really need to understand in order to follow

28:13

the rest of the conversation, but I thought I'd add

28:16

in a little bit about that just because it's

28:18

quite fun. since the beginning of philosophy, that

28:20

being this question, what is

28:22

knowledge? And one of the most

28:24

common answers or one of the most popular

28:26

answers into the twentieth century going back to the

28:28

ancient Greek was that knowledge

28:30

is justifying true belief. So you have

28:32

to believe something. It's gotta be true and you

28:34

have to have good reason to think that

28:36

it's true. In nineteen sixty three, Edmund Gettya

28:38

published this paper that basically

28:40

to almost everyone's satisfaction kind of

28:42

demolished that definition of knowledge with a

28:44

really strong counter example. And the

28:46

cataract example is this. Imagine that I

28:48

walk into my colleague's

28:50

office say, and I see

28:52

them sitting at their desk. and I

28:54

formed the belief that my colleague, Neil,

28:56

say, he's in his

28:58

office. It'd be very natural to say I have a

29:00

justified true belief there because I've seen

29:02

Neil sitting at his desk. But

29:04

imagine that unbeknownst to

29:06

me, Neil has had an

29:08

amazingly realistic wax sculpture of

29:10

himself that he has placed in

29:12

his desk chair in his place, and I wasn't

29:14

looking very carefully. So I hadn't

29:16

realized that it wasn't actually Neil sitting at

29:18

the desk. But

29:19

also unbeknownst

29:20

to me, Neil is in his office. He's

29:22

hiding under the desk as part of a prank

29:24

involving this wax sculpture that he's

29:26

produced of himself.

29:27

Now, I believe that Neil was in his

29:30

room. He is

29:30

in his room. He's hiding under the desk. And I

29:32

had good reason to think that Neil was in his

29:34

office because I saw him there.

29:36

But

29:36

can I really be said to have known

29:39

that? Given that, what I saw

29:41

was the wax sculpture, so it's

29:43

only by pure coincidence that my belief

29:45

is true. There's not actually a real

29:47

connection between the justification that

29:49

I had for thinking that Neil was in the office and

29:51

the fact that he is. It's just luck that

29:53

he also happens to be hiding under his desk.

29:55

this is the case where it seems like one can have

29:57

a justified true belief, but it doesn't

29:59

really

29:59

feel like knowledge because the

30:02

truth of the claim is not connected to the

30:04

justification that I have in my mind.

30:06

That's a

30:06

getier case or a getier problem. It shows

30:08

up all over the place where one can think

30:10

the right thing, but for the wrong reason, Another

30:12

amazing thing is that Edmund Gettya published this paper,

30:15

his knowledge justified true belief in

30:17

nineteen sixty three, but

30:19

that's basically the only thing that he's known for doing. I I don't know

30:21

that he made any other notable contributions

30:23

to philosophy other than one of the most

30:25

famous arguments made in philosophy across the

30:27

entire twentieth century. So I

30:29

guess he's kind of the one hit one, the the the macarena of his fields,

30:32

so to speak. Alright. That's get your

30:34

problems. Let's go back to the

30:36

interview. I think there are some

30:38

killer problems for various positions

30:40

we might talk about some later.

30:42

Yeah. But yes, often it's more

30:44

a matter of accumulation. There are some

30:47

smaller problems, but they start adding up.

30:49

And overall, the

30:51

position doesn't

30:51

seem tenable. It doesn't seem to

30:54

best capture the data points. Yeah.

30:56

The people sometimes give

30:56

up on them because it feels like, okay. You you could

30:58

like patch the first three things kind of, but then just like

31:00

more and more cracks start appearing and you're, like, trying

31:02

to patch it up everyone. You're, like, it starts to feel

31:05

like more complicated. Just patch it. Yes. Epi

31:07

cycles. Right? Yeah. It feels like more complicated to patch the

31:09

theory than just to come up with a new one.

31:11

That's right. Some might say that that

31:13

happened to the justified true

31:15

belief account of knowledge that

31:17

that can't be quite right. It seems because of

31:19

get here and so on. And then we add an

31:21

Epicycle and another one and another one.

31:23

And if it goes too far, it starts to

31:25

feel like a degenerating research

31:28

program it's like, yeah, the explanation so long that it's lost.

31:30

It's original intuitive appeal. It's no longer

31:32

simple either. That's right. And even if

31:34

it turned out, alright, I

31:36

can't come up with any counter examples to

31:38

this tremendously long complicated

31:41

analysis, but do I really feel

31:43

it? Illuminate. Suppose that really

31:45

is knowledge is this

31:47

thing with many Epi cycles. Yeah.

31:49

Do I feel like I understand it better? Yeah.

31:51

Yeah. Not really. hey, listen.

31:53

Rob here with with another quick aside.

31:55

This one's

31:56

a fun one. We just use the term EpiCycles,

31:58

which

31:59

philosophy around quite a bit, but I think I

32:02

hadn't heard until I started talking to people

32:04

who'd done philosophy PhDs. That year

32:05

of EpiCycles, is basically you're adding

32:08

lots more complexity to a

32:10

theory in order to salvage it

32:12

from cases in which it doesn't match in reality or it

32:14

doesn't match your intuition. But really

32:16

what you want to do is throw out the theory

32:18

altogether and and then start again because it's the

32:20

wrong approach. It goes back to

32:22

how the ancients used to

32:24

predict the the the motions of planets

32:26

when they thought that everything was

32:28

going around the Earth one way or another.

32:31

Obviously, the planets weren't growing around the

32:33

Earth fundamentally. So how

32:35

did they manage to explain the apparent

32:37

motions of of the planets and then them coming

32:39

closer and then and then going further

32:41

away. Basically, they modeled the planets

32:43

traveling around the earth, but they were

32:45

also traveling in little circles

32:47

around the circle that they were traveling

32:49

around the Earth on. They were traveling at the same time on

32:51

two different circles. Then this allowed them

32:53

to match up the predictions of that model with their

32:56

observations of where the planets were. So the main

32:58

big circle that they were traveling on around the

33:00

Earth was called the deferrant or deferrant,

33:02

I'm not sure how it's pronounced. And

33:04

the little circles that they were traveling on around

33:06

that circle were called EpiCycles. I

33:08

think it I think it comes from Greek meaning,

33:10

yeah, circle moving on another circle.

33:13

anyway, so you can see how this has come to mean adding

33:15

complexity to a model in order to

33:17

salvage it when really it's it's the wrong model

33:20

to start. What they should done is that the

33:22

planets were moving in ellipses around the

33:24

sun rather than adding more and more circles

33:26

to try to match things up. Interestingly

33:28

though, by adding in enough Epicycle's like

33:30

this, they were able to make their predictions of

33:32

the planet's motions match almost exactly

33:34

that their observations because they

33:36

just had enough degrees of freedom in the model to allow

33:38

them to place the planets in in any particular place

33:41

at any particular point in

33:43

time. what can happen when you're you add a

33:45

lot of complexity to a model even if it's mistaken.

33:47

Okay. That's Epicycle's back to the show.

33:49

Okay.

33:49

Well, what what are some common moves that

33:52

philosophers make trying to debunk at a other

33:54

philosophers of ideas that you think are kind of overrated.

33:56

It's like not as strong an objection as as people

33:58

make out. Well, a whole

34:00

movement in philosophy see that I now distance

34:02

myself from. I think this speaks to your

34:04

question. Flossers love to

34:06

appeal to other worlds, and

34:08

in particular, similar

34:10

worlds. This may come up when we

34:12

talk about cataractials. The

34:14

standard analysis of cataractials

34:16

appeals to

34:18

most similar possible worlds, but not just

34:20

counterfactuals. Knowledge, we often

34:22

talk about so called safety and

34:26

sensitivity, And that's a a matter

34:28

of what's going on in nearby worlds where you believe something or where the

34:30

thing you believe is is true or not true.

34:34

And I I used to

34:36

just talk this way too. I used to love all this

34:38

talk of similar worlds

34:40

and and other worlds in general. And

34:42

now I've now i've jumped off

34:44

the bus and I think one should not be

34:46

casting everything in terms of

34:48

other worlds and similarity relations.

34:52

I prefer to do it in terms

34:54

of probability and stay in the actual world, probabilities anchored

34:56

here and it will give

35:00

my preferred accounts of things. It doesn't quite speak to your question, but I think

35:02

it's close. Okay? Yeah. Any

35:04

yeah. Any other advice or burning young philosophers in the

35:06

in the audience, but before you push on to concrete

35:09

concrete questions. But high value for

35:11

me in philosophy is clarity. I

35:14

really care about clarity. And by

35:16

the way, these heuristics, I think,

35:18

help in that mission as

35:20

well, trying to just really get clear on what a

35:22

position is and what possible

35:24

defects are.

35:26

And as I think SIRL you understand

35:28

what you're saying. Yeah. And I

35:30

would begin with that. Yes. I'm

35:32

not sure a hundred percent agree.

35:36

So philosophers do tend to just be absolutely obsessed with, like,

35:38

making sure that the thing applies to every case.

35:40

And, like, when you read philosophy papers, you really do

35:42

get this impression that it's like a long series

35:45

of like paragraphs added to, like, like, every objection that some

35:47

philosopher might raise, so there's, like, nothing that can be

35:49

said in response. So it's in, like, one sense that's

35:51

extremely clear. In another sense, it feels like maybe you're,

35:53

like, losing the phrase for freeze

35:55

sometimes. Yeah. Like, in considering off of, like, small object

35:58

like, clever, small object rather than, like, is

35:59

the is the core issue because of the

36:02

thesis sound. Yeah. Maybe being too

36:04

pedantic. Yeah. Yeah. yeah, come on. You know

36:06

roughly what I meant. But Yeah. Since some

36:08

degree, like, a philosophy is a kind of professional pedents.

36:10

That's kind of a The whole thing is to find the education.

36:12

That's right. And I'm sure

36:14

you know the way that philosophy is often right.

36:16

It's often in this very defensive

36:18

style because you're preparing yourself

36:20

for the most uncharitable objection because -- Yeah. -- you didn't

36:22

quite nail the point, you know,

36:24

given your wording, there's some counter

36:28

example. And, yeah, this should

36:30

be tempered with the principle of charity that you should try to give a charitable

36:32

interpretation of what's being said

36:34

and and look for more

36:37

interesting

36:37

more profound deeper objections.

36:40

Yeah. Yeah. It is the most challenging part

36:42

of, I think, interviewing philosophers is is that they

36:44

really wanna be right. And just like,

36:46

can you the love of God, say something wrong. Say something wrong, but less

36:48

words, please. Yeah. Right.

36:50

And, yeah, you you ask a question and, well,

36:52

let's not quite right the way you said it.

36:54

Yeah. But Yeah.

36:56

If if at least the the spirit of it's

36:58

conveyed that that is often good

37:00

enough. Yeah. I I suppose yeah. If you if

37:02

you get I guess if you get too sloppy in that direction, then you can't like do

37:04

philosophy so much anymore. But then you just become like

37:06

ordinary people who accept common sense and like

37:08

I'm not looking for like the little ways that

37:11

like end up you, like, investigate more deeply, it does actually demolish common

37:13

sense when you think about it properly. Yeah.

37:16

Okay. Let's push on to a topic that is

37:18

dear to all of our heart's probability. Yeah. But

37:20

kind of the core question I

37:22

really wanna ask here is whether

37:24

basicism as kind of as it's often practiced by people in

37:26

the audience, whether it's true in

37:28

some sense. Yeah. But before I

37:30

ask that, we should probably wind back a step. At

37:32

a high level, kinda what are the different

37:34

theories of what probability what

37:36

probability is? Like, what yeah. What what ideas do people

37:38

have about it? Yeah. This is what my

37:40

professor should have said when I asked

37:42

the question, what is

37:44

p? And he thought I

37:46

needed medication. this would be the

37:48

beginning of a reply. Let's

37:50

distinguish three main kinds of

37:52

probability. The first, let let's

37:54

call it objective chance. Out

37:57

there in the world, there's probability and it's mind dependent.

37:59

It doesn't care what

38:00

we think. So I think maybe of

38:04

radioactive decay. The

38:06

radium atom has a decay law. It's got

38:08

a half life of sixteen hundred years,

38:10

which is a probabilistic fact. It

38:13

doesn't care what anyone thinks. It's just

38:16

out there in the world. It's like mass and

38:18

charge. It's some property

38:20

out there. That's the first.

38:22

Yeah. Can I make sense? Yep. Yeah. Second one,

38:24

let's call it Oh, I guess, under that one, do we have

38:26

kind of quantum mechanics issues? It's like the

38:28

probability of an electron being here rather than

38:30

there. Is that that in the same

38:32

category? Yeah. And that's a big question in the interpretation

38:34

of quantum mechanics whether there really

38:37

are objective probabilities or

38:40

is in fact everything deterministic and really the

38:42

chances are all ones and zeros -- Okay.

38:44

-- on one view. Wow. But

38:47

Let's get that. Okay. Second

38:50

interpretation, let's call it

38:52

subjective

38:53

probability and That's

38:55

now more about rational agents, people like

38:57

us. Call it Credence,

39:00

if you

39:02

like. and it's degree of confidence. We

39:04

sometimes we outright believe

39:07

things, but it's often

39:10

our degrees of confidence are more nuanced than that.

39:12

We believe some things more than others as we

39:14

might say. We have degrees of belief, and that

39:16

that would be the second interpretation. But

39:20

he had not just anything goes, it seems these are rational degrees

39:22

of belief, and it'll

39:23

turn out according to Beijingism,

39:25

they're constrained by

39:28

probability

39:28

theory. So would there be other, like, the correct credence?

39:30

Well -- Yeah. -- excellent. This this this

39:32

will get us to a big issue in

39:36

Beijingism. at

39:37

one extreme, you've got, I guess, a

39:39

very permissive radical subjectivism,

39:42

where the only

39:44

constraint is a

39:46

bay the probability calculus. They'll shelter

39:48

bay, columnar of sections, something like

39:50

this. Like, everything's got a sum to one

39:53

or the probability something happening as one. That

39:55

that's right. probabilities are non negative. Yeah. They have a top

39:57

value of one they add in a certain

39:59

way. Yeah. Okay. Now that

40:02

seems very seems very permissive.

40:04

You know, I can assign

40:07

probability even one to,

40:10

you

40:10

know, a meteor quantum

40:14

tunneling through this lecture theater

40:16

before we're finished and going out the other side --

40:18

Yeah. -- as long as I get probability zero to it,

40:20

not doing so and so

40:22

on. And probability, very high probabilities to the

40:24

sun not rising tomorrow and

40:26

so on. And it

40:28

doesn't violate

40:30

any fundamental axioms are probably

40:32

That's right. Yeah. But it seems somehow

40:34

too unconstrained. Right. Now at

40:36

the other end of the spectrum, This

40:39

is the so called uniqueness thesis

40:41

that your

40:41

evidence uniquely

40:42

constrains you and there's

40:44

exactly one creams you should have and

40:48

in fact There was let's call it an Ere prior. No.

40:50

There was the correct

40:52

thing. Correct. Before you saw anything about it. probability

40:54

before any evidence, you should

40:58

start there. and just update it on your evidence as it comes

41:00

in. Now that seems too extreme

41:02

perhaps in the other

41:04

direction that given my

41:06

evidence, there's a sharp probability

41:08

I should give to it

41:10

raining tomorrow. And -- Yeah. --

41:12

if I said seventy one point two rather than

41:14

seventy one point one, I wrong to think of --

41:16

Yes. Yeah. -- that's right.

41:18

And you'd think that different people could

41:20

disagree to some extent,

41:22

but not according to this thesis, not if

41:24

they're rational. And then you've got all the

41:26

positions in between in this

41:28

spectrum, and we could then

41:30

have discussions

41:32

about just how much grievances are constrained.

41:34

Actually, this nicely brings us to the third

41:36

main interpretation. Let's call

41:40

it evidential probability. And

41:41

the thought is that

41:42

evidence does put

41:44

some constraints

41:46

on

41:47

on hypotheses or propositions

41:50

degrees of support. Let's

41:51

call them. Okay? And probabilities

41:53

measure these degrees

41:56

of support. So for example, maybe given your

41:58

evidence, it's very

41:58

probable that the

41:59

sun will rise tomorrow. Yeah.

42:02

And then we might say the evidential

42:04

probability of

42:06

Sunrise given your evidence is

42:07

high. So I haven't quite tracked that. Yeah. How is this

42:10

different than the previous

42:12

ones? Yeah. So the previous

42:14

one, we started with just subjective

42:16

probability. Yeah. And notice

42:18

how we

42:18

sort of morphed into the third one,

42:20

But first, we we said we had the

42:21

permissive radical subjectivism that

42:24

said anything It's it's up to

42:26

you. Yeah. Your choice. Leave whatever you

42:28

like. Yeah.

42:30

Your credence just run with

42:32

it and then update it appropriately. And that definitely

42:35

was not evidential probability.

42:38

And then probably when we get

42:40

to the other extreme, the

42:42

uniqueness thesis, then it does

42:43

seem that that would be some something very

42:46

much like evidential

42:47

probability that would would

42:49

constrain you. And then there are the positions

42:51

in between. So I I don't wanna make

42:53

a sharp division between

42:55

subjective

42:55

and evidential probability. Really,

42:58

it's a spectrum and this

43:00

corresponds to what you

43:01

might call subjective bayziness

43:03

or more objective basingism

43:05

and degrees of that as we move

43:07

down the spectrum? Yeah. Okay. So

43:09

so the spectrum between, like, the

43:11

subjective basicism and these

43:13

kind of evidential a reasonism. So, like, where you can

43:15

believe anything and where have to believe, like, one specific thing. I like both of them feel but I feel

43:18

pretty terrible in their own own

43:20

own way. And you're saying, like,

43:22

maybe the most plausible thing or the most intuitive thing.

43:24

It's gonna be somewhere in the middle where it's like, you could there's

43:26

a range of stuff that you can believe that's not stupid.

43:30

Yeah. Yes. but you can, like, go too far. And it's also not just like one specific thing, you know,

43:32

like an idiot. If you don't believe the exact exact

43:34

truth. Yeah. I guess, whenever you have a spectrum like

43:36

that, it's gonna feel a little

43:38

bit arbitrary. a point you draw on there.

43:40

So, like, how would we even begin to know, like, what what is the correct point along that spectrum? Yeah. Well,

43:42

we start adding some constraints

43:44

to to the radical

43:47

subjectivism. Maybe for

43:48

example, the principle of indifference. You might

43:51

think that's a kind of

43:54

evidential probability explain that? Yes. Okay. When your

43:56

evidence bears symmetrically

43:58

on a range of

43:59

possibilities, not favoring

44:02

any other then

44:04

you should give probability these cases. It's most

44:07

plausible in gambling cases

44:09

like Etorso coin head's

44:12

tails. My evidence doesn't favor heads over tails.

44:15

It seems I should give half

44:17

half to those possibilities. And

44:20

then we can complicate that and find

44:23

brain

44:23

some problem and then say, well,

44:25

either you have no

44:26

evidence So you should

44:29

give equal probability to the cases or you do have

44:31

evidence that

44:31

bears symmetrically on them and you

44:33

should give equal

44:34

probabilities. Now a

44:36

big discussion could be had. There there

44:39

meant to be various serious problems. There are

44:41

serious problems with the principle of indifference

44:43

as I just stated it. and

44:45

various people think it's bankrupt

44:48

because of these problems.

44:49

Yeah. But it's funny how

44:52

people often reach

44:53

for it intuitively, even

44:56

when they've disavowed it a minute

44:58

ago, for example, in the Monty Hall

45:00

problem, may maybe you know that. Yeah.

45:02

You know? behind one of

45:04

three doors, there's some prize, what probability

45:06

should you give to

45:09

it being behind a particular

45:11

door? And then the problem continues. Now

45:13

no one

45:14

says, oh, I give probability

45:17

one seventeenth to behind

45:20

door number one because I'm just unconstrained,

45:22

and that's what I feel like. And

45:24

one one seventeenth, you feel the

45:27

pull of the principal in the difference.

45:29

I should give third, if you've just a

45:31

moment ago, disavowed the

45:32

principle of indifference. So it seems like

45:34

in some restricted cases, at least,

45:38

Yeah. It

45:38

has some pull. But I suppose one we've been talking here

45:40

about, like, what you should believe or just this is, like, smuggling

45:42

in this idea that there is, like, anything that you

45:45

should believe. We're, like, would be, like, practically, brought

45:47

in, like, ethics before, like, some ethical considerations almost into, like, into what

45:49

you should believe. And and and maybe that'd be too much

45:51

to get into here. This we

45:54

may be getting into ethics later

45:56

too, which is not my area

45:58

of specialization, but I'm always happy

46:00

to try. Okay. With that kind of

46:02

scene setting about what probability might be out of

46:04

the way. Real quick, I wanna ask, you know, me and

46:06

my friends, when we're like hanging out, when

46:08

we're chatting, watching the news or talking about events in the world. You know, I might say something

46:10

like I think that's like an eighty percent chance that Boris

46:12

Johnson is gonna resign in the next week or

46:14

two. And someone else would say no,

46:16

I think seventy percent, and then we, like, go

46:18

and check the news and, like, moment as to resign, and we're, like, okay, I think it's, like, eighty five percent now.

46:20

Yeah. How are you doing? How

46:22

are you doing right now? Yeah. Okay.

46:26

But are we doing the right thing? Is is this like the correct thing to do?

46:28

Or are we just playing some game that's like fun

46:30

for us and is like not really any better

46:32

than any other approach? or or at

46:35

least like not like uniquely privileged as the correct approach. Yeah. So I am

46:37

a big fan of Beijingism. I guess

46:39

I

46:39

say on Mondays,

46:42

Wednesdays, Fridays, I

46:43

call myself a baysian, Tuesdays,

46:46

Thursdays, Saturdays, I'm not so

46:48

sure. Today's Saturday. Today's

46:50

Saturday. Okay. Maybe I'm not

46:52

so sure. But look, I think there's something right about

46:54

this. We have these

46:56

degrees of confidence. I think

46:58

we have to allow this. It's not just

46:59

all or nothing belief

47:02

It does seem there are better and worse ways to

47:04

manage these degrees of

47:06

confidence. There are various good reasons

47:09

to think that they should obey probability theory. We may talk

47:12

about that Dutch books, for

47:14

example. There are ways

47:14

that they should update, so called

47:18

conditionalization. And we can then have disputes about how much

47:20

constraints there should be on

47:22

the priors that you have we

47:25

we had a bit of that discussion before. Yeah. But it it

47:28

seems like a very good model and it's

47:30

very fertile too. Lots of

47:32

good things are closely

47:34

related to this. Maybe soon we'll talk about decision

47:36

theory, another thing that I'm fond

47:38

of, and probabilities figure

47:40

centrally in that. And so I

47:41

think it's a good good place to

47:44

start. Hey,

47:44

listeners. One more definition. The

47:46

term

47:46

Dutch book is from

47:49

gambling. It's a set of odds or bets that when created

47:51

by a bookmaker, ensure that the bookmaker is

47:53

going to make a profit. Now, how is

47:55

that relevant to decision procedures and

47:58

beliefs and and all of that kind of

48:00

thing. So

48:00

one weakness that set

48:02

of ideas about grievances or

48:05

decision making could have is

48:07

that someone could be presented with a series of bets that they could be

48:09

offered to make or a series of trades that they

48:11

could be offered to make. that

48:14

would cause them to just constantly get worse off and worse

48:16

off. Basically, they have less and less money until

48:18

they bankrupt. How could that happen?

48:20

how could that happen So

48:21

normally, in philosophy, a standard thing is

48:24

that with preferences say, is that you would

48:26

assume transitivity. So if you think a

48:28

is better than b, and you think b is

48:30

better than c, and you should also

48:32

think that a is better than c.

48:34

Now you might

48:34

want to say, I don't want to buy this

48:36

idea of transitivity. I want to think that

48:38

I could believe that a is better

48:40

than b that b is better than c,

48:42

but also that c is better than a. So

48:45

you have kind of a circle here where you'd be

48:47

willing to give up c in exchange for b.

48:49

you'd give up b in exchange for a, but you'd also

48:51

give up a in exchange for c. But one

48:53

of the reasons why giving up this

48:55

principle of transitivity isn't very

48:57

desirable. is that if you have circular preferences like

48:59

that, then it's possible for someone to just

49:01

keep trading with you. So if you think b

49:03

is better than c, then you'd be willing to

49:06

give up c and potentially pay

49:08

a bit of extra money in order to get

49:10

B. But you can see that someone could just

49:12

keep trading you, b for c, a

49:14

for b. c for a

49:16

and so on and so on and so on in a

49:18

circle until you were left with no money. So

49:20

you said you might end up with c again, but then you've

49:22

lost all the other things that you traded as we were

49:24

going through this circle. where each time you thought things were getting better, but then you just end

49:26

up back where you started. So when

49:28

philosophers say that a set of ideas would allow

49:30

you to be

49:32

Dutch booked, They're saying that they're inconsistent some someone

49:34

to in principle offer you a series of exchanges

49:36

that you would all accept because you

49:38

think that they are good

49:41

because individually, they look good, but then

49:43

collectively, they would clearly just leave you

49:45

better off, potentially just just bankrupt. Okay.

49:47

Back

49:47

to the show. Yeah. Go

49:49

go go go go go go go go go go go go go go go

49:51

go go go go go go go go go go go

49:53

go go go go go

49:55

go go go go go go But for some of

49:57

the week, you're not into vaziness -- Yeah. -- or not into like this approach. Yeah. Okay. Let let's

49:59

do that one first. Like, what what are the reservations

50:01

that you have? Yeah. We

50:04

start with some

50:06

excimatization of probability, and

50:08

Colmogorff is is the

50:10

standard. Okay? And

50:14

he excimatized unconditional probability first and

50:16

then conditional probabilities defined in

50:18

terms of unconditional probabilities. The

50:20

probability of a given b

50:22

is a

50:24

ratio probability

50:25

of A probability of B,

50:26

assuming that the probability of

50:28

B is positive. I actually

50:31

be other way around. I think the conditional

50:34

probability is the basic notion,

50:36

the fundamental notion. I think

50:38

there are problems

50:40

with Colmogorov's exmeritization,

50:42

as I've just put it, he did have

50:44

further subtleties, which I can't get into

50:48

here. But two kinds of problem. Remember I had this

50:50

proviso provided that the

50:52

bottom line of that ratio is positive. You

50:54

can't divide by zero. But here's

50:56

now another problematic

50:58

feature of the standard theory with

51:01

real valued probabilities. Yeah. It

51:03

seems that probabilities zero

51:05

events can happen

51:08

Now

51:08

that's not intuitive. We normally think if something

51:10

can happen, it

51:11

must have positive probability. Yeah. Or

51:13

what what's an

51:16

example? Yeah. Okay? Think, for example, of the

51:18

radio atom

51:19

decaying exactly

51:21

at noon tomorrow,

51:24

say, what's the probability

51:26

of that? On the standard theory

51:28

where it's real valued probabilities,

51:30

in this case, an exponential

51:34

decay law, The

51:34

probability of it decaying exactly at

51:36

noon is zero. Now

51:38

it decaying in

51:39

some infinitesimal region

51:42

around noon, that could be something more. But

51:45

noon itself, that

51:47

point gets probability

51:48

probability zero

51:49

or or throw a dart at a dartboard.

51:52

What's the probability that it hits

51:54

randomly? It hits the

51:56

exact center

51:58

Yeah. Okay. So this really didn't do much math at university. This

52:00

is this is this is this classic thing. So imagine

52:02

that we're gonna randomly choose a real number

52:04

or, let's say, any number between zero and

52:06

one. the probability of any

52:08

being any specific one of them -- Yep.

52:10

-- any specific number is zero because there's,

52:12

like, uncountably infinite any numbers. Indeed,

52:14

I think the probability of you picking like

52:16

randomly picking a number that could ever even be written down is zero.

52:19

Right? Yeah. Well, you think it's computable? Yeah. And

52:21

it's not computable. Right? Yeah. And there are only

52:23

cannibalizing many of those and Okay.

52:25

Okay. So you're saying each of these, like, specific

52:27

numbers has a probability of being chosen of zero or

52:29

any any specific example that you pick a zero. And yet, we know

52:31

that one of them will chosen. Yes. Okay.

52:34

So yeah. Okay. So it's a bit like the lottery

52:36

paradigm. It is. It's like an uncountable

52:38

lottery paradigm. And this is a

52:40

puzzling feature. And

52:42

there is this this rather strong intuition.

52:44

Come on. If if it can happen,

52:46

it should get some positive probability.

52:48

We want to distinguish it from

52:50

an impossible event and

52:52

it seems the way to do that is, well, it's got greater probability. And

52:54

actually, this is another way in

52:57

which we might go

52:58

away from this

53:00

numerical call megal effect immunization. You

53:03

might say more fundamental is

53:06

comparative probability. And now the

53:08

primitive is something like x is

53:10

more

53:10

probable than y or maybe

53:12

better still

53:13

w given x

53:15

is more probable

53:16

than y given z or

53:18

at least is probable and now

53:20

make that the fundamental notion

53:23

and then

53:23

we can maybe recover the numerical

53:26

theory out of certain axioms and so

53:28

on on those fundamental

53:30

comparative probabilities. Yeah. hey, here

53:32

with another definition. We just use the term

53:34

primitive, a philosophical primitive.

53:36

In philosophy,

53:37

a primitive notion is

53:39

a concept that is kind of fundamental

53:42

and can't be broken down and defined in terms

53:44

of other previously defined

53:46

concepts.

53:46

In geometry, for example, a

53:48

point or a line or contains or

53:50

potentially space might be primitive notions that

53:53

one can't really break down and define in terms

53:55

of other notions. They're kind of the

53:58

starting point. Okay. Back

53:58

to the show. I'm just thinking about the the

53:59

the, like, choosing a specific number case. Okay. So so it's

54:02

it's actually quite a bad situation because

54:04

you're saying, So normally,

54:06

with basicism, we're we're thinking we got a prior, we

54:08

got like a prior probability that any number be chosen,

54:10

and then we update a lot based on the evidence.

54:12

Yeah. But because our prior and any any number is gonna

54:14

be zero. And when you, like, multiply anything by

54:17

zero, it's still zero. So so

54:19

random number gets chosen, you're like, you have

54:21

your prior you observe the and you still think

54:23

it wasn't chosen because it would be it was impossible for any number to be chosen,

54:25

whatever it was. Well, it's like, quite bad. Impossible

54:27

in this probabilistic sense, and that's

54:29

the trouble that and it

54:31

seems that probability, so to speak,

54:34

has blurry vision. It does not

54:36

distinguish between the genuine impossibilities

54:38

-- Yeah. -- and these very

54:40

unlikely, but in some good

54:42

sense possible cases. And this

54:44

is related to my

54:46

worry about the ratio formula, again, you divide

54:48

by zero. Now what happens

54:50

if you learn in this

54:53

experiment where you randomly

54:55

choose a real number from say zero

54:57

one. You learn its value, but it's something

54:59

you antecedently gave

55:02

probability zero. If you just

55:04

looked at the ratio

55:06

as standardly understood as

55:09

involving

55:09

a ratio of real

55:11

numbers, It was zero divided

55:12

by zero, it is zero that you'd get that particular

55:14

number. Now how do you update on

55:16

that? How do you, as we say, conditionalize

55:18

on something you originally gave?

55:21

probability zero. Now I have to

55:23

say that this quickly gets us into

55:25

very sophisticated mathematical refinements.

55:28

Colmogorff himself was well aware of this problem

55:30

and he had sophistication. People bring on

55:32

hyperreal numbers. They bring on

55:33

richer number systems that are meant

55:35

to preserve this

55:38

intuition that if something's possible, it'd it'd better have positive

55:40

probability -- Yeah. -- and we can

55:42

let that debate unfold. But it's

55:44

it's

55:44

just to say, now this is Saturday,

55:47

you know, I'm saying, I'm just

55:49

trying to bring out there are various problems

55:51

with just this simple statement. straightforward.

55:54

It seems like. Just

55:56

follow Colmogorff probabilism says

55:57

your probabilities should

55:59

obey these axioms well. It's

56:02

more complicated. should

56:03

we take conditional probability as primitive?

56:06

Do we have to worry about the probability

56:08

zeros? Do we enrich the

56:10

number system beyond

56:11

the reels, which will take comparative

56:14

probabilities as basic lots of

56:16

debates to be had. Yeah. That this might be

56:18

a stupid frivolous question. But is it is it

56:20

maybe that I guess it not

56:22

possible. Is it possible to have a

56:24

probability that's like a negative

56:26

probability or like a probability above one

56:28

or like Well, I'm just thinking, you know, obviously, we have imaginary

56:30

numbers now, like, off the real number line. Yes.

56:32

Like, is is any of this coherent?

56:34

Yeah. Well, some people

56:36

think so Feynman thought they could be

56:38

negative probabilities.

56:40

And, of course, you're not obeying

56:43

on the Gaurav. the chromogor effect

56:45

amortization or thou shalt have non

56:47

negative probabilities. There

56:49

are some thoughts

56:52

along these lines that there's something that behaves probability

56:54

like some function that seems

56:56

to have probabilistic properties. And

57:00

then you see that it sometimes goes negative. There are meant to be some

57:02

physical examples of this. And then you

57:04

say, well, those are the negative

57:07

probabilities. There are some problems with

57:09

this,

57:09

just to take one,

57:12

consider the

57:13

usual formula for independence. Two

57:15

events A and

57:15

B are independent, just in

57:18

case the probability of A and

57:20

B equals the probability of A

57:22

times the probability

57:24

of B. now

57:24

suppose you have independent negative probability

57:27

events, their

57:29

product, something negative times,

57:31

something negative. Yeah. is

57:34

positive. Alright. Yeah. That seems to be

57:36

a problem if if you think the event

57:38

itself and maybe the conjunction of

57:40

it with something else has negative

57:42

probability. How does independents pan out?

57:44

Yeah. Huge, you know,

57:46

issue we could get into there too. Yeah. Are

57:48

there any other downsides to

57:50

bayzunism that important or or or way on you at all? Here's

57:52

one thing that just

57:53

bothers me a bit, and I'll throw

57:55

it out there. As a

57:57

slogan, I'll say, subjective bay

57:59

zionism is anchoring

57:59

and adjustment, and I

58:01

need to explain what I mean

58:03

by that. Anchoring and

58:05

adjustments are heuristic that

58:07

often use when estimating some

58:10

quantity, they're given the so called

58:12

anchor some starting point for

58:14

thinking about the value of

58:16

that quantity and then they adjust until they reach an estimate

58:18

that they find plausible. The trouble

58:20

is that sometimes the

58:21

anchor is in highly

58:24

irrelevant to the quantity, and it just

58:26

should be ignored, yet it

58:28

still influences the

58:30

final estimate. the adjustment

58:32

is insufficient. And there are a couple of

58:34

classic examples, which I can give you. To

58:36

our skin condiment, had a famous study.

58:39

They asked people to watch the

58:41

spin of a roulette wheel, which was rigged to

58:43

land

58:43

on either ten or

58:46

sixty five. And

58:48

then they were asked whether the percentage of African countries

58:50

in the United Nations was

58:53

higher or lower

58:56

than

58:56

the number that they saw. And then they were asked

58:58

to estimate the percentage. Okay.

59:00

Those who saw a low number

59:03

tended

59:03

to give substantially lower estimates

59:06

for the percentage than those who

59:08

saw a high number.

59:10

And look, of course, they knew

59:12

that the RULET number, the anchor

59:14

provided no information whatsoever

59:16

about the percentage, yet it still

59:18

influenced their estimate. And

59:20

that

59:20

just

59:22

seems absurd. That's just seems crazy.

59:24

There's another famous

59:25

study. It was Arieli and Co.

59:27

They asked NBA students

59:30

at MIT to write

59:32

down the last two digits of

59:34

their Social Security number. And

59:36

then they were

59:36

asked whether they would pay this

59:38

number of dollars for some product

59:40

say, a bottle of wine box of fancy

59:43

chocolates and so

59:43

on. And then they were asked, what

59:46

was the maximum amount they were willing

59:48

to pay for

59:50

the product. Those who wrote down higher

59:53

two digit numbers were

59:54

willing to pay substantially more

59:58

And of course, they knew that their Social Security number

59:59

was completely uninformative

1:00:02

about the value of the product, but still

1:00:04

they anchored on it and

1:00:07

it influenced their final valuation. Okay. So the

1:00:09

idea is that the residue of the

1:00:11

anchor remained even after the

1:00:13

adjustment of thinking well,

1:00:15

how valuable is this product really? Okay.

1:00:18

Now these seem to be paradigm cases

1:00:20

of irrationality. Okay. But

1:00:22

now consider consider a putative

1:00:24

paradigm of rationality,

1:00:27

subjective

1:00:27

bayziness. Okay? Here

1:00:28

you start with a prayer That's

1:00:32

your initial probability distribution

1:00:34

before you get any information. And

1:00:36

the only constraint on this

1:00:38

is that it abaze the probability calculus.

1:00:41

That that's the version

1:00:43

I'm thinking of.

1:00:44

Okay. That's your anchor. Your

1:00:45

prayer is your anchor. And

1:00:47

then you get some information and you

1:00:50

update by conditionalizing on

1:00:52

it, as we say. So your

1:00:54

new probabilities are your old

1:00:56

probabilities conditional on that

1:00:58

information? That's your

1:00:59

adjustment. But the trouble

1:01:01

is that your prior

1:01:03

has no evidential value. It's it's

1:01:06

not based on any

1:01:08

information and you know this. That's what

1:01:10

makes it a prior. and its

1:01:12

residue remains even

1:01:14

after the adjustment often.

1:01:16

Now we can imagine that your

1:01:19

prior was even determined by the spin

1:01:21

of a roulette wheel or by your Social Security

1:01:23

number. As long as it obeys

1:01:25

the probability calculus, and

1:01:28

still it influences your final probabilities, your posterior

1:01:31

probabilities as we say. And now the

1:01:33

worry is, why isn't that

1:01:36

just as absurd as before. We were laughing

1:01:38

at the people in the

1:01:40

African United Nations experiment or

1:01:42

the wine and chocolate experiment.

1:01:46

what's the relevant difference? And look, there are

1:01:48

things that one can say, but I

1:01:50

just put that out there as something

1:01:52

that that needs some attention. I

1:01:55

think

1:01:55

in theory, if you get a lot of empirical

1:01:58

information over time, then the

1:01:59

influence of your

1:02:02

starting point. becomes more and more relatively irrelevant over time as this

1:02:04

kind of washed out by all these updates you're

1:02:06

making, you know, conditionalizing on things that you've

1:02:08

observed. So there's there's one thing, at least

1:02:10

if you you're around long enough and

1:02:12

collecting enough evidence to to move away

1:02:14

from the very first priority you started

1:02:16

with. I guess another difference that that I

1:02:18

imagine is that I think in theory you're meant to

1:02:20

start with something like an uninformed prior or I'm sorry. Which was

1:02:22

just to say a prior that is extremely

1:02:24

agnostic. I mean, like, is really pretending to

1:02:26

know all that much.

1:02:28

Now it's think it's a bit

1:02:30

hard to define exactly what is the appropriate, uninformed prior, but the hope is that

1:02:32

your views are gonna be very flexible

1:02:34

initially because it would be

1:02:38

presumptions, it would be foolish to think that before you look to any evidence, you

1:02:40

should have a really strong view about things. So maybe that's

1:02:42

one way in which the prior case

1:02:45

is well, the priors should hopefully be doing not that

1:02:47

much work. Even if we do concede that it

1:02:49

is largely arbitrary. Yep.

1:02:50

Excellent. Both good replies. The

1:02:53

first one was the washing

1:02:55

out of the prize in the long run. And

1:02:57

there are these famous convergence

1:03:00

theorems for Beijingism that

1:03:02

in the limit, under certain

1:03:04

appropriate conditions, effectively the

1:03:07

prior is completely washed out.

1:03:09

And that's good. But

1:03:10

that then

1:03:11

as Kain said in the long run, we'll all

1:03:13

be dead. And at

1:03:16

any point in our

1:03:18

finite lives, we will

1:03:20

not have reached that limit.

1:03:22

And the worry is that

1:03:24

the residue of the prior will remain

1:03:27

at all of these finite stages, which

1:03:29

is all we ever have.

1:03:31

Okay? So it's nice to know that there are

1:03:33

these theorems that we'll get there in the end,

1:03:35

but the problem is we're never at the

1:03:37

end. And regarding the second reply, and that that's certainly a good one.

1:03:40

Yes. I think actually that's the way to go that you

1:03:42

want some sort

1:03:44

of constraints beyond the

1:03:46

probability calculus on the

1:03:48

priors. And as you said,

1:03:51

maybe uninformative priors as we might

1:03:54

say, maybe there are some

1:03:56

constraints on what the price should be,

1:03:58

not just anything goes. And in fact,

1:04:00

there's the so called uniqueness thesis that

1:04:02

says, no, there's even exactly one.

1:04:04

There's only one rational starting

1:04:06

point, which is somehow, you know,

1:04:09

maximally uninformative, you might say,

1:04:11

For example, the principle of indifference might

1:04:13

kick in at that point. And now we

1:04:15

get into a good debate about

1:04:17

just how constrained prize should

1:04:19

be. So anyway, I raised anchoring and adjustment worry

1:04:22

as a concern for that completely

1:04:26

unconstrained version of

1:04:28

Beijingism that just said, thou shalt obey

1:04:30

the probability calculus. But beyond

1:04:32

that, it's okay, whatever you do.

1:04:35

it seems that you need to be a

1:04:37

bit more constrained than that. And then as

1:04:39

you say, the analogy to

1:04:41

anchoring an adjustment starts to to go away.

1:04:43

For example, we can't just spin a roulette

1:04:46

wheel or we we can't just

1:04:48

get your Social Security number and

1:04:50

make that

1:04:52

your prior. That's not the right starting

1:04:54

point. We haven't got five minutes left

1:04:56

on stage. So I wanted to give you a chance to

1:04:59

for the audience a few criticisms of fruquentism, which is

1:05:01

always. So firstly, like, what is fruquentism? And

1:05:03

secondly, like, what are some of the problems that we haven't yet mentioned

1:05:05

with it? Okay. Frequentism.

1:05:08

Remember my taxonomy of

1:05:10

objective probability, subjective probability,

1:05:13

evidential probability, frequentism would be

1:05:15

a version of objective. probability

1:05:17

out there in the world, mind

1:05:20

independence, there are these

1:05:22

probabilities. What are they? They're

1:05:24

relative

1:05:24

frequencies. Mhmm. To take a simple case

1:05:27

what's the

1:05:28

objective probability

1:05:29

that the coin lands heads,

1:05:31

let's suppose it's a fair

1:05:33

coin? Well, you toss

1:05:35

the coin a number see it lands and count the

1:05:37

number of heads over

1:05:39

the grand total. if

1:05:42

that number turns out to be a half,

1:05:44

then Bingo, you've got a chance

1:05:46

of a half for heads. Yeah. And

1:05:48

and now we generalize that. So

1:05:51

in general, the

1:05:52

probability of some, let's

1:05:54

call

1:05:55

it, an attribute relative

1:05:57

to some reference class So

1:05:59

attribute

1:05:59

a relative to reference class

1:06:01

r is the relative

1:06:04

frequency of a's

1:06:06

in that reference class. makes

1:06:09

sense, I think. And I think it may be still the most popular

1:06:11

account is among scientists.

1:06:14

Yeah. It's always scientist,

1:06:16

isn't it? They're the ones that They need to

1:06:18

talk to philosophers. Yeah. Absolutely. on so

1:06:20

many things. Yeah. Sorry. Okay. So this is kind of

1:06:22

a this has an intuitive appeal, and it's a bit like how

1:06:24

you're taught about probability. high school or something.

1:06:26

Yes, that's right. Yes. And we all know

1:06:28

that there's got to be some close

1:06:30

connection between probability

1:06:31

and frequency

1:06:34

and

1:06:34

frequentism posits the tightest connection of all

1:06:36

identity. And now we could distinguish

1:06:38

two kinds of frequentism.

1:06:40

You might call it actual frequentism,

1:06:43

you just look at what actually happens. You just,

1:06:45

in fact, toss the coin some

1:06:46

number of times -- Yeah. -- count the

1:06:49

number of heads divide

1:06:51

by the total of trials done. And then we

1:06:53

could

1:06:53

go hypothetical and

1:06:54

say, well, no, I really

1:06:56

meant some long run of heads

1:07:00

maybe I didn't get a long run,

1:07:01

so I go hypothetical, I imagine

1:07:04

counterfactually a long run

1:07:06

of trials and relative

1:07:08

frequency I would get maybe in the

1:07:10

limit. If I have infinitely many trials,

1:07:12

we have two versions. And

1:07:13

you probably want to ask why I don't

1:07:15

like -- Yeah. --

1:07:17

frequentism. I think version

1:07:18

of frequentism has the following kind of

1:07:20

problem. I think it's just built

1:07:22

into the very notion of probability

1:07:25

that fixing

1:07:26

the probability of something is compatible with

1:07:29

just any pattern and

1:07:31

any frequency of the corresponding

1:07:34

outcomes. Let's let's do it. Yeah. Yeah. Let's

1:07:36

do it for the coin toss. Let's suppose we

1:07:38

have a fair coin by which

1:07:40

I

1:07:40

mean the chance of heads as a half.

1:07:42

I

1:07:43

say that's compatible with any distribution of

1:07:45

heads and tails, including heads on

1:07:47

every toss, tails on

1:07:50

every toss, and everything in

1:07:52

between. And I can even tell you what the

1:07:54

probabilities of those outcomes are.

1:07:56

You know, it's one on two to the end

1:07:58

for end trials for each

1:08:00

exact sequence. But

1:08:02

it seems you can't say that

1:08:04

if you're a frequentist because

1:08:06

if the coin lands heads every

1:08:08

time, then that's probability one according to

1:08:10

frequentism. So there are various problems. We we

1:08:12

talked about the the problem of the single

1:08:15

case -- Yeah. -- earlier. there's

1:08:17

the problem of the double case. If I

1:08:19

toss a coin twice, then I can only have probabilities

1:08:22

of zero half

1:08:25

And one, off hand, I would have thought there could be other biases. And

1:08:27

as I like to

1:08:30

point out, it turns

1:08:32

out that

1:08:34

you cannot toss a fair coin

1:08:36

an odd number of times

1:08:39

according to frequentism, at

1:08:41

least this actual frequentism. because just

1:08:43

by definition according to them, if it's

1:08:45

an odd number of times, you can't

1:08:47

have exactly a

1:08:50

ratio of half of heads. Yeah. That

1:08:52

just doesn't seem – it seems pretty

1:08:54

weird. That seems pretty, pretty weird.

1:08:57

You'll also have I guess, a version of the the

1:09:00

gambler's fallacy. Suppose you

1:09:02

somehow know that

1:09:03

the

1:09:04

chance of heads is

1:09:06

a half of this coin and you

1:09:09

start tossing the coin and you

1:09:11

see a surprisingly long run

1:09:13

of heads as could happen. Yeah.

1:09:15

But if you know that somehow God tells you that

1:09:17

the chance of heads is a half,

1:09:20

you know that tails must be coming.

1:09:22

Oh, right. because they've got to make

1:09:24

up the run of

1:09:26

heads that's happened so far. Again, that was -- Yeah. -- actual frequentism. Now let's go

1:09:28

to the other kind,

1:09:31

the hypothetical frequentism. Yeah. But

1:09:35

now we have some counterfactual. This is not what actually happens. If

1:09:37

you were to toss the coin some large

1:09:39

number of times, maybe

1:09:42

infinitely many times, this

1:09:43

is what would happen. I think

1:09:45

for that, this is a

1:09:47

very weird counterfactual.

1:09:49

Imagine tossing an actual

1:09:51

coin like the

1:09:51

twenty cent coin in my pocket infinitely

1:09:54

many times. What would that even mean,

1:09:57

you know, that this coin would would

1:09:59

disintegrate before

1:09:59

then. So so we'd have to violate the

1:10:02

laws of nature so that

1:10:03

it would survive infinitely

1:10:06

long. I think it's very strange. I think there's a fact of

1:10:08

the matter of exactly how the the

1:10:10

queen would land in this infinite

1:10:14

sequence and even what it's frequencies

1:10:15

would be? Yeah. So you're trying to make this

1:10:17

like

1:10:17

very practical theory or that's just kind of a it's

1:10:20

virtue, but then it

1:10:22

seems to involve bizarre scenario that could never happen

1:10:24

to to back it up. Yeah.

1:10:26

Exactly. And I'll give actual frequentism

1:10:28

credit. At least, it was I

1:10:30

suppose practical anchored in the

1:10:33

world, gave you numbers that you

1:10:35

could ascertain. Yeah. Now when when the

1:10:36

problems start piling up and I gave

1:10:39

you a few of them, You start retreating

1:10:40

to this other version, the hypothetical frequencies, but

1:10:43

this seems to have other problems. It's

1:10:45

not practical. It's

1:10:48

not ascertainable. I

1:10:48

can't make sense of these counterfactuals. They seem

1:10:51

to be about the wrong thing about some idealized coin that would

1:10:53

never disintegrate and

1:10:55

what have you

1:10:56

what have you and

1:10:57

so put it all together and I

1:10:59

I frequentism is pretty bad. know there are lots

1:11:02

of frequentists out there read

1:11:05

my papers, the fifteen arguments against finite frequentism, finite fifteen arguments against

1:11:08

hypothetical -- Yeah. -- frequentism. I

1:11:10

I think it's in a bit of

1:11:12

trouble. Alright.

1:11:14

Well, we have to go upstairs because other people need the stage here. But,

1:11:17

yeah, we're gonna go chat about ways of

1:11:19

breaking expected value, counterfactuals, and why and

1:11:21

your your your many objections to

1:11:24

objective utilitarianism. But for now,

1:11:26

can everyone give random applause to to Alan? Thanks so much.

1:11:34

Alright. We're we're we're back in your

1:11:36

in your office, Alan. So I I was just

1:11:38

saying before we started recording that. In general,

1:11:40

I have a prejudice against doing interviews

1:11:43

in front of live audiences. because my my experience

1:11:45

listening to other other shows is that guests tend to kind of panned it to the crowd

1:11:47

a little bit, especially if they're talking about, like, charge issues. They

1:11:49

don't wanna have the courage to

1:11:51

say things of things wouldn't like. I

1:11:53

hope I didn't pander too much. No. No. I think Fortunately, we're we're mostly safe on this topic, except

1:11:55

perhaps for quizzes, although -- Right. -- you

1:11:58

probably have, like, sympathetic and unusually sympathetic

1:12:00

crowd. criticisms

1:12:02

or fruquintism. Hopefully, yes. Cool. But now

1:12:04

we can do the really hard hitting critical challenging

1:12:07

stuff. That was very good trouble. I'm

1:12:09

ready. Oh, okay. So before we came in

1:12:11

here, we were chatting about criticisms of fruquintism.

1:12:13

I guess one that you didn't bring

1:12:15

up, that jumps to mind for me. is

1:12:17

it it it seems like very odd that for Quenchism, it's saying like, okay, we've got like

1:12:19

one particular coin and we're saying

1:12:22

like, what is the

1:12:24

chance? that this coin is gonna land

1:12:26

heads or tails. It seems like it depends then on like all these other coins or like the same

1:12:28

coin and like

1:12:31

other points in time why

1:12:33

should the properties of this coin or, like, our knowledge of them,

1:12:35

like, depend on things far away in space and time.

1:12:37

It's very odd

1:12:39

in that respect. Yep. This radium

1:12:42

atom point to a particular atom -- Yeah. -- the case with probability a half

1:12:45

in sixteen

1:12:48

hundred years that seems to be an

1:12:50

intrinsic property of this atom. It seems

1:12:51

a little odd that its probability depends

1:12:53

on how all

1:12:56

these other atoms maybe very far away in space and

1:12:58

time happen to go decaying or not. Yeah. But I guess

1:13:00

the atom case sharpens it because with a

1:13:02

coin, you can flip it many times, but

1:13:04

each radium atom

1:13:06

can only decay once. That's it. And so you can imagine a scenario where what if there was there was only one radium or

1:13:08

like what if there was lots of

1:13:10

radium atoms and then you've got some frequency

1:13:14

then you, like, shrink it down such that now there's only one left. Yep. I

1:13:16

guess the fruquintis has to say now there's no

1:13:19

probability left anymore because there's just

1:13:21

one or zero. Yeah. Exactly. At that point, Yeah. It

1:13:23

seems very strange that probability depends on these

1:13:25

very extraneous facts. You'd think

1:13:28

it's just the the protagonist

1:13:30

is right here and now it's this Adam,

1:13:32

we're talking about -- Yeah. --

1:13:34

reminds me a bit of Hume's theory of causation about constant conjunction. And

1:13:38

take a paradigm case of causation like

1:13:40

I I put my hand

1:13:42

in a flame by accident and

1:13:46

I feel pain it seems somewhat odd to me to say,

1:13:48

well, what makes that causal claim

1:13:50

true is a fact about,

1:13:53

the you know,

1:13:54

these very disparate events across space and time, whether

1:13:56

putting hands in flames

1:13:58

were followed by

1:13:59

pains across space

1:14:02

and time? No. It seems like the protagonist Protagonist are

1:14:05

right here and now. Hey, listeners. Alan just

1:14:07

used the term constant conjunction. I

1:14:09

didn't know what that meant. But since that constant conjunction

1:14:11

is a relationship between two events where

1:14:14

one event is always invariably

1:14:16

followed by the other. So if

1:14:17

the occurrence of a is always

1:14:19

followed by b, and a and b are said

1:14:21

to be constantly conjoined. So in this case, I guess, you got the putting your hand in the

1:14:23

fire is always associated with

1:14:26

it with it being burned. And

1:14:28

I think cubes suggested that causation is just a

1:14:30

matter of constant conjunction. Okay. Back to the show. I see. So

1:14:32

so this is

1:14:34

an account of causality where

1:14:36

saying, the flame

1:14:38

causes the pain -- Yeah. -- if insufficiently, like, many cases or, like, hypothetical cases, the flame

1:14:41

and the

1:14:44

pain occur related really strongly. Yeah. Well So

1:14:46

saying, like, what does that got to do with it? Yeah. That's yeah. So who had a version of causation like that,

1:14:48

this account involving constant

1:14:50

conjunction? I think that frequentism

1:14:54

actual

1:14:54

frequentism, especially, is quite a lot like that.

1:14:56

Mhmm. And

1:14:57

I have the same reaction just

1:14:59

as you did that, look,

1:15:01

we should just be

1:15:03

staring at my poor hand and

1:15:05

the flame or the the radium atom, it seems odd

1:15:08

that its its chance

1:15:10

depends on

1:15:10

these maybe very distant

1:15:13

maybe very distant

1:15:14

facts and health, they they pan out. Yeah. Okay.

1:15:16

I guess causality is its own

1:15:19

With buddulamax. So that's a

1:15:21

big topic. Let's go back to probability.

1:15:23

Yeah. I think that's that's probably enough of fruquintas and people can go and check out

1:15:25

your your papers demolishing it. Yep. demolishing it, I

1:15:27

guess, thirty different ways and

1:15:29

maybe some extra my original paper was called thirty

1:15:32

arguments against fricotism. Mhmm. And I

1:15:34

I sent it in and I was

1:15:36

told it was it was a good

1:15:38

paper, but it was much too long. In fact, it twice as long as what could publish. So they

1:15:40

said that you need to

1:15:42

cut it. It was easy. fifteen

1:15:46

arguments against finite frequentism, fifteen arguments

1:15:48

against hypothetical frequentism -- Right. -- going to

1:15:51

okay. So if people people will often

1:15:53

cite both, you get double the citation. Absolutely.

1:15:55

Yeah. I should've got a mobile that's some more

1:15:58

I actually well, apparently, this was a big

1:16:00

problem in genetics. where you would have people

1:16:02

who were doing like whole genome studies and they decided to they they realized that they could that the studies of,

1:16:04

like, the effects

1:16:07

of different genes have break it,

1:16:09

like, in one paper for every chromosome. So they potentially get, like, thirty

1:16:11

different papers out of basically, like, exactly the same study. Yeah. That

1:16:15

that's how you you pump up your citation, your

1:16:17

various markers of

1:16:20

productivity. Yeah. Yeah. Okay. So what

1:16:22

you got from fruquintisum? I'm wondering

1:16:24

like Are there

1:16:26

other ways that, like, I could in practice start, like

1:16:28

reasoning differently? You know, start, like, in my daily life, thinking about the

1:16:30

probability of Boris Johnson being deposed in in different ways. I guess,

1:16:34

The adjustment that I'm, like, most familiar with with sync, we will make, is going from these points, estimates, probabilities to,

1:16:36

like, ranges and so on.

1:16:38

Yeah. Yeah. I'll I'll be glad

1:16:42

talk about that. That's right. Then you might say

1:16:45

this sharp

1:16:46

probabilism where you're

1:16:47

supposed to assign a

1:16:50

sharp real number is just psychologically

1:16:52

implausible. It's not something that we could do. Take

1:16:54

again the case of my probability of rain tomorrow. It's

1:16:57

not sharp to infinitely

1:16:59

many decimal places. what

1:17:02

do I say? What's the probability of

1:17:04

rain? Well,

1:17:05

it's zero point six

1:17:07

ish. It's in the region

1:17:09

of zero point six Now the

1:17:11

first move you might make is to say, well,

1:17:13

the probabilities should be intervals,

1:17:15

maybe point five to point seven

1:17:17

in my case. Yeah. But in

1:17:20

a way, that just makes the problem of

1:17:22

precision worse. So now you've got two precise numbers, the endpoints of the interval -- Right. -- point

1:17:25

50000

1:17:28

and point 70000 Yeah. That doesn't seem

1:17:30

to quite And that's the problem. Yeah. I suppose I suppose if

1:17:32

you wanted to defend it, you

1:17:35

would say, well, you've got two two numbers now

1:17:37

that you've chosen, but, like, they're not as important somehow. Yeah. Is that no.

1:17:39

Yeah. Not not look at convinced. Well, you you could say

1:17:41

that or or you could say

1:17:43

these probabilities get determined

1:17:46

by something else. Like, maybe there

1:17:48

are

1:17:48

the judgments that I make that I've

1:17:50

been frozen would say. Yes. And now

1:17:52

you just look at all of

1:17:54

the probability functions that

1:17:56

respect my judgments, and they

1:17:59

will form

1:17:59

a set, probably not just a

1:18:02

singleton set. but

1:18:03

the set itself will have some sharp boundaries and

1:18:05

it could well work out, but that

1:18:07

set has a boundary

1:18:09

point five and point seven and we we

1:18:11

represent my credence with in principle. Yeah.

1:18:14

And, yeah, I I may

1:18:16

not so easily access these

1:18:18

probabilities too. It may be unbadtered

1:18:20

in prospecting as Williamson would say, maybe my

1:18:22

credences are not luminous -- Right. -- to myself.

1:18:24

But I might

1:18:27

still have them and

1:18:28

they they might have these forms like intervals

1:18:30

or or sets. Yeah. So it gets something that's

1:18:35

appealing about saying, you know, the probability of raining camera tomorrow is between

1:18:37

point five and point seven on a in

1:18:39

a practical sense is that it

1:18:41

helps to indicate your level

1:18:44

of uncertainty to other people, whereas if you just say point

1:18:46

it's point six. Mhmm. Well, I mean, first of all, someone laughed at you because it sounds so precise. It

1:18:48

sounds like ridiculous to be to be so

1:18:50

sure. I mean, they're less like they're laughed

1:18:53

you if if you give a range. Yeah. I guess,

1:18:55

actually, it it does potentially indicate something technical, which is like how quickly you

1:18:58

would update your beliefs as

1:19:00

you get new information. If you have like a very wide range and

1:19:02

you're saying, well, a wide range of point estimates would be plausible and reasonable.

1:19:04

And so, you know, as I see the weather

1:19:06

report, I'm gonna, like, shift a lot. really

1:19:10

feel like it's also it's interesting. If you say it's like point six, in some sense, you're making a claim that you're like a hundred percent sure that it's point

1:19:12

six. And then you should say, well, I and you'll just

1:19:14

never change your mind about that even after it rains or

1:19:16

doesn't. I'm

1:19:19

not sure committed to that. I think it's okay.

1:19:22

You've got the point six

1:19:25

credence initially and then you conditionalize, as we

1:19:27

say, you update that, as the evidence comes in, like,

1:19:30

like, maybe you see the

1:19:31

rain for example. So, yeah,

1:19:33

that becomes a new

1:19:35

sharp value of one,

1:19:37

that's that's okay. But I guess it would be a

1:19:39

misunderstanding to

1:19:39

interpret someone who's saying the probability

1:19:42

of it raining in camera tomorrow

1:19:44

is sixty

1:19:46

percent with one hundred percent probability. That's like not

1:19:49

what's being claimed. Yeah. Well, that brings

1:19:51

us to another

1:19:52

issue with another

1:19:54

choice point, by the way, for varieties of

1:19:57

bayesianism, whether you allow

1:19:59

higher order

1:19:59

probabilities, do you have, for example,

1:20:02

credences of credence probabilities or probabilities in

1:20:04

general. And you could say no, that

1:20:05

doesn't make sense or that maybe they

1:20:08

collapse down to

1:20:10

just the first order probabilities

1:20:12

But you could say, no, I

1:20:14

have probabilities about various ways the world could be, including

1:20:18

what

1:20:18

my credence is r. Yeah.

1:20:20

Because that's part of the world. Why not have

1:20:22

intermediate credences for that too? Alright.

1:20:23

So maybe the thing that it feels

1:20:25

more like you're doing when

1:20:27

you introspect and try to, like, give

1:20:29

these ranges to actual questions. Is your inspect you're like you you pull like in

1:20:31

different numbers in your mind and then

1:20:34

see how much the mind

1:20:36

revolves at that number. So if you say,

1:20:38

like, the probability of rain tomorrow is one percent, then you're, like, no, that's, like, that's too crazy. And then you,

1:20:40

like, kind of, have a,

1:20:42

like, level of, like, craziness all

1:20:45

of these different numbers. And then that gives you some

1:20:47

sort of distribution like, numbers plausible. of what you think you ought to

1:20:49

believe, that's kind of maybe what you're measuring.

1:20:51

Yeah. And maybe we

1:20:55

could

1:20:55

compare your credences to say Lotteries. What do

1:20:57

you think is more probable? Rain

1:20:59

tomorrow or I, you

1:21:01

know, say, a hundred

1:21:04

ticket lottery tickets

1:21:04

one to sixty. One of

1:21:06

those is the winner. Yeah, it feels

1:21:09

maybe slightly higher

1:21:09

than that, but now I

1:21:12

make it one

1:21:14

to seventy or maybe slightly lower than that

1:21:16

and maybe I can somehow hone in

1:21:19

on what my probability is. That's a

1:21:21

way of a listing -- Yeah. --

1:21:23

means from myself. Yeah. Okay. So, yeah, a

1:21:25

philosopher's working on any adjustments to how we do these things that could

1:21:27

possibly affect how I reason about uncertain events,

1:21:29

like on a day to day basis,

1:21:31

that might like actually

1:21:34

help me live better. Starting I suppose with the imprecise credences, okay, maybe it's too much

1:21:36

to ask of you

1:21:38

to have the sharp probabilities

1:21:43

and update by conditionalizing all the time. But this

1:21:45

was meant to be a

1:21:47

friendly amendment. Jeffrey calls

1:21:49

it bayesianism with a

1:21:52

human face. And

1:21:53

it seems more psychologically plausible that you've got these

1:21:55

ranges of probabilities, you know, intervals

1:21:56

or sets. So that's

1:21:59

one kind of

1:22:00

humanizing. guess

1:22:02

so so you were saying but but you objected to that or you

1:22:05

offered the objection that well, now you've just chosen

1:22:07

two numbers. You've made it, like, you now

1:22:09

you've got double double the problem. Yeah. Is is that a

1:22:11

good objection interview? Well, I I think I think it has to be taken

1:22:13

seriously, but but now maybe things

1:22:15

start getting worse. 0II

1:22:17

don't want to have this

1:22:19

exact sharp interval from

1:22:21

point five to point seven in

1:22:23

my example. Maybe what I should have is

1:22:26

a

1:22:26

probability distribution over numbers that's not smooth.

1:22:28

It's smooth and

1:22:30

maybe it hits a peak somewhere in the middle near point six and it tapers off towards the edges and

1:22:32

maybe doesn't just stop it sharply

1:22:34

at point five and point seven.

1:22:39

but now we just raise the problem again. So, really,

1:22:41

I've got this sharp exactly

1:22:43

that sharp probability function over the

1:22:45

-- Yeah. -- range of values.

1:22:47

Usually, you're on you're unsure about the

1:22:49

value of the probability that you should give to each probability. And so -- Yeah. -- and and we have

1:22:51

us -- Okay. -- uncertainty all all the

1:22:54

way up. That's right or all the way

1:22:56

down. And

1:22:58

then one reply might be, well, look,

1:23:01

we're

1:23:01

just representing things. We're

1:23:03

providing models. So don't reify

1:23:05

this so much. Don't take this all literally that

1:23:07

this has to be in your head. But

1:23:09

these models, you know, with

1:23:11

various levels of sophistication,

1:23:13

may better or

1:23:15

worse represent what things

1:23:16

in what Going any My brain

1:23:18

is doing some Right. Right. Right. Hey, listeners. Rob here with another definition. We just

1:23:20

use

1:23:23

the term Raytheying something or ratification is

1:23:25

the mistake of imagining or representing that something

1:23:28

that is

1:23:30

really just an abstraction. making the mistake of thinking that it's material

1:23:32

or concrete thing that's that's actually real,

1:23:34

where that isn't. I mean, so

1:23:38

inflow recursion actually not always a problem. Right? You could just say, well, there is just uncertainty

1:23:40

distributions all the way up. Yeah.

1:23:42

Right. And maybe that's actually fine.

1:23:46

And it like caches out. And I suppose you could, in fact,

1:23:48

represent those uncertainties, like, as far as

1:23:50

you like. And so they they could all

1:23:52

cash out to this point estimate. if you like, you

1:23:54

can go one level up and represent uncertainty there, and you can go another one. Yep. At some point, it doesn't feel like it's adding value to you to

1:23:56

do it any further. Yeah. If it

1:23:59

if it does point first, maybe

1:24:02

things stop at a fixed point or

1:24:05

maybe you get a bit more

1:24:07

information at each level you

1:24:09

go back. This is another of the heuristics, by

1:24:11

the way, you asked for

1:24:13

some more infinite regresses, a

1:24:16

technique often used. And often

1:24:18

infinite

1:24:18

regress is thought to be a bad thing and it's a fatal problem for a view if faces such

1:24:21

a regress. But

1:24:24

that's not always

1:24:26

clear, some some notions

1:24:28

seem to be well understood in

1:24:30

terms of infinite hierarchies like that.

1:24:32

Lewis' notion of convention is

1:24:34

like that in in terms

1:24:36

of common knowledge or common belief, which is

1:24:38

a recursive thing

1:24:39

about knowing of each other. what

1:24:43

they believe and so on for higher orders. And we don't

1:24:45

just say, well, that can't be right because we

1:24:47

have an infinite regress. I

1:24:50

mean, especially if the

1:24:51

if the regress converges on something where it's just like it just

1:24:53

becomes the same every time you're just like forever. Oh,

1:24:55

the fixed point. Okay. That's right. And then you

1:24:57

argued it's like, well, that's just fine. Yeah.

1:24:59

That's right. Yeah. Yeah. Okay. Interesting. Yeah. Okay. So

1:25:01

we've got these, like what are these calling the the range of probabilities? What's the term for that?

1:25:03

Yeah. Well, sometimes

1:25:07

more distribution on the probability? So

1:25:09

sometimes we call it the the presenter. Okay. Representative is the set of

1:25:12

probability functions. that

1:25:15

represent your grievances, and they're meant

1:25:17

to be

1:25:18

all of the

1:25:19

precipifications of

1:25:23

your imprecise. credence, but that are faithful to it, but then

1:25:25

fill in in all of the precise ways.

1:25:27

Yeah. So this really does feel

1:25:29

like a friendly amendment to me. I feel

1:25:31

like -- Yeah. -- this is kinda it's the same spirit, and we're just gonna, like, get a little bit

1:25:33

better or, like, represent high levels of uncertainty. All

1:25:35

good. That that's right. And and

1:25:37

again, this takes me back to

1:25:39

earlier when I was saying that I'm

1:25:41

Amazon on Mondays, Wednesdays, Friday and so on. Look, so many things deserve the

1:25:43

name, Amazon,

1:25:44

and

1:25:48

I I shouldn't really say that I've

1:25:50

jumped ship on on Tuesdays and today, Saturday just because I

1:25:52

I make certain choices in

1:25:54

that tree of choice points. Yeah.

1:25:57

Yeah. Yeah. It makes sense. Are

1:25:59

there any more radical departures? Oh, I suppose, are there people who are

1:25:59

probability nihilists? yes,

1:26:05

I suppose you could say that all there is is

1:26:07

just these all or nothing states for start when

1:26:10

it comes to credences, beliefs, as

1:26:12

we might say. Look,

1:26:13

there's I mean, some of the kind of

1:26:15

people

1:26:15

who who are just

1:26:17

like, look, there is what is actual

1:26:19

probability else probability zero. Yep. And that's kind of all that there is

1:26:22

to say about probability. And and you should believe the thing

1:26:24

that will happen, another thing that is true.

1:26:26

Yeah. You shouldn't believe the thing that is

1:26:28

false. and that's kind

1:26:30

of the end of the story. And that

1:26:32

just shows you that objective norms are sometimes tough to

1:26:34

live up to. Yeah. Right. Not not easy.

1:26:37

your your ought to be amnescient. So -- Yeah. -- it's

1:26:39

it's tough to be amnescient, but so that that's not the fault of the

1:26:41

norm. It just says the the norm

1:26:43

is is hard to to

1:26:47

to live up to. Well, that

1:26:48

does seem a little extreme, I

1:26:50

guess. It's certainly not

1:26:52

it's it's it's unhelpful even

1:26:54

if it's it's not giving you good advice, for example. Okay.

1:26:56

So that is quite a lot on

1:26:58

probability. I guess, let's move down the

1:27:00

track now to, I guess, an application

1:27:03

of probability estimates, which is expected

1:27:05

value. Yeah. We've got a whole cluster of questions around that. I guess to start

1:27:07

though, what is expected value? It's it's it's I turned that we throw around a

1:27:09

lot, but I think it's actually like

1:27:11

basically not used among

1:27:14

the general how I was like, it it is actually

1:27:16

quite technical in a way. Yeah. That's right.

1:27:18

And they'll quickly turn into a discussion

1:27:21

of expected utility. But Mhmm. Alright. It comes

1:27:23

up to especially in decision theory,

1:27:26

expected utility theory. And

1:27:28

you

1:27:28

have a choice among certain

1:27:30

options. What should you do?

1:27:33

And

1:27:33

let's assume that the world could be in various ways. They're very states of

1:27:35

the world, and you don't have control of of

1:27:37

what they are, but you

1:27:39

assign probabilities to the

1:27:42

various states. Yeah. And the

1:27:44

combination of a particular

1:27:46

action of yours and the

1:27:48

state of the world together

1:27:50

that

1:27:51

determines an outcome and you can value

1:27:53

the outcomes more or less. Yeah. And we

1:27:55

could put numbers, which measure

1:27:57

how much you

1:28:00

value Now

1:28:00

the expected value is a

1:28:01

weighted average of these values where the

1:28:04

weights are

1:28:06

the probabilities. So that turns out to be a

1:28:09

sum of products. You

1:28:11

take probability multiplied by

1:28:14

the value and add across all

1:28:16

of the states. And that weighted

1:28:18

average

1:28:18

is the expected value. And

1:28:22

now think of that as like a figure of merit.

1:28:24

That's how choice worthy

1:28:25

each of your actions. Hey,

1:28:28

listen. One quick definition.

1:28:30

Choice

1:28:30

worthy knows. is this philosophy jargon term where choiceworthiness

1:28:32

corresponds to the strength of the

1:28:34

reasons for choosing a given option.

1:28:37

How good choices is

1:28:39

this for us? Okay. back to the show. She

1:28:41

was Trust where he was another one of these. So he said no

1:28:43

no no no no more non philosophy. But would that That's

1:28:46

exactly where I've been. Yeah.

1:28:49

And and now you should

1:28:51

maximize that quantity, do whatever action or actions because

1:28:53

maybe

1:28:54

it's not one. We'll

1:28:56

they will yield

1:28:58

the highest value along that score. Cool. So I I guess, like yeah. To to make that concrete

1:29:00

really

1:29:01

simple, if you

1:29:03

had a bat where

1:29:06

you got like one dollar if coin heads, comes it's fair

1:29:09

coin, then the

1:29:12

expected value I

1:29:14

guess, in dollars in this case is one dollar and

1:29:16

a half or 111 dollar fifty. That's right.

1:29:18

And of course, so normally, we'd we'd rather talk

1:29:20

about utility or well-being or something because we don't value

1:29:23

dollars the same as as as especially as the amounts become larger or maybe you

1:29:25

don't value dollars at all. So utility is the

1:29:27

thing where it ultimately caches out. That

1:29:29