Paradoxes That Break Your Brain

Truth should be simple, until you try saying “This statement is false” out loud and your brain ties itself in knots. We sit down as a dad and daughter duo to explore paradoxes that have haunted philosophy, logic, maths, and science for centuries, and we do it in the most honest way possible: by admitting when we’re confused, laughing at the wording, and trying again until something clicks.

We start with what a paradox is and why so many of them are really about language, definitions, and self-reference. That takes us straight into the liar paradox, then into Zeno’s Achilles and the tortoise, where infinity behaves in ways our intuition simply was not built for. From there we get stuck into identity with the Ship of Theseus, asking whether something stays the same when every part gets replaced, and we bring it down to earth with a band analogy that makes the problem feel uncomfortably real.

Then we hit the big hitters: Russell’s paradox, the barber paradox, and Schrödinger’s cat, where quantum mechanics turns “observation” into a serious question about reality and measurement. We jump into time travel with the grandfather paradox and the bootstrap paradox, pulling apart causality and origin, before ending on Karl Popper’s paradox of tolerance and what it means for free speech, hate speech, and living in a society where boundaries protect the very idea of tolerance.

If you like philosophy podcasts, critical thinking, and debates that stay respectful while still going deep, press play. Subscribe, share Bonus Dad, Bonus Daughter with someone who loves a good brain teaser, and leave us a review with your favourite paradox.

Transcript

Intro Banter And Soundboard Bits

SPEAKER_01 0:00

Hello and welcome to Bonus Dad.

SPEAKER_05 0:02

Bonus Daughter, a special father-daughter podcast with me, Hannah.

SPEAKER_01 0:05

And me, Davy, where we discuss our differences, similarities. Share a few laughs and stories. Within our ever-changing and complex world.

SPEAKER_05 0:13

Each week we will discuss a topic from our own point of view. And influences throughout the decades.

SPEAKER_01 0:18

Or you could choose one by contacting us.

SPEAKER_05 0:20

Via email, Instagram, Facebook, or TikTok. Links in bio. Hello and welcome to a very special podcast episode. Why do you keep laughing at the word special?

SPEAKER_01 0:30

Because it's like it is a special episode, of course it is.

SPEAKER_05 0:33

Every episode is special.

SPEAKER_01 0:35

I know, but it doesn't work.

SPEAKER_05 0:36

And then when I don't say it, you make a comment. If I say it, you laugh. I can't win.

SPEAKER_01 0:40

But the thing is That's the paradox in itself. It is, it is. But the the funny thing is, is about the like every single episode, it always starts the same because we have the five second silence beforehand and then the clapper board. And I can just every the start, I can just see your eyes, your little eyes just kind of looking at the timer, and then the clapperboard they go, and it's welcome to a very special episode.

SPEAKER_05 1:02

You know what? You start doing the intro, huh?

unknown 1:04

Huh?

SPEAKER_05 1:06

You F it up every time. Uh we're gonna be talking about paradoxes today.

SPEAKER_01 1:11

Yeah, this was another one of your ideas.

SPEAKER_05 1:13

Was it?

SPEAKER_03 1:14

It was I have removed that from my brain.

SPEAKER_04 1:25

Yeah, I I I that goes on for a while.

unknown 1:33

Okay.

SPEAKER_05 1:34

Every time we do uh a noise board thing, you don't have to play them all.

SPEAKER_01 1:37

Oh sorry, okay.

SPEAKER_05 1:40

John Cena. Every time I hear that one, I think of John Cena.

SPEAKER_01 1:48

Yeah.

SPEAKER_05 1:49

You can't see me.

SPEAKER_01 1:51

Do you know what that reminds me of now?

SPEAKER_05 1:53

No.

SPEAKER_01 1:54

Good evening! This is Gaber of the Duck!

SPEAKER_05 1:59

How many times did you have to record that?

SPEAKER_01 2:01

You have no idea how many times I have had to I I've listened to those and and redone them last, yeah.

SPEAKER_05 2:08

I still think John Cena is funny.

SPEAKER_01 2:09

Yeah.

SPEAKER_05 2:11

Anyway.

SPEAKER_01 2:13

Anywho. Anywho. Anywho. So moving swiftly on. Yes. So this was one of your ideas.

SPEAKER_05 2:18

Apparently so.

SPEAKER_01 2:19

Yes. And you've you're actually uh oh, you got you got it up on the screen. I can see your little tab on there, so I can see you're looking at the same document as me. Yes.

SPEAKER_05 2:26

I love it when you see someone else in there. Have you uh I don't know, do you use Google Docs at work at all?

SPEAKER_01 2:31

No, we well we use we obviously we use Microsoft 365, but 365, but what we we do share a lot of documents and people do work on them at the same time. So it's funny when you see like has this workbook uh open and they're on sell so and so. So sometimes I do sit there and go, what are they doing? Especially if it's a document that I've written and I see someone in there and they're doing things because actually, this is one point. When do you do you have people put comments on there or rewrite the document?

SPEAKER_05 2:58

Yeah, that's the kind of point of what I do for work. Yeah, I know, but do people rewrite your document or do you have comment boxes where somebody will say a comment saying um So on Google Docs you can do edit, you can give them editing uh rights so they can just full edit it, or you give them suggestion so they basically you can see the changes they've made to the crossing out part and track changes, basically, what you get in word. What I was gonna say about Google Docs is if someone's in there but they don't have a Google account, they can still access it through the link, it will come up with anonymous and then a random animal. So you will just get anonymous badger looking at this document or anonymous Ardvark. And there's not a really obscure, like there'll be like I don't know, I can't think of an obscure. Yeah, like uh anonymous axolot or something, like, and you're like, what the hell? Like it just comes up with this like anonymous beaver, and I just it just makes me laugh every time. Whatever animal that it's selected, it just makes me chuckle. I know, but it makes me laugh every time like anonymous octopus, like it's just so funny to me. Um, it's like when um have you seen Last One Laughing now? Yes, yeah, it's like when Bob Mortimer calls the seagull Ruth, it absolutely got me.

SPEAKER_01 4:09

He was just like this is my cheeses, always pleases.

SPEAKER_05 4:12

This is my seagull, Ruth. Oh god, just just so got me because I was trying not to laugh. Mitchell and I tried not to laugh through his whole joke around and um and and Ruth got me. He he went before I did, but uh Ruth I went the same time as um uh Diane Oh Diane Morgan Philomena Kunk.

SPEAKER_01 4:31

Yeah, Philomena Kunk.

SPEAKER_05 4:32

I love uh honestly have you watched all the conk on earth, conk friends?

SPEAKER_01 4:36

I love the conk on earth it's good. So um it says here that King Arthur came a lot. Did he? So so uh uh yeah, somebody who I know is actually one of the guests on on there. Oh no way, yeah, is a professor. Do they have are they told not to they know, and he he's he said it's so hard.

SPEAKER_05 5:00

Yeah, because he's funny.

SPEAKER_01 5:01

Literally so because it's a lot of it is improv.

SPEAKER_05 5:03

Because they have to be so serious, it's like well, and you can see some some of them are like trying to hide their smile, yeah, um, and coming up with something, but yeah, I bet that's really difficult as the expert on there. Yeah, yeah.

SPEAKER_01 5:14

Yeah. Was it the same as the normal man? About about the same as teaspoon? Yeah, she's great. Anyway, paradoxes.

What A Paradox Really Means

SPEAKER_01 5:24

Paradoxes. So I've written, so I take it away. I haven't written them, obviously, because they are real paradoxes. So I have I have uh Googled 10 paradoxes and we're going to discuss them.

SPEAKER_05 5:36

Let's go. What is a paradox?

SPEAKER_01 5:38

Oh it is paradox difficult. It's it's I don't know how to explain that.

SPEAKER_05 5:45

I'm surprised you didn't Google that first.

SPEAKER_01 5:46

Yeah, I they're kind of you could argue they're brain teasers. Yeah, they're like something that you try and work out. It's a statement that you try and work out in your head, but it's you can't work it out. Yeah. And they're and we there are actually a lot of what's the words, kind of like physics, maths, and mathematicians, and a lot of experts have actually tried to figure some of these paradoxes out. Um, but some of them you just can't. But they do base, they are based in a lot of a lot of way with the way that we think about it.

SPEAKER_05 6:12

Oh, I think a lot of them are semantics. Yes. Yeah.

SPEAKER_01 6:16

Yeah, yeah. It's and a lot of it is is wording as well. So let's take the first one, which is from so the origin of this one, we believe it's an ancient Greek paradox.

SPEAKER_05 6:27

Would you like to know the definition of a paradox? Go on, give it the actual property A paradox is a statement, proposition, or situation that seems self-con contradictory, illogical or absurd, but upon closer inspection may reveal a deep truth or a hidden complexity.

SPEAKER_01 6:43

There you go. I like that.

SPEAKER_05 6:44

That was a really nice way of describing it. Thank you, Google.

SPEAKER_01 6:47

I like that dictionary.

SPEAKER_05 6:48

Oxford language dictionary, actually.

SPEAKER_01 6:50

Collins. Uh Collins Oxford Language Dictionary.

SPEAKER_05 6:54

It just says Oxford. I don't know about the Collins part. I think Collins is the publisher of the dictionary. So Oxford do the dictionary. Yeah.

SPEAKER_01 7:01

Collins is the publisher. I believe.

SPEAKER_05 7:04

Like Bloomsbury.

SPEAKER_01 7:06

Oh, like Bloomsbury. Who publishes the Harry Potter books? Yes.

SPEAKER_05 7:09

And Avatar.

SPEAKER_01 7:10

Oh.

SPEAKER_05 7:10

And Penguin books, and they publish everything.

SPEAKER_01 7:12

Yeah, they do. They do. You can self-publish a lot of stuff now, can't you?

SPEAKER_05 7:16

Are you going to publish your book? We're not talking about that on this podcast.

SPEAKER_01 7:19

Oh, right, okay. Not yet. Alright, okay.

SPEAKER_05 7:21

It's under wraps.

SPEAKER_01 7:22

Oh, alright, okay.

SPEAKER_05 7:23

Tie a bow on that.

SPEAKER_01 7:24

Alright, we'll move that one. Sorry.

SPEAKER_05 7:25

Under the bed.

SPEAKER_01 7:26

Okay.

SPEAKER_05 7:26

In the loft, in the attic.

SPEAKER_01 7:28

Like monsters with with the monsters. Scary monsters. It's coming. Creeps. So is Christmas. Um the firstly before Christmas.

The Liar Paradox And Truth

SPEAKER_01 7:36

So the first paradox is called the liar paradox.

SPEAKER_05 7:40

Liar, liar, parents are fine.

SPEAKER_01 7:42

This comes from ancient Greece, uh, and offered often attributed to a guy called Epimendes, I believe. Is it you're you're quite up on Greek philosophers. Epimendes. Epimendes. Yep. Um, so the the statement, the paradox itself is very small. It's only four four words, and it is this statement is false. That's the paradox. So the problem with this particular statement is if it's true, then it must be false. But if it's false, it must be a true statement.

SPEAKER_02 8:13

Oh man.

SPEAKER_01 8:14

Yeah. So essentially that's problematic. So essentially, you're stuck in a loop of trying to work it out. So Bertrand Russell.

SPEAKER_02 8:24

Ah.

SPEAKER_01 8:25

Yes, I know Bertrand Russell. He tried to eliminate the self self-reference using a type thing called type theory, basically saying that statements can't talk about themselves directly.

SPEAKER_02 8:37

Yeah, that makes a lot of sense.

SPEAKER_01 8:38

Is that is that the kind of what he said came came up with? And then Alfred Tarski introduced the hierarchies of language that a statement can only be judged true from a higher level system, similar to what Bertrand's saying.

SPEAKER_03 8:50

Okay.

SPEAKER_01 8:50

Yeah. So what it really means is he's saying is that truth isn't as simple as true or false.

SPEAKER_05 8:56

Mm-hmm. Yeah.

SPEAKER_01 8:57

Which we know that anyway.

SPEAKER_05 8:59

Uh that would have been my point, actually. Um, because uh uh you can believe something to be true, yeah, but it actually could be false. It's your own truth.

SPEAKER_00 9:10

Yeah.

SPEAKER_05 9:11

Which comes into this because truth truth isn't true or false because the truth mo your truth might not be the truth.

SPEAKER_01 9:18

Exactly. What is truth? Because it's all about perception versus perspective as well. Yes. Yeah, that that comes into it. And do you know something? I I and again, I'm not saying that I'm a scientist in any way, shape, or form, but I'm I'm quite happy to say things to put my hand up and say I'm wrong about something. I heard something the other day, and it made me change my perspective on something that I knew to be true.

SPEAKER_06 9:46

Right.

SPEAKER_01 9:46

Okay. So this is also in one of the tales, I reference it in one of the tales.

SPEAKER_06 9:51

Okay.

SPEAKER_01 9:51

And in the Morning Star one, saying about the difference between ideas and beliefs, and the fact that I prefer ideas because you can change an idea, but you can't change a belief. Yeah, which is well my whole uh thing about religion. I heard somebody come up from a from a different perspective the other day, and I was like, actually, that makes sense.

SPEAKER_03 10:13

Go on.

SPEAKER_01 10:14

Right. Difference between belief and knowing. You know something to be true, you know it, but if you believe something to be true, there's still an element of doubt.

SPEAKER_04 10:24

Doubt, yeah.

SPEAKER_01 10:25

And that kind of I I listened to this the other day and I was like, actually, yeah. So that's going one step further. So you've got so now I see it as a three-tiered thing.

SPEAKER_05 10:34

Oh, okay.

SPEAKER_01 10:35

As three-tiered. So ideas, beliefs, knowing.

SPEAKER_05 10:40

Yeah. I guess knowing could also be false if you are.

SPEAKER_01 10:44

Well, no, if you know, if you definitely, definitely know, but that's if you're sure that you definitely know. Well you can't.

SPEAKER_05 10:52

Can you be a hundred percent certain that I am Hannah, your daughter sitting right here?

SPEAKER_01 10:56

Yeah. Well.

SPEAKER_05 10:58

I could be a mirage.

SPEAKER_01 10:59

You could be a figment of my imagination. In fact, I could have been doing this entire podcast by myself, yeah, and everyone's only hearing a one-sided conversation, and you are actually a figment of my imagination.

SPEAKER_05 11:08

You are the main character.

SPEAKER_01 11:10

Main character energy.

SPEAKER_05 11:11

Main character energy.

SPEAKER_01 11:12

Yeah. So there you are.

SPEAKER_05 11:15

Nice.

SPEAKER_01 11:15

Yeah. So I like that now. I've got another three-tiered approach. Idea, belief, knowing.

SPEAKER_05 11:20

Nice. You learnt from your mind.

SPEAKER_01 11:22

Yeah. There you are. Um, so yes. Uh so what has is that messed with your head?

SPEAKER_05 11:28

A little.

SPEAKER_01 11:28

A little.

SPEAKER_05 11:29

But yeah, I I think I don't think a statement can talk about itself. I agree with Bertrand Russell.

SPEAKER_01 11:33

Yeah. Do you need the the well on one of my bios, honestly? It said 99% of the statistics are made up.

SPEAKER_03 11:40

Yeah.

SPEAKER_04 11:42

Yeah. Okay.

SPEAKER_01 11:44

Next one. Okay.

Achilles And The Tortoise Confusion

SPEAKER_01 11:46

So this is Achilles and the Tortoise.

SPEAKER_05 11:49

Achilles.

SPEAKER_01 11:50

Yes. So this one I I still can't quite get my head around this.

SPEAKER_05 11:53

Okay.

SPEAKER_01 11:54

What it means. So the origin of this one is uh from 5th century BCE, so 500 years before the birth of uh Jesus Christ.

SPEAKER_05 12:04

Jesus.

SPEAKER_01 12:04

Jesus. Uh, and the statement is a faster runner can never overtake a slower one because they must first reach where the slower one was.

SPEAKER_05 12:14

Hold on.

SPEAKER_01 12:14

Exactly.

SPEAKER_05 12:15

I might need to reread that.

SPEAKER_01 12:16

I can't get my head around this.

SPEAKER_05 12:18

A faster runner can never overtake a slower one because they must first reach where the slower one was.

SPEAKER_01 12:27

Yeah. So basically, to overtake the tortoise, Achilles must first reach where the tortoise was, but by then the tortoise has moved slightly ahead.

SPEAKER_05 12:37

Lapping the tortoise?

SPEAKER_01 12:38

And this so that will then repeat infinitely. It splits motion into infinitely many steps. And the calculus tried to res try to resume it. So that the infinite steps can still sum up to a finite distance. And that was developed by Isaac Newton and Wilhelm Leibniz. But I can't get my head round it.

SPEAKER_05 12:58

But that suggests that Achilles started after the tortoise.

SPEAKER_01 13:03

No, a faster runner can never overtake a slower one because for because they must first reach where the slower one was. Again, this is a maths problem, which is why I can't I can't comprehend this.

SPEAKER_05 13:12

I can't comprehend this at all. I'm gonna stick up my hand and say I don't understand.

SPEAKER_01 13:16

Yeah.

SPEAKER_05 13:17

I don't understand what the problem is.

SPEAKER_01 13:19

I nearly even took this I I know I nearly even took this out because I don't get it.

SPEAKER_05 13:24

Infinity behaves in ways our intuition isn't built for. It's forced humanity to invent calculus.

SPEAKER_00 13:29

Yeah.

SPEAKER_05 13:30

I I I I think I would need something visual for this one.

SPEAKER_00 13:33

Yeah.

SPEAKER_05 13:34

A faster runner can never overtake a slower one because they must first reach where the slower one was.

SPEAKER_01 13:42

Yes. So essentially every time it cat it the talks talks, but they go, I I can't get my head on it.

SPEAKER_05 13:48

In a race, they start on the same line, right?

SPEAKER_01 13:50

Yeah.

SPEAKER_05 13:51

They're like this. Linear. Let's go with linear.

SPEAKER_00 13:54

Yeah.

SPEAKER_05 13:54

Which I don't think this was what this paradox means. So I guess I guess what they're saying is no, it never overtakes. It's already past.

SPEAKER_01 14:03

I don't know.

SPEAKER_05 14:04

Because if you think, if they if they both start the same line, I feel really dense right now. He doesn't need well, he doesn't need to overtake. If you look at the f the start line, that technically overtake is wrong because he's not overtaking, they started the same and he's faster. So yeah, it's right. I get it now. Now I've used my hands. Right. Let me let me explain. Let me explain. I think for the video watching. Sorry, sorry. I think this is what they're saying. So if you think Achilles and a tortoise are on the on the start line of a race, the gun goes off, they both start, and Achilles obviously pulls ahead because he's a man, uh, fast man, presumably. There is no overtake because they're at the same.

SPEAKER_00 14:47

Okay.

SPEAKER_05 14:47

They started, he it's not like he's lapped him and then overtaken him. Yeah. They started at the same and fall forward. So yeah, he can never overtake him because this line is always moving.

SPEAKER_00 14:58

Yeah. Okay.

SPEAKER_05 14:59

I do get it. I do I think I needed my hands to represent the start. Well done.

SPEAKER_01 15:05

Well done for working that one out.

SPEAKER_05 15:06

Yeah, I think I think that's what it means. Yeah, you can't he's not over. I think again, it's semantics, is the word overtake. He's not overtaking him, they're starting at the same point.

SPEAKER_00 15:14

Yeah.

SPEAKER_05 15:15

But then, yeah, if he overtakes, that start point is moving. If he was still lap. I think.

SPEAKER_01 15:21

Okay. So the next one is also a Greek uh philosophy.

Ship Of Theseus And Identity

SPEAKER_05 15:26

All the Greeks.

SPEAKER_01 15:27

And this is what why I said stick a pin in what we were saying in shower thoughts. Stick a pin in it.

SPEAKER_05 15:32

Ship of thesis.

SPEAKER_01 15:33

If all parts of a ship are replaced over time, is it still the same ship? So this has been debated in metaphysics and identity theory, and modern versions appear in the philosophy of the mind. It's basically saying what what defines identity? Is it continuity, material, or something else? Now you could even argue that you yourself as you are now are not the same person that you were when, say, 20 years ago, because your body regenerates constantly over time, apart from your teeth. Cells die and reborn.

SPEAKER_05 16:10

So I I have thoughts on this.

SPEAKER_01 16:13

Okay.

SPEAKER_05 16:13

And it's right. It's about not my my not my theory is right, but when he says that it's about the identity, continuity material or something else. Yeah. Continuity, sorry. I think it's the realm of something else. Because as you're replacing parts of that ship over time, those say the first plank of wood you replaced, as opposed to the last plank of wood, maybe 10 years have passed.

SPEAKER_00 16:38

Yeah.

SPEAKER_05 16:39

When that bit of wood, that first bit of wood was put into the ship with the identity of that ship, call it HMS Hannah. Bonus dad, bonus daughter.

SPEAKER_01 16:48

Okay.

SPEAKER_05 16:49

HMS B D B D, that has been part of the ship known as bonus dad, bonus daughter or HMS B D B D, right? So by the time you get round to doing that last plank, that's already had the identity of the ship. And therefore, just putting in that last plank, the identity still continues throughout.

SPEAKER_01 17:08

I'm gonna throw one in.

SPEAKER_05 17:10

Go ahead.

SPEAKER_01 17:10

Okay. That ship has been replaced over time.

SPEAKER_03 17:13

Yes.

SPEAKER_01 17:14

Yeah. All of those planks of wood are in the storeroom. We now build a ship out of those planks of wood, which is all the original of HMS B DBD. Which one, which ship is there now two ships? Which one is the HMS B DBD?

SPEAKER_05 17:33

Yeah. I think if you restore from all those I mean, I mean the suggestion would be that it's unlikely that those bits of ri wood would make a ship because they would have needed replacing.

SPEAKER_00 17:46

Yeah.

SPEAKER_05 17:47

So my question would be the quality of those materials that were left behind. Yeah. If someone was to rebuild as best they could, it would be more of a statement of a memorial of the original ship as opposed to the actual ship.

SPEAKER_01 18:02

Got another one for you. Oh god. Let's put this in human terms. Oh no. Right. There's a band.

SPEAKER_04 18:08

Yeah.

SPEAKER_01 18:09

Let's call the band BDBD.

SPEAKER_04 18:11

Okay.

SPEAKER_01 18:12

Right. And that band consists of myself, you, your mum, Mitchell.

SPEAKER_03 18:18

Okay.

SPEAKER_01 18:19

Mitchell leaves the band. We get a new member in.

SPEAKER_03 18:22

What did he leave?

SPEAKER_01 18:23

Uh Creative Differences. Right, okay. Right. Okay. Mitchell leaves the band. Creative Differences. We then pull in Archie.

SPEAKER_05 18:30

Yeah.

SPEAKER_01 18:31

Okay. After a little while, you leave the band.

SPEAKER_05 18:35

Why did I leave?

SPEAKER_01 18:35

You leave the band because Mitchell created because uh Mitchell decided or you decided you wanted to back Mitchell up. Okay. It was a very short period of time. Right, got you. So you and Mitchell have now left the band. Wovey joins the band.

SPEAKER_05 18:47

Okay.

unknown 18:48

Okay.

SPEAKER_05 18:48

She would never.

SPEAKER_01 18:49

Carry on. She wouldn't. So your mum then leaves the band. See where I'm going with this?

SPEAKER_05 18:55

You're basically describing Panic at the disco right now.

SPEAKER_01 18:57

Yeah. So, and then I leave the band, but another person. So you've now got None of the original members. None of the original members, but they're still called BDBD. But we're outside and we decide we're going to restart another band. But we're the originals. So which one, which band is BDBD?

SPEAKER_05 19:15

Whatever was contrary contractually obligated to use the BDBD band name. That is my God's honest answer. I don't not sure if you can do it in human terms, because we're bound by other things like contracts and stuff like that. I thought you meant pulling a person apart and putting them together because then I would say, well, wherever their mind was, would be the person. It's it's yeah.

SPEAKER_01 19:37

So that one is a paradox.

SPEAKER_05 19:38

I think it's ongoing history and identity of the boat. And if you're replacing bits, presumably they're broken. So how could you possibly build a ship out of the broken parts would be counter your Yeah. Yeah.

SPEAKER_01 19:55

So Bertrand Russell.

Russell’s Set Problem And Barber

SPEAKER_01 19:59

The Russell's paradox.

SPEAKER_03 20:01

Ooh.

SPEAKER_01 20:01

The statement is the set of all sets that do not contain themselves, does it contain itself?

SPEAKER_05 20:08

Come again.

SPEAKER_01 20:08

So this is this is another maths. So the core problem is so consider the set of all sets. So if it contains itself, it shouldn't. If it doesn't, it should. So this is a maths, this is another maths problem.

SPEAKER_05 20:18

When does this ever come up in anyone's life? So right, uh when I think of a set, I think of Monopoly, right?

SPEAKER_00 20:24

Yeah.

SPEAKER_05 20:25

So I've got uh the greens. So you've got Oxford Street, Bond Street, yeah, and uh Regent Street.

SPEAKER_00 20:32

Yeah.

SPEAKER_05 20:33

That is a complete set.

SPEAKER_00 20:34

Yeah.

SPEAKER_05 20:35

So the set of all sets, so the whole of the Monopoly board.

SPEAKER_01 20:39

Yeah. Is a set.

SPEAKER_05 20:41

Is a set. The set of all sets that do not contain themselves, does it contain itself? Um I've lost my monopoly analogy now. Yeah. I don't know how to get from I'm not sure on this.

SPEAKER_01 20:52

Again, this isn't a maths one. So we leave that one and move on.

SPEAKER_05 20:55

Yeah.

SPEAKER_01 20:56

Yeah. Okay. Let's go with something that we can get our head round. The barber paradox.

SPEAKER_05 21:01

Okay.

SPEAKER_01 21:02

Right. So, again, this is Bertie again. Oh, a barber shaves everyone who does not shave themselves. Does he shave himself?

SPEAKER_05 21:13

The barber shaves everyone who does not shave themselves.

SPEAKER_01 21:19

Yeah.

SPEAKER_05 21:19

Does he shave himself? The barber shaves everyone.

SPEAKER_01 21:23

Who does not shave themselves? So does he shave himself? Does the barber so does the barber his his own barber? But the definition is the statement is that the barber shaves everyone who does not shave themselves.

SPEAKER_05 21:36

But if they shave themselves and they're not the bar Yeah, okay, okay.

SPEAKER_01 21:40

Yeah.

SPEAKER_05 21:41

Oh. I mean, if I were the barber, I wouldn't shave my own barber.

SPEAKER_01 21:44

Oh, it does actually say here this is a simplified version of Russell's paradox to show logical inconsistency.

SPEAKER_05 21:50

Oh. These these are connected.

SPEAKER_01 21:52

Yeah. So the problem isn't the barber, essentially, it's the definition of what barber is. It creates a logical impossibility. So it's Where that it's the definition of the barber that falls down. Whereby the definition is the barber who shaves everyone who does not shave themselves. That definition itself is what is the is what is the problem.

SPEAKER_06 22:10

Mmm.

SPEAKER_01 22:11

So it's a bad essentially it's a bad definition.

SPEAKER_05 22:14

Yeah.

SPEAKER_01 22:14

Isn't it?

SPEAKER_05 22:15

It's a shit statement.

SPEAKER_01 22:17

It's a shit statement, yeah.

SPEAKER_05 22:18

Again, not sure where this has come up in his life. No. Uh other than the barber shop. Maybe he's in a quartet.

SPEAKER_01 22:24

I was thinking to say exactly that. Oh, my favourite.

Schrödinger’s Cat And Observation

SPEAKER_05 22:29

Schrdinger's cat.

SPEAKER_01 22:30

Schrdinger's cat.

unknown 22:31

Okay.

SPEAKER_01 22:32

So this comes from a guy called Irwin Schrdinger in 1935. And the statement is a cat in a box is both alive and dead until it is observed.

SPEAKER_04 22:41

Yeah.

SPEAKER_01 22:42

So basically, it's it's a quantum level reality statement, essentially. So the cat in a box is linked to a quantum event until it's until it is observed, it is both alive and dead. And why Schrdinger proposed it is to show how absurd quantum mechanics seems when it's scaled up.

SPEAKER_04 23:01

Yeah.

SPEAKER_01 23:03

So the interpretation is that Copenhagen's like observation collapses reality.

SPEAKER_05 23:08

It does, yeah. So I think And then you've got the many worlds.

SPEAKER_01 23:11

So both outcomes happen in different universes. And the inter and the other one is the interaction with the environment resolves the state.

SPEAKER_05 23:19

It does, yeah. Reality makes By opening the box and or hearing the purrs, scratches, bangs.

SPEAKER_01 23:27

Yeah.

SPEAKER_05 23:27

Or lack of.

SPEAKER_01 23:28

Exactly. So what what what this why this one is such a head teaser? Because when on this on the shape of it, on the face of it, you think, well, no, that that that makes no sense at all. That the cat is either alive until unless it's observed. But what it really means is that reality may not be definite until it is measured. And that observation itself may play a fundamental role in existence. That's what messes with your head.

SPEAKER_05 23:53

Yeah. Nothing nothing is anything until it's observed, right?

SPEAKER_01 23:57

Exactly that. Yeah.

SPEAKER_05 23:59

Which is problematic.

SPEAKER_01 24:01

Very problematic. Thoughts?

SPEAKER_05 24:05

Oh, it's just a tough one. Can't, yeah. It's not that I can't get my head around it, like I understand what it's saying, but I just it's it's so much more deeper than what it is on the face of it. Yeah. This this has been a head scratcher for a while, to be honest.

SPEAKER_01 24:18

Yeah. Um it's my favourite paradox. It's great.

SPEAKER_05 24:21

It's a great one.

SPEAKER_01 24:22

Yeah.

SPEAKER_05 24:22

Erwin Schrdinger. Didn't know his first name was Irwin.

SPEAKER_01 24:26

Erwin. Erwin Schrdinger.

SPEAKER_05 24:28

Uh oh, one of my favourites coming up.

Time Travel And The Grandfather Paradox

SPEAKER_01 24:31

Grandfather Paradox.

SPEAKER_05 24:32

Wee wee.

SPEAKER_01 24:33

Yep. So this is this this actually came from a lot of science fiction stories.

SPEAKER_05 24:38

This was in um Futurama as well. It was.

SPEAKER_01 24:42

Uh so if you travel back in time and prevent your grandfather from meeting your grandmother, how do you exist? So this is almost like the premise of Back to the Future.

SPEAKER_06 24:55

Isn't it?

SPEAKER_01 24:56

So this is it, it's basically saying that time travel challenges causality.

SPEAKER_05 25:01

You could be your own grandfather.

SPEAKER_01 25:04

Yeah. So even in Terminator, in the original Terminator, so old mate goes back, sleeps with Sarah Connor, which creates John Connor. But where is the time loop? Where is the origin of that loop?

SPEAKER_04 25:17

Yeah.

SPEAKER_01 25:18

Um so basically, yeah, the the core problem of the grand grandfather paradox is that you go back in time and you prevent your own existence. So if you go back in time and stop your grandfather from meeting your grandmother, you stop existing. Which means if you stop existing, you don't stop, you don't go back in time and stop your grandfather from meeting your grandmother, therefore you do exist.

SPEAKER_05 25:41

My theory on time travel, the way the way that I underst the way I'd like to understand time travel if it was a concept, would be that no matter what you do in the past cannot change your present. Because if so, if that if that statement was true, then that you could change the past, then you would cease to potentially exist. And everything that you know in the world beyond. So it it doesn't irk me a little bit in in futuristic films.

SPEAKER_01 26:14

Or the timeline would split.

SPEAKER_05 26:15

Yeah. This is this is this is the other running theory.

SPEAKER_01 26:18

Yeah.

SPEAKER_05 26:18

That's what irks me in films a little bit is when they go back into the future, uh, sorry, back into the past, they change something. They come back to a drastically different future. Like, how would he have got there if if that was the case? Yeah, they'd still have to get to the point. So, yeah, if you did sleep with your grandmother and then that's creating. No, I'm just saying, I I did say jokingly, you could be your own grandfather. I don't think you can stop them from meeting. No matter what happens, no matter what you do, even if you kill your grandfather, there must be oedipus. Yeah, very Oedipus, but if you do kill your grandfather, presumably before they can procreate, you will be created somewhere.

SPEAKER_00 27:04

Yeah.

SPEAKER_05 27:05

No matter what where that line is, there will be a creation of you somewhere.

SPEAKER_01 27:10

Oh, that's just giving me an idea for another tale.

SPEAKER_05 27:13

There you go, enjoy. It's how I tackle time travel in my brain.

The Heap Paradox And Language Limits

SPEAKER_01 27:18

So the next one is called the heap paradox. Heap. Heap paradox. So if you remove one grain from a heap, it still leaves a heap. So when does it stop becoming a heap?

SPEAKER_05 27:33

Depends on your definition of heap, doesn't it?

SPEAKER_01 27:35

This is the same thing, like almost like when when is a hill become a mountain?

SPEAKER_05 27:39

When does a few become several?

SPEAKER_01 27:41

Yeah.

SPEAKER_05 27:41

It's the definition of heap.

SPEAKER_01 27:43

Yeah.

SPEAKER_05 27:43

I think heap refers to the shape. I guess once that shape is not a heap, like a point, like a mountain point. I have a hair in my eye and it's really annoying. I wonder Yeah, I I think it's more of a definition of the word heap.

SPEAKER_01 28:00

Okay, so language is an interesting thing.

SPEAKER_05 28:03

Yes.

SPEAKER_01 28:04

Myself and Anya had an interesting conversation a couple of nights ago. Because Anya was talking, and she's absolutely right here, the limitations of the English language.

SPEAKER_04 28:15

Yeah.

SPEAKER_01 28:16

So did you see her story the other day?

SPEAKER_04 28:18

I did actually, yeah.

SPEAKER_01 28:19

Where there are different versions of her name.

SPEAKER_04 28:22

Yeah.

SPEAKER_01 28:22

And I said to her, I asked her, I said, like, what what in what and she said in in Polish, basically, the the people would use a different version of her name and it would tell her, sorry, Anya, if I've got this wrong, it would tell her what where their mental state was with her at that time. It's almost like it's a if it's like familiarity, depending on the type of name that's it.

SPEAKER_05 28:45

It's like a feeling that's associated with the word or or the name in this case.

SPEAKER_01 28:51

The usage of the name tells Anya if they've used that position similar to like me. So if because my name is my real my official name is David. David, yeah. Yeah. I don't like that name. I hate that it's just but you you've got the different iterations of my name. David, Dave, Davy. Depending on what someone calls me.

SPEAKER_05 29:09

You know, yeah, you know the context of the context behind it. Yeah.

SPEAKER_01 29:13

Yeah.

SPEAKER_05 29:14

Yeah. Most of your family, well, your immediate family call you Davy.

SPEAKER_00 29:18

Yeah.

SPEAKER_05 29:19

I think the older generation of our family call you David.

SPEAKER_01 29:23

Yeah. What does No one calls me Dave?

SPEAKER_05 29:26

I feel like Nana does.

SPEAKER_01 29:27

Oh she yeah, I think she does.

SPEAKER_05 29:29

She's I think she's the only one.

SPEAKER_01 29:30

Yeah. Yeah. But it's but it just goes to show the limitations of the English language. So like in other languages, there are so many different words for different things.

SPEAKER_04 29:42

Yeah.

SPEAKER_01 29:43

I mean, in in Gaelic, for example, right? So love it, love obviously is is a word in Gaelic. But there's also another word of in in in Gaelic is keeper of my heart.

SPEAKER_03 29:56

Oh, that's sweet.

SPEAKER_01 29:58

Yeah.

SPEAKER_03 29:59

Linguistically.

SPEAKER_01 30:00

Linguistically, yeah. And and that's such a beautiful way to say it. And it's it's got that that real kind of definite, you know, it's not just that love. It's like you are the keeper of my heart. Yeah, it's it's a bit more. It's a bit more.

SPEAKER_05 30:11

And even in in other same with I love you and I'm in love with you.

SPEAKER_01 30:16

But in other languages, there I come like let's say say like um Italian. So there might be 20 different words in Italian for one thing, but they all mean something different, but they're all referring to the same thing. The English language is very limiting.

SPEAKER_05 30:30

Yeah.

SPEAKER_01 30:30

And this is kind of again this going back to the heap.

SPEAKER_05 30:33

Yeah. That's what I mean about the heap. Like it's it's your definition of what constitutes a heap.

SPEAKER_01 30:38

We're very simplistic in the English language. Yeah.

Bootstrap Paradox And No Origin

SPEAKER_01 30:42

Um the moving on to the bootstrap paradox.

SPEAKER_05 30:46

I never heard of this one.

SPEAKER_01 30:47

Yes. Uh this is uh basically an object or piece of information exists without origin. So essentially it's like me going back to Shakespeare with an entire copy of his book written now and giving it to him. His play, uh his plays, so it's causality. Again, which is the origin? Which came first, the writer or the book?

SPEAKER_05 31:17

This is very chicken, isn't it?

SPEAKER_00 31:20

Yes.

SPEAKER_05 31:21

Of all the things you could do as a time traveller, that just feels like the weirdest one.

SPEAKER_00 31:25

Yeah.

SPEAKER_05 31:26

Um tough one. Tough one.

SPEAKER_01 31:29

I think this was in the Doctor Who episode once.

SPEAKER_05 31:31

Oh, this yeah, I think this is in Futuramour as well. Oh. Uh it does break the idea that everything must have a cause.

SPEAKER_01 31:39

Mm-hmm.

SPEAKER_05 31:40

An origin, a writer. Yeah. I don't I haven't got on. Yeah, that's what I mean. It's very chicken egg-gy, isn't it? Mmm. I I can't I'm struggling to comment on this one really. I um exists without origin. Like a time traveller giving Shakespeare's own works.

SPEAKER_01 31:59

Yeah. What do you think? I can see the cogs going round with it.

SPEAKER_05 32:03

Presumably before he wrote it. So he he got the books.

SPEAKER_01 32:06

Yeah, he would got the books before he wrote it.

SPEAKER_05 32:08

He would essentially be plagiarizing himself, right?

SPEAKER_01 32:10

Essentially, yeah.

SPEAKER_05 32:12

Uh but he did write them at some stage.

SPEAKER_01 32:16

Did he though?

SPEAKER_05 32:16

Well, he believes he did.

SPEAKER_01 32:17

Well, where's the origin of them? He believes he believed it, yes.

SPEAKER_05 32:21

Maybe it's a belief system.

SPEAKER_01 32:23

Mm-hmm.

SPEAKER_05 32:24

Mm-hmm.

SPEAKER_01 32:26

So we've got one more.

SPEAKER_05 32:28

Last one.

Paradox Of Tolerance And Free Speech

SPEAKER_01 32:29

This is the paradox of tolerance. And this is Carl Popper wrote this one.

SPEAKER_05 32:33

Ooh, Mr. Popper.

SPEAKER_01 32:34

And the statement is unlimited tolerance may lead to the disappearance of tolerance. So basically, what it means is that a society must limit intolerance to remain tolerant. So basically, well, okay, so if a society tolerates everything, freaking Christ, hang on. Yeah, if a society tolerates everything, including intolerance intolerance, it risks being destroyed by intolerant groups.

SPEAKER_05 33:01

Right. So what it's saying is we sh should stand up for things that we believe in.

SPEAKER_01 33:10

Yes. So when you're looking at free speech debates, laws against hate speech, democratic safeguards, it's saying that freedom isn't unlimited, it requires boundaries to survive.

SPEAKER_05 33:21

Yes. I hate it when people say, oh, it's a free country. I hate that expression. Because yes, it is a free country, sure. But you also have an obligation to be a fing nice person. That's another pound in the swear jar. But do you disagree?

SPEAKER_01 33:38

I don't disagree at all.

SPEAKER_05 33:39

Because I think this is what annoys me about this whole free speech thing. Uh sorry, I feel like I've got a lot of things. Oh, there we go.

SPEAKER_01 33:44

I'm just gonna sit down.

SPEAKER_05 33:45

I feel like I've got angry about this. But I I really, I really detest people that are like, oh, it's a free country, we can do what we want.

SPEAKER_01 33:50

We can say them what we want.

SPEAKER_05 33:51

No, you can't I don't I don't think that that mentality is correct because if it I just I just wish people would be kinder to each other. And I think there's just a yes, we can go too far with with intolerance, maybe perhaps might be the better way of saying it. Like we can go too far, we can be too politically correct, we can be too much of this. And I and I am starting to see it with the censorship stuff and the things like that. Right. I do think people have the right to say what they what they need to say, but do it in a way where you are limiting the harm of others as much as possible.

SPEAKER_01 34:30

The thing is about debating. So I'd put this. When I think everything should be up for discussion.

SPEAKER_05 34:38

Yeah.

SPEAKER_01 34:38

Everything everything should be about for you.

SPEAKER_05 34:39

It's okay to disagree. We disagree on things.

SPEAKER_01 34:41

There you go. And it's about it's about disagreeing and it's about respecting that other person's you can and I've said this many times, there are people who I know I inherently disagree with what this my grandmother's calling. I'm do you need to answer that? No.

SPEAKER_04 35:00

Okay.

SPEAKER_01 35:01

That's a paradox in itself. Yeah, so people can inherently disagree, but they can still respect that person. Yeah, I don't know. Just because they disagree with somebody on some somebody on something on one subject doesn't mean to say that they still don't like the rest of that person. They just you if if everybody agreed on everything all of the time, the world would be a very boring place.

SPEAKER_02 35:20

Yeah.

SPEAKER_01 35:20

But it's respectful.

SPEAKER_02 35:22

Being respectful.

SPEAKER_01 35:23

Being respectful and arguing-being a twat. Yeah. Arguing respectfully with somebody. Yeah. It's as simple as that. And that's why you can have debates, you can have discussions. Don't get personal with it.

SPEAKER_04 35:34

Yeah. Yeah.

SPEAKER_01 35:36

Agree to disagree. Yeah. And it's fine. People can disagree all the time.

unknown 35:41

Yeah.

SPEAKER_01 35:41

That's how I look at it.

SPEAKER_05 35:42

It's fine. I think it's fine for people to disagree. It's fine to have differing opinions. Otherwise, we wouldn't be in this world. Are you okay?

SPEAKER_01 35:49

Yeah, no, she's now leaving a voicemail.

SPEAKER_05 35:53

Hopefully it's not important.

SPEAKER_01 35:54

No, it won't be important. No, I know I know why she's calling me. It's because she went out yesterday, so she's probably telling me about what she did yesterday. Well, yeah. Sweet.

SPEAKER_05 36:02

Um, but yes, yeah, I think I think I think what annoys me when people say, Oh, it's free country, it's this, it's that. Well, yeah, but we still have like society to um conform with in the most basic form at least of of common decency. That's all I'm that's all I'm saying. Exactly. That's all I'm saying.

SPEAKER_01 36:19

Exactly that, yeah.

Favourite Paradoxes And Wrap Up

SPEAKER_05 36:21

Whoa, let's go.

SPEAKER_01 36:22

So that that's it. That was the last one. Yeah. That was the last one. So um Blitz for them. Which which is your favourite?

SPEAKER_05 36:29

Which one do you Well there's there's two I didn't understand. And then I thought I understood it, but now that I'm looking back at it, I'm wondering if it's if I'm right. And people are gonna be like, she's dumb as shit. I think I'll always like Schrdinger's cat.

SPEAKER_01 36:42

Yeah, Schrdinger's cat's my favourite. Yeah, I think it's just because of the connotations behind it.

SPEAKER_05 36:46

It it's it's fun to talk about the ship as well.

SPEAKER_01 36:49

Yeah.

SPEAKER_05 36:50

I think I think it it also depends on the complexity of the thing that you're replacing parts of. Like we talked about the broom. The broom, the handle and it's only a handle and a brush, right? So I would say that's probably not the same broom. Okay. I'm gonna say it. But the ship is huge. And if you're replacing several parts of that, that's like saying the Titanic isn't the Titanic anymore. If they replace the engine of it, it's still the Titanic. Yeah, I know it's in the bottom of the ocean, but whatever. They've recreated the Titanic, but they're not calling that the Titanic, they're calling that the recreation of the Titanic. You know, I think I think it is all to do with the language used, but yeah, I think I think when when the object becomes more complex, yeah, there is more room for that debate to to be a debate. That's that's quite funny. That's yours. I did like the ship one.

SPEAKER_01 37:42

You like the ship one? I like Schrodinger's cap.

SPEAKER_05 37:44

Yeah, I know, I know you do.

SPEAKER_01 37:45

Yeah, that's fine. There you go.

SPEAKER_05 37:47

Is that it?

SPEAKER_01 37:48

That's it.

SPEAKER_05 37:48

Sweet, okay. Well, if you enjoyed this episode of bonus dad, bonus daughter, we've got plenty more in the bank and on YouTube. If you're not watching us on YouTube already, um see our beautiful faces. Um the outro. Thanks for joining us on bonus dad, bonus daughter. Don't forget to follow us on all our socials and share the podcast with someone who'd love it. We are available on all streaming platforms. See you next time. Bye-bye.