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1 hour ago, HawkMan said:

Ship Of Theseus. 

Ancient Greek mariner Theseus has a ship  made entirely of wooden planks,  except sails etc. As each plank gets old he replaces it with a new plank. The old planks are stored in a warehouse. One by one he replaces the planks, all the time he has a sea worthy vessel. Eventually all the planks are replaced . Call this the Renovated Ship. Question is is this still the Ship Of Theseus, with no original plank. Now suppose he goes to the warehouse and rebuilds the ship using the original planks, call this the Reconstructed Ship. Which is the Ship of Theseus,  the Reconstructed or Renovated? The Reconstructed has the original planks,  the Renovated has a continuous timeline  of existence back to the original.  This is the puzzle of the Metaphysics of Identity. See vid for more.

 

 

Isn't this like Trigger's broom in only fools? 🙂

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A father tells a group of children that at least one of them has a muddy face. " Step forward if you have a muddy face" he tells them, and repeats this request until those with muddy faces steps forward. If there are 'x' muddy children then 'x' will step forward at the ' xth' request, ie if 2 then 2 will step forward at 2nd request, or 4 at 4th request. Why?

We are assuming the children have logical thought processes,  are honest and believe all the other children are likewise. 
But if the father doesn't tell them at the outset that at least one has a muddy face, this will not happen, even if there is more than one muddy face, so that everyone can see there is at least one ,and knows what the father doesn't tell them. Why?

Edited by HawkMan
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5 hours ago, HawkMan said:

A father tells a group of children that at least one of them has a muddy face. " Step forward if you have a muddy face" he tells them, and repeats this request until those with muddy faces steps forward. If there are 'x' muddy children then 'x' will step forward at the ' xth' request, ie if 2 then 2 will step forward at 2nd request, or 4 at 4th request. Why?

We are assuming the children have logical thought processes,  are honest and believe all the other children are likewise. 
But if the father doesn't tell them at the outset that at least one has a muddy face, this will not happen, even if there is more than one muddy face, so that everyone can see there is at least one ,and knows what the father doesn't tell them. Why?

Okay, this is going to be tricky to explain. 

Let's start with just 1 child being mucky. 

All the children can see each other so when the request is made the mucky child can see all the others are clean and they can all see he is mucky so he steps forward, knowing it must be him that is mucky and when the statement isn't made again the other children know they are not mucky. 

----

I'll see if I can explain this in a slightly more complicated way. 

Let's take 3 children. 2 have mucky faces, 1 doesn't for the sake of this explanation. 

They can all see each other so the one that is clean can see the others are mucky and the mucky ones can see one is clean and one is mucky. 

The first time the request is made no children step forward because they don't know if they themselves are mucky. 

When the request is made for a 2nd time the 2 mucky children (children A and B) step forward because they both think the same thing. That is that they (let's take child A's thought train) can see child C is clean and child B isnt and A thinks that B must think A too is mucky or B would have stepped forward at the first request, ie my first example. (and vice versa for B's thought train). 

----

Something like that, that is a very complicated puzzle, I know what I mean, apologies if the explanation is a bit rubbish. 

Edited by The Hallucinating Goose
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36 minutes ago, The Hallucinating Goose said:

Okay, this is going to be tricky to explain. 

Let's start with just 1 child being mucky. 

All the children can see each other so when the request is made the mucky child can see all the others are clean and they can all see he is mucky so he steps forward, knowing it must be him that is mucky and when the statement isn't made again the other children know they are not mucky. 

----

I'll see if I can explain this in a slightly more complicated way. 

Let's take 3 children. 2 have mucky faces, 1 doesn't for the sake of this explanation. 

They can all see each other so the one that is clean can see the others are mucky and the mucky ones can see one is clean and one is mucky. 

The first time the request is made no children step forward because they don't know if they themselves are mucky. 

When the request is made for a 2nd time the 2 mucky children (children A and B) step forward because they both think the same thing. That is that they (let's take child A's thought train) can see child C is clean and child B isnt and A thinks that B must think A too is mucky or B would have stepped forward at the first request, ie my first example. (and vice versa for B's thought train). 

----

Something like that, that is a very complicated puzzle, I know what I mean, apologies if the explanation is a bit rubbish. 

You're pretty much on the right track.
In scenario 1 the father tells them that at least one is muddy. If there is just one muddy child, he will see no muddy faces and assume he is muddy and step forward, the others stay still. If there are two muddy faces, then everyone stays still at the first request because they can all see at least one muddy face, and don't know if they are muddy. But as no one stepped forward they conclude there must be more than one muddy face. Those two that can only see one muddy face conclude that they must be muddy, so two step forward.
If three faces are muddy, three can see two, the others see three. When no one steps forward after the second request because they can all see two at least, the conclusion is there must be more than two, so the three that see two muddy faces step forward, three at the third request, and so on ad infinitum.
In the second scenario the father doesn't tell them that there is at least one muddy face, so there is no common knowledge. If there is one muddy face, the kid that can't see a muddy face has no reason to think he must be muddy. If there are two, the same, they cannot reason as in scenario 1. For example if two are muddy, Angela and Mary, at the second request Angela cannot reason that Mary didn't step forward at the first because she saw Angela 's face was muddy, so she cannot reason that there are just two muddy faces when she sees only one other which is muddy.
This is the difference between Universal and Common knowledge. For example, traffic lights, I know that red means stop, but I need to know that everyone else knows and they know that everyone else knows or the system breaks down. If everyone knows how traffic lights work that is Universal knowledge but that isn't enough, if no-one knew that everyone else knows how they work it would be chaos. The children have common knowledge in scenario 1 because the father's statement was public.
Taken from this book if you're interested in more brainteasers like this.

 

download.jpeg

Edited by HawkMan
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49 minutes ago, HawkMan said:

You're pretty much on the right track.
In scenario 1 the father tells them that at least one is muddy. If there is just one muddy child, he will see no muddy faces and assume he is muddy and step forward, the others stay still. If there are two muddy faces, then everyone stays still at the first request because they can all see at least one muddy face, and don't know if they are muddy. But as no one stepped forward they conclude there must be more than one muddy face. Those two that can only see one muddy face conclude that they must be muddy, so two step forward.
If three faces are muddy, three can see two, the others see three. When no one steps forward after the second request because they can all see two at least, the conclusion is there must be more than two, so the three that see two muddy faces step forward, three at the third request, and so on ad infinitum.
In the second scenario the father doesn't tell them that there is at least one muddy face, so there is no common knowledge. If there is one muddy face, the kid that can't see a muddy face has no reason to think he must be muddy. If there are two, the same, they cannot reason as in scenario 1. For example if two are muddy, Angela and Mary, at the second request Angela cannot reason that Mary didn't step forward at the first because she saw Angela 's face was muddy, so she cannot reason that there are just two muddy faces when she sees only one other which is muddy.
This is the difference between Universal and Common knowledge. For example, traffic lights, I know that red means stop, but I need to know that everyone else knows and they know that everyone else knows or the system breaks down. If everyone knows how traffic lights work that is Universal knowledge but that isn't enough, if no-one knew that everyone else knows how they work it would be chaos. The children have common knowledge in scenario 1 because the father's statement was public.
Taken from this book if you're interested in more brainteasers like this.

 

download.jpeg

That hurt my head! 😂

Yeah I might have a look at that book. Despite this not really being my area of study it is something that interests me so thanks for the recommendation! 👍

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On 23/09/2020 at 14:21, HawkMan said:

Ship Of Theseus. 

Ancient Greek mariner Theseus has a ship  made entirely of wooden planks,  except sails etc. As each plank gets old he replaces it with a new plank. The old planks are stored in a warehouse. One by one he replaces the planks, all the time he has a sea worthy vessel. Eventually all the planks are replaced . Call this the Renovated Ship. Question is is this still the Ship Of Theseus, with no original plank. Now suppose he goes to the warehouse and rebuilds the ship using the original planks, call this the Reconstructed Ship. Which is the Ship of Theseus,  the Reconstructed or Renovated? The Reconstructed has the original planks,  the Renovated has a continuous timeline  of existence back to the original.  This is the puzzle of the Metaphysics of Identity. See vid for more.

 

 

I never did have a go at this when you first posted it. I haven't watched the vids so don't know if they explain it. 

In my opinion, the ship with the new planks is the ship of theseus, that is the renovated ship isn't it? The reason I think this is because replacing the planks just one by one means that they are being added into the original ship and thus become part of it while the old planks are taken away and lose their status as part of the ship. 

If every plank was replaced at the same time then you would just be constructing a new ship because you would just put all the new pieces together without integrating them with any part of the old ship. And in the same respect you wouldn't be taking apart the old ship and reassembling it because there would be no need to do that so the original ship would still exist as it always had. 

Unless the argument is they are both the ship of theseus because he constructed both of them? But no, I think my first explanation is good enough here. 

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On 13/10/2021 at 08:48, The Hallucinating Goose said:

I never did have a go at this when you first posted it. I haven't watched the vids so don't know if they explain it. 

In my opinion, the ship with the new planks is the ship of theseus, that is the renovated ship isn't it? The reason I think this is because replacing the planks just one by one means that they are being added into the original ship and thus become part of it while the old planks are taken away and lose their status as part of the ship. 

If every plank was replaced at the same time then you would just be constructing a new ship because you would just put all the new pieces together without integrating them with any part of the old ship. And in the same respect you wouldn't be taking apart the old ship and reassembling it because there would be no need to do that so the original ship would still exist as it always had. 

Unless the argument is they are both the ship of theseus because he constructed both of them? But no, I think my first explanation is good enough here. 

This being a metaphysics puzzle about identity there is no particular right answer and genuine disagreement by Philosophers about this. Do objects survive  change is the question.  We survive change although every molecule of us continually changes,  atoms destroyed and replaced,  but our identity integrity is intact.  Someone can also dismantle a car, into bits then rebuild it and it would remain the same car. As for Theseus and his ships. The Reconstructed ship has all the original components even though its existence has been discontinuous,  ie while it was in the warehouse,  but it would be harsh not to award that the " honour " of being the original. The renovated ship has a continuous line of existing going back to the original so that too has a case. Some metaphysicians accept both are claimants to be the original. The vids will explain better than I can. I got into Metaphysics about 10 years ago,  a fascinating subject and has intruiging if kooky puzzles. Such as this: if you dip your toe in a river one day, then go back the next day and do it again at the same place,  are you dipping your toe in the same river? Well yes and no, same river but different water. Water from yesterday has flowed away so it can't be the same waters,  but what is a river? What makes The Thames a coherent object,  is it the water or the channel of mud that the water flows along. Identity again,  it changes constituents ie the water but remains the Thames. I can recommend Metaphysics if you like metaphorically bashing your head against a brick wall of puzzlement.

Edited by HawkMan
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45 minutes ago, HawkMan said:

This being a metaphysics puzzle about identity there is no particular right answer and genuine disagreement by Philosophers about this. Do objects survive  change is the question.  We survive change although every molecule of us continually changes,  atoms destroyed and replaced,  but our identity integrity is intact.  Someone can also dismantle a car, into bits then rebuild it and it would remain the same car. As for Theseus and his ships. The Reconstructed ship has all the original components even though its existence has been discontinuous,  ie while it was in the warehouse,  but it would be harsh not to award that the " honour " of being the original. The renovated ship has a continuous line of existing going back to the original so that too has a case. Some metaphysicians accept both are claimants to be the original. The vids will explain better than I can. I got into Metaphysics about 10 years ago,  a fascinating subject and has intruiging if kooky puzzles. Such as this: if you dip your toe in a river one day, then go back the next day and do it again at the same place,  are you dipping your toe in the same river? Well yes and no, same river but different water. Water from yesterday has flowed away so it can't be the same waters,  but what is a river? What makes The Thames a coherent object,  is it the water or the channel of mud that the water flows along. Identity again,  it changes constituents ie the water but remains the Thames. I can recommend Metaphysics if you like metaphorically bashes your head against a brick wall of puzzlement.

The river thing makes me think of the way I think when I visit historical sites, and essentially the reason I get so excited and goosebumpy (don't know if that's a word) about history. The example I always think of is when I visited Nuremburg a few years ago and went to the Nazi Rally Grounds. I walked up all the steps to the podium where Hitler stood to give his speeches and I stood back from it for a second and then stepped forward, then that shot of adrenaline I get from history kicked in. I was actually standing in exactly the same spot, on the same concrete that Adolf Hitler stood on, I felt that mud or rubber from his boots was still on that concrete and I was essentially touching the most evil and treacherous person in human history. But was it the exact same concrete and the exact same spot, probably not, most probably the concrete had been worn away over the years and any mud from his boots would have been washed away years ago but it was the same podium and the same location and the concrete I stood was at least part of the structure that was first built so it was that same thing Hitler stood on. Most people don't understand why I get so exhilarated by these kind of thoughts. 

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Note: Dr Who fans will recognise where I got this puzzle from!

You are an explorer and have discovered a hitherto unknown pyramid in Egypt. Unfortunately you are locked in the chamber, air is running out and you are going to die.
You have made an Earth shattering discovery, the myths about the ancient gods possibly being alien space travellers is true. Aliens were responsible for this pyramid, two robots of theirs are in the chamber with you. Being an expert on hieroglyphics you discover a message written on the wall, a way to escape the tomb. Two levers are on the wall, and the message says one lever pressed will bring release, the other instant death. The robots know which lever is which. Before deciding which lever to press you are allowed to ask one robot, one question, and only ONE. However one robot is programmed always to lie, the other always tells the truth. What is the one question you must ask to determine which is the death lever and which is the lever of life?

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24 minutes ago, HawkMan said:

Note: Dr Who fans will recognise where I got this puzzle from!

You are an explorer and have discovered a hitherto unknown pyramid in Egypt. Unfortunately you are locked in the chamber, air is running out and you are going to die.
You have made an Earth shattering discovery, the myths about the ancient gods possibly being alien space travellers is true. Aliens were responsible for this pyramid, two robots of theirs are in the chamber with you. Being an expert on hieroglyphics you discover a message written on the wall, a way to escape the tomb. Two levers are on the wall, and the message says one lever pressed will bring release, the other instant death. The robots know which lever is which. Before deciding which lever to press you are allowed to ask one robot, one question, and only ONE. However one robot is programmed always to lie, the other always tells the truth. What is the one question you must ask to determine which is the death lever and which is the lever of life?

Ask the one robot " what would the other robot advise"?

The lying robot would tell you the wrong answer i.e. pull the death lever

The truthful robot would say " the lying robot would say pull the death lever"

Therefore the other lever must be the safe one.

Edited by Bearman

Ron Banks

Midlands Hurricanes and Barrow

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9 hours ago, Bearman said:

Ask the one robot " what would the other robot advise"?

The lying robot would tell you the wrong answer i.e. pull the death lever

The truthful robot would say " the lying robot would say pull the death lever"

Therefore the other lever must be the safe one.

Correct, as Tom Baker put it, 

" if you're the truth one that's the death switch,  or if you're the automatic liar you're trying to deceive me so that's still the death switch,  so the other one is the one we want"

Edited by HawkMan
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