Philosophy problem dealing with logic...nice practice for computational logic

In my philosophy course the other day, my professor proposed a very interesting problem. Let me share it with you fellow AntiOnline gurus:

(I'll explain variables as I go)

A man named Theseus once sailed the seas in his ship dubbed the T.S. After many years of sailing, his ship fell into disrepair. He decided to take it to the nearest port city to have it restored. Once he arrived there, he docked his ship in Harbor A. Over a period of 1000 days, where A0 is the ship in Harbor A on Day 0 and A1000 is the ship in Harbor B on day 1000, a single wooden plank was removed each day, and replaced with a new one. Everytime this occured, however, the old plank removed from the ship in Harbor A was used to build a ship in Harbor B identical to the T.S. On Day 500, A500 is built with half new planks and half old, and B500 (the ship in Harbor B on day 500) is halfway finished, from the ground up, with the old planks removed from Ship A. On Day 1000, two completed ships are docked in Harbors A and B. The question is...which ship is the T.S.?

Think along the lines of characteristic identity and numerical identity...and how do you define when something begins and something ends.

Cheers,
gilgalad

Whichever one has the little metal plaque with the name and license info.
:cool:

Neither one is, if every single part of the ship in harbor A was removed. if it still has some parts, then it is still the TS, but if not one single part of the original ship is remaining then it is no longer the TS.

The ship in harbor B is an exactly duplicate of the orignial TS using the original parts, but if the ship was in that bad of condition, it won't be sailing anywhere. If every part of the ship in harbor A was completely replased, then the ship in harbor A is a duplicate, but would be T.S. 2, but it could still bear the name TS as it is the only ship that sales with that name on it.

It all depends on your origional philosaphy, if western then neither (as #1 was rebuilt and none of the origional remain, #2 isn't a ship as it wont sail.) if eastern then #1 as even rebuilt its still the same ship.

A man named Theseus once sailed the seas in his ship dubbed the T.S. After many years of sailing, his ship fell into disrepair. He decided to take it to the nearest port city to have it restored. Once he arrived there, he docked his ship in Harbor A. Over a period of 1000 days, where A0 is the ship in Harbor A on Day 0 and A1000 is the ship in Harbor B on day 1000, a single wooden plank was removed each day, and replaced with a new one. Everytime this occured, however, the old plank removed from the ship in Harbor A was used to build a ship in Harbor B identical to the T.S. On Day 500, A500 is built with half new planks and half old, and B500 (the ship in Harbor B on day 500) is halfway finished, from the ground up, with the old planks removed from Ship A. On Day 1000, two completed ships are docked in Harbors A and B. The question is...which ship is the T.S.?

Think along the lines of characteristic identity and numerical identity...and how do you define when something begins and something ends.

harbor a = old TS
Harbor b = a1000

Both ships are the T.S. The ship in harbor b is made of the same planks from the original T.S. The ship in harbor a is the new T.S., which was completele rebuilt from the ground up. The ship in harbor a is the one Theseus will use to keep sailing, since the old one is a wreck. The ship in harbor b is the ship Theseus brought to get repaired. Identity dosen't define who the ship is, or isn't. Like your name. If I ask who you were, you would tell me what your name was. This is because we associate our identity with ourselves. However, this dosen't define WHO we are, which was what my question was. ;) I'm still thinking about your second question.. I'll get back to you later on that one. Cheers. :D

This puzzle dates back to Heraclitus and his river-statements: the world is constantly changing, and Heraclitus wondered if someone could step into the same river twice. Heraclitus concluded (although there are different interpretations for his conclusion) that yes, one can step into the same river twice, even if the water you step into has changed.

The "solution" to the puzzle (although it is generally accepted amongst philosophers that there simply is no solution to this problem) depends on whether you accept the view that the identity of an object depends on the identity of the parts that compose the object, or not.

If you deny that view, then you'll be faced with problems as the one posted here. Deny that view, and there is no solution for your puzzle, simply because there will never be a "standard" agreement on where to draw the line ("Does a ship with one replaced bolt make a different ship? With two replaced bolts? Three? A different engine?")

If you agree with that view, then the "solution" is simple: none of the boats are the same, and the TS doesn"t exist anymore.

You question is full of assumptions. What really makes the T.S. the T.S. Is it that you can percieve it as so by interpreting the light waves which bounce off it with your eyes and brain? If that is the case, then the T.S. is only an image in your brain. Therefore, it is neither Ship A or B, it is merely the mental image you built of the T.S. when you decided to name it. Vague enough for ya?
-NeuTron

Here is some reading about Heraclitus

I agree with Heraclitus's philosophy about the material world. It is in constant change. He also says everything moves and nothing is at rest. Heraclitus concluded that you could NOT step into the same river twice.

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The idea is this: since the composition of the river changes from one moment to the next, it is not the same river for any length of time at all. Everything is like a river in this respect. That is, nothing retains its identity for any time at all.

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(taken from here )

Negative is right, if you accept this point of view, then neither ship is the T.S. However, according to the ancient Jewish way of thinking they both are the T.S. It just depends on which view you accept. If none, then Negative is right again. There is no solution because there isn't a standard agreement on where to draw the line. Which is what I think, there is no solution.

I believe I once heard of a man, doing a life sentence for murder,
who argued, after a number of years, that he should be released,
since he was no longer the same person who had comitted the
crime. After so many years, this is physically true. Every molecule
of your body has been replaced by fresh ones rebuilt from the food
you eat.

I think identity is more than just the parts, but more than the
name tag too.
:cool:

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Every molecule
of your body has been replaced by fresh ones rebuilt from the food
you eat.

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I appologize for straying off-topic, but if that were true we would all have the key to mortality. ;)

Man, I love hearing the answers of other people. To be honest, I still don't have an answer to this question. I proposed an answer that the T.S. is actually B1000, but the question remains: when does something cease to be and becomes something else? One reply in particular, Remote_Access' response, was my initial one. My professor told me that is wrong, though, because of a fundamental numeric identity theorum:
If x = y and y = z, then
x = z
And because the T.S. has an essence (so to speak) there can only be one exactly like it, and that is itself. The T.S. can't coexist with another T.S. However, the conclusion that neither of the ships are the T.S. can still be a legitimate answer :).

How is that wrong? Because the professor is the teacher and he says so? Numeric identity theorum is a bunch of crap.

If a Red M&M = Blue M&M and
Blue M&M = Green M&M
Then a Red = Green M&M

M&M's have an essence and there's millions of those. They're all the same. That's like saying there is only one red M&M and it can't coexist with another one because it has an "essence". :p

It's wrong because there can't be more than one thing. Yes, there can be multiple red M&M's, but no two are exactly the same. Therefore, the numeric identity theorum is not a bunch of crap. The teacher isn't right because SHE says so, she's right because what she says makes logical sense. :) If you had a twin, of course the twin would look like you...but does that mean the twin is you?

Cheers,
gilgalad

According to this "theorum", a red and a green M&M is the same thing. There CAN be more than one thing. There is more than one M&M in the world. Of course the twin wouldn't be me but you just said there can't be more than one thing so there for I don't even have a twin because he wouldn't be able to exist... :D

Really, as in all philosophy, it's hard to find an absolute truth in dealing with abstract concepts. It's all about terminology. I just wanted to see what people thought. Concerning the answers to the question, though, it's been a fun run.

gilgalad

Indeed, indeed. :D

I'm takeing intro to philsophy and trying to get into debateing my point of view. It's a fun class, quite different from the other ones. Instead of being taught what to think and memorizeing trivial things, we're learning how to think and why we think that way. I look forward to more philosophic discussions.

Cheers,
Remote

First the assumption that the two ships are identical is an incorrect assumption. As stated earlier no two objects can be exactly the same. Also to consider - any two objects when compared to each other exclusively, at a given point in time, will always have the same difference. So the real T.S. is actually the difference between two ships. Wink, Wink.

*gasp* what thought provoking input... :o

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Originally posted here by OverdueSpy
First the assumption that the two ships are identical is an incorrect assumption. As stated earlier no two objects can be exactly the same. Also to consider - any two objects when compared to each other exclusively, at a given point in time, will always have the same difference. So the real T.S. is actually the difference between two ships. Wink, Wink.

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Hear, Hear...Well stated. I raise my brandy glass to you sir!

They wont be the same ship.. they will have different captains..

It is like cloning yourself.. is the clone you? no.. Are you still you? .. yes.. While the Clone may have similar characatistics, and the personality traits will be similar.. the clone will have a different "Captain".. that is a different consiousness..

In the case of a ship.. had they cloned the captain and crew as well, then my idea falls in a screaming heap.. .. cloning the consiousness of a person.. the final link to being able to teleport..

Cheers

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Originally posted here by gilgalad
...
fundamental numeric identity theorum:
If x = y and y = z, then
x = z
...

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Quote:

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Originally posted here by Remote_Access
...If a Red M&M = Blue M&M and
Blue M&M = Green M&M
Then a Red = Green M&M

M&M's have an essence and there's millions of those. They're all the same. That's like saying there is only one red M&M and it can't coexist with another one because it has an "essence". :p

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You are saying to fundamentally different things.
If x=y and y=z, then x=z, is very different than a RED M&M being a GREEN M&M.
2+2=4 and 3+1=4, so 2+2=3+1, but RED is not GREEN. Red is a M&M, and Green is a M&M, but red is not green. That is like saying a dog is an animal and a cat is an animal, therefore a dog is a cat.

R_A, you have shown one ot the primary fallacies of logic..., one that I should remember the name of, but then I graduated and as you said, Philosophy taught me to think, not regurgitate. It is also making it very difficult to find a job...(funny that in the current economy no one want a guy with a BA is Philo... :p ). But as you made that mistake here in the tender loving environment of the Cosmos Forum, you won't make it in class, and perhaps you can: 1 catch someone else on it, or 2 find out the name of it and re-educate me so that I can forget it again.

Negative already beat me to the punch on my comment (as he ususally does), so I had to wait for someone to say something that could draw me back into the conversation.

Good conversation.

Peace,
Dhej

Copi would call that the fallacy of an Undistributed Middle.

All dogs are animals, all cats are animals, therefore all dogs are cats.
Animals is the middle term. Both dogs and cats share the common property of being animals, but according to the rules of logic, they may be different. And they are...

All reds are M&Ms, all greens are M&Ms, therefore all greens are reds... don't think so ;)

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If x = y and y = z, then x = z

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or

[ ( x = y ) ^ ( y = z ) ] -> ( x = z )

this IS true. mathematically speaking. you can't substitute english for mathematical variables and expect it to hold true.

you are saying that x EQUALS y ... so they are exactly the same thing. and if y EQUALS z then x must also equal z.

it is a completely different thing if we replace the equals with -> meaning IF x THEN y. then we are allowed to substitute english. though it may not make sense in english, it does in logic.

[ ( x -> y ) ^ ( y -> z ) ] -> ( x -> z ) this is a hypothetical syllogism straight from the rules of inference.

here we are saying;
if x then y and if y then z therefor if x then z
if it is raining i wear a coat and if i wear a coat i am warm. so if it is raining i am warm.
it works logically for the M&Ms too! but makes even less sense in english.

I think that the T.S. is whichever ship that you decide to name the T.S., but neither is the same old ship that Thesius had. :D

You guys think too much. It's very confusing :confused:

I generally agree with rcgreen,

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Whichever one has the little metal plaque with the name and license info.

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By the way, he should fire those workers. One board a day! Sheesh! :D

lol...I absolutely love that answer.