NationStates Jolt Archive

For those of us who are bored, let us have pointless philosophical thought cycles that never end, and share our endless thought cycles with others. Here is my example:

Everyone is a little weird.
There is no "normal".

Therefore, being weird is normal and being normal is weird. So, I am normal, which is weird, which is normal, which is weird, which is normal... you get the idea.

If everyone is different, then there is no such thing as normal.

If everyone was normal, then there would be no such thing as different.

Phil: What Lil says is true.

Lil: What Phil says is false.

Therefore, if what Lil says is true, then what Phil said is false, meaning that Lil was wrong, meaning Phil was right...

For those of us who are bored, let us have pointless philosophical thought cycles that never end, and share our endless thought cycles with others. Here is my example:

Everyone is a little weird.
There is no "normal".

Therefore, being weird is normal and being normal is weird. So, I am normal, which is weird, which is normal, which is weird, which is normal... you get the idea.

Thankfully, my mind is free from such philosophical nightmares :eek:

And, if I may for a moment address those few who are undoubtedly compelled to challenge me: Bring it on, bitches!

Here's an interesting one:

Find the smallest whole number that requires, in order to be specified, more words then there are in this sentence.

The paradox isn't immediately apparent.

EDIT: Well, I don't know if it's fully relevant, but it's cool anyway.

Why is it that

"Fools rush in where Angels fear to tread"
yet
"He who Hesitates is lost"

This statement is a lie.

I am a pathological liar.

The statement above is a lie.

You will be hanged at noon next week on Friday.
The choice of day will be a surprise to you.

More!

Quine's paradox:
“Yields falsehood when preceded by its quotation” yields falsehood when preceded by its quotation.

Everyone is unique.

Here's an interesting one:

Find the smallest whole number that requires, in order to be specified, more words then there are in this sentence.

The paradox isn't immediately apparent.

EDIT: Well, I don't know if it's fully relevant, but it's cool anyway.
Clever.

You had there for a bit.

For those of us who are bored, let us have pointless philosophical thought cycles that never end, and share our endless thought cycles with others. Here is my example:

Everyone is a little weird.
There is no "normal".

Therefore, being weird is normal and being normal is weird. So, I am normal, which is weird, which is normal, which is weird, which is normal... you get the idea.
There are degrees of "weirdness," if you operate in this paradigm. There's more than one type of being "weird."

Personally, I think those categories are kinda dumb. That's just me.

My head hurts :headbang:

For those of us who are bored, let us have pointless philosophical thought cycles that never end, and share our endless thought cycles with others. Here is my example:

Everyone is a little weird.
There is no "normal".

Therefore, being weird is normal and being normal is weird. So, I am normal, which is weird, which is normal, which is weird, which is normal... you get the idea.

No, because there are different kinds of weirdness. The "norm" is one single way to be.

No, because there are different kinds of weirdness. The "norm" is one single way to be.
Well, I never said it was a perfect example... if there is such a thing.

Well, I never said it was a perfect example... if there is such a thing.

I think perfection is like infinity. Useful for theoretical work, but doesn't exist in reality.

Well, Russell's paradox is possibly the most famous example of this sort of circular reasoning, so here it is :

Let R be the set of all sets which do not contain themselves as a member.

So, for instance, the set of all cows is in R since the set of all cows isn't a cow. On the other hand, the set of all things which aren't cows is itself not a cow (fairly obviously since it lacks an udder and never chews its cud), so it is contained inside itself, and hence, is in R.

Now, for the interesting part: Is R in R? If it is, then it contains itself, which contradicts it's being a member of R, but if R doesn't contain itself then by definition it is a member of R.

Anyway, the conclusion is that you have to be careful how you define sets if you want them to be logically consistent.

Here's an interesting one:

Find the smallest whole number that requires, in order to be specified, more words then there are in this sentence.

The paradox isn't immediately apparent.

EDIT: Well, I don't know if it's fully relevant, but it's cool anyway.

Nope. I don't get it.

Nope. I don't get it.
Well, if such a number existed, then it could be specified by "the smallest whole number that requires, in order to be specified, more words then there are in this sentence", which has fewer words than the original sentence, thus that number can't be the smallest such number, even though it was by assumption.

This terminates quickly though, because we conclude that no such number can exist.

Why can't it just be a number with 20 words in it? The logic is questionable if the original question can't be answered and is thus not a paradox.

Well, if such a number existed, then it could be specified by "the smallest whole number that requires, in order to be specified, more words then there are in this sentence", which has fewer words than the original sentence, thus that number can't be the smallest such number, even though it was by assumption.

This terminates quickly though, because we conclude that no such number can exist.


ahhh... right. Got it.
(tisn't my fault, I've been awake for much too long...)

Adapted from Martin Gardner, and I am not sure if it is originally his.

Scene 1. The Breakfast table, April 1st, Two brothers, one 16 the other 10.

16 year old - I'm going to fool you today, o brother of mine.
10 year old - You won't catch me now you done told me.

Scene 2. Bedroom, April 1st, 11 pm.

Mom - Why won't you go to sleep
10 yo - Because Tom said he would fool me and he hasn't even tried.
Mom - Tom, come fool the child so we can all get some sleep.
Tom - I said, I'd fool you. You believed me, I didn't fool you, so I fooled you.

Was he fooled?

You will be hanged at noon next week on Friday.
The choice of day will be a surprise to you.


I think this one works better if given in the form;

You will be hanged at noon next week on Wednesday, Thursday or Friday.
The choice of day will be a surprise to you.

If there is no uncertainty about the day then there is no reason to present the second stipulation. If there is uncertainty than the conivcted man can reason that if he isn't hung on Wednesday or Thursday, then he can't be hung on the Friday (as it wouldn't be a surprise), and following on from this that he can't be hung the day before, or the day before that. Thus he 'knows' he won't be hung. Having convinced himself of this, on a perfectly logical basis, he is then able to be surprised when he is actually hung on one of the three days.

I think this one works better if given in the form;

You will be hanged at noon next week on Wednesday, Thursday or Friday.
The choice of day will be a surprise to you.

If there is no uncertainty about the day then there is no reason to present the second stipulation. If there is uncertainty than the conivcted man can reason that if he isn't hung on Wednesday or Thursday, then he can't be hung on the Friday (as it wouldn't be a surprise), and following on from this that he can't be hung the day before, or the day before that. Thus he 'knows' he won't be hung. Having convinced himself of this, on a perfectly logical basis, he is then able to be surprised when he is actually hung on one of the three days.

I think the original version posted works fine too actually. If the executioner tells you that you'll be hanged on Friday at noon, and tells you that you'll be surprised, then if you believe both statements, the natural conclusion is that he's lying because the two statements seem mutually inconsistent. So you do end up being surprised because he was telling the truth!

The revised version has the advantage that you have to go through a little bit of clever reasoning to realize that the statements are on the surface mutually inconsistent, so it's less obvious what's going on.

The essence of the two is identical though - if you believe the executioner then he must be lying, and if you don't believe him, then he's telling the truth.

We're all a little wierd in our own little wierd way. :D

I think the original version posted works fine too actually. If the executioner tells you that you'll be hanged on Friday at noon, and tells you that you'll be surprised, then if you believe both statements, the natural conclusion is that he's lying because the two statements seem mutually inconsistent. So you do end up being surprised because he was telling the truth!

The revised version has the advantage that you have to go through a little bit of clever reasoning to realize that the statements are on the surface mutually inconsistent, so it's less obvious what's going on.

The essence of the two is identical though - if you believe the executioner then he must be lying, and if you don't believe him, then he's telling the truth.



Wheeee! Paradoxal cunundrums are fun! :D :D :p :headbang:

I am not he who writes this words