[subversion]

Originally Posted by <<>>

'There is a wrong interpretation by you all: all sets contain themslves in that they contain all their members and these are the set, but this is not containing itself, it's just being itself.

You contradict yourself. You say that all sets contain themselves and then proceed to say that they do not contain themselves. So which is it Guille?

[subversion]

Originally Posted by <<>>

The containing about which russell' paradox is about is that a set's cnditions for members includes the set itself.

Does something not always meet it's own criteria for existence, except necessarily for something that doesn't exist, i.e. nothing?

[Guille]

Originally Posted by subversion

You're wrong, the cookie always contains itself in order to be a cookie. Why do you say that the cookie does not contain it's own self? Do you mean to say that the cookie does not belong to itself? You might not want to tell the cookie that

The simple answer to the paradox is that all things logically contain themselves and if something doesn't it is nothing, i.e. the empty set. Doesn't that make perfect sense?

Answers aren't always simple, nor is simplicity always the answer. In fact, to explain something in a simple way, we have to go the complex way. But this simple explanation you give is just inventing things up. I'm tired of trying to explain you what 'contain' means in set theory, and that the logical meaning is not the same as the metaphysical. And that being is not the same as containing. But you stay in your view, that's ok, but please don't keep on teasing me.

[subversion]

Originally Posted by dustin_archibald

I don't know if someone already said this, in this thread; there is a lot to read and understand.

One way to avoid Russell's Paradox is to prove that it isn't a paradox at all.

One way we can do this (prove it's not a paradox) is by proving that it's based on a false assumption; that sets can contain themselves, more specifically, sets have the ability to contain themselves. How do we do this? We need to prove that a set cannot contain itself; that it cannot exist if it contains itself.

A second way to do this (prove it's not a paradox) is by proving that it's based on a false assumption; that a set cannot contain itself; a set does not have the ability to contain itself. How do we do this? We need to prove that a set must contain itself; that a set cannot exist without containing itself.

If you can prove that either (one or the other) assumption is incorrect, the paradox will fall apart since it is based on a false assumption

Answering the question "Does the set of all sets contain itself?" is important since, in my opinion, it is the only set with the possibility of containing itself.

You are exactly right Dustin! One of the two options you mentioned can solve the paradox by proving it is irrelevant (which is how I think I solved it). However, I think the option that we need here is the one where we "prove" that sets must contain themselves. The reason we must prove this instead of the opposite is because in order for a theory of everything to exist, there must be a complete set, and in order for a complete set to exist, it must contain itself. Therefore according to the law of positivity, which assumes that the theory of everything must exist (because it is not just good, but the best thing), the complete set must also exist and it must contain itself in order to be complete, and therefore sets must contain themselves in general. Therefore any set which does not contain itself is an empty set and synonymous with all other empty sets.

[subversion]

Originally Posted by <<>>

I give you these proof: the set of all Dustins is not a Dustin itself, therefore it doesn't contain itself. The set of of all sets that have infinite to 0 members contains itself, as it has a number of members (even if it's infinite). By the first I proof that sets have the ability to not contain themselves, and by the second I proof that sets have the ability to contain themselves.

Yet again, the set of all Dustins may not be a Dustin itself, but the set of all Dustins isn't supposed to be a Dustin necessarily. The only thing the set of all Dustins is supposed to be in order to exist is the set of all Dustins. Therefore as long as the set of all Dustins is the set of all Dustins (i.e. it exists) then the set contains itself.

As for your other example, what if their are no sets that have zero to infinite members. Then the set of all sets that have infinite to zero members could be empty and thus wouldn't necessarily contain itself.

Thus I conclude that you have not proven that sets cannot contain themselves. Take this for example, is your body the contents of Guille's body? Well, I should hope so if you consider yourself to be alive.

[subversion]

Originally Posted by <<>>

Answers aren't always simple, nor is simplicity always the answer. In fact, to explain something in a simple way, we have to go the complex way. But this simple explanation you give is just inventing things up. I'm tired of trying to explain you what 'contain' means in set theory, and that the logical meaning is not the same as the metaphysical. And that being is not the same as containing. But you stay in your view, that's ok, but please don't keep on teasing me.

I'm not teasing you, I'm just trying to make you get over your ignorance. If there is a valid disproof of my argument that everything contains itself all you have to do is tell me why you think that everything cannot contain itself, everything. Please if you want to prove me wrong don't get upset, just do it. Prove to me that everything does not contain everything. Because if everything does contain everything then my solution to russell's paradox must be correct. Won't you please just give me some credence and stop acting all jealous. I can't tell you all the theory of everything if you can't see that everything must contain itself. If everything didn't contain everything, then it wouldn't be everything, right? So work with me here ok? Alright, now all you have to do is answer a very simple and straightforward question so please just take this seriously. What is the container of everything, and must everything be it's own container? If everything does not contain itself, then what does contain everything? If you believe that nothing contains everything, I can tell you that you are exactly wrong, because nothing cannot possible contain something. Furthemore, believing that there is nothing which contains everything is believing that the TOE does not exist. So again, what contains everything? If it is not everything itself, then what is it?

[protheory]

Hi everybody, I'm posting my own ideas about Russell's Paradox and by definition all other paradoxes that take the same form, such as The chicken and the egg, and Is this a question?

I have answered both of these other paradoxes on my site here... http://www.protheory.com/Paradox%20Answers.htm

And here's my answers to Russell's Paradox...

Russell's Paradox

Introduction

Is the ultimate set of all sets a member of itself or not?

This paradox appears to be singularly unsolvable.

Philosophy

Russell's paradox relates to a branch of philosophy called set theory.

Sets

As its name suggests this theory uses the idea of categorising all parts of a problem into different sets or groups.

Rules

The rules for creating these sets are infinitely debatable, it depends what method you choose to divide your different objects, ideas, or answers.

Relative

All details are relative in other words.

Assumed

The sets were assumed to be hierarchical and this is where the paradox arises from.

Paradox

The paradox within set theory and many similar theories is whether the set of all sets is a member of itself.

Example

Is the word "word" a word?

Summary

Russell noticed it was impossible to conclusively prove beyond all doubt that the highest possible set was or indeed was not a member of itself.

The Problem

Is the set of all sets a member of itself or not?

Tha Answer

Problem

It cannot be unchangingly proven that the set of all sets is a member of itself.

Answers

Whichever "yes or no answer" you choose another person such as myself could state the opposite with equal conviction.

Three

We need to use three simultaneous answers at all relative times to be totally accurate, and to account for the fact that all energy within the universe may perform three simultaneous actions at any one time.

Is the set of all "sets" a member of itself?

1. The set of all sets is a member of itself.

2. The set of all sets is not a member of itself.

3. The set of all sets is neutral.

Simultaneously.

Am I wrong?

I simultaneously oppose, agree with, and neutralise all criticism ad infinitum.

My point is literal.

There is no point creating a theory of everything that doesn't work.

This is my own exploration of this paradox, according to my own TOE which I have been posting about here... http://www.toequest.com/forum/your-t...heory-com.html

I hope you find my theory an interesting point of view on this much studied subject.

Thanks.

PRO

[Canute]

Russell acknowledged that G. S. Brown's 'calulus of indications' did away the need for his theory of types. Perhaps it is worth a look. It was presented in his Laws of Form (1969), and there is quite a lot of discussion online.

[protheory]

Originally Posted by Canute

Russell acknowledged that G. S. Brown's 'calulus of indications' did away the need for his theory of types. Perhaps it is worth a look. It was presented in his Laws of Form (1969), and there is quite a lot of discussion online.

Thanks for the information about this Canute, I'll definitely take a look at it online

I posted in this topic as I noticed some interest about Russell's Paradox, I think that the same paradoxical principle runs through many other similar paradoxes, some of which I have written about on my site http://www.protheory.com/Paradox%20Answers.htm

What do you think about it all?

PRO

[Canute]

Originally Posted by protheory

Thanks for the information about this Canute, I'll definitely take a look at it online

I posted in this topic as I noticed some interest about Russell's Paradox, I think that the same paradoxical principle runs through many other similar paradoxes, some of which I have written about on my site http://www.protheory.com/Paradox%20Answers.htm

What do you think about it all?

PRO

I agree that most paradoxes tend to have a lot in common. But I can't get my head around your approach yet.

I feel the correct answer to R's paradox was given by my teeenage son, who knows almost no mathematics. He asked me one day for an example of a paradox (for a song lyric). I mentioned Russell's paradox and spent five minutes explaining it, talking about sets of all sets that do not contain themselves, whether it contains itself or not etc., and probably confused the issues more than necessary as usual. At the end he said, well, the paradox only arises because we invented sets.

I thought this was rather a good comment, and it is not far from the solution presented by G. S. Brown. Paradoxes, it seems to me, do not exist in nature, but are artefacts of errors in the way we conceive of it.

Canute