Russell's Paradox

[Pro]

Russell's Paradox.

[Pro]

It's pretty much impossible for me to rewrite the protheory.com topics in full as I'd end up just making it too complicated so for now please just take a look at this original archive from my website and then you can ask me any questions below here

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?



The 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.

[thrillz]

That is not Russell's Paradox.

The answer to the question 'Does the set of all sets contain itself?' is irrefutably yes. No contradiction is derived from that answer. 'All sets' is an all-encompassing definition.

Russell's Paradox concerns the question:

Does the set of all sets that do not contain themselves contain itself?

Here the answers yes and no both lead to circular implications and absurdities.


Now, I have two (not three) responses to what you have tried to achieve by creating this website and your 'theory'. One you might come to appreciate, one you won't.


'Nice' response

You are clearly interested in mathematics and the workings of the universe and that at least is to be applauded. If only more people were, or at least were comfortable admitting so. You claim to not have had a formal education in mathematics, physics or philosophy at an undergraduate degree level, which puts you at a big disadvantage for reasons you won't readily understand.

At university studying Maths, Physics or Philosophy, the most important thing you learn regarding your chosen subject isn't the specific teachings within it, but the overall logical use of it in general and with regards to the other two. Time on a philosophy degree, for instance, isn't spent wondering whether God exists or what acts are ethically sound. It is spent teasing out the ambiguities within and strengthening our understand of logic in general. The key teaching is that any logical system (that is, environment where we might wish to deduce things logically) requires axioms (basic assumptions). For instance, when philosophers get together and talk about the world they all silently agree for the moment that the axiom "The world exists" holds. If one of them turns around and says 'No, you can't possibly prove that because you can't even prove that the world exists' then he would get annoyed glares from his colleagues (and his funding cut).

All logical deduction stems from axioms. They are, if you like, the rules by what logical deduction should be conducted. Adding some or taking some away can screw everything up (eg adding the axiom 1=0 means that every number equals every other number and now numbers are meaningless).

Mathematics takes this logical framework and creates many different worlds. For instance, in what's known as Euclidean Geometry it is an axiom that any parallel lines don't intersect. Properties about Euclidean geometry are deduced from this axiom. In Hyperbolic Geometry on the other hand, all the axioms of Euclidean Geometry hold except that parallel lines CAN intersect. This creates an entirely new mathematical world with different properties. We could create systems where the shortest distance between two points isn't a straight line. Such systems are studied in mathematics.

Finally, Physics takes these mathematical systems and looks to them for frameworks for modelling the observable world we see around us. Physics isn't too bothered with any mathematical systems where the shortest distance between any two points isn't a straight line, because that doesn't fit the observable world. So, by the time all this logic is being applied to physics many axioms are already being assumed. When physicists talk about things it would be crazy to suddenly ignore a logical axiom such as 'The World Exists'. There wouldn't be any point for them to do so.

Now from what I can see, what you have done with your theory of everything is take questions (for instance the Poincaré Conjecture) rooted in systems that do have axioms (such as the axioms of mathematics in a well-defined space) and then asked the same question in your system where every question is reducibly both right, wrong and neutral (whatever that means). The crux of this is that your 'theory of everything' doesn't apply at all to anything anyone cares about. It is a philosophical side-show. A logical 1=0 with no useful applications whatsoever.


'Nasty' Response

So, please, with all of this in mind, stop wasting everyone's fucking time. No, you have not created a theory of everything. You have not answered unanswerable questions and the Clay Math Institute aren't about to start sending you millions of dollars. Your idea isn't even original. There's a reason people put stock into BScis and DPhils you know.

I've never seen such rubbish displayed with such blind enthusiasm.

[Pro]

Well that was a bit different. I'm not trying to say everything suddenly becomes meaningless. I'm trying to say that if you really want to know then this is the ultimate structure of logic.

I've never lied about my knowledge or lack of it, nor have I criticised anybody else for either condition. The practical applications are subtle and I can't list them all right now, you've got me there cold.

If anybody tries to say my theory has no practical applications I'll use my stock response of three worded answers probably, although I'm not really sure how to proceed any more.

People spend their time building critiques against me, inaccuracies in my descriptions of other people's works, not my own. They say my theory has no practical use, it's inaccurate, it's neutral and blurry, but in the end it's all the same thing.

The axioms and basic assumptions you speak of are ok for almost every other application apart from the TOE. Why? The TOE is plural and so trying to force assumption onto it doesn't just work, it works, doesn't work plus neutral.

So if I'm to learn the laws of logic the word law puts me off immediately as it seems to apply an unchanging commodity, much like the axioms.

So, please, with all of this in mind, stop wasting everyone's fucking time. No, you have not created a theory of everything. You have not answered unanswerable questions and the Clay Math Institute aren't about to start sending you millions of dollars. Your idea isn't even original. There's a reason people put stock into BScis and DPhils you know. I've never seen such rubbish displayed with such blind enthusiasm.

I've written a theory about how everything is three things and you've written singularly about it, do you see where I'm coming from here?

I don't mind if I've mis-quoted somebody by mistake, or I've stated a problem wrong by accident on here or whatever. I'm just fed up with getting the same responses lately, people try to pin singularities on me

[TriPower]

Originally Posted by thrillz 'Nasty' Response I've never seen such rubbish displayed with such blind enthusiasm.

Thrillz - this response betrays a total lack of understanding of the logical structure of Protheory.

It's been awhile since you posted the above but I hope you read this!

Protheory is based on recognition of three simultaneous possibilities - all of which have the potentiality to apply in any given circumstance.

(1) p is the case (+)
(2) ~p is the case (-)
(3) Both p and ~ p is the case (0)

Now you will immediately shudder at the sight of this seeming CONTRADICTION at (3) as ask : How can something be both p and not p.

(3) p + ~p = 0 (Truth value is neutral - not true but not false either).

~(p) + ~(~p)
= ~p + p
= 0

Consider this hypothetical situation : You hold up a cup and ask: Is this a cup? But then the cup slips from your fingers and breaks into several pieces (which can be clued back together). How can the question be answered now?

(1) Yes it is a cup!
(2) No - it is not a cup!
(3) Well it is not a cup but it also is not the case that it is not a cup.

See how the three simultaneous possibilities can be applied and we can say: true, false or not true and not false without contradiction.

My favorite example is: Does God exist?

(1) Yes God exists! (False - no proof)
(2) No - God does not exist (False - no proof)
(3) Well it is not the case that God exists - because there is no proof. but then again, it is not the case that God does not exist because there is not proof. (True)

Therefore the answer to God's existence is indeterminate (neutral - not true and not false) at this stage. If we are searching for falsity then this is the only logically correct answer.

Once you can conceptually grasp both p + ~p = 0 Protheory will make absolute sense.