## Mummy, Mummy, what’s Russell’s Paradox?

Discussion of articles that appear in the magazine.

Moderators: AMod, iMod

Philosophy Now
Posts: 753
Joined: Sun Aug 29, 2010 8:49 am

### Mummy, Mummy, what’s Russell’s Paradox?

A_Seagull
Posts: 520
Joined: Thu Jun 05, 2014 11:09 pm

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Well it shows that the concept of sets is logically flawed.

Philosophy (nor even maths) needs the concept of sets anyway.

-1-
Posts: 1026
Joined: Thu Sep 07, 2017 1:08 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Okay... so then... what's your argument, what is your point, and what is your question for debate. These three things are required for new original posts, and you provided zero for three.

It's not too late, please improve your chances of the post not getting removed. Make something out of it, I beg you.

Eodnhoj7
Posts: 1274
Joined: Mon Mar 13, 2017 3:18 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

I never understood how sets could be observed as the foundation of number theory when the set, in itself, is "1". It always appeared to me, and I will be in the minority probably, that sets are merely structural extensions of 1 as a means to "try" to justify "1". I think set theory is full of sh"t.

It always appeared to me that one would need prior sets to justify the original set, ad-infinitum, with each set in itself being "1". In these respects "1" must continually reflect itself ad-infinitum through perpetually every other number in order to justify itself as a foundational number. Wittgenstein observed this logically with "every tautology in itself is composed of another tautology".

Everything we understand of math is strictly unity and multiplicity with 1 being the median dimension of both. 1 as positive provides the foundations for addition, multiplication and exponentiation. 1 as a negative provides the foundation for subtraction, division and exponentiation.

This is considering multiplication is the addition of addition through 1 as positive and exponentionation is multiplication of multiplication. Vice versa for subtraction, division, roots.

Addition is summation as unity whose negative dual is subtraction as "deficiency". Multiplication/Division and Exponentiation/Root is the observation of multiplicity as form of indivduation through the propogation of "units" as parts. 1 is the medial point for this and simultaneously acts as a dimension of proportion in itself.

Considering 1 is the root for all number, as both unity and unit, it manifests a dualistic nature of definitionless definition. Infinity follows this same structure as numberless number.

I placed the argument in the math/logic section of the forum, but 1 must be proportional to infinity as both provides the foundations for proportion itself.

Arising_uk
Posts: 10936
Joined: Wed Oct 17, 2007 2:31 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Eodnhoj7 wrote:I never understood how sets could be observed as the foundation of number theory when the set, in itself, is "1". ...
I'm well out of my depth with respect to Mathematics but I thought the ground for sets with respect to numbers was zero or { }, i.e. the empty set?

Eodnhoj7
Posts: 1274
Joined: Mon Mar 13, 2017 3:18 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Arising_uk wrote:
Mon Dec 18, 2017 1:07 am
Eodnhoj7 wrote:I never understood how sets could be observed as the foundation of number theory when the set, in itself, is "1". ...
I'm well out of my depth with respect to Mathematics but I thought the ground for sets with respect to numbers was zero or { }, i.e. the empty set?
Then what is the set? So the set is empty, that means the set exists. I am not arguing against you, but the logic for set theory requires the set to act like a "vessel" of number that is equivalent to one. What is the vessel but "1"?

It is not an argument that you have to be an expert in to understand.

Arising_uk
Posts: 10936
Joined: Wed Oct 17, 2007 2:31 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Eodnhoj7 wrote:Then what is the set? So the set is empty, that means the set exists. ...
Does zero exist?
I am not arguing against you, but the logic for set theory requires the set to act like a "vessel" of number that is equivalent to one. What is the vessel but "1"?
Zero, it is an empty set.

I think this idea of a "vessel" misleading as a set, as far as I can tell, is just a group of things with no need to put them in an actual box.

Eodnhoj7
Posts: 1274
Joined: Mon Mar 13, 2017 3:18 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Arising_uk wrote:
Mon Dec 18, 2017 2:08 pm
Eodnhoj7 wrote:Then what is the set? So the set is empty, that means the set exists. ...
Does zero exist?
It is not "anything". The observation of 0 is an observation of non-existence, which can only be observed relative to one.

I am not arguing against you, but the logic for set theory requires the set to act like a "vessel" of number that is equivalent to one. What is the vessel but "1"?
Zero, it is an empty set.

I think this idea of a "vessel" misleading as a set, as far as I can tell, is just a group of things with no need to put them in an actual box.

But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".

Arising_uk
Posts: 10936
Joined: Wed Oct 17, 2007 2:31 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Eodnhoj7 wrote:It is not "anything". The observation of 0 is an observation of non-existence, which can only be observed relative to one.
It can be relative to the absence of any number of things?

But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
And in all cases there is no thing around them, just lots of objects?

Eodnhoj7
Posts: 1274
Joined: Mon Mar 13, 2017 3:18 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Arising_uk wrote:
Tue Dec 19, 2017 1:17 am
Eodnhoj7 wrote:It is not "anything". The observation of 0 is an observation of non-existence, which can only be observed relative to one.
It can be relative to the absence of any number of things?

Relation is absence of structure. We can observe zero as the limit of 1 as "non-being" is the limit of being. This duality between 1 as "being" and 0 as "nonbeing" allows a synthesis as gradation or "deficiency" which we observe in fractals and negative numbers.

But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
And in all cases there is no thing around them, just lots of objects?
According to set theory it has to be further sets, unless there is something I am missing.

Arising_uk
Posts: 10936
Joined: Wed Oct 17, 2007 2:31 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Eodnhoj7 wrote:Relation is absence of structure. We can observe zero as the limit of 1 as "non-being" is the limit of being. This duality between 1 as "being" and 0 as "nonbeing" allows a synthesis as gradation or "deficiency" which we observe in fractals and negative numbers. ...
Nothing about 1 and 0 leads to fractals nor negative numbers I'd have thought? As none of these things exist.
But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
According to set theory it has to be further sets, unless there is something I am missing.
No idea as like I say mathematics not my thing but you said sets needed '1' to be the foundation of numbers and from what I can grasp they need '0' not '1' to define numbers.

Eodnhoj7
Posts: 1274
Joined: Mon Mar 13, 2017 3:18 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Arising_uk wrote:
Tue Dec 19, 2017 4:26 am
Eodnhoj7 wrote:Relation is absence of structure. We can observe zero as the limit of 1 as "non-being" is the limit of being. This duality between 1 as "being" and 0 as "nonbeing" allows a synthesis as gradation or "deficiency" which we observe in fractals and negative numbers. ...
Nothing about 1 and 0 leads to fractals nor negative numbers I'd have thought? As none of these things exist.

But isn't that what a set is, a "dimension" or "boundary" limit? We observe the same for "groups" or "categories".
According to set theory it has to be further sets, unless there is something I am missing.
No idea as like I say mathematics not my thing but you said sets needed '1' to be the foundation of numbers and from what I can grasp they need '0' not '1' to define numbers.
The set as empty may be zero {0}, but what about the set itself { }? If it is not a number, but a function of number, it needs a form to extend from, in this case "1". Zero is not a foundation, because zero is nothing. I understand that is what they may argue, but it is irrational as zero is absent of an definition.

Arising_uk
Posts: 10936
Joined: Wed Oct 17, 2007 2:31 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Eodnhoj7 wrote:The set as empty may be zero {0}, but what about the set itself { }? If it is not a number, but a function of number, it needs a form to extend from, in this case "1". Zero is not a foundation, because zero is nothing. I understand that is what they may argue, but it is irrational as zero is absent of an definition.
Again, not my field but from what I see { } is the empty set, {0} is 1 in numbers so they appear to think zero is a number and given it is a number symbol I guess they are correct?

Eodnhoj7
Posts: 1274
Joined: Mon Mar 13, 2017 3:18 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Arising_uk wrote:
Tue Dec 19, 2017 4:33 am
Eodnhoj7 wrote:The set as empty may be zero {0}, but what about the set itself { }? If it is not a number, but a function of number, it needs a form to extend from, in this case "1". Zero is not a foundation, because zero is nothing. I understand that is what they may argue, but it is irrational as zero is absent of an definition.
Again, not my field but from what I see { } is the empty set, {0} is 1 in numbers so they appear to think zero is a number and given it is a number symbol I guess they are correct?
http://www.straightdope.com/columns/rea ... -a-number/

Thats the thing, some people say zero is a number and others say it is not. One is a number, plus it provides a foundation.

Would zero be a number without the set? That is the question I ask, because if it requires a set to be a number than the set itself must be a number conducive to one.

Arising_uk
Posts: 10936
Joined: Wed Oct 17, 2007 2:31 am

### Re: Mummy, Mummy, what’s Russell’s Paradox?

Eodnhoj7 wrote:Thats the thing, some people say zero is a number and others say it is not. One is a number, plus it provides a foundation. ...
I think you're on shaky ground if you are looking to provide a foundation for Mathematics as Russell and Whitehead tried with Logic and only partly succeeded, mainly with the numbers as it happened.

Zero is only not a number if you stick with the natural numbers but if you do that you can't have the negative numbers, et al, which I doubt you'd want?
Would zero be a number without the set? ...
What are numbers in our Mathematics, functions. What do you think they are?
That is the question I ask, because if it requires a set to be a number than the set itself must be a number conducive to one.
Not sure what you mean here but, as best I understand it, a set doesn't have to be a number as it can be the empty set { }.

### Who is online

Users browsing this forum: No registered users and 2 guests