Dunno if this is relevant...
Anyway, in his later years Plato was increasingly influenced by the Pythagoreans, and he paid more attention to the mathematical aspect of his philosophy.
In his essay "Concerning Good" (Norwegian Title "Om det Gode"), he argues that the ideas could be divided in to two or three elements (or facts). Human eg. would be described as 1.) a living being 2.)without wings 3.)with two feet.
However, the number 1(hen in Greek) could not be divided. Plato concluded that this had to be the mathematical expression for "good", as it cannot be divided, but can in fact divide all other numbers, as he meant this virtue was the basic element of all other ideas.
The Norwegian writer and philosopher Egil A. Whyller has written a lot about this.
chrdani wrote:Quote:
I propose a new line of though. Ommism. Everything is one. There is just one thing, and that thing is called everything. All the rest is just sub-dividing.
You should be careful about proposing a set that contains "everything". According to "Russel's Paradox" (after the mathematician Bertrand Russel), there exist two types of sets:
1. Sets that do contain themselves
2. Sets that do not contain themselves
The set of all sets of type 2 cannot be properly defined without reaching a contradiction.
One set cannot contain everything, without containing itself. Thus the universial set in Set Theory is always defined.
'Sets' that can or cannot contain themselves are not sets.
Quote:'Sets' that can or cannot contain themselves are not sets.
Maybe it was an unclear explanation.
Check it out for yourself:
http://plato.stanford.edu/entries/russell-paradox/
Quote:'Sets' that can or cannot contain themselves are not sets.
Maybe you understood the example, you just forgot that I was talking about a paradox?
Dunno, however it is not very easy to understand anyways....
chrdani wrote:Quote:'Sets' that can or cannot contain themselves are not sets.
Maybe you understood the example, you just forgot that I was talking about a paradox?
Dunno, however it is not very easy to understand anyways....
Set theory is all to pot. Set theory is confused beyond the level of understanding we use in infant school. I would not listen to anything the mathematicians or 'philosophers' have to say about sets. They have all got it wrong.
Everything need not be a set. It can be a list.
JJ wrote:
Quote:Set theory is all to pot. Set theory is confused beyond the level of understanding we use in infant school. I would not listen to anything the mathematicians or 'philosophers' have to say about sets. They have all got it wrong.
Everything need not be a set. It can be a list.
Yeah yeah yeah... everything old is drek. Nobody knew anything. Right.
So, how is a list not a set, or, isn't a set a list?
Joe(one set of settled elements)Nation
Hey, Joe, what'cha doin' here? Picking up some fresh fruit and veggies at the agora?
Merry (I am therefore I think) Andrew
chrdani
I think that Everything can be a set or not, according to the definition we give.
If we say that everything is just atoms, then EVERYTHING is a set, that is not part of itself (because, as you pointed very well, everything, in this case, is not an atom).
But if we say that EVERYTHING is just all that is, then we have not a set (there are no common elements) but, as Jones said, just a list.
In Descartes dualism, there are only bodies and souls. If we made a set of souls and a set of bodies, both would not be part of themselves (the set of souls is not a soul ...).
Then, EVERYTHING would be the set of two sets that are not part of themselves. But EVERYTHING, being a set, is part of itself (a set of sets).
So, EVERYTHING would be a set that is part of itself, but containing only sets that are not part of themselves.
Then, how can a set that is part of itself be the set of the sets that are not part of themselves?
From this, I think Jones is right. EVERYTHING cannot be a set. Only a list, but with the problems I have mentioned in my last thread.
Joe Nation wrote:JJ wrote:
Quote:Set theory is all to pot. Set theory is confused beyond the level of understanding we use in infant school. I would not listen to anything the mathematicians or 'philosophers' have to say about sets. They have all got it wrong.
Everything need not be a set. It can be a list.
Yeah yeah yeah... everything old is drek. Nobody knew anything. Right.
So, how is a list not a set, or, isn't a set a list?
Joe(one set of settled elements)Nation
A list is not a set if I don't make a set of all the things in the list.
I can say set theory is all to pot at the basic level because
1. It is.
2. People understand set theory as much as they understand me when I say set theory is all to pot.
I didn't put it strongly enough. There is no set of everything, and nothing that is predicated by 'all' can be put in a set. The name of a set must show precisely what it is a set of. 'All' and 'everything' do not indicate the particular cases of each object.
dunno if I misunderstod this, val:
Quote:If we say that everything is just atoms, then EVERYTHING is a set, that is not part of itself (because, as you pointed very well, everything, in this case, is not an atom).
If you say that everything is just atoms...then your set as an abstract idea is just atoms, and therefore it is a part of itself.
I least that is what I think when I see it...but then again, I'm only a cluster of atoms
