Russell's Paradox: The Achille's Heel of Solipsism?

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The discussion revolves around the philosophical implications of solipsism and its potential conflict with Russell's paradox. The original poster questions whether solipsism, which posits that only one's mind is certain to exist, can withstand logical scrutiny, particularly in light of Russell's paradox, which suggests that a set cannot contain itself. Participants debate the nature of the mind in relation to sets, with some arguing that the mind should not be viewed as a set of all things, as this leads to contradictions. They explore concepts like fuzzy sets and multi-valued logic, suggesting that if the mind is modeled as a category rather than a set, the paradox may be circumvented. The conversation also touches on the limits of human consciousness and memory, proposing that the mind operates as a subset of a greater subconscious. Ultimately, the discussion highlights the complexities of defining existence and reality within the frameworks of philosophy and logic, questioning whether the universe or the mind can be coherently understood as singular entities.
  • #91
Originally posted by Mentat
Fine, and this most certainly doesn't apply to an atom (or even a proton, for that matter). Look at the definition, and put it up against what I've been saying about quantum Uncertainty and fluidity of quark movement...
"A substance that does not flow perceptibly under moderate stress"...a proton (and, more Way LESS importantly, as the "Model for exemplary solidity" is the PROTON, NOT the quark! [/color] importantly, a quark) does flow perceptibly under moderate stress. Remember, at the quantum level there are no real "particles" but "wavicles" which behave both as particles and as waves.

"has a definite capacity for resisting forces which tend to deform it"...surely you're not going to say that the collapse of the wave-function of a fundamental particle, under rather minute stress (in quantum terms) still allows it to meet this criterion. Words in my mouth?, NO! I said PROTON! the above is proven FASLE in respect of Protons inasmuch as the energies required to "bust em up", But maybe you just don't know anything about that...[/color]

"and under ordinary conditions retains a definite size and shape"...size, maybe; but shape?! No way. Are you still talking about quarks? or Protons? in this statement, cause if your saying shape in a proton is changing over time, please PROVE IT![/color]

EDIT P.S. The reference to "Flow perceptibly" is a distinguishement from "fluidity" which is not to be confused with 'deformation' from impact(s)...even a Quark Does not "flow" as a "fluid" more likened to a gel...sticky...
 
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  • #92
Originally posted by Mr. Robin Parsons
followed by;

Follow your own advise please.....because when (and now you warrant the offence as you are attempting to place words in my mouth, that come from you, NOT me!) an "Idiot" pretends to do someone elses's thinking for them, well what they really see is simply the inside of themselves...and BTW justify 'idiot'? the first quote does that, well...you do it to yourself...

P.S. You'll notice that the dictionary definition follows what I have been saying, and I notice you cannot prove otherwise, either...nothing more then a (very) poor loser, with the inclusion of the obviousness of the sadness that you don't seem to even be concerned in finding the answer, but more defending what you have been taught by "others"...how sad, and un-Scientific...

Watch the personal remarks, please. They're never warranted and were only produced ever since the side-tracking (partially my own fault ) of the this thread...which is why Mumeishi would be asking us to "move on".
 
  • #93
Originally posted by mentat
Watch the personal remarks, please. They're never warranted and were only produced ever since the side-tracking (partially my own fault ) of the this thread...which is why Mumeishi would be asking us to "move on".
A small piece of advice, please direct your remarks at the person initiating the event, maybe you hadn't noticed (as per friendship) but it is mumeishe's "ridcule" that started this, your remark about "what has age to do with it" didn't help either, but does tell me what you do know about it...(by your hand)...
 
  • #94
Originally posted by Mr. Robin Parsons
EDIT P.S. The reference to "Flow perceptibly" is a distinguishement from "fluidity" which is not to be confused with 'deformation' from impact(s)...even a Quark Does not "flow" as a "fluid" more likened to a gel...sticky...

You see how this is all that showed up when I hit "quote"? That's because you typed within the quote-box again...please don't do that, it makes it very hard to respond coherently.

As it is, the proton may be your model for solidity, but a while ago it was the atom, and it isn't really relevant either way. Neutrons have been shown to posses exactly those "wavicle" properties as the fundamental quarks have, except at a less noticable level. Protons must be the same (though I don't personally know for sure if experiments have been conducted on the proton).

I never mentioned the ability to "bust up" a proton, but the ability to deform it. Ever heard of "decay"?

Last, but not least, when I remarked about its "shape" I was talking about the fact that the proton may be a hadron of point particles, or it may be a hadron of vibrating strings. It (the whole proton (though that's like speaking of "the whole solar system" as a separate entity from "planets revolving around star", IMO)) also "changes" form to be a "wave" in some experiments, while it shows up as a "particle" in other experiments (again, this is an assumption, but it is based on having actually read about the experiments done on Neutrons which are hadrons too).
 
  • #95
Originally posted by Mr. Robin Parsons
A small piece of advice, please direct your remarks at the person initiating the event, maybe you hadn't noticed (as per friendship) but it is mumeishe's "ridcule" that started this, your remark about "what has age to do with it" didn't help either, but does tell me what you do know about it...(by your hand)...

Mumeishi didn't initiate the insults, and my opinion on that is not biased, but based on having looked back to make sure...he only said that we should move on.

And what does my comment about age have to do with it? I didn't insult you. In fact, I could have been (though I wasn't) insulted by the implication, on your part, that I must be less intelligent than you simply because I'm younger than you.

Indeed, an older person has had more opportunity to become wise, but that just makes it all the more inexcusable that so many haven't. It doesn't mean that a younger person has had no opportunity to gain wisdom, and it doesn't mean that they haven't taken better advantage of this opportunity than someone thrice their age.
 
  • #96
Originally posted by Mentat
Mumeishi didn't initiate the insults, and my opinion on that is not biased, but based on having looked back to make sure...he only said that we should move on. And what I would really like to know (possible the Mentors too) is how he kept it from registering the EDIT!...cause if you look at my posting, just below his "Lets move on", you will see that I had Captured his Ridicule of me (Insult) so his having edited his post "Sans notation", well really suspicious, don't you think? nevermind I can no longer trust him for anything he types on these pages unless I keep copies of every single thing, OYE he ain't worth it![/color]
EDIT: Oooops, my mistake he deleted the insulting one, I got it now...[/color]

And what does my comment about age have to do with it? I didn't insult you. In fact, I could have been (though I wasn't) insulted by the implication, on your part, What part, the part where I apologised to you?[/color] that I must be less intelligent than you simply because I'm younger than you. Insecure? why don't you try reality, nothing to do with intelligence, But with "KNOWLEDGE" as that is a time dependant aquisitional 'thing', so age, does make a (for your sake I put "potential") difference.[/color]

Indeed, an older person has had more opportunity to become wise, Start back at "knowledgable" please...wisdom's another thing altogether)[/color] but that just makes it all the more inexcusable that so many haven't. It doesn't mean that a younger person has had no opportunity to gain wisdom, and it doesn't mean that they haven't taken better advantage of this opportunity than someone thrice their age.

For you to be able to take advantage of the opportunities that I have had in my lifetime, you would need live 47 years. Just because you can "take better advantage then someone thrice their age" (IF that's true) doesn't mean you have caught up to them, even if you went at twice my pace, you would still be behind me, I have had 47 "opportunity years", if you were working at twice my pace you would have had 30, three times my pace and you are still short at 45...get it?
 
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  • #97
Heck I even got the error/EDIT wrong, mumeishi's ridicule, it's still there...
But while I am here, I had gone looking and found this...
(as I do want for accuracy)

Originally found at http://hep.bu.edu/~superk/pdk.html" site..

Because the exchanged particle is so heavy, the proton lifetime predicted by grand unification models is extremely long... about 20 orders of magnitude longer than the age of the universe!

No events have been observed and a limit on the lifetime has been set to be over 10^(33) years

the bottom statement coorelates to other sites "times" for proton decay, the 1033 years, others range it at 6.5 x 1031 years, but clearly, a long duration particle.

Clearly I had had it wrong when I had stated that it was in the 10to the 40's something as it is some time shorter then that...
 
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  • #98
Originally posted by Mr. Robin Parsons
For you to be able to take advantage of the opportunities that I have had in my lifetime, you would need live 47 years. Just because you can "take better advantage then someone thrice their age" (IF that's true) doesn't mean you have caught up to them, even if you went at twice my pace, you would still be behind me, I have had 47 "opportunity years", if you were working at twice my pace you would have had 30, three times my pace and you are still short at 45...get it?

You obviously missed the point.

First off, I wasn't referring to myself when I said the "take better advantage than someone thrice their age" comment.

Secondly, you have not taken advantage of every chance to gain more knowledge that you've been presented with in your life, and thus your age is not a good marker for how hard I have to work to catch up with you.

Lastly, wisdom is indeed different than knowledge, but most people think that both come with age, so I use them interchangeably in this context. I know that knowledge is an aquisitional thing, but if you spend very little time reading (and I'm not saying you do) for 47 years, but just let the time pass you by, while I'm learning more and more each day (this part is true), then I will indeed surpass you in knowledge. There's nothing wrong with that. If you did take advantage of every opportunity to gain knowledge throughout your lifetime (or even went at the same pace that I've been going at) then you'd be far beyond me...but have you really worked that hard? If you have, I commend you. If you haven't, then I request that you not comment on my age.
 
  • #99
Originally posted by Mentat
First off, I wasn't referring to myself when I said the "take better advantage than someone thrice their age" comment. Ahem, any reference to age, once introduced as it has been in this conversation, which (BTW) is about to cease, is taken as "in reference to the conversations direction". (that a Normal practise for most people) I would have thought you 'capable enough' to recognize thusly, and NOT try to use debating tactics with me, again, but...[/color]

Secondly, you have not taken advantage of every chance to gain more knowledge that you've been presented with in your life, and thus your age is not a good marker for how hard I have to work to catch up with you. It was an e-x-a-m-p-l-e to make the point that, (BY YOUR ADMMISSION) you hadn't understood, or so you said...[/color]

Lastly, wisdom is indeed different than knowledge, but most people think that both come with age, so I (Erroneously, as they are not interchangable, one is a product of the other...maybe!)[/color] use them interchangeably in this context. I know that knowledge is an aquisitional thing, but if you spend very little time reading (and I'm not saying you do) for 47 years, but just let the time pass you by, while I'm learning more and more each day (this part is true), then I will indeed surpass you in knowledge. There's nothing wrong with that. If you did take advantage of every opportunity to gain knowledge throughout your lifetime (or even went at the same pace that I've been going at) then you'd be far beyond me...but have you really worked that hard? If you have, I commend you. If you haven't, then I request that you not comment on my age.
You can never, in the entirety of your lifetime, surpass the 'minutia' of the "time of my life" as the "time of your life" must exceed the "time of my life" to accomplish that, after that, we begin into the realms of "Quality of knowledge" and importantly "Application(s) of Knowledge"...Oh yes, please try to remain true to your 'stated form', as you are the one who had told me he made "no conclusions" right?? cause I've seen a few since then.

The older person always "knows more" as they have been alive longer, after that 'quality' counts! Quality of the 'Knowing' that they acquire in simply being alive.

As for your last "two" lines, I don't know, neither do you, my comment on your age, if yourecall, was in the acceptance and the offering of apologies, and my acknowledgment (honesty) that I could recognize that this is an "unfairness", me debating, with you because of My Age, the rest, your defensiveness, well get over it mentat ( ) there are lots of people out there, and NO ONE has an absolute corner on the market for "Smarts".

After all, Smart people Intelligent people, Knowledgable people, and even Wise people (an Oxymoron? he hee ) share what they know, that sort of flattens the curvatures that have been getting smaller and smaller with the increasing populations...
 
  • #100
Well I'm older still, and my opinion is that it's possible to be wrong at any age, one just become able to do it with better arguments as time goes on, and in emergencies can always resort to being patronising.
 
  • #101
Originally posted by Canute
Well I'm older still, and my opinion is that it's possible to be wrong at any age, one just become able to do it with better arguments as time goes on, and in emergencies can always resort to being patronising.
Well, I would agree with the first part, "wrong at any age" is definitely real, as there is no 'age' that brings 'perfection' of action/activity/speach...but not with the last line, as that ends up as 'not educational' nor 'good modelling', but usually simply an indication of someone with either, 'no answer', or 'not the patience' to help the other to see simply their viewpoint.
(Sometimes I have "lacked the patience" too...sooo...)
 
  • #102
Originally posted by Mr. Robin Parsons
You can never, in the entirety of your lifetime, surpass the 'minutia' of the "time of my life" as the "time of your life" must exceed the "time of my life" to accomplish that

My point is that I don't need to exceed the amount of your lifetime in order to exceed the amount of your knowledge.

...after that, we begin into the realms of "Quality of knowledge" and importantly "Application(s) of Knowledge"...Oh yes, please try to remain true to your 'stated form', as you are the one who had told me he made "no conclusions" right?? cause I've seen a few since then.

It's called a Working Assumption. I wouldn't post it if I didn't want you to try and prove it wrong. I'm open to any logical debate on the matter, but that's not what I'm getting from you.

The older person always "knows more" as they have been alive longer, after that 'quality' counts! Quality of the 'Knowing' that they acquire in simply being alive.

As for your last "two" lines, I don't know, neither do you, my comment on your age, if yourecall, was in the acceptance and the offering of apologies, and my acknowledgment (honesty) that I could recognize that this is an "unfairness", me debating, with you because of My Age, the rest, your defensiveness, well get over it mentat ( ) there are lots of people out there, and NO ONE has an absolute corner on the market for "Smarts".

Even if that person is the oldest man alive. I'm not trying to be defensive, I'm trying to get you to stop making statements about people's ages since this can only serve to both offend the younger person and weaken your stance (by making you seem arrogant, and seem like you think you are justified in being arrogant because you're older).

I'm sorry if it bothers you for me to disagree with you, but that's the purpose of the forum: logical debate (not "I state what I think and you state what you think; we all make funny remarks about each other's views and move on").
 
  • #103
Originally posted by Mentat
My point is that I don't need to exceed the amount of your lifetime in order to exceed the amount of your knowledge.
O.K...And my point is that time is going to prove you wrong...Who's opinion do you think is more qualified? (And why?...then again, don' respond, please!)[/color]

It's called a Working Assumption. I wouldn't post it if I didn't want you to try and prove it wrong. I'm open to any logical debate on the matter, but that's not what I'm getting from you. Possibly? because you are not presenting it as an "open assumption" but rather as a conclusion...my opinion...[/color]

Even if that person is the oldest man alive. I'm not trying to be defensive, I'm trying to get you to stop making statements about people's ages since this can only serve to both offend the younger (Why? are you offended by the truth? by your own age? what is off-end(ing) you?) [/color] person and weaken your stance This is contrary to what you have written below, as this is not supposed to be about stances, but 'facts of Science' and "The description that approximates the truth of those scientific observations" the best, it is NOT 'won' by "Stance" it is learned in exchange...[/color] (by making you seem arrogant, and seem like you think you are justified in being arrogant because you're older).

I'm sorry if it bothers you Not in the least![/color] for me to disagree with you, but that's the purpose of the forum: logical debate (not "I state what I think and you state what you think; we all make funny remarks about each other's views and move on"). Is that what your exclusively doing??[/color]

Ab BTW "...Justified in being arrogant..." How is attempting to ensure that 'the best possible answer is presented' being 'arrogant'? arrogance presents itself as right because it says it is, the path I have followed is to attempt to show the "...description that approximates the truth of those scientific observations..." as in mumieshi attempted to ridicule me with one of the most common lines in an internet science forum, "You think all Science is wrong..." that I followed up on by simply posting the right information (dictionary reference) (as best as I could) and you, "couched immaturity" as you are showing yourself to be(?), call me arrogant for it?? what an arrogant (somewhat educated/book-read) little Boy you truly are presenting yourself as...no wonder it is so difficult for you...it is really becoming obvious that your opinion on age seems to be the only way you will accept it, maybe we can talk again when your in your twenties + +...cause as I stated and clearly,
Originally posted par moi
(SNIP)[/color]...which (BTW) is about to cease...(SNoP)[/color]

C:\Ya.*
 
  • #104
You see, if the Mind ß the Set of all things that exist, then how can the Mind itself exist at all?

Isn't existence relative? The mind itself cannot exist at all from the perspective of outside the mind. However, from inside the mind the mind is ALL that exists. The paradox, taken this way, comes closer to supporting the idea than disproving it.
 
  • #105
I'd say you've got something there. The Cosmos is also the set of all sets. I wonder if that's a coincidence. They're the only two things whose existence is so self-referential that it doesn't seem to be logical.
 
  • #106
there is an article on a different kind of TOE in which mathematical existence is postulated (or conjectured) to be physical existence. we may be some mathematical component called self aware structures in a larger structure. the set of all sets, which i repeat can exist in fuzzy logic, seems way more adequate than necessary to capture not only our universe but a multiverse where each universe operates differently.

the thing about self-referentialism is interesting.

let x be a single word.

define D recursively:
D(x,1) is the set of all words in all possible definitions of x.
for n>0, D(x,n+1) is the set of all words in all possible definitions of all words in D(x,n).

if {x}∩D(x,1)!=Ø then the definition is self-referential and i'll bet most would consider it useless.

i also bet that for all x, there is an n such that {x}∩D(x,n)!=Ø so all words are, in that case, defined somewhat self-referentially.

i know it's a stretch, but i bet there are a few words that "generate" all other words along with the rules of grammar. i wonder if those generators would be synonyms and how many there are.

anyway, i suppose this article has to do with spooky action at a distance; it's about the hologramic theory of the universe:
http://www.water-consciousness.com/must/must_article33.htm
i know this is a stretch, but...
The holographic paradigm also has implications for so called hard sciences, like biology. Keith Floyd, a psychologist at Virginia Intermont College, has pointed out that if the concreteness of reality is but a holographic illusion, it would no longer be true to say the brain produces consciousness. Rather, it is consciousness that creates the appearance of the brain as well as the body and everything else around us we interpret as physical.

this sounds a lot like solipsism to me, though solipsism i think postulates that there is only one consciousness. I've kind of melded the two into the suspician that it is just one consciousness all connected though there appears to be separation analogous to the perceived separation between islands in the ocean: under the "awareness barrier" (ie the water), it's all connected.

what would be a good name for this island? phoenix.

what would be a good name for the whole consciousness, if it is all connected? hmmm... i think people have been giving it names for a while now; take your pick.
 
  • #107
Welcome to Buddhism.
 
  • #108
Originally posted by Canute
I'd say you've got something there. The Cosmos is also the set of all sets. I wonder if that's a coincidence. They're the only two things whose existence is so self-referential that it doesn't seem to be logical.

The cosmos is not a set of sets. It doesn't exist as its own entity, and thus needn't be referred to seperately at all (it is merely a convenient way to refer to everything all at once).
 
  • #109
Originally posted by phoenixthoth
there is an article on a different kind of TOE in which mathematical existence is postulated (or conjectured) to be physical existence. we may be some mathematical component called self aware structures in a larger structure. the set of all sets, which i repeat can exist in fuzzy logic, seems way more adequate than necessary to capture not only our universe but a multiverse where each universe operates differently.

the thing about self-referentialism is interesting.

let x be a single word.

define D recursively:
D(x,1) is the set of all words in all possible definitions of x.
for n>0, D(x,n+1) is the set of all words in all possible definitions of all words in D(x,n).

if {x}∩D(x,1)!=Ø then the definition is self-referential and i'll bet most would consider it useless.

i also bet that for all x, there is an n such that {x}∩D(x,n)!=Ø so all words are, in that case, defined somewhat self-referentially.

i know it's a stretch, but i bet there are a few words that "generate" all other words along with the rules of grammar. i wonder if those generators would be synonyms and how many there are.

anyway, i suppose this article has to do with spooky action at a distance; it's about the hologramic theory of the universe:
http://www.water-consciousness.com/must/must_article33.htm
i know this is a stretch, but...


this sounds a lot like solipsism to me, though solipsism i think postulates that there is only one consciousness. I've kind of melded the two into the suspician that it is just one consciousness all connected though there appears to be separation analogous to the perceived separation between islands in the ocean: under the "awareness barrier" (ie the water), it's all connected.

what would be a good name for this island? phoenix.

what would be a good name for the whole consciousness, if it is all connected? hmmm... i think people have been giving it names for a while now; take your pick.

Well...lifegazer would just call it "the Mind". This sounds a lot like his beliefs.
 
  • #110
(snoop)It [the cosmos] doesn't exist as its own entity(crop)

what does exist as its own entity and how do you know?

how do you know the cosmos doesn't exist as its own entity?

(and what I'm mainly getting at is...) how do you know the mind exists as its own entity while the cosmos does not, if that is your position?

using russell's theorem in two-valued logic, the set of all sets doesn't exist as its own entity either; so i can see the similarity, at least superficially, between your version of the "not as its own entity" cosmos and the universal set. anyway, though, if the universe is not black and white, a universal set can exist which would appear to remove the achilles heel from solipsism and any attempt to argue with the "paradox" to prove the cosmos can't exist if it is likened to the universal set.

when the facts contradict the axioms, change the axioms. adding a third truth value is sufficient to resolve russell's paradox and poof, the universal set could be the universe or the mind. indeed, if there's a bijection of some sort between the universe and the universal set and the mind and the universal set, then there would be a bijection between the universe and the mind. furthermore, in my investigation of the universal set, i argued that any set in bijection with U is U, hence we would have a stronger statement than bijections:
universe=U=the mind.
if all my premises + 3 valued logic are working right, that is.

by the way, i think some easterners, perhaps buddhists, have a third answer other than yes/no or true/false. mu. this could be viewed as the third truth value and as far as i can tell it removes several paradoxes. the sacrafice is that not all statements are either true or false. but that seems to gel with the "real world" anyway, doesn't it?

does a tree falling with no one to hear it make a sound? muuuuuuu.

btw, what are good references to buddhism; i figure i should read some of it...

yeah, the hologram is kind of like their view of the illusion. where I'm at in my research now is what's outside the hologram??
 
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  • #111
Originally posted by phoenixthoth
what does exist as its own entity and how do you know?

how do you know the cosmos doesn't exist as its own entity?

Because no entity can contain itself and I equated "cosmos" with "Universe" which is semantically equal to "everything"...ergo, it would have to contatin itself.

(and what I'm mainly getting at is...) how do you know the mind exists as its own entity while the cosmos does not, if that is your position?

Well, my position is that the mind of the Solipsistic paradigm is supposed to exist as its own entity.

using russell's theorem in two-valued logic, the set of all sets doesn't exist as its own entity either; so i can see the similarity, at least superficially, between your version of the "not as its own entity" cosmos and the universal set. anyway, though, if the universe is not black and white, a universal set can exist which would appear to remove the achilles heel from solipsism and any attempt to argue with the "paradox" to prove the cosmos can't exist if it is likened to the universal set.

when the facts contradict the axioms, change the axioms.

Ah, and that's the kicker. There are no facts that support the Solipsistic paradigm. There are just no facts that contradict it either.

adding a third truth value is sufficient to resolve russell's paradox and poof, the universal set could be the universe or the mind.

What is the third truth value, and how does it resolve russell's paradox?

by the way, i think some easterners, perhaps buddhists, have a third answer other than yes/no or true/false. mu. this could be viewed as the third truth value and as far as i can tell it removes several paradoxes. the sacrafice is that not all statements are either true or false. but that seems to gel with the "real world" anyway, doesn't it?

But, what does "mu" mean?
 
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  • #112
Because no entity can contain itself and I equated "cosmos" with "Universe" which is semantically equal to "everything"...ergo, it would have to contatin itself.
why not?
Ah, and that's the kicker. There are no facts that support the Solipsistic paradigm. There are just no facts that contradict it either.
maybe you're an agnostolipsist then? there's someone who posts in "what's the proof that god exists" whose name starts with mu who has decided that there must be a default position when there isn't evidence either way having to do with which explanation is simpler and other things. I'm of the mind that there is no default. there's no question that polyism (aka, eg, science) is more useful than solipsism but that, to me, doesn't prove its correctness in the grand scheme of things; it just proves it's more useful. similarly, an auto repair man doesn't need to know the theory of everything to fix the car whose forces are predicted by but that doesn't mean a more satisfying under-picture of reality isn't closer to the truth.
What is the third truth value, and how does it resolve russell's paradox?
in russel's theorem, you have a set S such that S ∈ S if and only if S ! ∈ S. if S ∈ S is true or false, the if and only if is false. this false was the consequent of the premise, "there is a set of all sets." the theorem proves that no set can exist.

however, in 3-valued logic (not to mention fuzzy logic), a third truth value makes things different:
let P be the statement the universal set exists and is a set and let Q be S ∈ S.
consider P -> (Q <-> ~Q) which is the symbolic form of russell's theorem. now, if Q is T or F, then we have the following conclusion:
[ P -> (Q <-> ~Q) ] -> ~P. this actually works for any P and Q in 2 valued logic but in this case it proves that there is no set of all sets. what if we let P possibly be T, F, or M and Q possibly be T, F, or M? can any definitive conclusions be made?
(i'm referencing my article on 3-valued logic i mentioned earler here.)
the following crappy table starts with (truth values for P and Q)||(truth values for Q <-> ~Q)||( [ P -> (Q <-> ~Q) ] )||( [ P -> (Q <-> ~Q) ] -> ~P ):
1. TT||F||T
2. TM||M||M
3. TF||F||T
4. MT||F||M
5. MM||M||M
6. MF||F||M
7. FT||F||T
8. FM||M||T
9. FF||F||T

note how the final statement is no longer a tautology (ie always T). hence it no longer conclusively proves ~P, ie no universal set. it is M in the cases when (PQ) are (TM), (MT), (MM), and (MF), which correspond to yes universal set & maybe S &isin; S, maybe there is a universal set & S &isin; S, maybe there is a universal set & maybe S &isin; S, and maybe there is a universal set and S ! &isin; S
But, what does "mu" mean?
what does T mean? what does F mean? mu is just the truth value that isn't true or false. one could also take it to mean maybe (undecidable with given premises) and one could also take it, in response to a question, as "that's an absurd question to my language that it can't answer definitively."
 
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  • #113
Originally posted by phoenixthoth
why not?

Since an entity can be said to contain many things, but never itself...I don't understand how you could work it so that an entity contained itself. A jar (fore example) may contain water or anything else you wish to put in it, but you could never put it inside itself, could you?

what does T mean? what does F mean?

T means that the proposition is true...that it should be held as correct until disproven. False means that it is not T. What can "mu" mean? If "mu" doesn't mean T, then it means that "T is not the case" (right?) and must thus be equal to F, according to my definitions thereof.

mu is just the truth value that isn't true or false. one could also take it to mean maybe (undecidable with given premises)

If something is undecidable then it is true "if and only if" some other proposition, isn't it?

and one could also take it, in response to a question, as "that's an absurd question to my language that it can't answer definitively."

But something that is assigned a truth value is answered definitively. If you assign the "mu" truth value, then you've definitely answered it, "mu".
 
  • #114
Not sure if this is helpful or not.

As far as I understand, 'mu', in the original Cha'an/Zen sense meant something like, 'the question is absurd' or 'I unask the question', hence it might be an appropriate (if dogmatic and thus probably unenlightened) answer to koans such as 'what is the sound of one hand clapping?' or 'who were you before your parents were conceived?'. Famously it was the answer given by one master to the question 'does a dog have Buddha nature?', but that's probably partly a joke since the Chinese 'Wu' is close to the sound a dog makes.
 
  • #115
Since an entity can be said to contain many things, but never itself...I don't understand how you could work it so that an entity contained itself. A jar (fore example) may contain water or anything else you wish to put in it, but you could never put it inside itself, could you?
i know what you're dealing with with this perspective. i know it's hard to intellectualize an entity that is self-containing and whose all definitions are self-referential and seemingly useless. what we're talking about can't really be defined exactly except as perhaps the universal set. there are two analogies that aren't perfect that might help you imagine an entity that contains itself:
1. a set with nonstrict inclusion. a set is always a subset of itself though NOT a proper one. there are no sets i know of that are proper subsets of themselves.

2. the outer most atoms in the jar are containing, in a sense, what's within the inner layers.

2 is inherintly flawed as an analogy because it's a finite object. we're talking about an infinite object here (even if it's just a bunch of empty space out there) and just how the rules of the macroscopic don't at all apply to the realm of quantum mechanics, the finite intuition on objects not being able to contain themselves doesn't apply to infinite entities. does that help you understand? it's not really something i can prove to you. and no one can, i don't think. i don't think anyone can prove this entity whose name does NOT matter (the universe, the universal mind, the universal set, God, etc) contains itself. the words are either going to be helpful or a stumbling block towards understanding. go and talk on the news about the universal set and they'd laugh me off the set (pun intended) with russell's paradox which 3 valued, east/west logic dissolves and answers the imponderable "does God exist?" it's just like all the other koans because you cannot prove either answer. and I'm sorry that we can't prove it to you, we really are. we wish we could. we try.

my conjecture is that that the answer is mu expresses the fact that free will has been built into "it": you are free to choose your own beliefs.

T means that the proposition is true...that it should be held as correct until disproven. False means that it is not T. What can "mu" mean? If "mu" doesn't mean T, then it means that "T is not the case" (right?) and must thus be equal to F, according to my definitions thereof.
simple. as you said, false means not T. well, mu means not T and not F. you can have a mu2 if you want, though i don't think you need it for russell, where mu2 is not T and not F and not mu. it doesn't just mean "T is not the case," it also means "F is not the case." all I'm requiring you to accept for proof, which is actually by definition not a proof because it uses mu, is the adoption of a possibility besides true and false. koans explain exactly why we need a third truth value and so do statements like "i always lie" and "jennifer love hewitt is beautiful," although i find that to be a weak example. actually, fuzzy logicians use infinitely many truth values modeled after the [0,1] interval where 0=F, 0.5=mu, and 1=T, though I'm fairly sure they're not using it to answer koans or solve (russell's) paradox; I've heard it useful for elevator and brake design.

in truth, there is only truth. there is no such thing as false. everything that isn't true is just true to a lesser extent, so to speak. i can't really formulate this correctly. I'm trying to get a transcendence of opposites here. like hot and cold. cold is really just absence of heat. same with true and false.

If something is undecidable then it is true "if and only if" some other proposition, isn't it?
perhaps some undecidable statements are equivalent to each other. in my investigation of the universal set, i found that the statement U equals the power set of U is equivalent to "russell's paradox is a nontautology."

But something that is assigned a truth value is answered definitively. If you assign the "mu" truth value, then you've definitely answered it, "mu".

i agree with that. i must have made a false statement ;) if it seemed otherwise. from that perspective, is anything undecidable? you're at least deciding it's undecidable. i love little logic circuits (aka paradoxes) like that. i think the word paradox means "language is inadequte."

we are all limbs on the same tree. that tree can have any name you want. some popular and less popular names are:
God
consciousness
all that is
christ consciouenss
the tree of life
the tree of knowledge
the blunt truth
the real truth
Truth
the universe
the multverse
Reality
objective reality
the universal set
the Self
the universal mind
the mind

different branches but all on the same tree. this is not a new idea at all. the name of this branch is phoenix. one tree. unity.
 
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  • #116
Originally posted by phoenixthoth
i know what you're dealing with with this perspective. i know it's hard to intellectualize an entity that is self-containing and whose all definitions are self-referential and seemingly useless. what we're talking about can't really be defined exactly except as perhaps the universal set. there are two analogies that aren't perfect that might help you imagine an entity that contains itself:
1. a set with nonstrict inclusion. a set is always a subset of itself though NOT a proper one. there are no sets i know of that are proper subsets of themselves.

A set is always a subset of itself? How so? If there is set S, and we say that all of the solipsists in the world belong to that set, the set of all solipsists cannot belong to S can it? IOW, S does not belong to (since I can't get the symbols to work )S.

simple. as you said, false means not T. well, mu means not T and not F.

Illogical. If F=notT then notT=F, it is commutative. Therefore, mu cannot equal "notT" without becoming equal to F. Right?

in truth, there is only truth. there is no such thing as false. everything that isn't true is just true to a lesser extent, so to speak. i can't really formulate this correctly. I'm trying to get a transcendence of opposites here. like hot and cold. cold is really just absence of heat. same with true and false.

But sometimes there is a complete absence of truth, right? There can be an "absolute zero" of truth, can't there?

i agree with that. i must have made a false statement ;) if it seemed otherwise. from that perspective, is anything undecidable? you're at least deciding it's undecidable. i love little logic circuits (aka paradoxes) like that. i think the word paradox means "language is inadequte."

Yeah, I think paradoxes are really fun. You should read Raymond Smullyan's books. He's very big on paradoxes and coercive logic.

we are all limbs on the same tree. that tree can have any name you want. some popular and less popular names are:
God
consciousness
all that is
christ consciouenss
the tree of life
the tree of knowledge
the universe
the multverse
Reality
objective reality
the universal set
the Self
the universal mind
the mind

different branches but all on the same tree. this is not a new idea at all. the name of this branch is phoenix. one tree. unity.

I'm one of the last people you usually ever hear saying this, but that's pretty deep.
 
  • #117
I'm not sure we're coming at Russell's paradox from the right direction. There is no problem with the set of all sets that contain themselves containing itself, as far as I know. After all the cosmos must qualify as such a set.

The paradox concerned the set of all sets that do not contain themselves.

Phoenixthoth

It's great to see someone struggling with the words. I think I know what you're trying to say and I sympathise (and agree). Unfortunately it isn't sayable, as everyone from Chuang Tsu onwards has said.
 
  • #118
yes and consider the possibility that the problem is not with the axiom of a universal set but with the subsets axiom. you need both to arrive at the contradiction in 2 valued logic. perhaps the set S in russell's paradox is not a subset of U. perhaps it does not exist and so considering it as if it does is an error. now if it did exist, then it would automatically be a subset of U, but it doesn't.

in 3-valued logic, it can exist as a "fuzzy" subset of U.

the choice seems to be thus:
1. drop the axiom that there is a universal set.
2. modify the subsets axiom so that properties that lead to contradictions do not result in subsets.
3. adopt logic with at least 3 truth values and keep the subsets axiom as it is, including fuzzy subsets and the universal set.

to some binars, 2 may be the most appealing.
to the fuzzies, 3 is the most appealing.
to some binars, 1 is the most appealing.

words can only approximate the real truth but i feel that the approximation can be done arbitrarily well.
 
  • #119
A set is always a subset of itself? How so? If there is set S, and we say that all of the solipsists in the world belong to that set, the set of all solipsists cannot belong to S can it? IOW, S does not belong to (since I can't get the symbols to work )S.
i took "contain" to mean a subset of and you took it to mean is an element of. well, U is an element of U and a subset of U and i know of no other such sets with this property. remember that non-U intuition just can't apply to U. every set is a subset of itself while few sets in some sense are elements of themselves. for example, for no ordinal or cardinal are they elements of themselves and that covers a lot of ground right there. if i were to pick a new symbol for the cardinal number of U, i'd like just aleph or omega or alephomega for it is the beginning and the end. (my website alephnull kinda translates to AO.)


Illogical. If F=notT then notT=F, it is commutative. Therefore, mu cannot equal "notT" without becoming equal to F. Right?
ill-2-valued-logic, yes. binary logic and the law of excluded middle of t xor f does not apply. check out the other thread on multi-valued logic for more info on this. it's in the logic section of this site, i think. the same question was raised there. there is a modified version of xor which stipulates that one formula cannot have two different truth values simultaneously. however, the way to assign truth values is general so in a sense, using two different equally consistent systems of assigning truth values that i call perspectives, they can have two different truth values simultanously. from the perspective of binary logic, the excluded middle is maintained. intuitively speaking, "phoenix is beautiful" is true from one perspective and not true from another perspective.

all perspectives must be generalizations of binary logic or else it will be nonsense in my opinion.

But sometimes there is a complete absence of truth, right? There can be an "absolute zero" of truth, can't there?
see one of my posts in the other thread i mentioned. i argued that all logic is not just reducible to binary, it is reducible to unitary:
T
~T
~(T v ~T)
etc.,
so i metaphorically said that there is only white and degredations of white (like heat and absence of heat) and so absolute black, while it can be approximated arbitrarily well, can never be attained. this is only one perspective though. in another, strict binary logic, or in short, any finite list of the above degredations of truth except just the first one, does attain absolute black. notice though that absolute white is always there? It Is.

Yeah, I think paradoxes are really fun. You should read Raymond Smullyan's books. He's very big on paradoxes and coercive logic.
;)

a battle avoided cannot be lost
--sun tzu


I'm one of the last people you usually ever hear saying this, but that's pretty deep.
it's literally as deep as it gets. now that's not to say my ego is so big that i think i came up with something really deep. this is just a reflection of what I've realized while pondering the imponderables and reading about theism, buddhism, abrahamic religion, mathematics, psychology, and stuff like that. it's not at all new. organic posted the same thing about a tree a while ago and that's what inspired me to write it in that way.

a battle avoided cannot be lost. that's to say you must surrender in order to win. but you're only exchanging the lesser for the greater. what you're really surrendering is all delusions which are products of the ego. you're sublating the ego.
 
  • #120
I can't follow all the set theory terminology I'm afraid, being a mathematical ignoramus.

I'm not very keen on the term 'fuzzy sets', since there is nothing at all fuzzy about them. You're talking about the 'middle way' of Buddhism and other non-dual epistemologies. Ultimately you're talking about exploring the reality beyond the illusion of duality. It's a well researched area of knowledge with an existing terminology and very clear cut concepts.

Have you explored non-dual ontology/epistemology? You may be re-inventing the wheel.
 

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