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

[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...

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.

 

[Canute]

Welcome to Buddhism.

 

[Mentat]

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).

 

[Mentat]

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.

 

[phoenixthoth]

(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??

 

[Mentat]

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?

 

[phoenixthoth]

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."

 

[Mentat]

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".

 

[Mumeishi]

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.

 

[phoenixthoth]

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.

 

[Mentat]

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.

 

[Canute]

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.

 

[phoenixthoth]

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.

 

[phoenixthoth]

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.

 

[Canute]

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.

 

[phoenixthoth]

I am not reinventing or discovering anything. nor did I ever.

it is all a synthesis of what I've read and thought.

and yes, I've gone into the study of nonduality. recommended books are
power vs force
the eye of the I: from which nothing is hidden
I: Reality and subjectivity
the above are authored by david hawkins.

the article on be-ness by duerden at http://www.duerden.com

someone in the church didn't want you to read that and it was excluded from the bible. it takes all their power away completely yet it is perhaps the most essential part.

if you read these core works, i think that would be enough on their own to stimulate you in the right direction. reading the above would take under a month but understanding them may never happen.

 

[phoenixthoth]

check out max tegmark's view on the theory of everything:
http://www.physicsresource.com/showproduct.php?product=37&sort=1&cat=2&page=1

in it, he posits that mathematical existence is physical existence and that we are "self aware structures" that are mathematical in nature. (like the matrix??)

i conjecture that the universal set U is a self-aware structure. it would appear that if any sets posses self aware structure, then U must also. however, since i don't have a precise definition of what a self-aware structure is, i can't prove that. tegmark ended his paper with an open problem of finding an example of a self-aware structure and U must be an example, though the goal now would be to find the smallest such structures. i have no idea how small they are though i suspect that all sets posses at least a weak form of self awareness structure, even the empty one though it would be limited only to self awareness and not awareness of anything else. i suppose everything would have to be aware of all its contents and all sets with nonempty intersection with them. hmm... all sets have nonempty intersection with U, hence U is infinitely aware, aka omniscient.

from these observations, i postulate that if there is set containing my computer screen and if there is a set that contains me, they have a nonempty intersection because i am aware of my computer screen (which would also mean my computer screen is aware of me, at least weakly!).

please tell me I'm not suffering from a nash-type delusion!

 

[phoenixthoth]

Originally posted by Mumeishi
And here I thought you was a Christian. Crowley is cetainly an interesting character. Do you find this philiosphy persuasive?

i haven't been a christian for 12 years now. i find his philosphies influential though i don't think he did the best job of explaining things though his solipsistic manefesto can help one realize that they are a part of God.

i am an agnostic-theist which means i believe what i cannot prove nor disprove. a delusion, perhaps?

let me expound a bit on my illusion theory. i think that thinking everything is an illusion is a helpful step towards reaching a state of unity but it is not quite correct. what's more accurate is that there are infinite degrees of consciousness and when the whole of consciousness is projected onto a lesser consciousness, part of the whole, one is not aware of the whole picture. what we see aren't quite illusions: they're icons/symbols. icons are real but a very incomplete part of the whole truth, which is the whole consciousness itself which is also as real. this consciousness has decided to interpret that projection as a computer screen that I'm looking at. but the real "action" is going on "upstairs."

 

[Canute]

Originally posted by phoenixthoth
I am not reinventing or discovering anything.nor did I ever.

If you say so. Still, seems to me you are.

and yes, I've gone into the study of nonduality.

It doesn't seem so from your links.

 

[phoenixthoth]

no, it doesn't seem that way, does it?

this was a recent event, the crossing over into nonduality. i had been in unity before and you can't really lose it or ever not be in it but you can believe you're not in it, as well as not be aware you're in it and not know what it's called, and beliefs can be powerful. i have believed i wasn't in it up until recently. a kind of absurd question is do i know I'm in it or do i think I'm in it? how do i know i even exist, if i want to ask such questions...

more about illusions: i think time might be an illusion that corresponds to the expansion of awareness of U which is static. growing yet not growing. revealing yet not revealing. does that make any sense? but perhaps expansion of awareness and any perception of change is a complete illusion. i doubt it though if a particle can have a dual wave- and -particle like structure, then perhaps U can have a dual static and dynamic structure.

it depends on your perspective, really.

on one hand, f(x)=x^2 is not constant. it's derivative is not identically zero which is our arbitrary definition of constant.

on the other hand, f={(0,0),(1,1),(2,4),...} is constant. there is no derivate concept for sets as far as i know.

dead and alive.

i'd like to ammend/change what i wrote about the philosophy of unity being "as deep as it gets." in fact, i think that if there is a rabbit hole in wonderland, then being in the state of unity is like finding the entrance to that rabbit hole. or like reaching the base of mt. olympus. the hole/mountain gets a lot deeper/taller after that. if we all live on a tree of knowledge, then i think it's infinite and there will never be a state of omniscience attained by a human in life. when i wrote "that's as deep as it gets," that suggests otherwise. that couldn't have been more in error.

 

[phoenixthoth]

back to the tree analogy that we're all connected somehow:
http://www.themessenger.info/MAR2002/WynnFree.html

by the way, the axiom of foundation can be used to prove that for no sets x is x an element of x.

 

[Canute]

Originally posted by phoenixthoth
check out max tegmark's view on the theory of everything:
http://www.physicsresource.com/showproduct.php?product=37&sort=1&cat=2&page=1

in it, he posits that mathematical existence is physical existence and that we are "self aware structures" that are mathematical in nature. (like the matrix??)

i conjecture that the universal set U is a self-aware structure. it would appear that if any sets posses self aware structure, then U must also. however, since i don't have a precise definition of what a self-aware structure is, i can't prove that. tegmark ended his paper with an open problem of finding an example of a self-aware structure and U must be an example, though the goal now would be to find the smallest such structures. i have no idea how small they are though i suspect that all sets posses at least a weak form of self awareness structure, even the empty one though it would be limited only to self awareness and not awareness of anything else. i suppose everything would have to be aware of all its contents and all sets with nonempty intersection with them. hmm... all sets have nonempty intersection with U, hence U is infinitely aware, aka omniscient.

from these observations, i postulate that if there is set containing my computer screen and if there is a set that contains me, they have a nonempty intersection because i am aware of my computer screen (which would also mean my computer screen is aware of me, at least weakly!).

please tell me I'm not suffering from a nash-type delusion! [/B]

I don't think you have delusions. I think you're bang on. I'd quibble about whether your computer is aware of you, prefering microphenomenalism to the idea of conscious thermostasts, and also over the bit about the empty set having self-awareness, since I think it is actually a pure non-dual experience, but they're small points.

 

[phoenixthoth]

i'd rather be wrong than delusional. thank you for suggesting that I'm right or wrong but not delusional.

does the empty set have SAS? hmm... indeed, how can a void have any structure, let alone SAS. i think there must be infinitely many levels of SAS and singletons could from a certain point of view have the most because there's so little to be aware of and the least because there's so little structure to be "complex" enough for SAS.

if a manifold has SAS, i conjecture that it's level of SAS is related to its dimension and if a set has SAS, to its cardinality.

i have virtually given up hope that the object {X is a set : X=X} is a set though I'm still trying. even if it's a proper class, i conjecture that it is somehow "aware" of all sets.

edit: max said that evidently no known structures have SAS. i think he says that because there is no evidence of selfawareness in any known structure. i disagree; i bet that lots of known structures have SAS, whatever that is. the big open problems are these: define SAS, prove it exists, give examples, give and prove the smallest example. my little pet conjecture is that the smallest SAS anything like human is roughly equivalent to the same amount of structure in a differentiable manifold or riemann surface of dimension under 10, like 5. but since i don't have a definition of SAS, i don't even know if any exist.

anyways, if math and physics and consciousness are all somehow connected, that would indeed by a theory of everything at least in a context where consciousness forms the basis of reality and i know that's probably a distortion of buddhism but i know many people believe/"know" that.

 

[Canute]

I agree with you that set theory is important in respect of explaining consciousness. Unfortumately I know almost nothing about it so can't follow you very well.

However I would argue that the empty set is not quite the right metaphor for fundamantal consciousness, although it's close. I'd also argue that the empty set cannot have SAS, since SAS requires self and non-self, awareness and object of awareness, and the empty set has insufficient parts to allow this. A Buddhist would say it is 'is-ness', the annihilation of self and therefore of self-awareness.

Another point about the empty set is that in set theory its existence is (I think) taken as axiomatic. To explain consciousness I suspect we have to do the same, and assume that the existence of consciousness is inevitable, axiomatic, and that 'nothingness' is impossible. That is, there is 'something that it is like' to be nothing.

It may be a scientifically uncomfortable idea, but as a theory it has considerable reach, since it nicely explains why anything exists.

 

[phoenixthoth]

Originally posted by Canute
However I would argue that the empty set is not quite the right metaphor for fundamantal consciousness, although it's close. I'd also argue that the empty set cannot have SAS, since SAS requires self and non-self, awareness and object of awareness, and the empty set has insufficient parts to allow this. A Buddhist would say it is 'is-ness', the annihilation of self and therefore of self-awareness.

perhaps then instead of the void being the fundamental consciousness, the fundamental consciousness is on the other end of the spectrum. I'm thinking maybe the proper class of all sets or the category of all categories. but in some sense, just binary logic is the biggest structure for it is the most general with the fewest constants and fewest axioms and all of math uses it. I'm working on a way to remove russell's paradox, going back to the subject of this thread and the main problem is that in ternary logic, the proof by contradiction is no longer valid but then again neither is modus ponens standard deduction. i think i found a way to get around this problem so that a universal set, a set of all sets, can exist in the context of ternary logic, a logic with a third truth value. this unviersal set U would be on the other end of the spectrum from Ø and perhaps it is the fundamental consciousness. even if U is not a set and my work proves to be invalid, U is still a proper class and does "exist" mathematically which, in max's theory, means it physically exists. one way or another, i suspect there is some uberstructure that contains all SAS's and whatever it is is the fundamental consciousness.

one may argue that it is "obvious" that we're not "living" in a set because a set is static yet we are dynamic. i have an analogy as to why sets have a dual dynamic and static nature but i think i shared it already. now I'm viewing that analogy as somewhat weak. all it does for me now is suggest that it's conceivable that sets can have a dual dynamic and static nature.

Another point about the empty set is that in set theory its existence is (I think) taken as axiomatic. To explain consciousness I suspect we have to do the same, and assume that the existence of consciousness is inevitable, axiomatic, and that 'nothingness' is impossible. That is, there is 'something that it is like' to be nothing.

you are correct, it is an axiom. the existence of the universal set would also be an axiom. mathematical existence means a structure exists if its existence is free from contradiction. i agree wholehartedly that nothingness is impossible. does it make sense to say that the thing that is empty is not nothingness? this is a subtle point. the thing that is empty sort of contains nothingness and it's not that the nothingness exists, its the thing that contains nothing that exists.

this doesn't have to do with "no mind" does it?

It may be a scientifically uncomfortable idea, but as a theory it has considerable reach, since it nicely explains why anything exists.

indeed (on both points).

 

[Canute]

Originally posted by phoenixthoth
perhaps then instead of the void being the fundamental consciousness, the fundamental consciousness is on the other end of the spectrum. I'm thinking maybe the proper class of all sets or the category of all categories.

Absolutely. Thus emptiness/fullness and the two Brahman.

(Didn't get any of the next bit)

you are correct, it is an axiom. the existence of the universal set would also be an axiom. mathematical existence means a structure exists if its existence is free from contradiction. i agree wholehartedly that nothingness is impossible. does it make sense to say that the thing that is empty is not nothingness?

Yes, and no. As the set of all sets, (or the set of all empty sets), emptiness is actually its own container. There is no 'thing that is empty'. But I agree that emptiness is not nothingness in metaphysical/cosomlogical terms.

(If I descend into insanity before you do let me know).

this is a subtle point. the thing that is empty sort of contains nothingness and it's not that the nothingness exists, its the thing that contains nothing that exists.

That seems like the right way of thinking about it but the wrong thought. But this stuff is nearly impossible to talk about.

this doesn't have to do with "no mind" does it?

Everything imho.

Canute