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

  • Thread starter Mentat
  • Start date
  • #126
1,569
2
back to the tree analogy that we're all connected somehow:
http://www.themessenger.info/MAR2002/WynnFree.html [Broken]

by the way, the axiom of foundation can be used to prove that for no sets x is x an element of x.
 
Last edited by a moderator:
  • #127
1,515
0
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.
 
  • #128
1,569
2
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.
 
Last edited:
  • #129
1,515
0
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.
 
  • #130
1,569
2
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).
 
Last edited:
  • #131
1,515
0
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
 

Related Threads on Russell's Paradox: The Achille's Heel of Solipsism?

  • Last Post
Replies
18
Views
3K
  • Last Post
6
Replies
133
Views
24K
  • Last Post
Replies
19
Views
4K
Replies
18
Views
21K
Replies
1
Views
3K
  • Poll
  • Last Post
3
Replies
59
Views
9K
  • Last Post
2
Replies
32
Views
11K
  • Last Post
4
Replies
91
Views
12K
Replies
28
Views
8K
Top