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

  1. Nov 24, 2003 #1
    I had always taken it for granted that nothing could disprove Solipsism, but now I think there may be an actual logical problem with it!

    I understand that I could easily be wrong, and that's why I'm posting it: for constructive criticism.

    Alright, now, the first think I might have gotten wrong is the name...Russell's paradox is the paradox that states that no set can contain itself, isn't it?

    If so, then isn't this a huge (possibly fatal) blow to Solipsism (which dictates that there is nothing that exists, except for what exists in my mind)?

    You see, if the Mind ≡ the Set of all things that exist, then how can the Mind itself exist at all?

    Any comments, constructive critiques, or corrections are appreciated. :smile:
     
  2. jcsd
  3. Nov 24, 2003 #2
    first of all, that something contradicts an arbitrary contrivance such as logic means nothing. but i don't think solipsism leads to russell's paradox so that issue is moot.

    here's russell's paradox. one can view it as a theorem and not a paradox. it's based on the tautology
    [p→(q↔¬q)]→¬p.

    p says ∃U∀x(x∈U). in this context, this means U is a set containing all other sets.

    by the subsets axiom, S={x∈U:x!∈x} is a set.

    q will be the statement S∈S.

    note that for all (sets) z, z∈S↔(z∈U∧z!∈z). one can show that since z∈U is true for all z, this is equivalent to z∈S↔z!∈z. now taking z=S, we have that S∈S↔S!∈S, a statement of the form q↔¬q which was a consequence of p. conclusion? ¬p. in other words, it is not the case that there exists a set U such that for all (sets) x, x∈U. in other words, for all sets U there is a set x such that x!∈U.

    there is, however, a class of all sets and a category of all sets and a category of all categories (in that situation the difficulty is relieved by the absence of an equivalent "subsets axiom" but i'm no category theory person).

    when one moves to multi-valued logic such as one in which truth values aren't just 0 (F) or 1 (T) but anything in [0,1], the truth value of the statement S∈S under basic assumptions is 0.5; S is considered a fuzzy set.

    in solipsism, one hardly claims that their mind contains all sets; just perhaps sets related to the universe. but, then again, if the mind is better modeled by a category than a set, then the whole question of whether it is somehow equivalent to the set of sets is moot.
     
    Last edited: Nov 24, 2003
  4. Nov 24, 2003 #3
    The 'mind' can simply exist as the (small) reflector of 'all things' in the greater mind.

    Just like you have memories, in you, that are not in your 'presently conscious mind', but you can re-call them. Your mind equvalently works out to be a "subset access system" of your own, greater, mind.

    Put it this way, for the totality of 'mind' you still cannot concieve of the actuality of an Avogadro's number, as that number exceeds all of the Neurons, and neuronal connections, (even neurotransmitters rates, as individualized counts) that exist within a humans mind.

    Your mind, like everyones mind, has limitations upon it, hence it would be difficult, at best, to prove (or disprove?) solipsism, by that methodology.
     
  5. Nov 24, 2003 #4
    oh yeah, and about that snip/snop quote, it can exist it just wouldn't be a set in two valued logic.
     
  6. Nov 25, 2003 #5


    Ok...I'm not that good at symbolic logic, but I understood most of that . Anyway, isn't the end result that there can be no set of all sets?

    That's bad semantics, since the term "Universe" means "everything".

    I didn't understand the "category of sets" thing, could you please clarify?
     
  7. Nov 25, 2003 #6
    Re: Re: Russell's Paradox: The Achille's Heel of Solipsism?

    That doesn't help at all, since the "greater mind" would have to be a set of all sets", and would still fall into Russell's paradox...besides, Solipsism makes all things the function of my own mind, thus the thing that I'm supposed to be "reflecting" should also be a function of my mind...IOW, there is no objective reality, nothing outside my own mind.
     
  8. Nov 25, 2003 #7
    How else would you have me establish validity? I'm not trying to discover "truths", just validity, and this seemed like a valid argument. But, is there some other way to check its validity by another method completely (besides logic)?
     
  9. Nov 25, 2003 #8
    Re: Re: Re: Russell's Paradox: The Achille's Heel of Solipsism?

    But you have missed my simple point of the fact that not all things exist in your mind simultaneously, (consciously) ergo you MUST be dealing with a 'subset' (Conscious) of the 'greater set' (Sub-Conscious) even if the entire 'greater set' is in your mind only!
     
  10. Nov 25, 2003 #9
    the *blank* of all things just isn't a set unless you allow fuzzy sets to exist. the mind would just not be a set.

    could you substitute the word "universe" for "mind" in a nonsolipsistic theory? in essence, whatever you call the thing that contains (or is equivalent to) the thing of all things has the same problem the mind does in solipsism.

    either way, the problem is resolved by realizing that the *blank* of all things that exist just may not be a set.

    http://mathworld.wolfram.com/Category.html

    anyway, if a theory (science, set theory, logic) can't make sense of the truth, it doesn't make the truth nontruth, it just points out limitations in the theory.
     
    Last edited: Nov 25, 2003
  11. Nov 26, 2003 #10
    From the Solipsist's viewpoint I would like to know how your mind goes about generating information that you, in your mind, are completely unaware of, prior to it's presentation to you, by another!

    How does that work??
     
  12. Nov 26, 2003 #11
    a modified solipsism is that reality is like a dvd and you are the laser beam that reads the disc. you're the only one that exists; everyone else is just a bunch of 1's and 0's on some disc (perhaps a hologram). the whole of reality is in some sense only present in one moment but the illusion of time is created as you (the laser) shifts awareness from one point on the "disc" to another. there are no other minds, just illusions of minds. perhaps the mind created this hologram and perhaps it didn't. maybe it wasn't created but has always existed out of time. generally speaking, i'm not sure if it is thought that the mind isn't generating stuff prior to your experience of it and there would be no others to present it to you. i'm not sure if it is thought that the mind is what creates things. perhaps it is the creator (the laser beam and the disc) and perhaps it is just the only perceiver (just the laser beam).
     
  13. Nov 26, 2003 #12
    Re: Re: Re: Re: Russell's Paradox: The Achille's Heel of Solipsism?

    I'm sorry, I don't understand what you're getting at. If we are always dealing with subsets of a greater set, that set would still have to hold all of reality at once, wouldn't it?
     
  14. Nov 26, 2003 #13
    What's a "fuzzy set"? Besides, the mind isn't really the set; all things that exist are "mindful" things, according to Solipsism, but then the mind itself must also be a "mindful" thing. That's my point.

    No, the Universe is not an entity. The word "Universe" just refer to everything.
     
  15. Nov 26, 2003 #14
    Re: Re: Re: Re: Re: Russell's Paradox: The Achille's Heel of Solipsism?

    The 'subset' presently being dealt with, is the activity currently going on in your mind, but that is not the entirety of the 'greater set' (in your mind) that contains all of the other things you can remember, even though that 'greater set' exists, presently, (dormant? or just quiet?) within you.

    But the Solipsis determines that that greater set carries all of the knowledge that Exists, and then what?? presents that through others, to itself?? Why the need of the redundancy?
     
  16. Nov 26, 2003 #15
    Re: Re: Re: Re: Re: Re: Russell's Paradox: The Achille's Heel of Solipsism?

    Uh...you goin' somewhere with this? You're making good points, but they're scattered, so...what are you trying to say?
     
  17. Nov 26, 2003 #16
    some people think the universe is an entity. not necessarily a conscious entity though some think it is but its consciousness doesn't resemble ours.

    a fuzzy set x, to me, is a set such that there is another set y such that the statement y∈x is neither true nor false but some other truth value. for example, in russell's "paradox," you have S and the statement S∈S has truth value not equal to 0 or 1 and so if a set of all sets exists, you have to accept the existence of fuzzy sets. fuzzy sets and a universal set or crisp sets and no universal set. one can also show that the powerset of the universal set would equal the universal set and the cantor diagonal argument which usually proves that there is no function from a set to its powerset (which would show that the identity map from U to P(U) isn't onto which would contradict their equality) actually reduces to russell's theorem and the fuzzy set S; again, no contradiction if more than two truth values are allowed. i wonder if P(x)=x implies x is the universal set... the universal set itself, btw, is crisp though it has fuzzy subsets.
     
  18. Nov 26, 2003 #17
    Re: Re: Re: Re: Re: Re: Re: Russell's Paradox: The Achille's Heel of Solipsism?

    Scattered?, Humm, ya mean like seeds??

    Solipsism requires that the universe act in a redundant fashion with respect to "education of self", and requires that your mind contain the either the entirety of the Universe, or the knowledge of the entirety of the Universe which, on simple numerical values alone, it cannot.

    As for the rest, simply put in your language of 'set theory', your mind and its functions, your consious mind, (as I previously said) "the subset" that is active in "the greater set" (subconscious) that is the 'entirety of your mind' which includes all of your memories etc. etc.

    Does that help?
    (perhaps what you need is really some time to think about it....sleep on it, see what develops tomorrow, or later still.......)
     
  19. Nov 26, 2003 #18
    or that your mind is the entirety of the universe.
     
  20. Nov 26, 2003 #19
    And how then does it go about hidding 'itself' from 'itself'? as clearly we do not know the entirety of the Universe, right?
    (or are you perhaps laying the claim??)
     
  21. Nov 26, 2003 #20
    whatever appears hidden doesn't exist.
    either that or perhaps its a kind of dissociative amnesia.
    we are the entirety of the universe but are not aware of it (unless we are). i can control the sun no more than i can control my toenail growth. a mind doesn't have to completely be aware of itself, know itself, or control all of its parts.
     
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