UFO Conjectures

Saturday, February 02, 2008

UFOs as “Entscheidungsproblem”


Mathematician David Hilbert’s “entscheidungsproblem” (decision problem) applies to algebraic and calculus conundrums mainly, but also applies to the UFO phenomenon: results cannot be conclusively proved, which Kurt Gödel established with his paper, “On Formally Undecidable Propositions of Principia Mathematica and Related Systems.”

Hilbert and Gödel determined that what seems logical from outside a system was not necessarily true (or logical) within a system itself.

UFOs as a systematic phenomenon can be seen in that same light; that is, UFOs may appear to be real from a vantage point apart (outside) of the phenomenon but from within the phenomenon itself may not be real at all, or more “real” than anyone can imagine.

Carl Jung’s view that flying saucers are primarily a psychological manifestation doesn’t work here, as that view is from without the phenomenon but pretends to gather its truth from within the phenomenon, where conclusions can’t be made.

(Jung’s view from within is a chimera: a view from outside the phenomenon that appears to be from inside the phenomenon but is hardly that at all.)

The problem is unresolvable since no one can get inside the phenomenon (and never has been able to do so) to determine what the phenomenon’s real parameters are.

Looking at UFOs from outside has allowed for myriad conjectures as to what the things are.

And “truths” of what UFOs are have been argued, and determined, by various factions of the UFO community.

But such “truths” are not the real truth as such truths are not provable (or determinable) from within the phenomenon itself, which has remained beyond the scrutiny of observers and UFO investigators.

The brilliant recluse, Jacques Vallee, the intellectual Jerry Clark, and the highly intelligent Stanton Friedman can pose hypotheses about what UFOs are, and those hypotheses can be seen as true by others looking at UFOs outside the phenomenon itself.

But without access to the inside of the phenomenon, the “system” as it were, UFOs remain undecidable, and present the “entscheidungsproblem.”

No logic or (true) reality can be determined from within a system (UFOs) itself, and any truth determined from without a system (UFOs) has got to be false by virtue of a lack of an ability to encompass a total truth of a system, mathematical or otherwise.

This means that the totality of the UFO truth is beyond the ken of anyone, even those who (some named above) are skilled in logic, intelligence, and even Jungian intuition.

Mathematical truth, as noted, cannot be encompassed by even powerful logical systems [The Universal Computer: The Road from Leibniz to Turing by Martin Davis, W. W, Norton, N.Y., 2000, Page 118].

And UFO truth also cannot be encompassed by powerful logical systems (take note Richard Hall) so conjecture is futile, as it has been and will be.

Thus, pursuing the phenomenon is an act of folly, a madness that even Jung underestimated.


  • Well thank you and also thank Carl for me but I will continue my folly. I don't like people telling me its a waste of time to think a certain way because we have a theory which is proof of an answer.

    I think they do that in fundlementlist religions didn't they?

    Joe Capp
    UFO Media Matters

    By Blogger Joseph Capp, at Sunday, February 03, 2008  

  • Joseph, you maverick...

    Far be it from us to try and curb your unique thought processes.

    Our comments are meant for the UFO hoi polloi, of which you are not one.


    By Blogger RRRGroup, at Sunday, February 03, 2008  

  • According to what you've gleaned, do you think that there exists a method which allows one access to the inside of the phenomenon?

    By Blogger Brandon, at Monday, February 04, 2008  

  • Brandon:

    If Godel is correct, and everyone thinks he is, no -- one cannot every permeate the UFO system, just as no one can ever permeate the mathematical system -- using logic.

    That's the loop-hole, however...

    Godel says that a system can't be corroborated (or proved) using logic.

    So if one wants to get inside the UFO phenomenon, they would have to enter by way of something other than logic or ratiocination.

    What that would be is anyone's guess, and since ufology doesn't contain any persons (so far) who are looking at the phenomenon from a unique, obtuse vantage point, we contend that the pursuit of the mystery is sheer folly.

    By Blogger RRRGroup, at Monday, February 04, 2008  

  • Gödel showed that within a rigidly logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or undemonstrable within the axioms of the system.



    Don't confuse logic with the axioms of the system, Rich.

    You are misreading Gödel if you do so. As long as we reduce the system to a set of AXIOMS which we all agree with, we are fine.

    By Blogger Epinoia, at Monday, February 04, 2008  

  • Epinoia:

    The axioms are the logic of the system(s).

    By Blogger RRRGroup, at Monday, February 04, 2008  

  • Sorry, Rich. The Axioms are the elements of the system upon which the formal system of logic is used. You are incorrect.

    By Blogger Epinoia, at Monday, February 04, 2008  

  • Epinoia...

    You seem to misunderstand Godel's argument, which derives from Hilbert.

    The system's "logic" is comprised of axioms and all the mathematical parameters that make up the unfathomable mystery of arithmetic (math).

    This is what Godel strives to make clear: that no formal (or informal) logical approach can get at the profound mathematical truth.

    This means, in part, that a scrutiny of axioms themselves will not bring anyone closer to the truth of math or, rather, mathematical "truth."

    The (mathematical) system is closed to logical processes, and axioms, which are the basic structure of mathematical logic, are of no help at all.

    You are trying to encrust a complex argument with a simplistic view that goes wanting, if you are familiar with Hofstadter's "Godel, Escher, Bach: An Eternal Golden Braid."

    But there I go again, mentioning a book that you should have read before engaging in this discussion.

    Forgive me.

    By Blogger RRRGroup, at Monday, February 04, 2008  

  • I have read Hofstadter's book, and attended the very school and campus that he taught at.

    The axioms are the elements of the system. Logic is the tool one uses on the elements of the system. They are not the same.

    If you want to suggest that Logic itself cannot be proved, then fine. But that's not Gödel's point.

    I'm curious if you have ever taken a formal logic course?

    By Blogger Epinoia, at Monday, February 04, 2008  

  • Epinoia...

    Here's the argument, which you tend to stray away from (as you did with the "gays don't see UFOs" post):

    The formalities of logic (which in math uses axioms, in part, to provide arithmetical logic) cannot encompass the full scope of mathematical truth, as noted in my reference to Davis' book.

    This same situation, in the UFO realm, is analogous to the Godel/Hilbert/Turing view(s) about math.

    You would drag me into a discussion about the Godel construct, as you had hoped to do with the gay agape/eros thrust.

    The argument here is about UFOs, and the impossibility of getting at the truth of them from without the phenomenon, nor from within the phenomenon, which is the crux of the UFO continuing mystery.

    Your slipover to Godel's view on math, which you seem to miss (even though you had proximity to IU), is not pertinent; it was just a jumping off point for my view on UFOs, as the opening graphic on the post hinted at.

    (Shall I show you pics of my college text books from philisophy classes re: logic?)

    By Blogger RRRGroup, at Monday, February 04, 2008  

  • The formalities of logic (which in math uses axioms, in part, to provide arithmetical logic) cannot encompass the full scope of mathematical truth, as noted in my reference to Davis' book.

    Don't confuse 'mathematical truth' with logic, and we'll do just fine. I might also remind you that you're the one who brought up Gödel, and then proceeded to misconstrue his position into something which very much resembles insanity.

    If you want to justify your own flavor of insanity/sophistry, you'll need something more than logic with which to do it.

    By Blogger Epinoia, at Monday, February 04, 2008  

  • E:

    Thank you for the advice, and perceptive observations, albeit a bit oblique, as usual.

    By Blogger RRRGroup, at Monday, February 04, 2008  

  • You have decided to merge UFOs and Gödel, and you have the audacity to call me oblique? Now that's rich! =P

    Gödel's incompleteness theorem has been with us for quite some time now, yet we still make gains in all sorts of systems. One would think that the same limitations would apply to all sorts of other systems -- biological, geological, astrophysical, etc. Yet we still pursue these endeavors as a species, and few would consider them 'sheer folly'.

    By Blogger Epinoia, at Monday, February 04, 2008  

  • E:

    You make an astute observation, but I think there are some "mysteries" that can't be fathomed no matter how hard we try, such as the existence of God (or not), the exact place of consciousness, life after death, the denouement of Amelia Earhart (and Jimmy Hoffa) -- to name a few.

    UFOs fall into this unresolvable area -- for me.

    You (Joseph Capp and a few others) think otherwise.

    That is your right. But for me it is folly, that takes the place of actual existential responsibility; an escape INTO reality as psychiatry tells us.

    Now I'm off to other (responsible) duties.


    By Blogger RRRGroup, at Monday, February 04, 2008  

  • You have this wrong (my credentials -- a degree in math with a concentration in logic, and I'm now an engineer at Google).

    Gödel's theorem talks about formal systems of reasoning -- in other words, abstract things like mathematical systems. It most certainly isn't applicable to any real-world things in the slightest -- because you can never prove a real-world theory, you can only amass evidence for it.

    It's perfectly easy to construct physical systems where there are no hidden issues -- where there are no unsolvable problems.

    Perhaps we'll be able to work out every detail of UFOs. Perhaps we'll never get anywhere. Gödel is silent on this matter.

    For the deep background, Gödel's Theorem really says:

    For any sufficiently complex mathematical system that's "omega-complete", there's a statement that is true but cannot be proven within that system.

    "Sufficiently complex" basically means you can do arithmetic (there really aren't any interesting mathematical systems that can't be made to do arithmetic).

    "Omega complete" is an interesting technical condition: it means that you cannot define infinite, irreducible, inconsistent statements.

    This is actually very reasonable. Such a statement would look something like:

    There exist a number x such that property P holds;
    and 0 is not that number;
    and 1 is not that number;
    and 2 is not that number... (forever).

    And we clearly don't want this to happen.

    By Blogger Tom, at Monday, February 04, 2008  

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