Gödel and Determinism

Reference: Is there an absolute Will?

Isene provides the following logic in his article:

  1. For a system to be deterministic, its underlying rules must be consistent.
  2. For a system to be deterministic, its underlying rules must be complete.
  3. No system of rules can be both complete and consistent per Godels Incompleteness Theorems.
  4. Thus, no system can be deterministic.

This is how I see it.

Godel’s incompleteness theorem applies only to axiomatic systems capable of doing arithmetic. I do not know if Godel’s argument can be extended to as complex a system as the universe.

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Definitions:

de•ter•min•ism (noun)
1. the doctrine that all facts and events exemplify natural laws.
2. the doctrine that all events, including human choices and decisions, have sufficient causes.

axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.

complete
A set of axioms is complete if, for any statement in the axioms’ language, either that statement or its negation is provable from the axioms.

consistent
A set of axioms is (simply) consistent if there is no statement such that both the statement and its negation are provable from the axioms.

e·nu·mer·ate verb (used with object)
1. to mention separately as if in counting; name one by one; specify, as in a list: Let me enumerate the many flaws in your hypothesis.
2. to ascertain the number of; count.

effectively generated
A formal theory is said to be effectively generated if there is a computer program that, in principle, could enumerate all the axioms of the theory without listing any statements that are not axioms. This is equivalent to the existence of a program that enumerates all the theorems of the theory without enumerating any statements that are not theorems.

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Gödel’s first incompleteness theorem states that:

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory…

Gödel’s theorem shows that, in theories that include a small portion of number theory, a complete and consistent finite list of axioms can never be created, nor even an infinite list that can be enumerated by a computer program. Each time a new statement is added as an axiom, there are other true statements that still cannot be proved, even with the new axiom. If an axiom is ever added that makes the system complete, it does so at the cost of making the system inconsistent.

There are complete and consistent lists of axioms for arithmetic that cannot be enumerated by a computer program. For example, one might take all true statements about the natural numbers to be axioms (and no false statements), which gives the theory known as “true arithmetic”. The difficulty is that there is no mechanical way to decide, given a statement about the natural numbers, whether it is an axiom of this theory, and thus there is no effective way to verify a formal proof in this theory.

This may mean that if this universe (with both its physical and spiritual aspects) can be expressed through a consistent set of principles, then there is a truth about this universe that cannot be demonstrated using those set of principles. That truth may look at this universe (as a whole) exactly for what it is. Such a truth may not be derivable from the set of principles that supposedly describe the universe.

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Gödel’s second incompleteness theorem states that:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.

The second incompleteness theorem does not rule out consistency proofs altogether, only consistency proofs that could be formalized in the theory that is proved consistent. The second incompleteness theorem is similar to the Liar’s paradox, “This sentence is false,” which contains an inherent contradiction about its truth value.

This may mean that this universe cannot contain the ultimate truth about itself. The ultimate truth is unknowable from the reference point of this universe.

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If we go by the definition of determinism that all facts and events exemplify natural laws, we cannot say for certain if that is true or not. In other words, not everything may be predictable ahead of its occurrence.

Manifestations may be related to each other in strict logical sequence meaning that any manifestation may be shown to follow from another manifestation. However, it may be impossible to determine how a manifestation may come to be on its own. This is another version of saying, “Absolutes are unattainable.”

So a system may be deterministic only in a relative sense. It can neither be absolutely deterministic, nor can it be absolutely non-deterministic. 

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Comments

  • vinaire's avatar vinaire  On July 20, 2012 at 3:00 PM

    The center of gravity of an object is essentially the resultant of all the force vectors acting on the molecules of that object. Similarly, a center of consciousness may be looked upon as the resultant of all mental forces and energies associated with you through awareness at that moment. This center of such mental forces and energies may be called SELF.

    A center of gravity is relatively stable compared to the moving particles of that object. Similarly, SELF may appear relatively stable compared to all the mental forces and energies, which are in a flux.

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  • vinaire's avatar vinaire  On July 21, 2012 at 5:19 PM

    There are no enemies or suppressive persons. There are inconsistencies only.

    It is paranoiac fixation on self that creates enemies or suppressive persons. Simply focus on inconsistencies and address them with KHTK Exercises. Everything will be well.

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    • Chris Thompson's avatar Chris Thompson  On January 11, 2013 at 7:34 AM

      Vin: There are no enemies or suppressive persons. There are inconsistencies only.

      Chris: This statement is consistent for the context of this thread. “Suppressive person” can be a placeholder in the context of “war” or “doing battle,” etc.,.

    • vinaire's avatar vinaire  On January 11, 2013 at 10:09 AM

      That is correct. These concepts serve to sweep problems under the carpet. They are there because the problem is not being confronted.

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  • vinaire's avatar vinaire  On July 21, 2012 at 9:53 PM

    For most people, body is an intimate part of their self. The Scientology command, “BE THREE FEET BACK OF YOUR HEAD” may simply serve to jar, momentarily, one’s fixed attention on the body. It may give one a glimpse of what it is like when the attention is not fixed on the body.

    This command may not have any effect on a person whose attention is too fixed on the body, or whose attention is not fixed on the body in the first place. Those who are affected by this command may believe that they have suddenly separated from the body and are ‘exterior’ to it. In actual case there is only a shift in viewpoint of the person. He didn’t even know how fixed his attention was on the body.

    Scientology uses strange vocabulary, such as, ‘thetan’ and ‘exteriorization.’ It believes that the person is a spiritual entity, called ‘thetan’, which has separated itself from the body, called ‘exteriorization’. But what has actually happened here is a relief from fixation on the body. This sudden relief may be surprising, but soon that feeling is gone.

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    • Chris Thompson's avatar Chris Thompson  On January 11, 2013 at 7:36 AM

      Check! I can use this.

    • Chris Thompson's avatar Chris Thompson  On January 11, 2013 at 7:44 AM

      Vin: “This sudden relief may be surprising, but soon that feeling is gone.”

      Chris: “Attention” seems to gravitate; to drift; to float; or zoom and to focus. We do seem to be able to use it, to direct it, to focus it; however, it can become fixated. This fixation reminds me of the way that a particle stream is focused by the magnetic fields in the collider at Cern.

      Or is “attention” analogous to the magnetic fields and “intention” analogous to the particle stream?

      • vinaire's avatar vinaire  On January 11, 2013 at 10:15 AM

        Attention seems to activate considerations when it is exterior to them. But when attention is fixated on considerations, the considerations maintain their status quo.

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  • vinaire's avatar vinaire  On July 22, 2012 at 6:21 AM

    One can probably handle a situation better once the attention is no longer obsessively fixed on it.

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  • vinaire's avatar vinaire  On July 22, 2012 at 6:29 AM

    One’s attention is usually stuck on those things one has been told not to look at. One was told that looking at those things would be bad or dangerous. This might be so, but it is better to look and handle whatever is bad or dangerous there.

    Going back and looking at those things, which one was told not to look at, might release that fixed attention. There is one caution. One should not just start to think about such things randomly. One needs to pick up one thing at a time and contemplate on what the mind brings up.

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  • vinaire's avatar vinaire  On July 22, 2012 at 7:19 AM

    Fixation in terms of space may express itself as being at certain locations.
    Fixation in terms of energy may express itself as feeling of rapid motion.
    Fixation in terms of mass may express itself as inertia in getting things done.
    Fixation in terms of time may express itself as as thought of permanence in the form of a self or soul.

  • vinaire's avatar vinaire  On July 22, 2012 at 8:01 AM

    In Scientology, there is this strange concept of thetan, which nobody really understands. There is nothing to understand really.

    Thetan is the abstract consideration of ‘being’. Thetan occupying a certain space is consideration of ‘that space being’. It is simply having attention on that space, which brings it into being.

    The attention becomes that space.

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    • Chris Thompson's avatar Chris Thompson  On July 22, 2012 at 8:12 AM

      as in the wave collapse?

      • vinaire's avatar vinaire  On July 22, 2012 at 8:49 AM

        We are working towards that. I don’t have a good grasp of attention and awareness yet.

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      • vinaire's avatar vinaire  On July 22, 2012 at 8:55 AM

        Why does music have certain affect on people? You may ignore the words of the song. But music has certain effect all by itself. These are sound waves being converted into neural waves and going deep into the mind. Maybe a smooth waveform penetrates deeper, Then there is the matter of resonance. There is a lot here to look at.

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        • Chris Thompson's avatar Chris Thompson  On July 25, 2012 at 1:43 AM

          Regarding music, I have long held that similarly consistent waveforms to the individual’s own waveforms are more pleasing to that individual. Said another way, the type of music that I like at particular time may be because it harmonizes with my mind . . . thus differences in taste . . . similar with food and other senses as well… the favorite waveforms are somehow similar to and resonate with our current mental states.

        • vinaire's avatar vinaire  On July 25, 2012 at 5:39 AM

          Yes. That seems to be the case.

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    • vinaire's avatar vinaire  On July 22, 2012 at 9:01 AM

      When Hubbard talks about a thetan occupying the same space as an object, it seems to translate simply as ‘becoming aware of that object’. I don’t understand why Hubbard uses such confusing vocabulary. There is no thetan. There is only attention and awareness.

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      • Chris Thompson's avatar Chris Thompson  On July 24, 2012 at 11:49 PM

        Yes, “be it” seems to mean “become aware of it.” And in addition to attention and awareness we need to consider focus. I was paying attention to my focus today and realizing that as I drive or read that I am focusing on no more than a couple degrees no more than about approximately 2 inches or 5 cm at arms length in front of my face. Everything outside those few degrees become peripheral vision extending outward to somewhere around 160 degrees or 80 degrees to the left and to the right of a perpendicular line in front of my face. This is really curious to me – there seems to be some zooming possible but I can clearly zoom and focus approximately 1/4″ outward to about 2 inches tops before the peripheral vision starts. I am really wondering about how to apply this data.

        • Chris Thompson's avatar Chris Thompson  On July 25, 2012 at 1:47 AM

          . . . but it may be more than just this. We may have to duplicate somehow its innate waveform — to become willing to let it in or to “go in” – like a key in a lock. Colors, temperatures, shapes, sizes, symmetries, weight, and so forth.

        • vinaire's avatar vinaire  On July 25, 2012 at 5:31 AM

          Check out Exercise 3 here, which I have added recently.

          KHTK EXERCISE SET 1 (new)

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        • vinaire's avatar vinaire  On July 25, 2012 at 5:40 AM

          I am studying COHA (Creation of Human Ability by Hubbard) at the moment. Hence these comments…

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        • Chris Thompson's avatar Chris Thompson  On July 25, 2012 at 10:42 AM

          ah!

    • vinaire's avatar vinaire  On July 22, 2012 at 9:08 AM

      There seems to be degrees of awareness about something. One may just think about something, or one may have intimate familiarity with that thing. Here we have have two different levels of awareness.

      ‘Occupying the same space as’ would simply mean a level of most intimate and complete awareness.

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      • Chris Thompson's avatar Chris Thompson  On July 24, 2012 at 11:52 PM

        . . . and I am wondering if this is or how this is related to focus and field of vision.

  • vinaire's avatar vinaire  On July 22, 2012 at 9:33 AM

    Havingness seems to have something to do with awareness in terms of senses that are grounded in reality, and not just in terms of mental speculation.

    Mental figure-figure in an effort to resolve some problem may lead to ‘a loss of havingness’ as one drifts into losing touch with reality.

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    • Chris Thompson's avatar Chris Thompson  On July 22, 2012 at 11:35 AM

      This can be accounted for mathematically as a fractal coordinate which iterates away into infinity from the X,Y axis.

      It can also be accounted for in Scientology processes when repairing “havingness” involves directing the PC’s attention back into the “real” world by having him do various drills like touching and noticing various objects in the immediate environment. This both reads on the e-meter and is readily apparent to the PC’s subjective awareness of his surroundings becoming more real to him.

      I am wondering if every phenomena everywhere may be within the descriptive bounds of the language of mathematics. And if it were, why is that?

    • Chris Thompson's avatar Chris Thompson  On July 24, 2012 at 11:54 PM

      Havingness is a physical manifestation regardless of the word you give it. I doubt it is confined to Scientology.

    • vinaire's avatar vinaire  On July 25, 2012 at 5:37 AM

      I find it useful to think of Havingness in terms of being in touch with reality. In that sense scientists shall have high havingness.

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      • Chris Thompson's avatar Chris Thompson  On July 25, 2012 at 10:41 AM

        . . . and what of meditating upon a dot on the wall?

        • vinaire's avatar vinaire  On July 25, 2012 at 11:12 AM

          That is what scientists seem to be doing… ha ha. Talk about the Higg’s particle…

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  • vinaire's avatar vinaire  On July 22, 2012 at 2:57 PM

    Mathematics is a wonderful tool to organize thought.

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  • vinaire's avatar vinaire  On July 22, 2012 at 3:01 PM

    The beautiful thing about Buddhism is that, like science, it is rooted in the senses derived from this universe. It does not stray into speculations as Scientology does.

    When one follows Buddhist exercises of Vipassana, there is never any loss of havingness.

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    • Chris Thompson's avatar Chris Thompson  On July 24, 2012 at 11:24 PM

      So you declare; however, that would be hard to prove.

      • vinaire's avatar vinaire  On July 25, 2012 at 5:18 AM

        I am more into looking and encouraging others into looking and recognizing inconsistencies. I shall leave proofs to Geometry.

        The deeper I get into Buddhism, the more I realize how much rooted it is in actual senses derived from this universe. Just look at the very first exercise about mindfulness in breathing. It keeps one grounded through awareness of breathing unlike OT TR0 of Scientology. Here one doesn’t do anything with breathing except for being aware of it. That awareness keeps one grounded in reality.

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        • Chris Thompson's avatar Chris Thompson  On July 25, 2012 at 10:38 AM

          So are we trying to stay grounded in reality or remove attachments?

        • vinaire's avatar vinaire  On July 25, 2012 at 11:06 AM

          It is like peeling the layers of an onion. To remove the top layer you have to be grounded in the layers beneath it. When the top layer is removed, the next layer becomes the top layer and the grounding shifts accordingly.

          It is all relative.

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  • vinaire's avatar vinaire  On July 22, 2012 at 3:21 PM

    R1-12: HAVE PRECLEAR MOCK-UP GENERATORS, POWER PLANTS AND SUNS TO GIVE HIM ENERGY, ON THAT GRADIENT SCALE, UNTIL HE IS TOTALLY CONVINCED THAT HE DOES NOT HAVE TO RECEIVE ENERGY FROM AN OUTSIDE SOURCE. (A COMPLETE REMEDY OF HAVINGNESS)

    This is a procedure in Scientology which seems to get into speculation. It is assumed that a person does not need energy from an outside source, but can generates one’s own energy.

    A more basic assumption here is that mental forces/energies are separate and independent of physical forces/energies. In actuality, a person is made up of a combination of physical and mental forces and energies. The body needs to eat and support the mind.

    The self is like the “center of gravity” of these physical and mental forces and energies. Self is nothing in itself. Self is part of this universe. There is exchange of energy between the self and the rest of the universe. The self cannot survive without the universe.

    What remedies havingness is to get really in touch with the real universe out there. The idea that a person does not have to receive energy from outside source is humbug. This process is going to condition the mind in a certain way.

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  • vinaire's avatar vinaire  On July 25, 2012 at 3:04 PM

    Hubbard says,“Considerations take rank over the mechanics.”

    I belive that considerations and mechanics go hand in hand. After all ‘mechanics’ is a consideration too. And the importance or unimportance of mechanics is also a consideration. So I do not buy what Hubbard is saying here.

    I agree that if there is an inconsistency to do with considerations and mechanics then one should be addressing that. Hubbard says, “… the mechanics have
    taken such precedent in man that they have become more important than the considerations and overpower his ability to act freely in the framework of mechanics…”

    This is not the problem with mechanics. Scientists have done a great job of understanding mechanics and have put that understanding to great use. This has been a hallmark of the western civilization.

    It is not the mechanics that are the problem. It is the ignorance of mechanics that needs to be addressed.

    The inconsistency lies in Hubbard putting mechanics down. Hubbard also declares MEST universe as a theta trap in his THETA-MEST theory. Hubbard is taking sides here by pitching Theta against MEST. There is something very wrong here with Hubbard’s theory.

    In my opinion Theta and MEST are part of the same overall system. One only needs to address inconsistencies that arise in the interaction between Theta and MEST. Neither Theta is superior to MEST, nor MEST is superior to Theta.

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  • vinaire's avatar vinaire  On July 25, 2012 at 5:53 PM

    R1- 6: HAVE PRECLEAR HOLD THE TWO UPPER BACK ANCHOR POINTS OF THE ROOM FOR AT LEAST TWO MINUTES BY THE CLOCK.

    This is an interesting Scientology process. When a person has his attention knowingly fixed on the two corners, it may so happen that he may let go of his unknowingly fixed attention on the body.

    This command may not have any effect on a person whose attention is too fixed on the body, or whose attention is not fixed on the body in the first place. Those who are affected by this command may believe that they have suddenly separated from the body and are ‘exterior’ to it. In actual case there is only a shift in viewpoint of the person. He didn’t even know how fixed his attention was on the body.

    ‘Exteriorization’ is simply a shift of viewpoint from body to outside the body.

    A similar shift of viewpoint is possible from the physical universe to “outside” the physical universe.

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    • Chris Thompson's avatar Chris Thompson  On July 26, 2012 at 7:39 AM

      hehe well, this is what hobbies are for, aren’t they?

      • vinaire's avatar vinaire  On July 26, 2012 at 9:40 AM

        I think you are right. 🙂

        My hobby at the moment is nit-picking Scientology.

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        • Chris Thompson's avatar Chris Thompson  On July 26, 2012 at 6:54 PM

          Yes, and a fruitful nit-picking it is being. 😉

        • Chris Thompson's avatar Chris Thompson  On July 26, 2012 at 6:56 PM

          Placing my attention from the things it is fixated on and onto “something else” is one reason that I play guitar. It is a hobby and a few minutes vacation — refreshing to have my fixed attention unfixed.

        • vinaire's avatar vinaire  On July 26, 2012 at 7:56 PM

          It is fun to look at COHA processes with the KHTK approach of looking with mindfulness.

  • vinaire's avatar vinaire  On July 26, 2012 at 9:52 AM

    Hubbard says:
    “Agreement with the physical universe brings about the consideration on the part of the preclear that two things cannot occupy the same space. It is this basic rule which keeps the physical universe ‘stretched’. It is not, however, true that two things cannot occupy the same space, and it is particularly untrue when the two things are an object and a thetan, since a thetan can occupy the space any object is occupying.”

    Hubbard’s assertion that two things can occupy the same space is false. A thetan is not a thing but a consideration. Hubbard even admits elsewhere that thetan is not a thing.

    .

  • vinaire's avatar vinaire  On July 26, 2012 at 2:36 PM

    The purpose of COHA processes is to bring an individual into thorough communication with the physical universe.

    Route 1 processes basically address fixed attention in the following order:
    (1) Fixed attention on things uppermost in the mind. (R1-5)
    (2) Fixed attention on (identification with) body’s location. (R1-4, R1-6)
    (3) Fixed attention on locations in the physical universe (actual locations). (R1-7)
    (4) Fixed attention on things regarded as bad or dangerous (actual things). (R1-8)

    Route 1 processes then exercise freed attention as follows:
    (5) Place attention on actual locations that are real to the person (do not suggest locations that are unreal) (R1-9)
    (6) Become aware of one’s tolerance of things. (R1-10)
    (7) Become aware of actual problems and solutions (not imagined ones) (R1-11)
    (8) Get thoroughly in touch with the physical universe reality. (R1-12)
    (9) Familiarize yourself fully with the body’s nerve structure. (R1-13)
    (10) Thoroughly examine one’s habits and patterns. (R1-14)
    (11) Thoroughly examine one’s impressions of the physical universe (R1-15)

    However, many of these processes are put together in a weird manner with weird vocabulary, and one may not be able to run them as intended. A PDF copy of COHA may be downloaded from Internet.

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  • vinaire's avatar vinaire  On July 26, 2012 at 6:30 PM

    Space itself can be havingness if one can view it as something.

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    • Chris Thompson's avatar Chris Thompson  On July 26, 2012 at 6:52 PM

      Yes, it is clear to me how this can be. My experience is of space being more significant and freeing to me than my experience of solid material things. Space in my memory has always seemed like something to me rather than nothing. Given the choice of a cozy cabin in a beautiful (thick) forest setting vs. a sod house out on the ocean of vistas of flat plains on the North Texas panhandle, I choose the wide open spaces.

      But I never quite thought about it in just that way before.

      • vinaire's avatar vinaire  On July 26, 2012 at 7:53 PM

        I got that realization while looking at R2-18 and R2-19 of COHA.

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  • vinaire's avatar vinaire  On July 26, 2012 at 8:03 PM

    There are simply locations, movements, objects and considerations about them. They have the property of attention and awareness by the very fact of existence. A combination of such things may produce the sense of ‘I’. This ‘I’ can be a problem or a solution from other viewpoints or its own. ‘I’ is a problem to degree it becomes inflexible. ‘I’ is a solution to the degree it induces flexibility. ‘I’ may be analyzed by breaking it down into locations, movements, objects and considerations. This is just a thought.

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  • vinaire's avatar vinaire  On July 26, 2012 at 8:37 PM

    Hubbard says:
    “Granting of Beingness (life) to something. The preclear is as well as he can grant life to things, an action which involves the creation of energy. The basic granting of beingness is the thetan duplicating himself as another thinking being.”

    In my opinion, Granting of Beingness would be letting something (or somebody) be for what it is, and making no efforts to alter it by adding or subtracting to it. You are not giving it life. It is what it is. You are not creating energy. The energy is already there. You are simply becoming aware of it.

    Thetan is just a label for a combination of locations, movements, particles and considerations. There are locations, movements, particles and considerations other than those, which make up your ‘I’.

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    • Chris Thompson's avatar Chris Thompson  On July 26, 2012 at 11:19 PM

      Like a fractal iteration, every moment that it has iterated makes the previous iteration recede into the past and possibly into oblivion. Thus as the resulting iteration, though similar yet is different. The language, the words which have been earmarked for a certain iteration at a certain moment also get left behind in meaning for the meaning is the iteration. As the newest iteration is different from the previous iteration, the old words naming previous iterations cease to be as correctly descriptive as they used to be and their essence becomes as lost as the previous iteration.

      Once not long ago I wrote to you that I was at the core the same unknowable static that I ever was and you wrote to me, “Are you sure?” As true as my statement of “I” was true to me then, it is no longer true to me. Rather than wearing my “i” like a garment, that “I” now looks as foreign to me as a stranger. It stands out in front of me like a worn and thread-bare suit on a rack.

      “This existence as it unwinds is becoming very different than I ever expected.” Now that statement I have said more than a few times in the past and it has retained its consistency.

    • Chris Thompson's avatar Chris Thompson  On July 26, 2012 at 11:20 PM

      There is a consistency to your statement of “granting beingness” which is pleasingly consistent to me and which is consistent with my statements about fractals above.

    • vinaire's avatar vinaire  On July 27, 2012 at 4:45 AM

      It is like peeling off the layers of onions. I don’t know how many layers there might be. 🙂

  • vinaire's avatar vinaire  On July 27, 2012 at 9:44 AM

    Hubbard: “In the mechanics of the granting of beingness we have ‘orientation point’ and the ‘symbol’. An orientation point is that point in relation to which others have location.”

    Vinaire: An orientation point is not something absolute. It is itself a location, so all locations are relative to each other including the orientation point.

    Hubbard: “It is also that point from which the space containing the locations is being created.”

    Vinaire: Locations are the properties of space. Therefore, the orientation point is part of the space. It does not stand out from the space and creates space.

    Hubbard: “In the orientation point we have our basic definition of space: ‘Space is a viewpoint of dimension’.”

    Vinaire: Dimensions are measurable properties. Anything manifested is perceived because of its dimensions. Space contains the viewpoint as well as the dimensions.

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  • Chris Thompson's avatar Chris Thompson  On July 27, 2012 at 12:32 PM

    . . . and something more is that the character of space is different from the character of matter. The manifestation and character of space seems to have something more in common with time than it does with matter or energy. Space-time is aptly named. I have to look at this some more.

    I am seeing a consistency in saying that the “propagation point” of light is not in motion. Thus resolving the mystery of c constant for all frames of reference. This is wound up in space-time such that resolving one of these may lead to making the other problems dissolve as well.

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