The Foundations of Mathematics

There is a fundamental axiom which may be expressed in the following two forms:

  1. There is a POINT.

  2. There is a UNIT.

A LINE may be expressed in terms of points. A SURFACE may be expressed in terms of lines. A SOLID may be expressed in terms of surfaces. All forms may be expressed in terms of solids. This sort of buildup may keep on going toward more variety and complexity of forms.

COUNTING may be expressed in terms of units. ADDITION may be expressed in terms of counting. MULTIPLICATION may be expressed in terms of addition. EXPONENTIATION may be expressed in terms of multiplication. Besides, the opposite of addition may be expressed as SUBTRACTION. The opposite of multiplication may be expressed as DIVISION. The opposite of exponentiation may be expressed as LOGARITHMS. This sort of buildup may also keep on going toward more variety and complexity of thinking.

The above two “axioms” underlie all mathematics. Mathematics underlies all our thinking. The ideas of location, God, soul, etc., cannot exist without the ideas of POINT and UNIT.

It seems to me that mathematical principles underlie all spiritual and physical principles, and the ideas of point and unit underlie all mathematical principles.

These two assumptions of POINT and UNIT, happen to be just assumptions. They are arbitrary.

And to believe in these assumptions as fundamental facts would be the fundamental inconsistency indeed.

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Comments

  • Chris Thompson  On December 3, 2011 at 11:45 AM

    I like how short this is. A nice clean statement. Very satisfying. Now you have reduced existence to the irreducible minimum? Clear-minded of you to spot the fundamental inconsistency as well.

    When I look at this I see a layer of judgement in “unit.” The judgement of “a singular” or “a one.” “Unit” has the added complexity of judgement underlying “value.” Do you see what I am saying? Maybe we should stop at “there is a point.” Now we would have the irreducible minimum of existence without judgement. But actually ” ‘there’ is a point implies ‘here’ is a point.” Here? There? A line– oops. Well, maybe from the point back to where?

    I am a point? I count the point? I have a unit of I? These are complete sentences and reduce “point” and “unit” to “I.” Hmmm. I am back where I started in the squirrel cage, am I not? I am at be, do, and have without trying very hard. But maybe there is usefulness in this as well. Maybe you should add a third axiom above — something like “movement” or “change.”

    So another axiom would be that we cannot solve a problem from the same level of consciousness that created the problem. And so on we go. Though my writing is less than cogent, I can see the usefulness of your breakdown to help understand mathematics and I think I will use it to help my kids.

    Maybe there should be a single axiom written as “A point exists uncoalesced.” Now it becomes abstract with no location. This could possibly be consistent with the wavefunction. Then it can come forth into its collapsed state and so forth.

    The basic inconsistency of your fundamental points the way toward your well-worn unknowable. If you answer me without writing the word unknowable I will reward you. (my basic inconsistency employs manipulation yet again.)

    Thank you for writing this. I was able to reason and have the thoughts I’ve written because of it — very enjoyable.

  • vinaire  On December 3, 2011 at 12:11 PM

    The above two forms seem to me the expressions for the same axiom, the exact wording for which excape me at the moment.

    Anyway, right now I am enjoying exploring the mind of Alan Turing. See

    Links Suggested by Readers

    .

  • Chris Thompson  On December 3, 2011 at 12:14 PM

    Yes, you wrote this.

  • allzermalmer  On December 4, 2011 at 3:21 AM

    Good blog. One point, is that you basically bring mathematics to underlying our thinking, and mathematics is based on Point and Unit. But the mathematical Point is a fiction. You won’t ever find anything like that existing, and it’s an abstract concept. And your right that it’s arbitrary, because it’s a convention. It’s an assumption about the world not found anywhere near the world.

  • vinaire  On December 4, 2011 at 6:50 AM

    Thank you. Basically, “point” in geometry is an abstraction for a location. Locations are represented by points on a map. At macro level, this concept seems to work, but when we get down to the atomic dimensions we have to resort to probability to define “location”. Same argument may be presented for “unit.” I am wondering if there are really well-defined particles at atomic dimensions. Does a photon have a well-defined boundary? I don’t think so.

    .

  • Kevin Osborne  On February 9, 2012 at 2:15 AM

    Existence is the difference between you and what you see.

    • vinaire  On February 9, 2012 at 8:27 AM

      So far I have found that existence is the result of speculation.

      .

  • IdealGoal  On October 9, 2012 at 4:30 PM

    Hi! Vinaire.
    Few questions first:
    – Isn’t counting already, an addition?
    – Could you define “God” and “Soul” only in terms of “point” and/or “unit”?

    Now, as you well said at the end: a “point” can not be considered without been “located”. That means that at least two other points does need to exist too.
    Yes, indeed, otherwise, if you have even two points, you don’t have any scale here, any unit than the unit of DISTANCE brought by the two points.
    Cause yes, you don’t have here any gauge to COMPARE!
    Are the two points at one thousand light-years or one picometre? Who can say that! Even per “pure consideration” would exist something like a “meter” to say that.
    Of course, we could call this distance in these two points “a meter”, and say “they are at this distance”. But what this statement would worth if we have no other point here?
    But now, having two points, having a distance, we can consider the space in-between and the infinite possibilities of locations for points.
    So, when we have two points, we have de facto an infinite set of possible points.
    I mean, it’s not: “first” we have two points and “then” we have “an inifinite”, we create them all in the same consideration.

    An other way to show this is how we can construct all the mathematics, but I really say “all”, on the concept of “VACUUM”.
    Yes, all the marvellous things you can find in mathematics, all based on… The Nothingness!
    How it’s possible?
    Well, “zero” represents indeed the concept of “Nothingness”!
    “Zero” in arithmetics, is the equivalent of “the vacuum set” in the Sets Theory. Indeed, it just two way, to “modes” to say the same in mathematics, as all the arithmetics has its equivalent and expression in geometry.
    I would say more: the arithmetics and all the Numbers Theory, CAN be deduced from the Sets Theory, but the opposite is not possible (or one may demonstrate the contrary if think I’m wrong).
    So, we have the “vacuum”.
    And what could we do now with this totally evanescent base?
    Well, to follow me well now, to go through the “nothingness”, demands at least for the first time to walk very closely into the paces of the guide 😉
    So, when we CONSIDER that a vacuum DOES EXIST, we consider too that “SOMETHING” exists: the “ENTITY” that were are considering; so that makes an “UNIT”, something we can talk about for what it is; so we have made a “SET”, we have made “A WHOLE OF NOTHING”.
    But now, look at this: we have “A” set, we have “ONE” set, indeed! We have “ONE”, the NUMBER, and the vacuum itself is “ZERO”.
    Hey! Did you think the story was finished?! Surely not but surely “yes” too!
    How this could be possible?!
    Because of the same reason than in the case of the postulation of a “point”: A POINT CAN NOT EXIST WITHOUT AN INFINITE NUMBER OF OTHER POTENTIAL POINTS, AND AT LEAST, THREE ACTUAL POINTS.
    Lets look “in the vacuum” again: (no, you don’t miss some “mass” there – Scientologist students will understand – cause no “mass” can symbolized a vacuum, only “the vacuum set”, “the vacuum set”?! Indeed!)
    So, remember now, we have “the vacuum” itself, the “ZERO”, and we have the set that consider the existence of the vacuum, so “now” we have TWO entities! which we can consider them as a whole, as a new SET, so that we have THE set which represents “THE NUMBER TWO”, and we say he HAS tow ELEMENTS; but so we can make an other set which contains there sets…
    You have perhaps understood: this goes TO INFINITE instantly, indeed, THERE IS NO TIME AT ALL in this CREATION, and when I wrote “now we have”, it was only about the TIME involved with the writing.

    So, here we come back at the beginning of the talk: AT THE SAME POINT YOU CONSIDER THE NOTHINGNESS FOR ITSELF, YOU CONSIDER IT AS AN UNIT, AND YOU POTENTIALLY CONSIDER A INFINITE OF SETS, AN INFINITE OF UNITIES.

    Now, as you have spoken about spirituality, dear Vinaire, lets see if we can make a parallel, a comparison, between these mathematics and what we could consider or “feel” what could be “THE ESSENCE OF THE SPIRITUAL”.
    Well, lets consider that we have “AN UNDEFINED WHOLE, UNDIFFERENCIATED, UNBOUND”, not because a “DIFFERENCIATION” or a “BOUND/LIMIT” would apply here, but just because it has NO SENSE here.
    Now, this “AN UNDEFINED WHOLE, UNDIFFERENCIATED, UNBOUND”, has one ability at least: TO DECIDE.
    “It” “DECISES” so to CONSIDER “ITSELF”, so “TO MAKE “ITSELF” EXISTENT FOR “ITSELF” “; what happen so?
    As we have seen, it’s potentially “AN INFINITE SET OF POINTS OF VIEW ON ITSELF, THAT “IT” CREATES AT THE SAME INSTANT”.
    So, all goes very simple now:
    Define that basically, “DISTANCE” IS A “DIFFERENCE”, then a “SPACE” IS CREATED IN BETWEEN EACH POINT OF VIEW AS “CONSIDERATIONS”, OR “VIEWPOINTS” IF AS “A LOCATIONS IN A SPACE”; A “SPACE” which is the “INIFINITE MATHEMATICAL SPACE OF ALL THE POSSIBLE LOCATIONS FOR A VIEWPOINT”.
    Then you just read “The Factors” of Lafayette Ron Hubbard, and could be it could bring you a interesting effect; and if “yes”, Just tell me 😉 Oh yes! For the “zero”, “nothingness”, but having the ability to “CONSIDER”, you have too his “First Axiom of Scientology” (1954).

    Note: Nothing in what I’ve just written has the vainglory for any absolute truth. It is here to be criticized ad libidum, as long as it is constructive reviews made in the purpose of the enrichment of “The Whole Set Of Viewpoints”, “The Infinite Set Of Viewpoints”, or “The Infinite”, and not to defend one’s only single.. point of view.

    • vinaire  On October 18, 2012 at 8:02 PM

      Hi IdealGoal, Sorry for this delay in answering you as I have been away on a safari in Africa.

      Let me answer your questions first.

      (1) Addition is “counting together.” It is the next step up from counting.

      (2) “God” and “soul” are described as beings. All beings have locations. A point is a location in space, and therefore, it provides a basis for the concepts of ‘God’ and ‘soul.’ God would be a unit to itself in monotheism. A ‘soul’ would be a unit when we are taking about many souls… a UNIT being ‘what is counted one at a time’.

      Here are some general definitions:

      (1) A POINT represents a location. All locations are points.
      (2) A LINE is a path traced by a moving point.
      (3) A SURFACE is a path traced by a moving line in a different direction.
      (4) A SOLID is a path traced by a moving surface in a different direction.
      (5) A UNIT is a particular length of a line, a particular area of a surface, or a particular volume of a solid.
      (6) A ZERO is simply a reference point on a dimension. It represents an absence of the unit of that dimension.
      (7) A VACUUM is unfilled space.
      (8) SPACE is not nothing. It is something like a container.
      (9) A SET is a collection of things. An empty set has no items in it.
      (10) SPIRITUAL is defined as the opposite of mechanical.
      (11) MANIFESTATIONS come about. We don’t know how a manifestation comes about from nothing. We may speculate about it but that would be speculation.
      (12) A CONSIDERATION is whatever that is considered. We do not know how a consideration appears, though we may speculate about it.
      (13) NOTHINGNESS is a consideration.
      (14) A DECISION is an act of considering.
      (15) MATHEMATICS is systematic thinking. It is a very fine system of logic.

      .

      • Chris Thompson  On October 18, 2012 at 9:37 PM

        Hi Vin, Please consider modifying (7) to “space with the solids removed.”

        • vinaire  On October 19, 2012 at 3:15 AM

          You may be right, but how do we define solids?

          .

        • Chris Thompson  On October 19, 2012 at 8:10 AM

          ah, I thought I was using your def, but let me see… just in the conventional sense when we draw a vacuum for whatever reason, we create pressure differential and draw out the gases. The gas particles are solid; however, rocky meteorites are solid and they seem to exist in the vacuum of space ok. so your point if well taken. well, anyway, what I was addressing is the word unfilled. How do you define that?

          Now I have to ask if a 1 cu meter meteorite residing in a 2 cu meter box with the air pulled out is residing in empty space? Or have we simply not pulled hard enough on the meteorite yet? This is making all sorts of conjecture about space bubble up!

          We begin with the premise that space is something. Therefore, it must always be filled with something even if just filled with its not quite defined self.

          I’m not saying it but I am holding a mental card in reserve about space that it too may be a fractal construct. In this model, atomic particles might qualify as “macro.”

        • idealgoal  On October 19, 2012 at 2:58 PM

          Hi! Chris Thompson.

          While reading your answer I think there is two concept which need to be differentiated:

          – the “SPACE” itself, and

          – the “UNIVERSE”.

          As I could see it, and how it’s works better in my mind:

          – The “Universe” exists in a “space”, but this space, as Buddhism has viewpoint stand it since a while, is a consideration of existence only given by, at least, a spiritual being who considers it exists.

          In other words:

          – “The space” is the container, “the Universe” the content.

          It’s while considering, the being assumes different “viewpoints” and “points to view” that he creates “space”(1), and as I said before, for me the most basic “space” is first the one of the consideration of DIFFERENCE, whatever it could be, which brings us to any mathematical space we can imagine and have imagined already.

          Then, having a “space”, the being can consider it is empty or full; just by one’s own consideration.

          This present Universe around, looks like there was an agreement about(2) the idea that the “common space” will be filled by an infinite levels of energies “starting” with the thinnest and lightest levels to go up to the biggest and condensed clusters of energies, that can be matter but not necessary: plasmas could be very dense and big, but matter needs a REPETITIVE LOCAL PATH of energy(ies), and we can even consider that many matter-flows are indeed energy-flows, like a water-flow.

          So, when we observe the Universe, we do though our own agreements about how the space is filled or not; which is each time a personal experience even if we can share the same perceptions with others beings while having the same considerations on it.

          What “fills” this common space, IS the “Universe”.

          The “Universe” could be created as finite/limited, or infinite; but the “space” itself could be unlimited/infinite, while in the same “time”, the “universe” could finite.

          So, if we talk now about “the Universe”, so I can answer that the present local universe, look to be indeed, made of these infinite levels of energies, which could be fractal, indeed. (3)

          On fractal stuff of you, I will study your work later, Chris Thompson, Don’t bother if it’s take time to me to come back of this specific subject I think very pertinent here.

          (1) See Axioms of Scientology 1954.
          (2) See works of Lafayette Ron Hubbard on the definition of “agreement”.
          (3) See work of Christian RICORDEAU: http://www.quatuor.org/english/fractal_34.htm

        • vinaire  On October 19, 2012 at 7:58 PM

          Chris, when one talks about a container being filled, one is considering liquids and gases that assume the same volume as that of the container. A space is considered to be filled with solid when the solid has the same volume as that of the container. A solid, such as the meteorite in your example is not filling the space of the container. Vacuum is measured by the density of particles present in space. The lower is the density the greater is the vacuum. This vacuum can vary in space from one location to another. There is no absolute vacuum.

          Energy and considerations are not material enough to be affecting a vacuum even if present.

          .

        • Chris Thompson  On October 19, 2012 at 8:13 AM

          Don’t we also have to ask whether the model of empty space can be something akin to a volume with some type of skin around it that possibly exihibits surface tension? ouch, hurt me brain on that.

        • vinaire  On October 19, 2012 at 8:16 AM

          See if the following makes sense:

          comment-5097

          .

        • Chris Thompson  On October 19, 2012 at 8:26 AM

          AWESOME!

        • Chris Thompson  On October 19, 2012 at 8:29 AM

          You’ve used the fractal beautifully!

      • idealgoal  On October 19, 2012 at 3:03 PM

        Hi!Vinaire. Great to see you back and thanks for your answers. Sorry if you have to patient too for my owns. Regards.

        • vinaire  On October 19, 2012 at 5:04 PM

          I love your contributions to this blog. Please continue.

          .

      • idealgoal  On October 19, 2012 at 10:07 PM

        Hi again, Dear Vinaire.

        I’m not agree with you: COUNTING is basically an ADDITION.

        It could be addition one by one, ten by ten, or whatever.

        See: when you count 1, 2, 3, etc., you just do 0+1=1, 1+1=2, 2+1=3, etc.

        Then, when we have the “quantification” of a set, we can or not, make bijections and compare the different sets to know how many elements the others contain, the “cardinal” of the set. You know this, right?

        And, base on this same principle, there are few important fundamental demonstrations about the “countability” and the comparisions of differents known sets of numbers, recursivity and so on…

        But fundamentally, if we speak about specific “natural numbers”, we have to have “a counting” base on the addition of 1 to the previous number/quantity.

        Regards

        • vinaire  On October 20, 2012 at 3:21 AM

          Counting is adding one more each time. It is a specific from of addition.

          But when one is adding 3 apples and 4 apples, one has already counted them separately. The next step is to put all these apples together, and count them as 7. This is what I meant when I said “adding is counting together.”

          .

      • idealgoal  On October 19, 2012 at 10:28 PM

        Vinaire, if you define “a BEING” as something having “a LOCATION” thus, for me, “God” is not “a BEING”, and for “a SOUL, it depends for me if you care only about, as Ron Hubbard said “awareness of awareness unit” or if you add to it the mind pictures and memories

        • Chris Thompson  On October 20, 2012 at 1:08 AM

          IdealOrg, I think the idea behind the omnipresent god is to have the the characteristic of being in every location.

        • idealgoal  On October 20, 2012 at 2:13 AM

          Yes, indeed, but it is not how I see “God”. “God” for me is not a location or all the possible locations, but the possible creator of; as “souls” can create their own space [space of the imagination, space “in” the mind] and decide to assume or not any viewpoint in it or even all, as “God” can assume any or all viewpoint in “His” creation, but “He” is not the locations themselves, the space and the Universe are both products of his own creations and considerations; from my viewpoints…

        • vinaire  On October 20, 2012 at 3:41 AM

          Here are my considerations:

          (1) A BEING has beingness. It is something manifested. All manifestations are finite relative to the background of no manifestations. Therefore, a being has to be finite.

          (2) All manifestations are located in the background of no manifestation. Therefore, a being has a location.

          (3) You are right in saying that “God” is not a being. Therefore, God is not a manifestation. We can only know what is manifested. God is, therefore, unknowable.

          (4) A soul, as defined in Christianity, is not the same thing as THETAN (awareness of awareness unit).

          (5) One can be aware of only that which is manifested. Awareness comes with manifestation. Without manifestation there is no awareness. Therefore, an “awareness of awareness unit” must be a manifestation. A thetan is a finite manifestation, especially when it is differentiated from other thetans.

          (6) God cannot be omnipresent if it is unknowable. “God being omnipresent” is a consideration.

          (7) Cause-effect or creator-creation are dipoles. Cause comes into being when effect comes into being. Creator comes into being when creation comes into being. Cause and/or creator cannot exist independently of Effect and/or creation.

          (8) God is unknowable. Therefore, any attributes assigned to God, such as “God can assume any or all viewpoint,” are created considerations.

          .

      • idealgoal  On October 19, 2012 at 10:39 PM

        So, “therefore”, “God” for me has very few to have with “points”, if it’s not about the ability to create any, and a “soul”, if “awareness of awareness unit” only, can locate or not itself, or create points too, as much as space, and if mind pictures, well, just look “where” you create your pictures and you could possibly locate them yourself somewhere outside at the front of the face but are “dimentional points” any way, and your own.

        • vinaire  On October 20, 2012 at 3:46 AM

          Considerations come about in an effort to define the unknowable.

          “Awareness of awareness unit” is such a consideration.

          .

        • Chris Thompson  On October 20, 2012 at 12:40 PM

          I would say that the effort to define the unknowable would be wasted.

        • vinaire  On October 20, 2012 at 1:33 PM

          But it takes the prize as the generator of considerations.

          .

      • idealgoal  On October 19, 2012 at 11:20 PM

        “God” for me, is both the fundamental state of undifined/ilimited/undifferenciated entity that exists without begenning nor end, which then produces by having reflexing consideration on itself, makes it appearing to itself: individualities/limited(points-like)/differenciated viewpoints on itself in infinite number, which are no more “God” but possible consisting elements for “souls”.

        These are “VIEWPOINTS”, not yet and not necessary “points to view”. (2)

        As could see it: “God” is like the hand for the fingers: fingers are “indépendant” in a way but are part of the hand any way.

        Then, we could even extrapolate that any spiritual path for “spiritual freedom” would consist of going from the level of awarness of mud under the bail, to the nail, to the finger, to the hand (of course, it doesn’t means anybody need to start from the mud 😉 ).

        Regards.

        Still, if I make a pause it in terms of days, it will not by lack interest…

        (2) See “Factors” of L. Ron Hubbard.

        • Chris Thompson  On October 20, 2012 at 1:15 AM

          Hey idealgoal, I think we came together on this one… god being like the hand to the fingers – independant yet still part of the hand. Nice metaphor. I am a sucker for metaphors.

          So I’m at a concert tonight with thousands of people and I’m wondering how it is that we share the reality of the venue and concert, etc., yet I cannot see from their point of view.

        • idealgoal  On October 20, 2012 at 2:46 AM

          Nice to know that my metaphor brough you something positive. 🙂

          For the common experience, could be you can try first to embrasse with your own space (the one you can fill by your awareness) the physical location of the bodies where the souls themselves consider they are located in most of the time, and try to feel what they feel and see, one by one and then like a whole. I think it could give good feeling IF these souls feel good too at this time 😉

          But we could go further and try to embrasse by one’s own space, any space, any being, and like few say “God” is Infinite Understanding and Love, to fill our extended space of such infinite Love, at least as much we can conceive it, and see if we feel good then: not to be the effect of the “others” but to create an positive effect in our own space that could possibly too, have a good influence on these said “others”. So, you have understood: I’m not so good myself at this practice! (Proof is in this blog now – see post to Vinaire).

          Regards.

        • vinaire  On October 20, 2012 at 3:57 AM

          To me, it is inconsistent to say that something exists beyond all existence; or to try to define something that cannot be defined. A consideration is generated that way.

          My motto is to see something for what it is.

          To me “God” represents that which we cannot know and, thus, define.

          All religions are basically theories about unknowable. The safest route is to see what is there for what it is, and keep resolving inconsistencies.

          .

  • IdealGoal  On October 9, 2012 at 4:46 PM

    Erratum: It’s from the Sets Theory, as you have see, that we can produce the arithmetics, but it is from the arithmetics we can deduce the geometry, and not the opposite. Sorry for the inversion.

    • vinaire  On October 19, 2012 at 3:31 AM

      Here are some more definitions:

      (1) SETS are collections of items.
      (2) An ITEM is any manifestation or consideration.
      (3) A NUMBER accounts for how many items there are.
      (4) ARITHMETIC is simply ‘skill with numbers’.
      (5) GEOMETRY is a study of relationships among locations in space.

      I am not quite sure what SPACE is and how do the various laws and constraints of geometry come about. It has to do with the basic axioms of geometry.

      .

  • IdealGoal  On October 9, 2012 at 7:37 PM

    “The Fundamental Inconsistency”:
    It is here that:
    – The NOTHINGNESS produces the “SOMETHINGNESS” (so, the existence);
    – The ZERO produce the INFINITE;
    – The “UNDIFFERENCIABLE” produces the INFINITE DIFFERENCIATION.
    And this, all in the same “TIME”, a “time” which has both “no DURATION” and INFINITE DURATION.

    If we see that “Inconsistency” may be taken as synonym of “contradiction”, and of “lie”, we could see that the whole reality is constructed on a lie.
    But in this case, how a logic, a “consistent” one, with “consistent” mathematics could exist?
    Well, we do not need to be “so” consistent at all, meaning that from a contraction we never deduce anything right or really precised.
    But who cares?!
    We CAN produce workable mathematics with an inconsistant theory, and arithmetics has been proved such!
    A nice article in the on-line Standford Encylopedia of Philosophy named “Inconsistant Mathematics” shaws that more we look at the fundamentals of the mathematics and of the logic, more we come in the both case to reinforce the importance of said “intuitive set-theory” and “intuitionist mathematics” and it is precisely what we were talking about here: that Inconsistency, IS the natural base of everything, I mean of any reality.

    “Priest (1987) and Priest, Routley, and Norman (1989) argued that the Liar* had to be regarded as a statement both true and false, a true contradiction”; Chris Nortensen, Standford Encylopedia of Philosophy. (* liar like: “this sentence is a lie”)

    • vinaire  On October 19, 2012 at 4:01 AM

      (1) How can NOTHINGNESS produce SOMETHING? I see an inconsistency there.
      (2) The same inconsistency has been worded differently many more times in the post above.
      (3) A consistent subject may emerge from axioms that are inconsistent. There may be consistent agreement over things that are inconsistent. A lot of people may believe that the earth is flat and not spherical. A lot of people may believe that the earth is spherical.
      (4) Believing in both sides of a contradiction is definitely an inconsistency.
      (5) Believing in a lie is also an inconsistency. In fact, believing in anything (instead of looking at it thoroughly) is an inconsistency.
      (6) Attention should be on resolving inconsistencies. What is consistent may be accepted for what it is without further attention. There is nothing to be resolved there.
      (7) A universe is there because something is consistent about it, but there is something inconsistent about saying that NOTHINGNESS has produced the universe.
      (8) Anything stands out in consciousness because there is something is inconsistent about it.

      .

      • Chris Thompson  On October 19, 2012 at 8:37 AM

        Nothingness has a similar inconsistency as unknowable.

        • vinaire  On October 19, 2012 at 8:49 AM

          Not really. With unknowable one simply doesn’t know, so how can there be inconsistency?

          The unknowable encourages one to keep looking and not become complacent with what one knows.

          .

        • Chris Thompson  On October 19, 2012 at 6:57 PM

          Precisely. What is it that we know about nothing?

        • vinaire  On October 19, 2012 at 7:02 PM

          Nothing is relative. It is absence of something we have in mind.

          .

        • Chris Thompson  On October 20, 2012 at 12:38 AM

          Yes, you are very correct. Is neti-neti otherwise?

        • vinaire  On October 20, 2012 at 3:08 AM

          “Neti-neti” would say that the unknowable is not even “nothing”.

          “Nothing” is a consideration. The unknowable is beyond consideration.

          .

        • Chris Thompson  On October 20, 2012 at 12:38 PM

          hehe, Not until you stop considering it is it beyond consideration!

        • vinaire  On October 20, 2012 at 1:31 PM

          “Neti-neti” is an excellent way of tracing the fractal in reverse. Somewhere along the way, one might hit the jackpot.

          .

      • Chris Thompson  On October 19, 2012 at 8:38 AM

        You have written too many good things for me to simply reply without study… well done! You are on fire! but I have to go to work.

      • idealgoal  On October 19, 2012 at 11:52 PM

        1) Because a “THING” can be defined as the creation from the “entity” which could not be itself “a thing”. So, the “source of any creation”, “God” for me here, by your own definitions can be labelled “spiritual” while “things” would be “material”. While “God” would “pre-exists” the “things”, the “NO-THING” creates the “THING”.

        • vinaire  On October 20, 2012 at 4:04 AM

          All I know is

          (1) There is manifestation,

          (2) There is speculation about how come there is a manifestation.

          (3) That manifests considerations, hypotheses, theories, etc.

          (4) Thus, manifestation appears to be a fractal.

          .

      • idealgoal  On October 20, 2012 at 12:07 AM

        2) I would not say here “inconsistancy” here any way, but more “paradox”, because only “seems” contradictory, because to be able to have “CONTRACTION”, or “INCONSISTANCE”, one needs to have a LOGIC, while here, no “logic” existing yet. Any way, for me it is quite acceptable that both “logic” and “unlogic” or “truth” and “untruth” could come from “neither logic or unlogic” or “neither true or untrue”.

        • vinaire  On October 20, 2012 at 4:11 AM

          A “paradox” to me, is an unresolved inconsistency. One needs to look at it more closely to see what is really there.

          I am not talking about LOGIC. It is simple LOOKING. Just see what is there.

          I see considerations.

          .

        • Chris Thompson  On October 20, 2012 at 12:41 PM

          Yes, and that paradox dissolves along with the inconsistency when it is spotted.

        • vinaire  On October 20, 2012 at 1:34 PM

          Right!

          .

      • idealgoal  On October 20, 2012 at 12:23 AM

        3) I’m not agree with you: by the definition itself of “INCONSISTENT AXIOM” in the subject of general logics, it is ONLY the inconsistency of the theorems produced by the logic applied on the set of axioms, which determines if the axioms are or are not “consistents”. Unless one has found a contradiction in the theory deducted from the axioms, nobody can seriously stated that the set of axioms is “inconsistant”.

        • vinaire  On October 20, 2012 at 4:24 AM

          I am not seeking agreement. I am simply looking at what is there without any expectations, presuppositions, speculations, etc.

          Axioms are simply seeking the most common denominator of what is there. For example, an axion would be: THERE IS MANIFESTATION.

          A theory may be presented as an axiom. But that does not make it an axiom. An axiom would be something that is actually there to be seen. A theory regarded as an axiom would be an inconsistency.

          Please see INCONSISTENCY & LOOKING

          .

      • idealgoal  On October 20, 2012 at 12:30 AM

        2a) Obviously, if I have tried to use différent approaches, it has been not sufficient and/or clear enough to communicate to you, dear Vinaire, my concept.

        • vinaire  On October 20, 2012 at 4:26 AM

          We all are doing our best to communicate what we see.

          We all are in the same boat. 🙂

          .

  • IdealGoal  On October 9, 2012 at 8:40 PM

    Probabilities, Location and Fondamental Physics:

    “From my viewpoints”…

    We have to differenciate a “MATERIAL POINT” from a “SPACIAL POINT”.
    A “material point” can only take specific locations in space, while a “space point” is any of the inifinite number of locations in a space how little we go or large (See concepts of “dimension point” and “viewpoint” in L. Ron Hubbard Scientology literature, especially again in his “Technical Dictionary”.)

    Tow concepts have to be differenciated the same way: the “UNIVERSE” and the “SPACE” itself.
    The “universe” could be bounded, completely localized, but the “space” in which the “universe” is inside, because of infinite qualities and while it is not what it contains, is “unboundable” and “unlocalizable”.

    So, a material point of energy, have to be described through probabilities because he looks to have such behaviour through our instrumentations and mathematical interpretations we make of the signal received by them.
    But, it’s not because you see only the white edges of the sea waves in the night are separed, that sea, as a continuum, doesn’t exist.
    If the present physic can’t “see” through its intrumentations a “continuity” that doesn’t means this “continuity” does not exist.

    Regards.

    • Chris Thompson  On October 18, 2012 at 9:48 PM

      Hi IdealGoal. Please consider whether in the beginning of the current ongoing Big Bang there could have existed pure space; possibly described as a liquid singularity.

      Today’s current version of space might be described as arid; when compared to the original.

      Space-Time might be first (I left them together because I can’t fathom splitting them apart);
      Energy condensing from the singularity next;
      Matter condensing from the energy next.

      Can you see any consistency in this?

      • vinaire  On October 19, 2012 at 4:40 AM

        The Big Bang could be an initial bounding consideration, within which other considerations then appear.

        Pure space would be UNKNOWABLE and thus UNBOUNDED, because any knowledge creates a boundary.

        SPACE-TIME would be space that is persisting. It would be persisting because it is considered and, therefore, it is bound in some way.

        .

      • idealgoal  On October 19, 2012 at 9:21 PM

        Hi again, Chris Thompson.

        Well, the problem looks to me is that I do not see the things as you do, even if I do not say you’re wrong I’m right.

        As stated before, for me there is a “SPACE” and there is a “UNIVERSE”.

        When you speak about liquid state and so on, you speak about the content; right?

        Any way, haven’t you imagined these possible pictures/film of a description of a said “Big-Bang”? Didn’t you place these pictures in “a SPACE”, a “SPACE” that you created “in your mind” (to make simple)? Didn’t you see that you could freely consider that this near spot like theoretical phenomena are LOCATED in THE SPACE YOU CREATE YOURSELF? Couldn’t you freely consider this SPACE infinite?

        For me it’s rather the same with this common local UNIVERSE through which we try to communicate to each other. The only think is that we don’t claim our property rights on the SPACE we are perceiving and locating this UNIVERSE.

        But who says that the “Big-Bang” theory is the only available and even the most coherent and powerful one ?!

        Regards

    • vinaire  On October 19, 2012 at 4:34 AM

      (1) A SPATIAL POINT is there because of the consideration of a matrix, which is space.
      (2) A MATERIAL POINT seems to be a spatial point with further considerations added to it. The added considerations make that spatial point unique in some way and subject to added constraints.
      (3) A DIMENSION POINT is simply a point on some dimensional scale. An example would be a certain temperature on a temperature scale.
      (4) A VIEWPOINT is simply a point used as a reference in evaluating all other points. It is like a stable datum selected for the moment.
      (5) SPACE is an integral part of a universe. A universe is built out of space.
      (6) A universe may be made up of material points within space.
      (7) Limitations or bounds come from considerations. A universe is bounded by considerations.
      (8) Space is unbounded to the degree it is unconsidered. There lies the UNKNOWABLE.
      (9) One may consider anything one wants, but with considerations come boundaries, and within those boundaries can be a universe.

      Regards,

      .

  • idealgoal  On October 20, 2012 at 12:34 AM

    4) yes, but as I have demonstrate just before: there is NO contraction where the logic not yet applies.

    • vinaire  On October 20, 2012 at 4:29 AM

      Looking requires no logic. It is simply seeing what is there.

      .

  • idealgoal  On October 20, 2012 at 1:34 AM

    5) Who needs to “believe” when one only need to proceed by extrapolations.
    “THE” only “lie” (but it is a way to say, the exact terminology is “paradox”) I need to make all then after perfectly coherent, perfectly consistent, is the base of the creation of “the beginning of any independent soul as parts of God”. And I remember you that the criterion for a mathematical theory to be valuable, is NOT if you feel good with the axioms of the said theory, but if it is coherent, consistent in its corpus: the consequencies of its theorems. And this is where you fall, looks to me Vinaire: you try to evaluate the axioms as “consistent” or “inconsitent” for themselves, while once again, it is what we can do with that will say if they are inconsistent. Any way, looks to me you have not made any serious studies of the references I’ve let here above, so what worth to discuss without deep enough knowledge of the work already done by professionals in the domain? If you have made, you would have seen that we are already much further in the thinest of the questions about “inconsistency”. But by not seeing already it is the corpus of a theory that proved the consistency of the axioms, you prove my own postulate (mathematical meaning) of your lack of fundamental studies about the subject of general logic. And what about “independent axioms”, about paradoxes which occurs indeed in the fundations of useful theories, like the sets-theory? What about non-demonstrable proposition in arithmetics? There are to kind of “madness”, for ordinary poeple: the one of the mad, and the one of the genius, cause in the eyes of “the normals” they both see and/or understand things they can’t see nor understand!
    Good journey in the land of the knowledge, sorry, I won’t accompagny you further, dear Vinaire…

    • vinaire  On October 20, 2012 at 5:13 AM

      A belief acts as a presupposition, which then influences one’s looking. It alters one’s recognition of what is really there.

      To extrapolate is to infer (an unknown) from something that is known. It is a conjecture yet to be verified by actual looking.

      God is the most fundamental belief that needs to be examined very closely by actual looking. If there are presuppositions in one’s concept of God, then that would color all further extrapolations from God. Those presuppositions will act as a filter from then on no matter how consistent rest of extrapolation is.

      I am not thinking of me or you, or any other participant, when I am discussing this subject. Please see Discussions and what needs to be avoided. So, your comment, “And this is where you fall…” tells me that you are deviating from this discussion. There should be no consideration of ego or of being right or wrong. There should simply be looking at what is really there.

      Please take a good look at what is happening here. My best wishes to you.

      .

  • vinaire  On October 20, 2012 at 2:33 AM

    This is a response to comment-5110 of idealgoal:

    (1) The universe precipitates out of the unknowable as considerations are made.

    (2) First, SPACE precipitates out of unknowable as the consideration of locations (as in a lattice or matrix) is made.

    (3) Next, ENERGY precipitates out at certain locations in space as further consideration of oscillations (as in waves) is made.

    (4) Next, MATTER precipitates out from certain oscillations as further consideration of increasing frequency (as in condensation) is made.

    (5) The source of a consideration would be the considerations, which it is derived from. The source of that consideration is not some ‘self’.

    (6) ‘Self” is a beingness created out of manifestingness of considerations. It may be looked upon as combining of manifestingnesses, similar to the combining of considerations themselves.

    (7) The source of original considerations is unknowable.

    (8) Space is there because we observe it to be there, and not because we consider it to be there.

    (9) The universe is an extension of space. Space is consideration of locations. Other considerations at a location define the various characteristics at that location.

    (10) The most basic “space” is unknowable. The next gradient of “space” are the locations. Space is created as locations are considered.

    (11) Energy waves are created as oscillation of locations is considered.

    (12) Matter particles are created as higher and higher frequency for oscillations is considered.

    (13) The particles themselves start to represent locations and the above process of further oscillation and frequency repeat as a fractal.

    (14) Thus, greater fixation of configurations of locations comes about, and we have fundamental particles, electrons, atoms, molecules, the periodic table, elements, compounds, and so on.

    (15) It is more than a ‘container-content’ relationship. It is an extention of unknowable into space, energy, matter. configuration, and universe.

    (16) A viewpoint is a construct like that of a being. It is the pattern of considerations at a location. It is an aspect of space.

    (17) A viewpoint denotes observation of space rather than creation of space.

    (18) Differences bring about manifestingness and knowingness. When there are no differences then there can be no manifestingness and, therefore, no knowingness.

    (19) Here we are looking at various fundamental dimensions of the universe: considerations, manifestingness, differentiation, multiplicity, combiningness, variety, etc.

    (20) Intuition is the creation of original consideration.

    (21) Imagination is the combining of existing considerations.

    (22) Visualization is further detailing of imagination.

    (23) Agreement is viewpoints going in resonance with each other.

    (24) Perception is a viewpoint resonating with what it is there. It is as much a function of viewpoint as it is a function of what is there.

    (25) Time is the endurance aspect of what is there in terms of space-energy-matter.

    .

    • vinaire  On October 20, 2012 at 2:43 AM

      Location, oscillation, and frequency seem to be the fundamental considerations underlying space, energy and matter.

      Time may have to do with the endurance of the manifestation of these considerations

      .

      • Chris Thompson  On October 20, 2012 at 12:35 PM

        The re-iteration has to do with time and the fractal iteration accounts for both change and motion.

      • vinaire  On October 20, 2012 at 1:28 PM

        It seems that we hardly know anything about space and time. There seems to be many, many facets to both.

        .

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