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Mieli dalyviai! Visa mano kūryba ir kartu visi šie puslapiai yra visuomenės turtas, kuriuo visi kviečiami laisvai naudotis, dalintis, visaip perkurti. - Andrius



Žr. Apimtys, Kategorijų teorija, Helmut Leitner See also: Definite, Indefinite, IndefiniteVDefinite, Define, Overview, Truth, Freedom, Forwards, Backwards, View, Scope, Unlimited, Definition, GoingBeyondOneself, AlgebraOfViews

Apibrėžimas yra:

Išėjimo už savęs eigos nustatymas, tad apimties nustatymas

  • Žinojimas - pasižiūrėjimas iš šalies - į išėjimą už savęs
  • Išsakytas apimtis (nieką, kažką, betką, viską) atitinkančiomis savybėmis
  • Įtvirtinimas apimtyje - grounding in Scope
  • the establishing of Scope and thus the distinction of the one who knows, assumes (and applies definition) and the one who is known, assumed (and to whom the definition is applied) so that they may be the same or different, the circumscription of NotWho in terms of NotWhat that assumes them, the negation of an assumption about Not Who. (Negation of Representations of Onesome) (Creation)
  • ... in Scope
  • Theory in a Scope
  • Knowledge given a Scope, and in particular, when the Scope is Nothing

Sandaros išvystymas tiesos lygmenimis, apimtimis:

  • Viskas, Visaregis, Netroškimai, Nedviprasmybės
  • To be defined is to be set in some way (and not some other way). Therefore definitions distinguish hard Truth from soft truth.

Sąlyginis buvimas viena

  • BeingOneWith in the extent of NotBeingOneWith

Apibrėžiama tai, kas už apimties, kas neviena - neigimu iškeliamas jo nevieningumas su tuo, kas apimtyje - tad svarstoma būtis, to kas už apimties

  • is of NotEverything, NotAnything, NotSomething, NotNothing.
  • comes before relationship (of Being One With)
  • negates where God goes to (Everything's properties, where God is not).
  • (NotFreedom) is negation of a property of not being alone (of NotGod, Everything), self-standing in a system's context, external limitations, acceptance from Beyond of Negation, the negation from beyond of NullActivity (of Willing), Questions taking up Answers, yielding Scope (Self) as the absolute limits of Activity. The Creator defines the Creation by self-defining himself as the negation of their creation, limiting his NullActivity, thus making room for their creation.
  • Creation, interference with NotGod, Questions taking up Answers.
  • Existence of God
  • Išėjimas už savęs, būtent įžvalgai išeinant už savęs į apimtį, iš neapibrėžtumo į apibrėžtumą.

Neapibrėžtas žvilgsnis ir apibrėžtas žvilgsnis

Apibrėžtumas susijęs su žinojimu. Žinome apibrėžtumą, jo lygmenis. Apibrėžtumas reiškiasi keturiais žinojimo lygmenimis. Tačiau galime žinoti ir neapibrėžtumą, tai ko nežinome.

Šis esminis skirtumas grindžia požiūrių grandinę? kuria visos sandaros išsivysto. Žinau, kad nežinau, kad žinau...

Indefinite and definite are the two Representations Of Slack, increasing and decreasing. Their scopes are the four Representations Of Everything: all, any, some, none.

It is crucial which direction we are thinking about in defining things.

Apibrėžtumas yra dangaus karalystės esmė - dieviškumo išgyvenimą žmogiškume.

Neapibrėžtas žvilgsnisApibrėžtas žvilgsnis
all suppositions are trueall suppositions are either true or false
Dievo žvilgsnisžmogaus žvilgsnis
Apimtis neapibrėžtaApimtis apibrėžta
the supposition identifies equally, unconditionally with all of its perspectives (like a nondeterministic automata)the supposition identify with Any of its perspectives (like a deterministic automata)
"all statements are true" - I suppose it is the (supposed) point which goes beyond into all perspectives
not a subset of itself, hence contradictory, as in Russell's paradoxa subset of itself
defined and identified, in its perspectives, as what it goes into, and so it is all of the perspectivedefined and identified, in its perspectives, as what it comes out from, and so it is one perspective among all of them
Immersed, empathetic and endlessframed, detached and finite
unlimited viewlimited view
unbounded viewbounded view
view of the Indefiniteview of the Definite
view of the unknownview of the known
has a scope, but the scope is not fixed, not definedscope is fixed, defined, established
not yet mirrored by structuremirrored by structure
increasing slack of scopedecreasing slack of scope
ever less definedever more defined
suppositions are indefinitesuppositions are definite
looking forwardslooking backwards
does not suppose God is goodsupposes God is good
the supposition includes within it all of its perspectivesthe supposition is one of its perspectives
is pregnant with all of its perspectives
differentiates its perspectives within itself prior to going out as themdifferentiates its perspectives upon going beyond itself
engages through and identifies with all of its perspectives equally, unconditionallyengages through and identifies itself with any one of its perspectives
God is all of his possibilitiesI am one of my possibilities
can distinguish morecan distinguish less
does not distinguish understandingsdistinguishes understandings
does not know ignorance directlyknows ignorance directly
transparentcan be opaque
keeps concepts separate, as in eternal life is the understanding of the goodness of God, the keeping separate of goodness and Godblends concepts, as in life is the goodness of God, the fact that God is good
allows for multiple tracks, thinking in parallelallows for one track (a one-track mind)
Leaves things hanging, allows them to be undefined for a while, or foreverCircumscribes everything, leaves nothing hanging
Defined by what it goes intoDefined by what it comes from
Open ended
Does not allow for a change in scopeAllows for a change in scope
Does not open up space for a quality, for the goodOpens up space for a quality, for the good
Takes sole responsibility for its suppositionsShifts some of its responsibility onto the quality
Acceptance of an indefinite scope
Allows for the indefinite separation, distinction, of perspectivesAllows for the definite separation, distinction, of perspectives
distinctions and separations are themselves suppositionsdistinctions and separations are themselves not suppositions, but are derivative

Viską žinoti

Definitions are at the heart of the quest to Know Everything.

To know is to have a definite scope. The Foursome is the structure that makes definite, that yields the truth of concepts.

To know everything is perhaps to have the view of the indefinite of the definite.

Definitions are complete only when there is an Observer. (RaimundasVaitkevicius)

Apibrėžimo būdai

How might we best define concepts, ideas, structures and such? Structure is relevant for making definitions.

  • Complex concepts may be defined in terms of simpler ones, primitive ones. But how do we define primitive concepts, the fundamentals?
  • Padalinimai: The divisions of everything serve to define issues as states of mind by presenting the relationships among the outlooks that are relevant.
  • Aplinkybės: Mind games: Topologies are defined by way of mind games.
  • Veiksmai: The structure of the divisions is also given by operations +1, +2, +3.
  • Kategorijų teorija is a tool for finding good definitions by thinking in terms of the morphisms that preserve Structure.


In my diagrams I've found it helpful to use colors.

  • Red indicates what I think is built into my mind, but I can't make coherent because ultimately it's inaccessible.
  • Green indicates what I think is built into my mind, and I can make coherent because it's accessible, and in fact, is evident in the world.
  • Yellow indicates what is not built into my mind, is optional, but is accessible, helps me think things through in a new light.
  • Blue is not given, not accessible, just a formalistic label.

My use of words and terms

I'll try to share more about my own outlook. What I'm trying to do is counter to how we're conditioned to think. Hopefully, I can help myself and others grow in our thinking. This means that I will diverge from how we usually think, and also, that I want, at some point, to relate to how we usually think, so that I and others might grow beyond that. This means that we'll give up how we usually think, or at least, expand beyond it, which is to say, give up on the restrictions that we place on our thinking.

For example, many people believe that it's not possible to think without words. Words do offer many advantages. However, we would not want to say that the deaf do not think, or that infants do not think. My work shows, at least to me, that it is possible to think in terms of concepts. For example, I can think the concept everything without making use of any particular word. I can think it because I can consider, intuit, reflect on its structural properties. This kind of thinking is much deeper than the manipulation or leveraging of words. Furthermore, I find evidence that concepts are universal and absolute, whereas words are quite unreliable and by nature have many meanings. So I think it's important to focus on the underlying concepts and not place too much weight on the names for these concepts.

Words or names are important as markers that we can manipulate. Sometimes I use abstract symbols, for example, I may refer to the levels of the foursome as +0, +1, +2, +3 or to the perspectives of the twosome as ! and ?. However, such symbols tend to be loaded with meaning at some point and in some way, and so we do not escape the question, what connotations to include in the name. Some terms I invent, especially if they are for original concepts, especially for the abstract structures that I uncover, for example: nullsome, onesome, twosome, threesome, foursome, etc. Although even here I use names that extend the meaning of existing words. Generally, I try to find the simplest, most familiar and understandable terms that capture the relevant intuition, but I give them an additional, often formal meaning. This approach is very common in mathematics, physics and the sciences. For example, the word or in everyday language is a bit vague, but tends to mean either... or... but not both, whereas in mathematics A or B means anything that is in at least one of A or B (or, in everday language, we might say for this A and/or B). Similarly, physics has taken everyday words such as force, mass, power, time, energy and given them very precise meanings which are quite unexpected and even counterintuitive for those who know only the everday usage. Indeed, people often think that everyday usage is somehow definitive when actually it is a social construct, a folk theory.

I try to express and ground concepts by way of structure, by way of their relationship with themselves, as then they do not depend on any larger context. That is why the divisions of everything are so central, because they are defined and described by the relationships between the perspectives, the parts which they organize. This is a great challenge, but I feel my efforts have been fruitful. I think of mathematics as the study of structure, and what I am doing is a sort of pre-mathematics, how structure arises out of concepts. Mathematics is important as a source of ideas. For this reason, I do draw on mathematics as a source of terms.

For example, in working with categories (as Kant would call them), I realized that it was not helpful to think of them as abstractions of things that we imagine. In fact, they were quite the opposite - they were backdrops, canvases, worlds which our imagination provided so that we could place something in it and imagine it in such a context. For example, there is a metaphor love is a journey, and here journey brings to mind an entire abstract world that an abstract journey conjures. Typically, a thing (or a word) may have a definition that can be pulled together as a single, definitive statement. However, a world is not described by a single, definitive statement. Imagine living on a sphere, or a flat plane, or a line, or on a torus. Each of these worlds has its own geometry, its own properties locally and globally. In mathematics, such a world is described not by one definitive statement, but rather by a set of rules, and that set is typically not special. The same world can be described, determined by a variety of different rules, none of which can claim to be special. It is only the world itself that is special. In mathematics, this kind of world is often talked about as a topology. Another word that I could use is circumstances. What I'm trying to convey is that a concept like many is not an abstract thing but rather a world or circumstance that we project things upon. For example, in defining language as a mapping you're relying on the concept of many, that there can be parallel relationships. With the [Topologies #] I have found a way to rigorously define concepts such as many.

Generally, what I'm trying to do is to find the existing words that best capture the intuition that I'm pointing to, and then extend, specialize, formalize their meaning further. Where possible I try to draw on everyday language. But I also extend terms from mathematics and other disciplines which themselves extend on the meanings of words from everyday life. This means that I can communicate to myself and others at least something of what I mean. And first of all, I am writing for myself, looking for terms which will help me capture my insights.

Also, this is all a work-in-progress, which means that many of the underlying concepts are underdeveloped, murky. Progress is made by getting a clearer understanding of the underlying concepts. Thinking about the terms is helpful but ultimately the issue to solve is deeper.

Yet truly it is exciting when ordinary everyday language can take on a deeper, more mature meaning. For example, the concepts whether, what, how and why are ancient. And yet we might come to understand that they are not accidental, that they express deep concepts.

The difference between deterministic and nondeterministic algorithms is relevant to the NPComplete problem.


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Puslapis paskutinį kartą pakeistas 2014 gruodžio 05 d., 13:39