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
Išėjimo už savęs eigos nustatymas, tad apimties nustatymas
Sandaros išvystymas tiesos lygmenimis, apimtimis:
Sąlyginis buvimas viena
Apibrėžiama tai, kas už apimties, kas neviena - neigimu iškeliamas jo nevieningumas su tuo, kas apimtyje - tad svarstoma būtis, to kas už apimties
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.
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.
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)
How might we best define concepts, ideas, structures and such? Structure is relevant for making definitions.
In my diagrams I've found it helpful to use colors.
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.