Kas yra apimtis?
Apimtys yra skirtumai tarp tiesos turinio ir jos išraiškos. Keturi skirtumai - viskas, betkas, kažkas, niekas - Dievo požiūriu veiksmu +1 iškyla ketverybe, tai tarpai tarp Dievo išeinančio iš už savęs ir Dievo išėjusio į save.
Apimtys tad išskiria:
Ryšys tarp pažinovo ir pažinimo lauko
Keturios apimtys išplaukia iš visko savybių
Mąstymas be jokio požiūrio
Visko savybes taip išdėsčius, galime aptarti visko žinojimą ir būtent jo santykį su požiūriais. Savybė S0 (Viskas neturi išorinių aplinkybių) tvirtina, jog visko nevaržo joks požiūris, tad visko žinojimas yra, pirmiausiai, žinojimas be jokio požiūrio, kas mums labai nebūdinga. Mes ištisai mąstome požiūriais, tad mums tenka įsivaizduoti, ką reikštų gyventi be jų, ir bandyti ištisai jų atsisakyti.
Tačiau mąstymas be jokio požiūrio tėra visko žinojimo pagrindas. Juk taip mąstydami, kaip kad Dievas mąsto, vis dėl to galime mąstyti ir požiūriu, tarsi užsidėdami akinius, ir žiūrėdami į viską per lęšį. Galime mąstyti požiūriu į požiūrį, ir netgi požiūriu į požiūrį į požiūrį.
Požiūriu, Aš mąstau betką.
Būtent Aš mąstau viską savo požiūriu, užtat mąstau betką. Betką nusako trys savybės: S1, S2, S3. Betkas neturi atrankos, vadinas, jo nevaržo požiūris į požiūrį.
Požiūriu į požiūrį, Tu mąstai kažką.
Tu, kaip toks, esi apibrėžtas Mano požiūrio pagrindu. Tavimi save varžau. Tavimi pripažįstu požiūrį į požiūrį, išgyvenu savo požiūrį į tavo požiūrį, ir pripažįstu tavo požiūrį į mano požiūrį. Tokiomis sąlygomis mąstau ir žinau kažką. Kažką nusako dvi savybės: S2, S3. Kažkas neturi vidinės sandaros, tai yra, neturi savyje galimybės save paneigti.
Požiūriu į požiūrį į požiūrį, Kitas mąsto nieką.
Kitas, kaip toks, yra apibrėžtas Tavo požiūrio pagrindu. Kitas varžo Tave, kaip ir Mane. Kitu pripažįstame požiūrį į požiūrį į požiūrį, tiek jo požiūrį į mūsų požiūrius, tiek mūsų požiūrius į jo požiūrį. Tokiomis sąlygomis mąstau ir žinau nieką, tai ko nėra, tai kas negali būti. Nieką nusako vienintelė savybė: S3. Niekas yra būtina sąvoka, kurios negalime atsisakyti, kuri tačiau neturi jokio turinio. Niekas yra būtent ta sąvoka, kuri be jokio turinio, tad kuri parodo, kad sąvokai turinys nebūtinas, kad ji gali būti tiesiog neteisinga. Žodžiu, yra tai, kas būtinai nebūtina, būtent nieko sąvokos turinys, neteisingumas. Tuom ir išsibaigia žinojimas. Taip ir prieiname prie žinojimo galo.
Viskas, betkas, kažkas, niekas. Dievas, Aš, Tu, Kitas.
Užtat visko žinojimas susideda iš žinojimo be jokio požiūrio, ir taip pat iš žinojimu požiūriu, žinojimu požiūriu į požiūrį, ir žinojimu požiūriu į požiūrį į požiūrį. Vadinas, Dievu mąstome viską, Manimi betką, Tavimi kažką ir Kitu nieką. Kažkas apima nieką, betkas apima juos abu, o viskas apima visus ir dargi save.
Keturių apimčių pagrindimas
A whole is the Scope of all perspectives: Everything
Niekas turi vidinę sandarą, tai tuštuma, tai nulybė.
When an Observer observes themselves, this relationship characterizes the ObservationalPlane between them. These are four scopes of access.
This relationship is completely formal. It gives the amount of opaqueness that separates the observer and the observed, the amount of perspective that is filtered out by self-reflection, by which the observer sees less than the observed. Note that the observer may, in a sense, see more by seeing less.
This yields the following properties:
We may also think of Indefinite as unbounded, Definite as bounded, Evaluated as closed, Unevaluated as open. Therefore:
Evaluated refers to the full or partial calculation that has taken place, as for a function. Evaluation is an obstacle to applying the Associative rule of CategoryTheory to the CompositionOfViews.
Another way to think about this is:
This is especially helpful in considering Christopher Alexander's PrinciplesOfLife, which is to say, the Topologies.
The four scopes may also be understood as:
Where they refer to the role of the observational plane that is between the observer and the observed. These terms are helpful in considering the Secondary Structures as generated by their relationships, and I should think more about that.
- You mention "relativeness" as the point of scope - great! Indeed, we may think of everything, anything, something, nothing as serving these purposes. Relative to "everything" - all statements are true! (Because a statement is just a narrowing down of the truth, and note that the state of everything is contradictory, thus not restricting the truth). So we may think of a statement as true (= obvious = not hidden) relative to:
- all contexts ("everything"=open+unbounded) if we think broadly enough, then truth wins out, everything is obvious, and there is no falsehood, there is nothing hidden - any context ("anything"=open+bounded) if we restrict to a particular context, there is a way to empathize with its truth, if necessary, by way of the relevant framing of everything - some contexts = not all contexts ("something" = "not everything"=closed+bounded), which is to say, it is sometimes true, and sometimes false, the usual way of looking at logic - no contexts = ("nothing"=closed+unbounded), then there is no context to distinguish truth and falsehood, and so they are equal in standing.
Note: In this way, the four scopes serve a most important structural function: they allow for the description of a "distinguished opposite". Perhaps the greatest structural challenge is defining a "distinguished opposite" - we want to be able to say that, on the one hand, good and bad are opposites, but on the other hand, good wins out, which is to say, there can be good without bad. One way to think about this is that God wants "all the good" - so some good does not require bad, but he's willing to take all the bad that might be needed so as to include every least bit of good. Structurally, this "distinguished opposite" is slack (note in English the interesting fact that "loosen" and "unloosen" mean the same thing, or that tightening and loosening are both representations of slack - decreasing and increasing). Slack is the "anti-structure" that dissolves structure so that it can collapse and doesn't keep growing in metalevels. What's new for me here is the idea that the point of the scopes (and what gives rise to them) is that they are what's needed for being able to look at truth as self-standing (as with everything) but also an equal opposite to falsehood (as with nothing). Apparently, all four scopes are needed - the two intermediate scopes "any" and "some" apparently restrict the question to individual matters - do we link back to the "true" and "false" of nothing or to the "all true" of everything - do we place the question in the conceiver or in the conceived?
Now, furthermore, these scopes make it possible to relate "God" and "godlet" in a symmetric way, and yet ultimately realize the primacy of God.
Apdorotojų apimtys: outlook, talk, work, life
I write about a tenfold structure (four PrimaryStructures and six SecondaryStructures) that I consider fundamental to all of life. In particular, I think it is associated with the ten commandments. I think of outlook, talk, work and life as four scopes for parsers (much as in "The Algebra of Copyright"). I associate four commandments with honor for what is beyond scope, and six of the commandments with not reducing one scope to another.
I decided I should try to make some progress on what I think is the all-encompassing structure. It consists of four levels and six pairs of levels. This structure came up in my work on "The Algebra of Copyright" and I think also in my work on "Spine for the Web". There are five other places where I have noticed it previously. So I am trying to look for unity and learn as I look.
In 1998 and 1999 I realized that the possible endeavors of our laboratory suggested a tenfold structure: four directions to foster caring, and six directions to foster thinking, where the latter where elevations from narrower scopes of caring to broader scopes of caring. I have used this for the structure of our working groups.
In 2000 and 2001 I realized that the many structures that I had observed throughout the years could all be organized by means of such a tenfold structure (four families of primary structure for transcending life, six families of secondary structure for engaging life). As part of this, I noticed that we could think of everything as having four representations, and anything as having six representations, where anything is everything plus slack. (Analogously, Life is the fact that God is good, where Life is the coherence (= the unity of representations) of anything, God is the coherence of everything, good is the coherence of slack.)
Theologically this was most attractive. I had earlier thought of the Ten Commandments as consisting of 4 positive commands (expressing Love God) and 6 negative commands (expressing Love your neighbor as yourself). Now I thought that this might be the same tenfold structure. So this would make evident that, from God's point of view, the Law is the Structure, and the most basic law is the most fundamental structure.
In flying out to the United States, I worked out some ideas in "The Algebra of Copyright" and came up with four levels (transcriber, proofreader, editor, author) and six pairs of levels (copy, interpret, transform, author, intend, perform). And I also came up with ten levels in "Spine for the Web", four initiators (intiative, relationship, individual, community) and six encouragers (kindword, frustration, evaluation; story, pattern, expression). So I am thinking that I should try to use these new insights to revisit this fundamental structure.
In particular, an important question is to understand the Ten Commandments. I have yet to find a structural interpretation that would explain how six of the commandments are to be understood as pairs from the other four. So I am looking to ideas from "The Algebra of Copyright".
One idea that I got just before my talk in Vienna, Austria is that we may think of there being an outputter, proofreader, editor, author who are parsing a creative work in different chunks, whatever can "stand alone" according to their parsing. For example, a proofreader can often get by reading a work sentence by sentence, whereas an editor might have to read paragraph by paragraph. Their parsing is characterized by the "scope" involved. Likewise, the character of a sign (for example, a word) - whether it is fulfilling the functions of an icon, index or symbol - may be given by the scope that it involves. If a word is a "symbol" within a work, then a proper understanding (or parsing) may require parsing the entire work.
I looked at the various examples that I have collected for this tenfold structure:
4 Levels 6 Pairs of Levels
They suggest that the four levels have to do with Creation, and what is unbounded, and beyond scope, whereas the six pairs of levels have to do with Co-creation, what is bounded, within scope. Here the scopes might be: nothing, something, anything, everything.
I took a new look at the Ten Commandments. Four of the commandments express Love God, and relate to the foursome: whether, what, how, why. Perhaps as Christ said: Love God with all your heart, mind, soul, body. They all seem to have to do with honoring God in different scopes:
The other six commandments express Love your neighbor as yourself. So I am looking for how they relate pairs of levels. I think it might be that they are saying that a broader level should not be subjected to a narrower level. Life should not be reduced to work, nor work to talk, nor talk to outlook. Just as in "The Algebra of Copyright", talk is a constructor on outlooks, work is a constructor on talk, life is a constructor on work. And there is a qualitative "phase transition" at each level that cannot be reduced away.
Here is one attempt to apply these ideas:
Here I cheated - I used the ordering given by the relationship I had observed between the commandments and the families of structures. I wasn't able to get this just by thinking it through. But it does kind of feel right. So maybe it's just a matter of letting it rattle around, find the right understanding (or words) for outlook - talk - work - life.
I like the idea of the "Love God" commands having us honor what is beyond scope, and the "Love your neighbor as yourself"commands of having us not conflate scopes. And
is a rather nice way to distinguish the scopes through which we parse our lives.
So this is rather satisfactory, and I will consider what this might suggest further about the big picture.
2004.12.13 A: Kaip keturi atvaizdai susiję su susikalbėjimu? D: Aš noriu būti su visais, būti vienas su jais, juos mylėti. Tad tai yra meilės sąlygos. A: Kaip suprasti, meilės sąlygos? D: Meilei reikia, kad galėtumėme gyventi vienas kitame. A: O ką tai reiškia? D: Išeiti iš savęs, ir iš savęs į kitą, ir iš kito į save, ir iš kito. A: Ačiū. D: Myliu.