This page was renewed and TSL is enabled. However, there are lots of areas not implemented yet. We shall add components here in stages sequentially. サイトをリニューアルし、TLS通信を有効化しました。しかしまだ未実装の要素が多々あります。順次追加してゆく所存で御座います。
An environment-En is a discipline constituted by ontology-G. In En, all the objects need to hold their existence, and when they no longer retain their existence as their own identity morphism, they are removed from the element in En. In environments, the operation of depriving identity morphism of existency from elements of their ontology is called ‘banishment’. The addition of a new element to En by self is called ‘generation’. What elements maintain its existence in the environment is called ‘continuance’.
‘Acceleration’ is used, for example, as follows.When an object-O(∈ outside of G)seeks to generate and maintain itself O'(∈G) or another object P in En, an object-Q which interferes with its generation or continuance is called an ‘obstruction’. When O maps O'and P by an isomorphism to (mega-)structure or environment which is not operated from Q, this environment or isomorphism is called ‘escape’. O' or P that were mapped to the escape-Es are generated or continued there. When mapping O’ or P ripened(= be not operated any obstruction during the generation or continuance) in Es to En by an isomorphism, we say that O' or P was ‘accelerated’ by escape-Es. This series of processes that letting an object be operated twice isomorphisms is called ‘acceleration’. 環境Enは、何らかの対象Gによって構成されたディシプリンである。Enにおいて、一切の対象は存在を保持する必要があり、存在を自己の恒等射として保持しなくなったとき、Enにおいて自己は要素から除かれる。何らかの環境において系の要素を《存在の恒等射を剝奪する＝排除する》作用を淘汰(banishment)と呼ぶ。自己が環境Enへ新たに要素を追加することを生成(generation)と呼ぶ。環境において存在を維持することを存続(continuance)と呼ぶ。
The description style of this text is a modification of categorical theory. Category theory takes a bird’s eye view of mathematics, so it is suitable for essential abstraction. Since the ontology shown in this text beyond Human's compass or has such intentionality, it is not appropriate to use Human-perceptual words. And then, if possible, in addition to Human-life familiar impression, exclude it mathematically in the following words. Desirably, meaning/signifié of these words shall be independent of any other context.
Several peculiar orthography used in this text are listed below. At this time, "A" and "B" are words, "N" is a number, "S" is half-sentence(phrase containing at least one noun and verb), "S." is a sentence(containing at least one noun and one verb and closing at the period), '(quotation) is attached for distinction.
We do not distinguish noun and verb so rigorously. It is obvious from the definition that [affect is enable to be a category | e is an affect; it is possible to construct a category E∋e which contains only an element e]: that is to say, it is rather natural not to distinguish between them. Similarly, we do not distinguish between singular or plural. Description style such that something is singular/plural is only a notation for simplication.
There is an object regarded as single on a certain scale, if we regard this object as a category; when any element in the object transits state by external affects, a collection of these elements is called "perceptual organ", and then, this perception affects to other elements in the object following its own transition, the codomain is called "computational organ". Sensu lato, category which has both perceptual organ and computational organ is "tribus".
By calling the transitional state of perceptual&computational organ due to external affects as "sensation", the sensed state is sustained, or that they are preserved in some way is called "experience". If [the experiences of individual tribus are integrated at a certain scale | there is a category containing the each experience as an element]; at this time, the category containing all the individual tribus that can be integrated about experience is also tribus by definition. When it is preferable to distinguish, the category containing is called "higher tribus" and the category contained is called "lower tribus". Sensu stricto, only higher tribus is called tribus.
A category is constructed with all existing objects as elements. At the moment, the identity(o∈O; identity:o→o: element-o does exist as o.) of each element is established not by o itself but by the maneuver of the constructor(-ego). Hence, [ whole | world ] which found in ontology is all existence that "as far as the constructor can recognize". Because of the possession of criterion to give identity for any object, constructor of (category of) ontology is particularly called "criterior".
All tribus are criteriors. If an ontology is constructed by a tribus which has finite perceptual/computational organ, [whole | world | all existence] is originally limited. Due to this limitation, all ontologies can be uniquely delineated the boundary. Alternatively, ontlogies constructed by particular criteria should be distinguished even if they have mutually same elements.
*If all existences are capable of giving themselves identity of existence by their own maneuver, they exists all owned. At this time, (category of) realism, a certain ontology, is constructed. All of ontology is part of this category, isn't it?
Among ontology, what is applied by law of excluded middle is "static". Law of excluded middle is a rule that allows only two states, both affirmation and negation of criterion, and excludes other states. When this works, all objects in the ontology are "closed". And for following argument, we call closed object "entity". In static ontology, all objects are entity. In this case, following two statements are validated.
i) Every entity does only exist, and things that do not exist can not be object/entity.
ii) Every boundary between arbitrary entities is always delineated and stable.
There are entities a and b. a is a and not non-a, also b. And, if the two entities are delineated their boundary, a is not b except when a is contained by b, likewise b is not a. Boundaries and relation of containing are not modified without maneuver of the criterior: it is required for constructor to maneuvre them explicitly.
*Entity is obedient to the criterior, because entity does not interfere/disturb with the ontology itself.
Ontology is not unique to the criterior, because this is also one category, so it has innumerable subcategories. However, the hugest ontology is determined as the ontology containing all objects that exist as far as the constructor can recognize. We call it "ess-sup (ontology)" or "Ontology" in capital letters, this subcategory (actually, more ordinarily used) is called "(ontology) system" or "ontology" in lower case.
By taking the part of ess-sup, it is possible to construct systems as many as the number of its power set. Including ess-sup, this series of systems is "monoscale", because there is only one scale about existing. It is "multiscale" that such a category has more than one scale; a multiscale system can be constructed by newly giving scales to these systems. Multiscale system or mutliscale itself specific to the system is called "structure". In a structure, other scales of existing scale are called "rules". In the elements of a structure, a category containing affirmative ones is called "discipline". These orthographies are as follows.