譬如天平：
|
It is similized to a weighting scale as:
|
| 國家應在公正之基礎，經正當之程序，以公平之處置，為平等之實現。 | The nation shall, on the just ground, in the due process, with the fair deal, do the equality. |
| 公正、正當、公平係平等之充分條件，故雖無上開三者，仍有平等之可能。 | The justice, the due and the fairness are the sufficient conditions of the equality, so even if we lack them, we can still do the equality. |
| 連續時空，係由無限命題所描述之圖像拼湊而成。 | A continuous space-time is pieced up by the images described by infinite propositions. |
| 時空之不確定性，係因命題間之不相容性所致。 | The uncertainty of a space-time is caused by the inconsistency among the propositions. |
| 本徵函數受個體觀察所致之崩塌，係個體基於自身選擇公理而自前開無限命題中選擇用以構成自我之相容命題所顯示之局部時空之連續圖像[1]。 | The collapse of an eigenfunction caused by an individual observation is the continuous image of the partial space-time displayed by the consistent propositions chosen from the infinite propositions by the individual basing on its choice axiom to consist itself. |
| [1] | 本徵函數自高維之時空崩塌為低維之圖像，所滅失之多元基底自當係因果之不確定性。 | When the eigenfunction collapses from a high dimensional space-time to a low dimensional image, the lost variety basis is of course the causal uncertainty. |
| 時間軸無差別於其他時空軸，亦受時空曲率分量之力迫，故可在因果路徑上經補外法發現其主導邊界條件，俾鎖定上開因果路徑之不確定震盪範圍；又，倘上開範圍近似離散量子態，則極可能力迫出完全預想圖。 | The time axis is not special among other space-time axes, and is also forced by the component of the space-time curvature, so we can discover by extrapolation its dominant boundary conditions in a causal route, in order to lock the uncertain vibration range of the causal route; furthermore, if the range approximates to a set of discrete quantum states, we can probable force a complete expectancy. |
| 回到目錄《後設猜想篇章節》。 | Back to the menu, The Table of Content of The Metahypotheses. | ||
| 第1篇第3章第3節 | Volume.1, Chapter.3, Section.3 | ||
| 現象⊃群體⊃廣義價值理論 | The Phenomena⊃The Colony⊃The General Value Theory | ||
| § 1 | I | 知識、資本及勞動，經下列測度，在價值空間中展現其正交性，俾描述廣義價值理論：
|
Knowledge, capital and labor show their orthogonality in a value space through the following measures, in order to describe the general value theory:
|
| II | 前項用詞定義如次：
|
The words in the preceding paragraph are defined as follows:
|
|
| § 2 | I | 客體多元向量，在相容邏輯系統下完全表示客體性質。 | The variety vector of an object completely expresses the properties of the object. |
| II | 多元向量之權係時變函數。 | Weights of a variety vector are time-variant functions. | |
| III | 多元向量之權在特定時間之值，等於其在前一瞬間之值與特定值之內積，故一旦在特定時間歸零，將從此恆為零。 | The value of a weight of a variety vector at a certain time equals to the inner product of its value at the exactly previous instant and a certain value, and if it once returns to zero at a certain time, it remains zero henceforth. | |
| IV | 多元函數之權在閔可夫斯基時空之映射，可相容表示為能量。 | The maps of the weights of a variety vector in Minkowski's spacetime can be consistently expressed as energy. | |
| § 3 | 知識，係由勞動以資本維持之。 | The knowledge is preserved with capital through labor. | |
| § 4 | 基於知識、資本及勞動之任意一者或任意兩者之準價值理論，可能互相不相容，而引發爭議。 | Quasi value theories based on any one or any two of knowledge, capital and labor are possibly inconsistent with each other, and cause issues. | |
| § 5 | 客體經廣義價值理論測定為價值向量，再經主體主觀加權為主觀價值向量。 | An object is measured to be a value vector by the general value theory, then is subjectively weighted to be a subjective value vector by a subject. | |
| § 6 | 客體價值，係其主觀價值向量之範數。 | The value of an object is the norm of its subjective value vector. |
第一節 系統外公理之客觀上存在及法律上需求 |
Section.1 The Objective Existence of Out-of-System Axioms and the Legal Demand therefor |
| 由歌德爾不完備定理可知人之邏輯有限，又由超越數數目可類推公理數目之無限不可數性，故理想國之生成，除我在〈科學革命宣言〉所謂「以遞迴更新方式無限逼近完備公理系統」外，別無他法。 | Godel's incompleteness theorems show us the finitude of human logic, and the number of the transcendental numbers implies the uncountability of the number of axioms, so the Republic can be founded only by means of "infinitely approaching a complete axiom system by recursive updates," what I have said in Scientific Revolution Declaration. |
| 人之活動具有動態性，而保障多元性[1]之法規系統[2]將隨之更新，納入未收錄之公理，盡可能合法化之，使系統外多元性不因被視為違法而遭受殲滅，俾穩定人之活動。惟遇有新舊公理相互矛盾時，則須由後設系統[3]出面依比例原則衡平取捨之，若且唯若納入上開衡平取捨之理由於上開法規系統。 | Human activities are dynamic, and a legal system[2] guaranteeing the variety[1] shall update itself along with them, accept the uncollected axioms, legalize them as possible, and save the out-of-system variety from being eliminated as deemed illegal, in order to stabilize human activities. However, when a new axiom is inconsistent with old ones, we shall request a metasystem[3] to make a balance or a choice between them according to the proportionality, that is, to accept the reasons of the balance or the choice into the legal system. |
第二節 關鍵威脅之阻卻 |
Section.2 The Critical Threat Blocking |
| 新公理在生成後，在由常規後設系統[4]納入前開法規系統前，前開法規系統基於舊公理運作可能視上開新公理為違法而威脅殲滅之。此時臨時後設系統[5]如認定上開殲滅不符比例原則，則應發動緊急救濟。 | After discovering a new axiom, and before accepting it into the legal system by the regular metasystem[4] specified by the legal system, the legal system working with old axioms is possible to deem the new axiom illegal, threatening to eliminate it. In this case, a provisional metasystem[5], if considers the threat is beyond the proportionality, shall launch an emergency remedy. |
| 緊急救濟在抵抗威脅時亦可能傷及舊公理，致生多元性之衡平取捨問題，故應依《逐項評論原則》分析上開威脅所涉及之引理、定理、公理等命題及其等對上開新公理之作用，俾確認關鍵威脅而有效阻卻之，並盡可能維持前開法規系統常規運作。 | An emergency remedy, while resisting a threat, is also possible to hurt some old axioms, bringing on the problem about making a balance or a choice of the variety, so we shall analyze the propositions about the threat, such as the lemmas, the theorems and the axioms, and their effects on the new axiom according to Term-by-Term Comment Principles, in order to confirm the critical threat, to effectively block it, and to keep the regular function of the legal system as possible. |
第三節 革命主體內部左右派之先天共存必要及其間及時切換 |
Section.3 The Necessity of the Innate Coexistence of the Left-wing and the Right-wing in a Revolutionary Subject and the Timely Switch between Them |
| 新公理雖可自成一格，但其無法脫離資源分配公理者[6]，如非經前開法規系統合法化納入，則必然萎靡至死，故其仍須在藉緊急救濟取得之短暫倖存期間內，與舊公理完成妥協而融合為新法規系統，蘊含上開新舊公理須自始相容。 | Even if a new axiom can create its own system, if it cannot escape from the resource distribution axiom[6], and if it is not legally accepted by the legal system, it will certainly degenerate into death, so it shall still, while a temporary survival period given by an emergency remedy, reach a compromise with the old axioms, to form a new legal system, and this implies the new axiom is necessary to be innately consistent with the old ones. |
| 臨時後設系統即革命主體或其協助者，縱內建前開相容性，應至遲於前開新公理遭受殲滅前，經搜尋其內建命題清單發現相容命題，藉以重新設定前開新舊公理之維生閥值；逾暫時前開倖存期間不為上開重新設定者，法規系統將續行殲滅。 | A provisional metasystem, which includes a revolutionary subject and its helpers, even if is built-in with the consistence, shall, before the new axiom is eliminated, search its built-in proposition list to discover a consistent proposition to reset life thresholds for the new axiom and of the old ones; if it fails to reset them within the survival period it, the legal system will continue the elimination. |
| [1] | 法規系統得或得不保障多元性。 | A legal system may or may not guarantee the variety. |
| [2] | 法規系統即屬蘊含哥德爾不完備定理之公理系統。 | Legal systems are axiomatic systems including Godel's incompleteness theorems. |
| [3] | 本文所稱後設系統主要係指專家學者。 | The metasystem in this article mainly means specialists and scholars. |
| [4] | 常規後設系統由法規系統指定。 | The regular metasystem is specified by the legal system. |
| [5] | 臨時後設系統之判斷對舊公理系統未必有拘束力。 | A measure made by a provisional metasystem is unnecessarily with a constraining force to the old axioms. |
| [6] | 蓋新公理能力太弱，受強後設系統牽制，不足以掠奪舊公理所占有之資源。 | Since the new axioms are so weak that they are dominated by the strong metasystem, and cannot snatch the resources from the old axioms. |
| 多元性，即多元基底數目，係本徵函數項數目。 | The variety, which is the number of the variety bases, is the number of the terms of an eigenfunction. |
| 個體維生目的在於維持自身多元性。 | An individual lives on purpose to preserve its own variety. |
| 個體維生所為之熵排放量不得逾越特定閥值，使上開個體成功維持之多元性不小於因上開熵排放而損失之多元性期望值[1]。 | The amount of the entropy emission from an individual living shall not beyond a certain threshold, such that the variety successfully preserved by the individual is not less than the expected value[1] of the variety lost as a result of the entropy emission. |
| [1] | 個體之熵排放未必傷及群體多元性，故須考慮期望值。 | An individual's entropy emission is not necessary to hurt the colonial variety, so we shall consider the expected value. |
| 回到目錄《後設猜想篇章節》。 | Back to the menu, The Table of Content of The Metahypotheses. | ||
| 第2篇第2章第1節 | Volume.2, Chapter.2, Section.1 | ||
| 運作⊃共識⊃評論之定義 | Application⊃Consensus⊃The Definition of Comment | ||
| § 1 | I | 評價，係對事物所為之測度。 | An estimate is the measure on a thing. |
| II | 前項測度之幾何性質，在本文中無特別規範。 | The geometric properties of the measure in the preceding paragraph are not specified in this article. | |
| § 2 | I | 評論，包括下列必要參照：
|
A comment comprises the following necessary references:
|
| II | 前項必要參照內建於評論接收人本徵函數者，得省略之。 | A necessary reference in the preceding paragraph may be omitted, if it is built-in the comment receiver's eigenfunction. | |
| § 3 | 評論非依前條定義為之者，應視為不當評論。 | A comment made as violating the definition in the preceding paragraph shall be deemed an improper comment. | |
| § 4 | I | 代表人，代表個體或群體。 | A representative represents an individual or a group. |
| II | 個體代表人之評論可不同於上開個體之評論；群體代表人之評論可不同於上開群體中任何個體之評論。 | The comment made by the representative of an individual can be different from the comment made by the individual; the comment made by the representative of a group can be different from the comment made by any individual in the group. |