Fires the first spear/gun for the world of this big struggle, is Feng Luoyi. 为这大争之世打响第一枪的,是冯落衣。 Although the song courtyard room has handed over to hold for as member even/including sect calculates in Lord first disciple what outside hand, but the song courtyard faction to legitimate, is calculates as before as before Lord direct descendant. This point, never because of what outside the factors or any others , but changes simply. 尽管歌庭斋已经交托给了身为连宗修士的算主首徒何外尔手中,但是歌庭派依旧是离宗正统,依旧是算主嫡系。这一点,从来就不会因为何外尔或其他任何一个人的因素而简单改变。 Perhaps hundred years later, the song courtyard room will turn into another appearance finally, but what outside person, is unable to reverse this stone after all. 或许百年之后,歌庭斋终将变成另外一个样子,但是何外尔一个人,终归是无法扭转这个石头的。 The member of song courtyard faction most core, has killed to get angry, deliberately planning is going linking the sect operation with inconsiderately is calculated routed that separation operation equates, integrates in them the attack range of inconsiderately calculating. 歌庭派最核心的修士,已经杀红了眼,处心积虑的将要将连宗算理同被不周之算所击溃的那部分离宗算理划上等号,将他们也纳入不周之算的攻击范围之中。 But first completes the achievement, actually Feng Luoyi this genius who has „inhuman” the name. 但最先完成成果的,却还是冯落衣这位有着“非人”之称的天才人物。 Therefore , Feng Luoyi found the brand-new mentality. 应当说,冯落衣找到了全新的思路。 They declared, the set theory beforehand mentality has the issue. 他们宣称,集合论之前的思路都有问题。 Should not from „completely”, but should from „not have” in starts. 不应该从“全部”,而是应该从“无”之中入手。 All „set”, must start from „null set”, constructs. 所有的“集合”,都必须从“空集”开始,进行构建。 The set that or only then starts to construct from the null set is recognized as the legitimate set. 或者说,只有从空集开始构建的集合才被承认为合法集合。 Set in addition, has the issue, inconsiderately is calculated took away the foundation in the air garret. 除此之外的集合,都是有问题的,都是被不周之算抽掉了根基的空中阁楼。 The finite set or the infinite aggregate, must start from „null set”. 无论是有穷集还是无穷集,都必须从“空集”开始。 The null set corresponds 0, corresponds 1 , corresponds 2. If all sets, have similar normal order including the infinite set, then, then can implement to exceed the infinite induction to be the same with the ordinary mathematical induction. 空集对应0,对应一,,就对应二。如果一切集合,包括无穷集合都有类似的良序,那么,那么就可以实施超越无限的归纳就和普通的数学归纳一样。 Then, to sect Zhigao the achievement „natural justice system” 【Zf axiomatics】, Its complete axiom, can during Yoshimoto gathers realizes. 然后,离宗至高成就的“天理体系”【zf公理体系】,其全部公理,都能够在良基集合之中实现。 This is Feng Luoyi proposition. 这就是冯落衣的命题。 This talent, successively with two papers, completed this great proof. 这位天才,先后用两篇论文,完成了这一伟大的论证。 Any proof structure must have the poor length, is no exception about the contradictory proof. But the infinite axiom natural number infinite set has the axiom, utilized the successor operation and null set operation. These two operations, in the operation of sect, have the correspondence continually. Therefore, these two operations, between continually the sect operation and leaves operations, is absolute. In other words , to the operation and even/including sect operation, actually has the consistent embodiment to quite a large extent. 任何证明构造都必须是有穷长度的,关于矛盾的证明也不例外。而无穷公理自然数无穷集合存在公理,之运用到了后继运算和空集运算。这两个运算,在连宗的算理当中,均有对应。因而,这两个算理,在连宗算理和离宗算理之间,是绝对的。换言之,离宗算理和连宗算理,其实存在着相当程度上的一致内蕴。 This is two operations „absolute quality”. 这就是两个算理的“绝对性”。 Therefore, if the infinite axiom has the contradiction, then this contradiction, „will have poverty” through one translation process, appears in the operation. 因此,如果无穷公理有矛盾,那么这个矛盾,也会通过一个“有穷”的翻译过程,出现在算理之中。 The infinite function axiom, is safe. 无穷功能公理,是安全的。 This paper one, is the large surface area of member even/including sect spits blood. 这篇论文一出,便是连宗修士的大面积吐血。 Everyone knows, even/including sect, especially few Li-school of modern Representative even/including sect, denies „infinite” and „the law of excluded middle”. Calculates Monarch to believe, the material world does not have the infinite object, the world of arithmetic should not have the infinite object similarly. 谁都知道,连宗,特别是近代连宗代表的少黎派,就是否认“无穷”与“排中律”的。算君认为,物质的世界不存在无穷的对象,算学的世界同样不应该存在无穷的对象。 This then shook even/including sect the foundation. 这便是撼动了连宗的根基了。 Innumerable even/including sect calculates the family/home to touch own ears and cheeks, wishes one could to write the paper immediately, counter-attacks Feng Luoyi. 无数连宗算家抓耳挠腮,恨不能立刻就写出论文,反击冯落衣。 However, quick, the Feng Luoyi second paper, makes all arguments cease all activities. 但是,很快,冯落衣的第二篇论文,就让所有的争论都偃旗息鼓。 „If takes infinite axiom the negative form to take the axiom, will have poor well-ordered in contradiction also more convenient manifestation above other axioms.” “如果取无穷公理的否定形式作为公理,有穷良序之中的矛盾也会更加方便的体现在其他公理之上。” „Therefore, in some sense, the infinite axiom is not vindicable, may not the card otherwise.” “因此,某种意义上来讲,无穷公理不可证明,也不可证否。” This, then like bolt from the blue, the town/subdues all even/including sect calculates that the family/home could not speak. 这一下,便如同晴天霹雳,镇得所有连宗算家都说不出话来了。 Generally speaking, „attesting to falsity”, is a now law immortal foundation is then. Does not have the attesting to falsity thing, without value of discussion. 一般来说,“可证伪性”,便是今法仙道的根基所在。不具备可证伪性的东西,没有讨论的价值。 However, the position of arithmetic, slightly is more special. 但是,算学的地位,却稍稍特殊一些。 These arithmetic do not talk clearly, own work, is „discovery” „invention”. 就连那些算学家自己都说不清楚,自己的工作,到底是“发现”还是“发明”。 In this regard, calculates that Monarch and king Qi have the completely opposite view absolutely. 在这一点上,算君和王崎绝对持有完全相反的看法。 Naturally, looks like in beautiful god that level, this struggle holds, is completely the joke. 当然,在美神那种层次看来,这种争持,完全就是笑话。 king Qi when encounters after the beautiful gods, then also had this tendency. 王崎在与美神遭遇之后,便也有了这种倾向。 He even said in the preface of formal linguistics, this argument, is the natural language chaos cannot withstand purely, must branch out „discovery” and „invention” two completely different concepts. 他甚至都在形式语言学的序言之中表示,这种争论,纯粹就是自然语言混沌不堪,非得分出“发现”和“发明”两个完全不同的概念。 But said no matter how, in the arithmetic domain, cannot prove the theory that may not attest to falsity, allows to exist. 但不管怎么说,在算学领域,一个不可证明也不可证伪的理论,是允许存在的。 But it seems like that the theology to be the same, is self-contained in own logic. 但它就好像是神学一样,在自己的逻辑里自成一体。 Even if wants destroying, is still very difficult to start. 就算想要将之摧毁,也很难下手。 Regarding the average person, this is one „does not know has anything” unknown region. 对于普通人来说,这就是一个“不知道到底有什么”的未知区域。 But Feng Luoyi skillfully skillful, he from the beginning, proved another point directly. 但冯落衣巧就巧在,他一开始,就直接证明了另一点。 The infinite axiom is safe. 无限公理是安全的。 „Does not know that inside has anything”, but is „safe”. “不知道里面有什么”,但是是“安全的”。 This also explained from one side, even/including sect critique to „infinite” concept, is really not meaningful. 这也从侧面说明了,连宗对“无穷”概念的批判,实在是没有什么意义。 But Chen by fine paper, was follows emits. 而陈由嘉的论文,也是紧随其后放出了。 This, let all leave member sect uncomfortably. 这一下,却让所有离宗修士难受了一阵。 Even some people cursed at the scene: „Rebel!” 甚至有人当场大骂:“叛徒！” To the rebel! 离宗叛徒！ In the past time, almost all member, sent to regard as the base naturally to the sect. King Sakiya had expressed clearly leave the standpoint of sect. 在过去的时光里,几乎所有修士,都将基派理所当然的视作了离宗。王崎也旗帜鲜明的表示过自己离宗的立场。 But now, as to sect member Chen by fine, published had the paper that clearly even/including sect favored. 而现在,身为离宗修士的陈由嘉,发表了带有明显连宗倾向的论文。 Does this make them not get angry? How can not get angry? 这又让他们怎么不怒？怎能不怒？ But gets angry compared with them, is actually many basic unit disciples in thousand machine pavilions. 但比他们更怒的,却是千机阁的众多基层弟子。 The theory of types erased Turing to be complete directly, erased the circulation. 类型论直接删掉了图灵完备,删掉了循环。 Turing human finds it very interesting actually, will treat as a topic arrangement to leave. 图灵真人本人倒是觉得挺有趣的,甚至将之当做一个课题布置离了下去。 But after thousand machine pavilion disciples discover this point, boils immediately. 但千机阁弟子发现这一点之后,就立刻沸腾了。 To them, without calculates the system that Turing complete, has not circulated, cannot imagine. 对于他们来说,没有图灵完备、没有循环的算器体系,是不可想象的。 They felt that oneself Saint territory was violated. 他们感觉自己的圣域受到了侵犯。 Past „free soaring”, turns now „brought the shackles to dance”. 过去的“自由飞翔”,如今就变成了“带着镣铐跳舞”。 Chen by „to the rebel” the call, makes noisily in thousand machine pavilions. 陈由嘉“离宗叛徒”的呼声,也在千机阁闹得沸反盈天。 Regarding this, Turing honorable person also only then smiles bitterly: „This was actually...... seems is I do not do right by that miss.” 对此,图灵真人也只有苦笑:“这却是……好似是我对不住那姑娘了。” Feng Luoyi shakes the head: „Goes by them noisily. Regarding these having no interest operation fellow, what kind of function the theory of girl has, their future association/will will know.” 冯落衣摇了摇头:“由得他们闹去。对于这些无心算理的家伙来说,那丫头的理论有怎么的作用,他们未来总会知道的。” „You were said that ‚theory of types’ integration ‚Turing will be complete’?” Turing honorable person smiled: „Whorl had thought for these days, may have the malignancy not to agree.” “你是说将‘类型论’纳入‘图灵完备’吗？”图灵真人笑了:“涡这几天想过了,或许会产生恶性不谐的。” „But king Qi told me, this can actually enormous reduction calculate the threshold of technique.” Feng Luoyi said. “但王崎跟我说,这却能极大的降低算器之术的门槛。”冯落衣说道。 Because there is a promotion of all phenomena on earth trigram article, he to his disciple's vision in this aspect, is the trust. 由于有了万象卦文的推广,他对自己弟子在这方面的眼光,还是信任的。 „Feared that these two do not moisten, at crucial moment messes things up.” Turing honorable person somewhat hesitates. With the theory of types associated language, has the fault slightly, the direct engine off, could be the security. But the method in those days using although will output the unknown result, however was because the member has known extremely well to this domain, therefore also rarely fell the chain at crucial moments. “就怕这两不沾的,关键时候误了事。”图灵真人有些犹豫。与类型论伴生的语言,是稍有错处,就会直接停机,算得上安全。而往日所用的法子虽然会输出未知结果,然是由于修士对这一领域已经熟稔,所以也很少在关键时刻掉链子。 But if really both unify...... 但若是真的两者结合…… Projects on the essential time what to do calculated the down? 打到关键的时候算器宕机了怎么办？ „If the Lord Buddhist musical instrument naturally discussed separately, however cultivation time, really had the advantage.” Feng Luoyi said. “若是主法器自然另说,但是修炼的时候,确实有优势的。”冯落衣说道。 Turing honorable person said with a smile suddenly: „Moon/Month cold brother now actually a having no immediate concern to oneself appearance. Don't you know? This ‚to the rebel’ wind, blew on you?” 图灵真人突然笑道:“月寒兄如今倒是一副事不关己的样子。你难道不知道吗？这一股‘离宗叛徒’的风,也吹到你身上了吧？” Feng Luoyi eyelid hangs down: „Is the old thing that some diehard...... swallow the ancient learning without digesting it. Inconsiderately calculates, without letting them sees clearly the truth, their also this.” 冯落衣眼睑低垂:“不过是些顽固分子……食古不化的老东西罢了。一个不周之算,都没有让他们看清楚真相,那他们也就这样了。” In fact, Feng Luoyi paper, to , has the opposition. 实际上,冯落衣的论文,在离宗内部,也并非没有反对之声。 Most starts also because of thousand machine pavilion member to Chen by the fine opposition, initiated another opposition. 最开始也就是因为千机阁修士对陈由嘉的反对之声,才引发了另一股反对之声。 Some felt to member sect, Feng Luoyi was insane. 有一些离宗修士都觉得,冯落衣是疯了。 He excluded „circulation” unexpectedly this concept! 他居然剔除掉了“循环”这个概念！ The circulation, widely has the concept in nature. The world breathes the spirit force circulation that represents, the circulation of the atmospheric circulation and water, is a circulation. 循环,是广泛存在于自然界之中的概念。天地呼吸所代表的灵力循环,大气环流、水的循环,都是一种循环。 Therefore, circulates this type of thing, should exist in the arithmetic in fact, it even is the key parts of ten thousand law family merit laws. 所以,循环这种东西,理应存在于算学之中实际上,它甚至都是万法门功法的关键部分。 „Circulation cannot be excluded the logic.” “循环是不能被剔除出逻辑的。” These leave member sect to say. 那些离宗修士如此说道。 Chen by and Feng Luoyi, walks to calculate lord „two roads” in „breaks refers to”. 陈由嘉和冯落衣,都是走算主“两条路”之中的“断自指”的。 Even two people also inspired to a certain extent mutually. 甚至两人也在一定程度上相互启发了。 But from the foundation, Feng Luoyi is most legitimate to sect, but Chen from calculating Monarch here accepted many even/including sect mentality by. 只不过从根基上来说,冯落衣是最正统的离宗,而陈由嘉则从算君这里接受了不少连宗的思路。 But they actually aimed at the same direction. 但他们却是指向了同一个方向。 Feng Luoyi never cares about this minor matter. He said to Turing honorable person: „Song courtyard sends internal not to have the opposition, was enough. Then, looks their?” 冯落衣从来就不在乎这点小事。他对图灵真人说道:“歌庭派内部没有反对之声,就足够了。接下来,就看他们的吧？” Turing honorable person shows neither approval nor disapproval. Everyone knows, the song courtyard faction at this moment, is sets at the deathtrap then to live. 图灵真人不置可否。谁都知道,歌庭派此时此刻,已经是置之死地而后生了。 Under steamroll that in inconsiderately calculates, they could not attend to many. 在不周之算的碾压下,他们也顾不得许多了。 However, Turing honorable person has not thought that the backwater that several days later, the song courtyard sent struck, unexpectedly came so violently. 不过,图灵真人并没有想到,数日之后,歌庭派的背水一击,居然来得如此猛烈。 In fact, is Feng Luoyi even/including sect, to operation frequent transformation the method, brought to their attention. 实际上,也就是冯落衣将连宗、离宗算理频繁转化的手段,引起了他们的注意。 They from this, refined a nameless logical level function. 他们由此,提炼出了一个无名的逻辑层面的函数。 „Double negation translations”. 【On Earth calls it „Goodall Cen” translation】 “双重否定翻译”。【地球上称之为“哥德尔-根岑”翻译】 „The supposition law of excluded middle has the contradiction, then can construct denial proof of this supposition”. “假设排中律有矛盾,则可以构造出这个假设的否定证明”。 „However law of excluded middle, then can equally in double negation eliminations”. “而排中律,则可以等价于双重否定去除”。 This is two has had the simple proof the thesis. 这是两条已经存在浅显证明的论题。 But at this time, the song courtyard faction gave a more further idea. 而就在这个时候,歌庭派提出了一个更进一步的想法。 „If from classical logic inside proof, increases the double negations, then this certificate, whether can equally in the constructive proof of intuitionism?” “如果从经典逻辑里面的证明里,添加双重否定,那么这个证明,是否可以等价于直觉主义的构造性证明？” In other words, if sends in the operation is „the law of excluded middle” some dispelling the song courtyard, then, this thing, whether equal constructive proof in few Li-school? 也就是说,如果将歌庭派算理之中属于“排中律”的部分祛除,那么,这东西,是否就等价于少黎派的构造性证明呢？ The answer is, yes. 答案是,“是”。 It uses the even/including sect operation of opposition law of excluded middle, determined law of excluded middle that even/including sect opposes, is safe. 它用反对排中律的连宗算理,确定了连宗反对的排中律,也是安全的。 With infinite axiom same security. 和无穷公理一样安全。 In other words ,...... 换言之…… Where does not compare including the sect operation to the operation security to goes. 连宗算理并不比离宗算理安全到哪里去。