The Infinite Form and the Spark of Truth – On the Materialist Dialectic in Badiou’s *The Immanence of Truths*

For the French Marxist philosopher Alain Badiou, his newly published 2018 work *The Immanence of Truths* may well be his last major philosophical opus. *Being and Event*, published in 1989, and *Logics of Worlds* (the second volume of the “Being and Event” series), published in 2006, used his distinctive mathematical-philosophical approach to attempt to find the possibility of moving toward a future communist society. Twelve years after the publication of *Logics of Worlds*, he has again published a monumental work of over 700 pages—*The Immanence of Truths*—indicating that this new book is the third volume of the “Being and Event” series. Perhaps Alain Badiou hopes that in this newly published third volume of “Being and Event,” namely *The Immanence of Truths*, he can bring his lifelong philosophical enterprise to a conclusion: that is, once we have touched upon the “infinite,” a genuine infinite, how can we bring about a change in the world, and how is such a change possible?

对于法国马克思主义哲学家阿兰·巴迪欧来说，2018年新出版的《真理的内在性》或许是他最后一部大部头的哲学著作了。1989年出版的《存在与事件》和2006年出版的《世界的逻辑》（即“存在与事件”系列的第二卷），用他特有的数学哲学方式，来尝试找到走向未来共产主义社会的可能性。在《世界的逻辑》出版了12年之后，他再次出版了一部长达700多页的巨著——《真理的内在性》，他表明这部新书是“存在与事件”系列的第三卷。或许，阿兰·巴迪欧希望在这本新出版的“存在与事件”的第三卷即《真理的内在性》中，将他一身的哲学事业告一个段落，即我们如果触及了“无限”，一个真正的无限之后，如何能让世界发生个改变，这种改变如何具有可能。

I. The Path to the Infinite

一、通向无限之路

“A single spark can start a prairie fire.” Badiou is indeed very fond of this famous saying of Mao Zedong, and in his works he has cited Mao’s “a single spark can start a prairie fire” on many occasions, whether in his early work *Theory of Contradiction*, or in his 1982 *Theory of the Subject*, as well as in the conclusion of *Logics of Worlds*. We cannot determine to what extent Badiou, when citing this famous saying of Mao, understood how, in 1930, the Chinese Workers’ and Peasants’ Red Army, in the arduous and difficult environment of the Jinggangshan period, persisted in the ideals of national liberation and communism, thereby finding hope in the spark of truth amidst the actual situation. Mao Zedong’s creation of “A Single Spark Can Start a Prairie Fire” was not only a response to the pessimistic mood then prevalent in the Red Army, but also an idealistic expression—that is, finding hope for a future ideal society from a faint firelight. It is perhaps this idealistic expression that sparked Badiou’s intellectual resonance. He knows that Mao’s “a single spark can start a prairie fire” was directed at the harsh environment of revolutionary struggle in China at the time, but its most fundamental aspect is a philosophical idea: the concept of seeing an infinite future from a finite spark of light. In fact, in *The Immanence of Truths*, Badiou cites this famous saying again in the introduction. However, he expresses dissatisfaction with the expression “Une seule étincelle peut commencer un feu de prairie” in the French edition of the *Selected Works of Mao Zedong*, and thus retranslates Mao’s passage into his own French: “l’étincelle qui jaillit du frottement localisé d’infinités disparates.” Badiou’s new translation differs little in the first half, but the two sentence structures are worlds apart. The former is in the active voice, meaning that the spark is the cause and the prairie fire is the effect; it is precisely by igniting the spark that the universal spark of the future illuminates the entire world—this is a way of ascending gradually from the finite to the infinite, and in Badiou’s early thought, he endorsed this approach. However, in *The Immanence of Truths*, the relationship in this sentence has changed; it can no longer be directly translated as “a single spark can start a prairie fire,” but rather as “the spark is the concrete flame burst forth by the omnipresent infinite.” In this new sentence structure, the spark is no longer the cause, but the result of the infinite descending into the human world. This logic is an inverted romanticism: first there is the form of the prairie fire, and only then the concrete spark. In Badiou’s view, when we can see the spark, it means the world has already changed. For communists, for revolutionary movements, it is not a matter of artificially creating the spark, but of being faithful to the spark, because being faithful to the spark means facing a more significant event, and the event is precisely the result excited by a new infinite or a new generic procedure. When Badiou quotes Paul Valéry’s poem “The Graveyard by the Sea” in *Logics of Worlds*, what he anticipates is not the tranquil and calm sea under the sun, but the waves swept in by the raging storm. This is the famous line at the end of Valéry’s “The Graveyard by the Sea”:

“星星之火，可以燎原。”巴迪欧的确十分喜欢毛泽东的这句名言，在他的著作中，曾经多次提到毛泽东的这句“星星之火，可以燎原”，无论是他早期的作品《矛盾理论》，还是1982年的《主体理论》，以及《世界的逻辑》的结论部分，都曾经提到了毛泽东的“星星之火，可以燎原”。我们无法判定，巴迪欧在引述毛泽东的这句名言的时候，在多大程度上理解1930年中国工农红军在井冈山时期在艰苦卓绝的环境中，如何坚持民族解放和共产主义的理想，从而在星星之火之中找到希望的现实处境。毛泽东《星星之火，可以燎原》的创造，不仅仅是针对当时红军中弥漫的悲观情绪，也是一种理想式的表达，即从微弱的火光中找到通向未来理想社会的希望。或许正是这种理想式的表达，促发了巴迪欧的思想感触，他知道，毛泽东的“星星之火，可以燎原”针对的是当时中国艰苦的革命斗争环境，但是最根本的是一种哲学理念，从有限的火光中，看到无限未来的理念。实际上，在《真理的内在性》中，巴迪欧在导论中再次引述了这个段名言，不过，对于法文版《毛泽东选集》中的表达Une seule étincelle peut commencer un feu de prairie，他表达了不满，从而用自己的法语重新翻译了毛泽东的这段话，即l’étincelle qui jaillit du frottement localisé d’infinités disparates。巴迪欧的新译法，在前半部分实际上区别不大，不过这两个句式却相差千里，前者是主动态，也就是说，星星之火是原因，燎原是结果，正是燃起了星星之火，才将未来的普遍性的火花照遍了整个世界，这是从有限逐渐上升为无限的方式，在早期巴迪欧的思想中，他是认可这种方式的。但是，在《真理的内在性》中，这句话的关系发生了变化，已经不能直接翻译为“星星之火，可以燎原”，而是“星星之火是无处不在的无限所迸发出来的具体的火花”，在这个新句式中，星星之火不再是原因，而是无限在降临人间时所激发出来的结果，这个逻辑是一种颠倒的浪漫主义，即先有了燎原的形式，然后才有具体的星星之火。在巴迪欧看来，当我们能看到星星之火的时候，说明世界已经发生了变化，而对于共产党人，对于革命运动来说，不是人为地去制造星星之火，而是忠实于星星之火，因为忠实于星星之火，就是面对一个更为重大的事件，而事件恰恰是新的无限或新的类性程序所激发的结果，当巴迪欧在《世界的逻辑》中引用瓦莱里的《海边墓园》的诗歌时，他所期待并不是那个在太阳下静谧而宁静大海，而是被狂风暴雨席卷而来的海浪，这就是瓦莱里《海边墓园》结尾处的名句：

My breast, drink in the wind’s new birth!

我的胸怀啊，畅饮风催的新生！

A fresh breath from the sea

从大海发出的一股新鲜气息

Revives my soul… O salty vigor!

复苏吧，我的灵魂……啊，咸味的魄力！

Let us run to the waves, and return reborn!

奔向海浪去吧，跑回来将是新生！

Truth and the absolute are by no means the calm surface of the sea under a gentle breeze and warm sun. This calmness is more like the disguise and concealment of montage; it brings order and tranquility, making people operate year after year, day after day, according to established apparatuses, and take this mode of operation as nature, as the universal, as the absolute, as truth. What Badiou wants to tell us is: no. Beneath the gentle breeze and warm sun, the sea also has storms, and the poetic imagery of “rocks piercing the sky, startling waves slapping the shore, rolling up a thousand piles of snow” [1]1 Plato, *Republic*, 515c–515d. [return to text]. If we remain only under the appearance of the calm sea, we degenerate into a finite existence. Only when torn apart by the storm, in the charm of saltiness, can we see the real, see the infinite. This is why Badiou calls on us in *Logics of Worlds* to “run to the waves.” There is another, more important reason: once we touch the real and the absolute, once we face those infinites that cannot be easily faced, our lives will be renewed. The waves bring not only “saltiness,” not only “frightening waves,” not only “terror,” but a “rebirth.” This is also why Badiou so appreciates the “fresh breath of the sea” in “The Graveyard by the Sea.” This “fresh breath” must by no means be simplistically understood as the sweetness of romanticism, nor as an uplifting progressive triumphal march, but as an elevation in the face of the genuine infinite. In this elevation, “my soul is revived.” When I face this world anew, “returning reborn.”

真理和绝对，绝不是和风煦日下的宁静的海面，这种宁静更像是蒙太奇的伪饰和遮掩，它们带来的是秩序与安宁，让人们年复一年，日复一日地按照既定的装置去运行，并将这种运动模式当成自然，当成普遍，当成绝对，当成真理。巴迪欧想告诉我们的是，不对，在和风煦日下，大海还有暴风雨，还有那“乱石穿空，惊涛拍岸，卷起千堆雪”的诗意，如果只在宁静的大海的外表下，我们就沦为一种有限存在，只有在被暴风雨撕裂，带着咸味的魅力中，才能看到真实、看到无限。这就是为什么巴迪欧在《世界的逻辑》中号召我们“奔向海浪去吧”的原因，还有一个更为重要的原因，一旦我们触及真实和绝对，一旦面对那些无法简单面对的无限，我们的生命会焕然一新，海浪带来的不仅仅是“咸味”，不仅仅是“惊涛骇浪”，也不仅仅是“恐怖”，而是一种“新生”，这也就是为什么巴迪欧十分欣赏《海边墓园》中的那种“大海的新鲜气息”的原因，这种“新鲜气息”我们决不能简单理解为浪漫主义的香甜，也不能理解为一种励志向上的进步主义的凯歌，而是一种面对真正无限的升华，在这种升华中“我的灵魂，得到复苏”，在我重新面对这个世界的时候，“跑回来将是新生”。

Whether it is Badiou’s rewritten “spark” or his final citation of Valéry’s “The Graveyard by the Sea”—“Let us run to the waves, and return reborn”—both are in fact expressing a new consciousness to us: if the subject once touches the infinite that is ordinarily untouchable, when facing the world anew, what will this world, or this world as the appearance of being, become? When Badiou introduces his book *The Immanence of Truths*, he repeatedly emphasizes that this is an inverted book. If *Being and Event* and *Logics of Worlds* are works that explore the path to the infinite from finite forms and the world, then *The Immanence of Truths* is precisely on the other side—that is, once we have come into contact with the event and encountered truth, how do we face the world constituted by finite beings?

无论是被巴迪欧改写的“星星之火”，还是他最后引述的瓦莱里的《海边墓园》的“奔向海浪吧，跑回来将是新生”，实际上都在向我们表达出一个新意识，倘若主体一旦触及了平常所无法触及的无限，在重新面对世界的时候，这个世界，或者说这个作为存在表象的世界，会变成什么样子？当巴迪欧在介绍自己的《真理的内在性》一书的时候，他反复强调，这是一本倒过来的书，如果说《存在与事件》和《世界的逻辑》是从有限的形式和世界去探索通向无限道路的著作，那么《真理的内在性》恰恰是在另一段，也即是说，一旦我们接触到了事件，遭遇了真理，我们会如何去面对有限的存在物构成的世界？

II. Truth in the Cave

二、洞穴中的真理

Perhaps we can borrow Plato’s metaphor of the cave and the sunlight in *The Republic* to illustrate the problem Badiou raises in *The Immanence of Truths*. The sunlight outside the cave represents the absolute and the existence of truth, while the vast majority of us can only, within the cave, take the fleeting shadows on the cave wall as reality, subordinate ourselves to these shadows, and form a common opinion (*doxa*). However, once someone steps out of the cave and sees the sunlight outside, they immediately feel the difference between truth and common opinion. Plato writes: “Consider, then, what would be the manner of the release and healing from their bonds and their folly, if something like this naturally happened to them: when one was untied and compelled suddenly to stand up, turn his neck around, walk, and look up toward the light, he would do all these things with pain, and because of the dazzling light, he would be unable to discern those things whose shadows he formerly saw. What do you think he would say if someone told him that before he saw empty phantoms, but now he is nearer to being, turned toward what is more real, and sees more correctly?”[1]1 Plato, *Republic*, 515c–515d. [return to text] In this passage from Plato, we perceive two things.

或许，我们可以借用柏拉图在《理想国》中用洞穴和阳光的比喻来说明的巴迪欧在《真理的内在性》所提出的问题。洞穴之外的阳光代表着绝对和真理的存在，而我们绝大多数人都是只能在洞穴里将穴壁上浮光掠影的影子当成了实在，并从属于影子，形成了一种俗见（doxa）。不过，一旦有人走出洞穴，看到洞穴之外的阳光，就立刻能感受到真理与俗见的区别。柏拉图写道：“看他们从枷锁和无知中释放出来并获得了痊愈，如同每人可能遇上了那类处境，如果以下这类事也发生在他们身上，当某人被松了绑，被逼迫突然站立起来，扭过脖子，开始行走，并且抬眼看到洞外的太阳，他很痛苦地做着这一切事情，而且，因为阳光耀眼，他不能认清那些他从前只捕风捉影谈到的东西，你想他说些什么，如果某人告诉他，从前，他看到的都是虚影，现在，他比以前更接近事物的本质而且已转而面对真实，他也就会看得更为正确。”在柏拉图的这段话中，我们感受到两件事情。

First, confronting truth is clearly more painful than confronting shadows on the wall. People do not voluntarily face truth; they can only turn around and face the sunlight outside the cave under the compulsion of some procedure and force. This is also the reason Badiou has insisted since *Theory of the Subject* that the subject is rare. Those who can see the shadows of truth are extremely few, and those who are willing to set aside the common opinion (*doxa*) of the cave, voluntarily move toward truth, and unite with the generic procedure of that truth are even fewer. Mathematics and philosophy are such procedures, but those truly willing to touch the path leading to the absolute and truth through mathematics are far too scarce. In other words, today there is no shortage of “philosophy”—that is, thought that disguises ordinary common opinion as philosophy. In Badiou’s view, this “philosophy” is actually an anti-philosophy; Nietzsche, Wittgenstein, and Lacan are famous masters of anti-philosophy. For instance, when Wittgenstein says, “What we cannot speak about we must pass over in silence,” in Badiou’s view, this “conclusion” precisely demands that we confine ourselves within the limits of finite common opinion (*doxa*), suspending all paths leading outside the cave. In evaluating Wittgenstein’s anti-philosophy, Badiou points out: “The anti-philosophical act is to let things show themselves, because ‘there it is’ is precisely what we cannot speak of in genuine propositions. If Wittgenstein’s anti-philosophical act can be properly called ‘archi-aesthetic,’ it is because ‘letting it be’ cannot express its pure being and clarity in propositional form, for the clarity of this pure being is something unspeakable, appearing only in works of non-thought form (for Wittgenstein, music is of course the most appropriate form).”[2]2 Alain Badiou, *L’Immanence des vérités* (Paris: Fayard, 2018), p. 45. [return to text] Badiou argues that Wittgenstein abolishes the form of philosophical thinking, holding that philosophy cannot lead us to truth, and reduces that truth to an unspeakable “archi-aesthetic.” This is in fact a kind of sophist under contemporary conditions, who confuses common opinion with truth, maintains a sense of mystery about the absolute and infinite outside the cave, preserves this mystery in the primordial unspeakable sensibility, and thereby cuts off the path to the external world. Thus, compared with art, which is a more intoxicating form, people seem to forget what Plato once reminded us of: the path to the truth outside is painful. In Badiou’s view, only mathematics in the strict sense has this function: “Only mathematics allows us to enter into a unified thought of the visible.”[3]3 Ibid., p. 48. [return to text] This is also why Plato wrote above the entrance to his Academy: “Let no one ignorant of geometry enter.” Mathematics is painful, but once, through the path of mathematics, one touches that seemingly untouchable truth, one can obtain a greater pleasure.

首先，面对真理显然比面对墙壁上的影子，会令人感到痛苦，人们不会自愿地去面对着真理，只能在某种程序和力量的督促下，才会转过身来，面对洞穴外的阳光。这也是巴迪欧从《主体理论》以来一直强调主体是稀缺的原因所在，能够看到真理的影子的人是极少数，而原因放下洞穴中的俗见（doxa），志愿走向真理，与那种真理的类性程序合体的人，更是少之又少，数学和哲学都是这样的程序，但是真正原因通过数学去触及通向绝对和真理的道路的人，实在太稀缺了。换言之，今天并不缺少“哲学”，即那种将平常的俗见伪装成哲学的思想，在巴迪欧看来，这种“哲学”实际上是一种反哲学，尼采、维特根斯坦、拉康就是著名的反哲学大师。比如当维特根斯坦说“对于不可说的东西我们必须保持沉默”时，在巴迪欧看来，这种“结论”恰恰要求我们局限在有限性的俗见（doxa）之内，悬置了一切通向洞穴之外的道路。巴迪欧在评价维特根斯坦的反哲学的时候指出：“反哲学行为就是让事物自己显现自己，因为‘在那里存在’恰恰使我们不能用真正的命题来言说的东西。如果维特根斯坦的反哲学行为之所以可以适当地称之为‘原-感性’（archi-esthétique），这是因为‘任其存在’并不能从命题上来表达它的纯粹存在和明晰性，因为这种纯粹存在的明晰性是一种不可言说的东西，只能在非思想形式的作品中出现（对维特根斯坦来说，音乐当然是最恰当的形式）。”巴迪欧对维特根斯坦取消了哲学思考的形式，认为哲学不能够带我们走向真理，并将那种真理化为一种不可言说的“原-感性”，事实上就是一种当代条件下的智者（sophist），他们混淆了俗见和真理，并让人们对洞穴外的绝对和无限保持神秘感，将这种神秘感保存在原生性的不可言说的感性之中，从而切断了通向外部世界的道路。这样，相对于艺术这种更让人沉醉的形式，人们似乎忘记了柏拉图曾经提醒过的，通向外面的真理的道路是痛苦的。在巴迪欧看来，只有严格意义上的数学才具有这个作用，“只有数学才能让我们进入到一种关于可见物的统一思想中”，这也是柏拉图为什么在他的学园门口要写上“不懂几何者，严禁入内”的原因。数学令人痛苦，但是一旦通过数学的道路，触及了那个看似无法触及的真理，能够获得更大的愉悦。

Secondly, in *The Immanence of Truths*, Badiou actually endows Plato’s allegory of the cave with a new meaning, and this is precisely the central theme of *The Immanence of Truths*. If *Being and Event* aims to pave a formalized path toward the outside of the cave, and *Logics of Worlds* aims to show how finite beings can walk this path, realizing the possibility of reaching the infinite from the finite perspective, then the final volume, *The Immanence of Truths*, is a return—that is, the story of how, after having attained the infinite, one returns to the cave. Because one has touched the form of truth and come into contact with the infinite, the things in the cave still exist, but they are no longer “let themselves show themselves” in Wittgenstein’s sense; for in Badiou’s view, there is simply no way for things to show themselves by themselves. From *Being and Event* onward, Badiou has maintained that the reason we see things as things, and being as being (*l’être en tant qu’être*), is precisely that they are re-presented by a structure of counting-as-one. Real being is indifferent being, a multiplicity and a manifold; we can only distinguish things and objects from one another through the conceptual tools or functions of counting-as-one. It is precisely through these functions and concepts of distinction that we can understand certain things as *things* (*chose*) and as *objects* (*objet*). The subject (*sujet*) is the one who creates these concepts and functions. In this way, Badiou actually inverts this relationship: the point is not that we piece things together bit by bit in experience to obtain the great capitalized Totality (*Totalité*) or the One (*UN*); rather, the objects in the cave are in fact all mediated by concepts, becoming the result of some operation of counting-as-one. Conversely, we can understand why Badiou, in *The Immanence of Truths*, transforms Mao Zedong’s “A single spark can start a prairie fire” into “the spark is the concrete flame burst forth by the infinite that is everywhere.” That is to say, as the truth procedure outside the cave changes, the objects inside the cave also change accordingly, becoming sparks of truth. In other words, once one returns to the cave, the real world has not changed; what has changed is the way of distinguishing and framing the world—that which in *Being and Event* is called the “state of the situation,” and in *Logics of Worlds* the transcendental T. The generic procedure of truth changes the entire formal framework, so that objects appear within the new framework and exhibit new states. All objects are immanent to form, immanent to the newly opened generic procedure of truth; any existing and appearing object is an object under the generic procedure. In this sense, we can say that all objects are immanent to truth. This is why Badiou titled his 2018 new book *The Immanence of Truths* and made it the third volume of the “Being and Event” series. It is not that things and ideas are beyond (*au-delà*) the formal framework; rather, all objects and ideas are framed by form and immanent to the framework of truth. Objects are beings realized by the formal framework or the generic procedure of truth; they can be re-presented, counted, and incorporated into the existing operational framework. Yet there also exists a pure multiplicity—a being of multiplicity that is not manifested by the formal framework. But this pure multiplicity is not only unspeakable (as Wittgenstein would say) but even imperceptible; even Wittgenstein’s “proto-sensibility” is powerless before such pure multiplicity, or indifferent multiplicity. In this way, through his truth procedure, i.e., the immanence of truth, Badiou distinguishes between objects that have been intervened upon by the formal truth procedure and the indistinguishable pure multiplicity, the pure being of multiplicity. Badiou believes that the purpose of philosophy certainly cannot be, as Wittgenstein would have it, to remain silent about what cannot be said; rather, we must create a form, create a generic procedure of truth, so that what was originally unsayable can be presented under a new form. Hence, Badiou points out: “This proves the immanence of truth, at the most diagrammatic level, in the most formal truth, inevitably provides the possibility for human thought, through suffering, to encounter the infinite.” From this perspective, the reason Badiou trusts mathematics so much is precisely that mathematics can provide us with infinite possibilities, allowing new possibilities to descend into the cave, liberating the multiplicity that exists there from its original vulgar opinions and gaining its own potential.

其次，在《真理的内在性》中，巴迪欧实际上赋予了柏拉图的洞穴比喻一个新的意义，这个也是他在《真理的内在性》中的主旨所在。如果说《存在与事件》在于为通往洞穴之外铺设好一条形式化的道路，而《世界的逻辑》在于如何让有限的存在物，走上这条道路，从有限的角度实现通向无限的可能性，那么最后的《真理的内在性》是返回，即在具有了无限之后，如何返回到洞中的故事。由于触及的真理的形式，接触到了无限，洞穴的中的东西仍然存在着，但是他们已经不再是维特根斯坦意义上的“让自己显现自己”，因为在巴迪欧看来，根本不存在物自己显现自己的方式，从《存在与事件》开始，巴迪欧就认定，我们之所以将物看成物，存在之所为存在（l’être en tant qu’être）恰恰是被一种计数为一的结构所再现的，真实的存在是无差分（indifférent）的存在，是杂多和流形，我们只能通过计数为一的概念工具或函数，才能将物和对象彼此区分开来，也正是有了这种区分的函数和概念，我们才能将某些东西理解为物（chose），理解为对象（objet），而创造这些概念和函数的人就是主体（sujet）。这样，巴迪欧实际上颠倒了这种关系，重点并不是我们在经验中一点点地拼凑来获得那个大写的总体（Totalité）或太一（UN），而是洞穴中的对象事实上都是被概念中介过的，成为某种计数为一运算的结果。我们反过来可以理解，为什么巴迪欧在《真理的内在性》中将毛泽东的“星星之火，可以燎原”变成了“星星之火是无处不在的无限所迸发出来的具体的火花”，也就是说，随着洞穴外的真理程序的改变，洞穴中的对象也随着发生变化，成为面向真理的星星之火。换言之，一旦重新回到洞穴中，真实的世界并没有改变，改变的是用来区分和架构世界的方式，那个在《存在与事件》中被成为“情势状态”的东西，也是《世界的逻辑》中的超验T，真理的类性程序改变了整个形式架构，从而让对象在新的架构中呈现出来，并表现出新的状态。所有对象都内在于形式，内在于新开启的真理的类性程序，任何实存的和显现出来的对象都是类性程序下的对象，在这个意义上我们可以说所有的对象都内在于（immanent à）真理。这就是巴迪欧将2018年的新书名定义为“真理的内在性”，并将其作为“存在与事件”系列的第三卷的原因所在。并不是物和观念超越于（au-delà）形式框架之上，而是所有的对象和观念都是被形式所架构的，内在于真理的框架。对象是被形式框架或真理的类性程序实现了的存在，它可以被再现，可以被计数，可以纳入现存的运算框架之中，但还存在着某种纯多，即并非由形式框架显现的多之存在，但是这种纯度不仅（像维特根斯坦所说的那样）是不可言说的，甚至是无法感知的，即便是维特根斯坦的“原-感性”，对于这样的纯多，或无差分的多也无能为力。这样，巴迪欧通过自己的真理程序，即真理的内在性，将被形式上的真理程序所介入的对象，与无法区分的纯多，纯粹的多之存在区别开来。巴迪欧认为，哲学的目的当然不能像维特根斯坦那样对不可言说的保持沉默，而是我们要创造一种形式，创造出真理的类性程序，让原本不能言说的东西可以在新的形式下呈现出来。所以，巴迪欧指出：“这证明了真理的内在性，在最具有图示性的层面上，在最形式的真理中，不可避免地为人类思想提供可能性，让人们历经磨难，去遭遇无限。”从这个角度来看，巴迪欧之所以如此信任数学，恰恰在于数学可以为我们提供无限的可能性，让新的可能性降临在洞穴中，让在那里存在着的杂多可以从原本的俗见中解放出来，获得自己的潜能。

III. From Language to Mathematics

三、从语言到数学

To achieve this goal, Badiou believes that the prestige of philosophy must be re-established. In his lifetime, Badiou has written two “Manifestos for Philosophy.” The first, *Manifesto for Philosophy*, was completed shortly after *Being and Event* in 1989, at a time when postmodernism and post-structuralism were in vogue. Thinkers of that era constantly declared that philosophy was dead: Lyotard turned philosophy into a grand narrative to be castigated; Bourdieu and Baudrillard both claimed to be engaged in sociological research, avoiding philosophy and metaphysics as much as possible. Since the anti-philosopher Nietzsche, philosophy had suffered unprecedented questioning. Badiou swam against the current; what he needed to do was to vindicate philosophy—not only does philosophy exist, but we are already inseparable from it, because we are situated within different truth procedures. However, after *Logics of Worlds*, Badiou wrote a second *Second Manifesto for Philosophy*, this time in 2009. The problem of this era had suddenly changed: people no longer announced the death of philosophy; on the contrary, many believed that philosophy was everywhere—stock trading has its philosophy, cooking has its philosophy, there is a philosophy of making money, a philosophy of governing people, and so on, ad infinitum. In Badiou’s view, this phenomenon is precisely the evil consequence of the former one: because postmodernism and post-structuralism had dissolved the legitimacy and justification of philosophy, philosophy became a label emptied of content, ready to be pasted anywhere. The distinction between Platonic philosophical ideas and vulgar opinions had ceased to exist. The prevalence of anti-philosophical currents made people no longer believe in the existence of truth, no longer enamored with eternity; philosophical ideas were deconstructed as grand narratives. People valued more what was immediately at hand, fixing their gaze on the transient world of existence, caring only for the fleeting glimmer in a single drink or a bowl of porridge. This way of viewing all things in the world solely through the finite, Badiou calls “democratic materialism.” In *Logics of Worlds*, Badiou explicitly states that the axiom of “democratic materialism” is: “There are only bodies and languages.” Whether it is the body (as in Merleau-Ponty) or language (as in the later Wittgenstein), both are finite; they cannot directly help us break the boundary of the finite to reach the infinite, but instead make us eternally linger on this shore of fragmented and atomized concrete bodies and linguistic fragments. Here again echoes Heidegger’s quotation from the poem by Stefan George: “Where the word breaks off, no thing may be.”

为了达到这个目的，巴迪欧认为，必须来重新建立哲学的威望。在巴迪欧的一生中，写过两部“哲学宣言”。第一部《哲学宣言》完成于《存在与事件》之后不久的1989年，那时，正好是后现代和后结构主义流行的时代，那个时代的思想家都不停地宣布哲学业已死亡，利奥塔将哲学变成了宏大叙事，加以挞伐，布尔迪厄和鲍德里亚都宣称自己从事的是社会学研究，对哲学和形而上学避之唯恐不及。自反哲学家尼采之后，哲学遭受了前所未有的质疑，巴迪欧逆流而上，他所需要做的是为哲学正名，不仅存在着哲学，而且我们已经与哲学密不可分，因为我们就处在不同的真理程序之中。不过，在《世界的逻辑》之后，巴迪欧再次写作了一本《第二哲学宣言》，时间已经是2009年，这个时代的问题突然发生了变化，人们不再宣告哲学的死亡，相反，许多人都认为哲学无处不在，炒股有炒股的哲学，烹饪有烹饪哲学，还有赚钱的哲学，治人的哲学等等，不一而足。在巴迪欧看来，这种现象恰恰是前一种现象的恶果，即由于被后现代和后结构主义消解了哲学的合法性和正当性，让哲学成为被掏空内容的标签，可以被随处粘贴。在柏拉图意义上的哲学观念与俗见看法之间的区分，已经不复存在，反哲学思潮的流行，让他们不再相信存在着真理，不再迷恋永恒，哲学的观念被当成宏大叙事遭到解构，人们更看重的是眼下的东西，将目光停留在转瞬即逝的实存世界当中，只看重一瓢饮，一碗粥中昙花一现式的微光。这种仅仅局限于有限来看待世间万物的方式，巴迪欧称之为“民主唯物主义”，在《世界的逻辑》中，巴迪欧曾十分明确指出，“民主唯物主义”公理是“只存在着身体与语言”。无论是身体（如梅洛-庞蒂），还是语言（晚期的维特根斯坦），都是有限的，它并不能直接帮助我们打破有限的界限通向无限，而是让我们永恒地逗留在碎片化和零散化的具体身体和语言碎片的此岸，这里再次回响起海德格尔引用的格奥尔格诗歌中的名言“词语破碎处，无物可存在”。

Clearly, Badiou attempts to go against the grain. He does not distrust poetry; in fact, Badiou has a profound literary background and is highly skilled at appreciating and critiquing poetry. He possesses deep expertise in the poetry of Mandelstam, Pessoa, Rimbaud, Paul Celan, and others. However, Badiou believes that the fragmented words of poetry do not lead us toward Heidegger’s unconcealment (aletheia) or the infinite absolute; they only cause us to become more lost in the fragments of words. Thus, Badiou proposes a mathematical path to rediscover the route to the infinite. In *Second Manifesto for Philosophy*, he again announces this plan: “Being is a multiplicity derived from the empty set, and only mathematics is the thought of being qua being. In short: ontology, and the etymological discourse on being, can be fully realized historically only through the mathematics of multiplicity.” Yet the philosophical problem today is precisely that philosophers are too far removed from mathematicians. However, calculus was invented by Newton and Leibniz, and topology had already emerged in the eighteenth century. Philosophers today are often unfamiliar with post-Cantor set theory, which is why Badiou insists on reconstructing philosophy through mathematics, especially set theory.

显然，巴迪欧试图反其道而行之，他并不是不信任诗歌，实际上巴迪欧有着深厚的文学功底，也是十分擅长欣赏和评论诗歌，他对曼德尔斯坦姆、佩索阿、兰波、保罗·策兰等人的诗歌都有着很深的造诣。不过巴迪欧认为，诗歌的词语碎片，并不会引领我们走向海德格尔意义上的无蔽（aletheia）或无限的绝对，只能让我们更加迷失在词语的碎片中。这样，巴迪欧提出了从数学的路径来重新寻找通向无限的路径，在《第二哲学宣言》中，巴迪欧再次宣布了这个计划：“存在是一个从空集中得出的多元，而唯有数学才是关于存在之为存在的思想。简言之：本体论，以及关于存在的词源学意义上的论述，在历史上，由于关于多元的数学才能使其彻底实现。”不过，今天的哲学问题恰恰是哲学家离数学家太远了。然而，微积分是牛顿和莱布尼茨发明的，而拓扑学在18世纪也已经出现，今天的哲学家往往不太熟悉康托尔之后的集合论，这也是巴迪欧坚持从数学，尤其是集合论来重构哲学的原因。

In the introduction to *The Immanence of Truths*, Badiou points out that twentieth-century mathematics provided philosophy with three important concepts that have not received sufficient attention from philosophers. The first concept is the generic set (ensemble générique), which grounds all thought of universality; to access the infinite, the generic set is necessary. However, Badiou believes that his discussion of the generic set was already completed in *Being and Event*, and this is not the task of *The Immanence of Truths*. The second concept is the theory of sheaves (la théorie des faisceaux) of the twentieth-century German mathematical genius Grothendieck, which Badiou discussed specifically in *Logics of Worlds*. The final concept, and the one discussed in *The Immanence of Truths*, is the grand infinite (grand infini). In Badiou’s own words, “This concept of the grand infinite, immanently approximating (approximation immanente) the absolute, will influence us for a long time to come.” This grand infinite concerns the absolute and the infinite; for Badiou, it is the foundation for reconstructing the entire ontology of philosophy.

在《真理的内在性》的导论中，巴迪欧就指出，20世纪数学为哲学提供了三个重要的概念，并没有引起哲学家们的足够重视，第一个概念是类性集合（ensemble générique），它奠定了所有普遍性思想的基础，如果要通常无限，就必须要有类性集合。不过巴迪欧认为，对类性集合的讨论，他在《存在与事件》中已经完成，这并不是《真理的内在性》的任务。第二个概念是20世纪的德国数学天才格罗腾迪克（Grothendieck）的层论，巴迪欧在《世界的逻辑》中进行过专门的讨论。最后一个概念，也是《真理的内在性》这本书讨论的概念，是大无限（grand infini），用巴迪欧自己的话来说，“这个大无限的概念，内在地接近于（approximation immanente）绝对，将会在很长一段时间里影响我们”。而这个大无限，涉及的就是绝对和无限，对巴迪欧，这就是重构整个哲学本体论的根基。

To reconstruct the philosophical grand infinite and allow philosophy to once again confront the real (le réel), a new materialist dialectic (dialectique matérialiste) is needed. Badiou declares very clearly: “All truths are produced immanently; no one can enclose them within the dominant finite forms. Only in the open philosophical materialist dialectic, only within its truth conditions (science, politics, love, art), starting from this concept, can we discover the possibility of not turning into its opposite, of not vainly hesitating in the shadows enclosed by finite scenes.” Precisely speaking, this new materialist dialectic simultaneously fights enemies on two fronts. On one hand, Badiou directs his critique at the absolute of transcendence, a notion that reduces all finite modes to a transcendence external to the world [in the Middle Ages, this transcendent being was God (Dieu); in modern philosophy, it might be Substance (Substance) or Nature (Nature)]. In short, there is an absolute One serving as the reference frame for philosophy and the various differentiated sciences of the world. On the other hand, with the rise of postmodernism, the linguistic turn, and other modern sophistries (sophistique), and with the deconstruction of concepts like the absolute and truth by postmodernism and post-structuralism, philosophy is regarded as a meaningless discourse, thereby confining meaning to finite beings (“there are only bodies and languages”). This is what Badiou calls “democratic materialism.”

为了重构出哲学上的大无限，让哲学再一次面对真实（le réel），需要一种全新的唯物辩证法（dialectique matérialiste），巴迪欧十分明确地宣告：“所有的真理都是被内在地生产出来的，没有人可以将其封闭在主流的有限形式下。唯有在开放的哲学的唯物辩证法当中，只有在它的真理条件（科学、政治、爱、艺术）当中，从这个概念出发，才能发现不会走向其反面的可能性，不会徒劳地在有限场景所封闭的阴影中踟蹰不前。”准确来说，这种新的唯物辩证法同时在针对两个方面的敌人作战，一方面，巴迪欧将批判的矛头指向超越性（transcendence）的绝对，这种观念将所有的有限的模式都还原为一个外在于世界的超越性［在中世纪的时候，这个超越性的存在是上帝（Dieu），在现代哲学中，这个超越性的存在，可能是实体（Substance），也可以是大自然（Nature）］。总之，有一个绝对的一作为哲学和世界上各种分殊科学的参照系。另一方面，随着后现代和语言学转向等现代智术（sophistique）的兴起，随着后现代主义和后结构主义对绝对、真理等概念的解构，哲学被视为一种无意义的论调，从而将意义局限于有限的存在当中（“只存在着身体和语言”），这就是巴迪欧所谓的“民主唯物主义”。

IV. Mathematical Form and the Possibility of Truth

四、数学形式与真理的可能性

Regarding the first conception, Badiou devoted considerable space in *Being and Event* to proving that “the One is not” (l’Un n’est pas). Badiou points out that in the original real world, there is only multiplicity and manifold, only the undifferentiated being of the multiple. Only when we invent a structure of counting-as-one can we see the world as “One” (Un). Therefore, Badiou says: “There is no One, only the count-as-one. The One, as an operation, is never presentation. It must be said very seriously: ‘One’ is a number.” Since the One is a counting structure, this counting structure eternally has exceptions relative to the real world. Badiou says: “There will always be exceptions relative to the counting structure, appearing in an incalculable form, a concrete rupture, which I call an event.” This necessarily implies that any structure of counting-as-one cannot exhaust all of the real; thus, the real has an eternal exception relative to the “One.” However, in the history of philosophy and theology, there has always been a desire to reduce all things in the world to a single origin, the One—for example, the Christian God, the Nature of natural law, and so on. From the perspective of this transcendental philosophy, the origin of the world is an external One; outside this One, there is no exception. Whether Spinoza’s Substance or Hegel’s Absolute Spirit, these are all variants of this One, but in fact none escape the relationship Badiou identifies between the real world and the One as a counting structure. Badiou believes that the mathematician Cantor’s contribution lies not only in proposing set theory but also in “distinguishing the infinite from the One, allowing for a form of infinite as ‘a multiple-without-One’ (un multiple sans-un).” The infinite we seek is not necessarily the One, not necessarily a single source; on the contrary, the infinite or the absolute may also appear in the form of multiplicity and undifferentiation. We cannot view the original real world, or the infinite world, as a coherent unity, nor does there exist a Gödelian concept of a constructible universe. If we need to construct a materialist dialectic on a new foundation, we must abandon this concept of the One, because when we assume an original One, we have already recognized an abstract formal structure that allows us to make the real world coherent, turning it into a One that is understood and grasped in our cognition. This is a new concept of the infinite, and also the concept of the grand infinite that Badiou repeatedly emphasizes. This is not Hegel’s “bad infinite,” but a world full of incoherence and plural truths (vérités). Relative to our counting structure, this world always has an outside. The goal of philosophical research is to seek possibilities outside our state of the situation’s structure—that is, those absolutes that abruptly appear in a paradoxical form within our framework of knowledge and language. Then the infinite has a destructive and annihilating meaning; the true infinite is an impossibility, namely: “The key point is that it is an impossible paradigm relative to the initially given image of a possible world; it is an infinite potential difficult to recognize, a novelty with destructive repression, and a paradoxical construction.”

对于第一种观念，巴迪欧在《存在与事件》中用了很大的篇幅来证明“一不存在”（l’Un n’est pas），巴迪欧指出，在原本真实的世界里，只有杂多和流形，只有无差分的多之存在，唯有当我们发明了计数为一的结构时，我们才能将世界看成是“一”（Un）。因此，巴迪欧说：“没有一，只有计数为一。一，作为一种运算，从来不是呈现。必须非常严肃地说，‘一’是一个数。”由于一是一种计数结构，那么这个计数结构相对于真实世界永恒地存在例外，巴迪欧说：“总会存在着相对于计数结构的例外，它会以不可计算的形式出现，是一个具体性的断裂，我称之为事件。”这势必意味着，任何计数为一的结构，实际上都不能穷尽所有的真实，这样，真实相对于“一”有着永恒的例外。但是，在哲学史和神学史上，存在在于总希望将世界上的万物都归结为一个起源，即太一，如基督教的上帝，自然法学派的自然等等。在这种超越论的哲学看来，世界的起源是一个外在的一，在这个太一之外，没有任何例外的存在。无论是斯宾诺莎的实体，黑格尔的绝对精神都是这种太一的变种，但实际上都没有摆脱巴迪欧所指出的真实世界和作为计数结构的太一之间的关系。巴迪欧认为，数学家康托尔的贡献不仅仅在于他提出了集合论，而且他将“无限和太一区分开来，可以存在着一种‘无一之多’（un multiple sans-un）形式的无限”。我们所追求的无限，不一定是太一，不一定是单一的源头，相反，无限或绝对也可能是以杂多和无差分的形式出现的。我们不能将原初的真实世界，或者无限的世界看成一个连贯的统一体，也不存在哥德尔那种可建构的全集概念。如果需要在新的基础上去建构唯物辩证法，就必须要摒弃这种太一的概念，因为在我们认为存在着一个原初的太一的时候，已经认定了存在一个抽象的形式化的结构，而这个结构让我们将真实的世界连贯起来，成为一个在我们的认识中被理解和把握的太一。这是一种新的无限概念，也是巴迪欧反复强调的大无限的概念，这不是黑格尔意义上的“坏的无限”，而是一个充满不连贯性的和复数真理（vérités）的世界，这个世界相对于我们计数结构，始终存在着一个外部，而哲学研究的目的，就是去寻找在我们的情势状态结构之外的例外的可能性，即那些突兀地以悖论性形式出现在我们知识和语言架构中的绝对，那么无限具有一种破坏性和毁灭性意义，真正的无限是一种不可能性，即“关键在于，那是一个相对于最初给定的可能世界形象的不可能的范式，它是难以认识的无限潜能，带有毁灭性压抑的新奇，以及悖论式的建构”。

The second enemy of the new materialist dialectic is clearly “democratic materialism.” Although in *Logics of Worlds* Badiou extensively criticized “democratic materialism,” rewriting the axiom of democratic materialism – “there are only bodies and languages” – into the axiom of materialist dialectics – “besides bodies and languages, there are also truths” – the problem with “democratic materialism” lies in the fact that, unlike the transcendental idea of the absolute One, its adherents do not believe in anything absolute. Thus, they not only negate concepts such as totality, absolute spirit, and God as the ultimate absolute One, but also negate the absolute and the infinite themselves, holding that the only reliable things are our bodies and the languages we use to speak. This is why Wittgenstein said “whereof one cannot speak, thereof one must be silent”: because language cannot guarantee certainty beyond its own limits. For Badiou, “democratic materialism” represents the other extreme: locking itself within fragmented finitude, believing in nothing beyond our finitude, beyond the bodies we can touch and the languages we can speak.

新唯物辩证法的第二个敌人，显然就是“民主唯物主义”。尽管在《世界的逻辑》中，巴迪欧对“民主唯物主义”进行了大量的批判，将“民主唯物主义”的公理“只存在着身体和语言”，改写成唯物辩证法的公理“除了身体和语言之外，还存在着真理”。“民主唯物主义”的问题在于，与超越论的绝对的太一观念不同，他们不相信任何绝对的东西。于是，他们不仅否定了总体性、绝对精神、上帝等作为终极的绝对的太一的概念，同时他们也否定了绝对和无限本身，认为唯一可靠的东西就是我们的身体以及我们用来说话的语言，这也是为什么维特根斯坦说“保持沉默”原因，因为语言不可能在自己的限度之外来保障确实性。对于巴迪欧来说，“民主唯物主义”代表着另一个极端，即自己锁死在支离破碎的有限性当中，除了我们的有限，除了我们可以触及的身体，可以言说的语言之外，他们不再相信任何东西。

Badiou believes that in *Being and Event* he had already dealt well with the problem of the One and the transcendental, opening the way for a formal ontology of the event, and that Cantor’s set theory and Cohen’s forcing method later resolved the philosophical-historical problem of the One, which Gödel’s constructible universe had posed. However, the latter task – the critique of “democratic materialism” – was not completed in *Logics of Worlds*. Although Badiou reconstructed the phenomenology of the event from the perspectives of category theory and topology, constructing the possibility of the event within finite things and objects, this phenomenology of the event is still insufficient to thoroughly critique the ideology of “democratic materialism.” Here, the problem Badiou needs to solve is finitude. To resolve the infinite and the absolute while avoiding falling back into the rut of transcendentalism and the One, it is necessary to carry out a thorough ontological critique of the concept of finitude. In this regard, Badiou’s disciple Quentin Meillassoux provided a good foundation in *After Finitude*, and many of Badiou’s arguments also reference Meillassoux’s research. How, then, does Badiou actually handle the problem of finitude?

巴迪欧认为自己曾经《存在与事件》中很好地处理了太一和超越论的问题，并为事件的形式本体论开辟了道路，以后康托尔的集合论和科恩的力迫法解决了哥德尔的可建构全集的哲学史上的太一问题。但是，对于后者，即对“民主唯物主义”的批判，在《世界的逻辑》中，并没有完成这个任务。尽管巴迪欧从范畴论和拓扑学的角度，重构了事件的现象学，在有限的事物和对象中，建构了事件的可能性。但是这种事件的现象学，还不足以彻底批判“民主唯物主义”的意识形态。在这里，巴迪欧需要解决的问题是：有限。如果要解决无限和绝对，同时避免重新陷落到超越论和太一的窠臼中，那么，就必须从本体论上，对有限概念进行彻底的批判。在这个方面，巴迪欧的弟子昆汀·梅亚苏在他的《有限性之后》中做了很好的铺垫工作，而巴迪欧的许多论述也是参照了梅亚苏的研究。巴迪欧究竟是如何来处理有限问题的呢？

In the introduction to *Immanence of Truths*, Badiou makes a startling claim. In contrast to postmodernism, post-structuralism, and the late Wittgenstein – these “democratic materialisms” – they hold that the most certain things are the finite things closest to us: bodies and languages. We can only touch this certainty; beyond it, we can neither perceive nor speak. Even the less radical versions (such as Habermas’s attempt to deal with the finitude of body and language under communicative reason, thereby constructing a framework of publicness that transcends the finitude of individual bodies and languages through intersubjectivity and discourse ethics) firmly believe that what is closest to us is most certain, and that we can only obtain greater publicness and universality from the most certain body and language. But Badiou argues: “The finite does not exist; it is merely the result of the multiple operation of the infinite.” This is indeed a claim quite different from our usual understanding. Moreover, Badiou even believes that contemporary “democratic materialism,” as an anti-philosophical trend and sophistry, actually establishes an “ideology of finitude,” and one of the goals of his *Immanence of Truths* is “the critique of finitude, which has become the most central fetishistic ideology of our time.”

在《真理的内在性》的导论中，巴迪欧就给出了一个惊人的说法。相对于后现代主义和后结构主义，以及晚期维特根斯坦这些“民主唯物主义”来说，他们认为最确定的东西就是与我们最接近的有限之物：身体和语言。我们只能触及这种确定性，对于这种确定性之外的东西，我们既无法感知，也无法言说。即便那些不太激进的版本（如哈贝马斯试图在交往理性下来处理身体和语言的有限性问题，从而试图用主体间性和商谈伦理的方式来建构一个超越个体身体和语言有限性的公共性框架），他们也坚信我们最接近的东西是最确定的，我们只能从最确定的身体和语言来获得更大的公共性和普遍性。但是，巴迪欧认为：“有限，并不存在，它不过是无限多元运算的结果。”这的确是一个与我们通常理解大相径庭的说法，不仅如此，巴迪欧甚至认为，当代“民主唯物主义”，作为一种反哲学思潮和智术，它实际上建立的是一种“有限的意识形态”，他的《真理的内在性》的目标之一就是“对有限进行批判，而有限已经成为了我们时代的最核心的拜物教意识形态”。

This is a very important judgment. When Badiou proposed in *Being and Event* that the One is an operation, a result of counting-as-one, how is finitude also understood as a result? For example, when we say there is an apple here, the apple is finite. But the reason we speak of the apple is not because the apple itself possesses this finite nature, but because within a given classificatory framework (the framework of counting-as-one), it is regarded as an apple separated from its surrounding environment. In other words, the reason we regard the apple as an apple is precisely because a representational framework, a framework of counting-as-one, exists beforehand. Only within this framework can we have knowledge of this apple, and can we see or perceive the existence of this apple. Otherwise, the apple is fused into the given world, unable to be separated from that world and become an independent finite object. All the bodies we see and all the languages we speak depend on an invisible framework, which constitutes the foundation of our understanding and grasp of the world, and is also the basis on which the object-world we see and understand operates. In this sense, we must say that the apple, as an individual finite object, is actually the result of the classificatory system we have established, and this classificatory system in turn is subordinate to a higher-order formal framework. Within this framework (whose essence is the structure of counting-as-one, or the One), beings are separated from the manifold environment and become independent finite beings.

这是一个十分重要的判断，当巴迪欧在《存在与事件》中提出一是一种运算，是一种计数为一的结果的时候，如何理解有限也是一种结果。例如，当我们说这里有一个苹果的时候，苹果是有限的，但是，我们之所以谈到苹果，并不是因为苹果本身具有这种有限的性质，而是在一个既定的分类框架（计数为一）的框架下将它视为一个与周围环境分离开来苹果。换句话说，我们之所以将苹果视为苹果，正是因为事先存在了一个再现框架，一个计数为一的框架，只有在这个框架下，我们才能对这个苹果有所认识，也才能看到或感知到这个苹果的存在，否则，苹果是融合在既定的世界中，无法从那个世界中分离出来，并独立为一个有限的对象。我们所有看到的身体，我们所言说的语言都依赖于一个看不见的框架，而这个框架构成了我们理解和把握世界的根基，也是让我们所看到所理解的对象世界得以运行的基础。在这个意义上，我们不得不说，作为个体有限对象的苹果，实际上是我们建立的分类体系的结果，而这个分类体系又进一步服从于更高阶的形式框架。在这个框架下（这个框架的本质是计数为一，或太一的架构），存在物从杂多的环境中分离出来，独立为一个有限的存在物。

If finite classification is subordinate to a given framework (in set-theoretic terms, the elements of the apple belong to a part or subset of a situation), then the problem lies not in the elements but in the classifying part. How the world is counted and classified becomes the most basic way we grasp and understand the world. What we call liberation is not purely about breaking visible boundaries, as Deleuze advocates, going to the great Outside to nomadize, using lines of flight to break up the ordered world. But Deleuze and Guattari both forgot that the subjects or objects in the present world are actually carved out under the mold of a formal framework; that is, their bodies and languages are highly compatible with the schizophrenic regime of capitalism. There is no nomadism outside the capitalist territory, because that kind of nomadism represents the breaking of individuated distinctions and the rules of finite counting, and also signifies the death of the individual – no singularity, only the silence of life.

如果有限的分类隶属于一个既定的框架（用集合论的话说，苹果的元素属于一个情势的部分或子集），那么问题并不在于元素，而是在于分类的部分。对世界如何进行计数和分类，成为我们把握和理解世界的最基本的方式。我们所谓的解放，不纯粹是打破可见的边界，像德勒兹主张的那样，到大外部去游牧，用逃逸线来打破秩序化的世界。但是，德勒兹和伽塔里都忘记了，现在世界中的主体或对象，实际上都是在一个形式框架的模子下雕刻出来的，也就是说，他们的身体和语言都是与资本主义的精神分裂症体制高度契合的，不存在着在资本主义辖域范围外的游牧，因为那种游牧代表着打破了个体化的区分和有限计数的规则，也意味着个体的死亡，没有独特性，只有生命的沉寂。

If one wishes to break the fetishistic form of consciousness of the finite, Badiou believes there is only one path: mathematics, formalized mathematics. That is to say, we must first create a form; even if this form has no object, it can become incarnate in the real world of existence, concretizing into new formal objects. Badiou always believes in the revolutionary effect of the event, because the event is an absolute exception: the structure of the prior state of the situation cannot count it as one, which necessarily implies the need to create a new structure to completely replace the prior structure. This is revolution in Badiou’s sense, a formal revolution. Again, take the example of mathematical form. In ancient Greece, people already understood the distinction between rational and irrational numbers and believed that rational and irrational numbers covered the entire range of numbers. However, in mathematics, there were still some problems that could not be solved within the entire range of rational and irrational numbers. The most famous of these was the problem of solving the quadratic equation \(x^2 + 1 = 0\). The great Indian mathematician Bhāskara believed this equation had no solution, because a negative number cannot be the even power of any number. It was not until the 16th century that the Italian mathematician Cardano introduced a new concept, the “imaginary number” (*nombre imaginaire*), thereby forming a concept opposed to the “real number” (*nombre réel*) composed of rational and irrational numbers. It is worth noting that in nature, we do not actually discover the concept of “imaginary numbers” because we have discovered some object of imaginary numbers. The emergence of the concept of “imaginary numbers” is in fact a creation of infinite form. Before Cardano invented the concept of “imaginary numbers,” we could not imagine the solution to the equation \(x^2 + 1 = 0\). Once the form of “imaginary numbers” appeared, not only could we find the square roots of negative numbers, but, more importantly, a new mathematical form was produced.

倘若要打破有限的拜物教意识形式，巴迪欧认为只有一条道路可走，这就是数学，形式化的数学，也就是说，我们先要创造一个形式，即便这个形式没有对象，但是它们可以在现实的实存世界中道成肉身，具体化为新的形式的对象。巴迪欧始终相信事件的革命性效果，因为事件是一个绝对的例外，原先的情势状态的结构无法对它进行计数为一的计算，势必意味着需要创造一个新的结构，来彻底取代原先的结构。这就是巴迪欧意义上的革命，一种形式上的革命。还是以数学的形式为例，在古希腊，人们已经理解了有理数和无理数的分别，并认为有理数和无理数涵盖了所有的数的范围。但是，在数学上，仍然有一些难题无法在全部的有理数和无理数的范围里解决，其中最有名的就是一元二次方程x2+1=0的解的问题，印度大数学家婆什伽罗认为这个方程是无解的，因为负数不可能是任何数的偶次方。直到16世纪，意大利数学家卡尔达诺才谈到了一个新的概念“虚数”（nombre imaginaire），从而与有理数和无理数构成的“实数”（nombre réel）形成对立的概念。值得注意的是，在自然界里面，我们实际上并不是因为发现了某种虚数的对象，才发现了“虚数”概念。“虚数”概念的出现，实际上就是一种无限的形式创造，在卡尔达诺发明“虚数”概念之前，我们无法想象方程x2+1=0的解，一旦出现了“虚数”这个形式，不仅我们可以找到负数的方根，更重要的是，产生了一种新的数学形式。

In fact, Badiou also uses this approach to respond to those critics who argue that within the scope of science he only values mathematics, not physics or chemistry. Indeed, in Badiou’s early works, when he discusses revolutions in the scientific field, he often refers specifically to mathematical revolutions. The important figures of scientific revolution he lists are mostly mathematicians such as Descartes, Gauss, d’Alembert, Galois, and Grothendieck; he basically never mentions any contributions from physics or chemistry (he only occasionally mentions the chemist Lavoisier, but he discusses not Lavoisier’s contributions to chemistry, but rather Lavoisier’s experiences during the French Revolution). If we understand Badiou’s critique of the “ideology of the finite,” it is easy to see why he prefers not to discuss concrete sciences like physics but instead directly addresses mathematics. In *The Immanence of Truths*, Badiou points out: “We see that, for many years, I have been engaged in arduous mathematical work, and I have concluded that we must insist that the root of all problems is the theory of the multiple (set theory), although we also acknowledge that theories of particular worlds, such as physics, are formalized through thinking in mathematical categories.” To a certain extent, this is both a prejudice against concrete sciences like physics on the part of Badiou, who is trained in mathematics and philosophy, and a consequence of the ontology Badiou himself has established.

实际上，巴迪欧也用这种方式回应了那些认为他在科学范围内只重视数学，而不重视物理学和化学的批评意见。的确，在巴迪欧的早期著作中，谈到了科学领域的革命，往往指的就是数学革命，他列举的科学革命的重要人物，大多是笛卡尔、高斯、达朗贝尔、伽罗瓦、格罗腾迪克等数学家，他基本上没有谈到任何物理学或化学上的贡献（他只有偶然一次提到了化学家拉瓦锡，但是他谈到的不是拉瓦锡在化学上的贡献，而是谈拉瓦锡在法国大革命时期的遭遇）。如果从巴迪欧对“有限的意识形态”的批判，就很容易理解他为何不喜欢谈物理学等具体科学而是直接讨论数学。在《真理的内在性》中，巴迪欧指出：“我们看到，多年以来，我都从事着艰苦的数学工作，我得出结论，我们必须坚持认为，所有问题的根源就是多的理论（集合论），不过我们也承认，关于特殊世界的理论，如物理学，通过数学范畴的思考得到形式化。”在一定程度上，这既是学数学和哲学出身的巴迪欧对物理学等具体科学的歧视，也是巴迪欧自己所设定的本体论使然。

Conclusion

结语

After the discussions in *Being and Event* and *Logics of Worlds*, Badiou gradually reveals to us his ambition: if there exists a future society, this society is not an exterior, nor a return to the Garden of Eden like “religion”—that is, a return to the embrace of the One and the absolute spirit—but rather, under the impact of the event as exception, it creates a new form, even if this new form is an empty set. However, because the new form is a generic truth procedure after the event, it constructs a new combination (generic set), continuously incorporating the subject into the new set, becoming incarnate under the mathematical form of the new set, concretizing into new objects. We can return once again to Badiou’s understanding of Mao Zedong’s “A single spark can start a prairie fire.” [13]13 “A single spark can start a prairie fire” (星星之火，可以燎原) is a phrase from a letter written by Mao Zedong in 1930, later used as a slogan to express the idea that a small revolutionary force can grow into a powerful movement. The reason a single spark can start a prairie fire is not that it itself represents a transcendent One, but that it belongs to the generic procedure of a new truth formed by the subject after the event. Because it conforms to the generic procedure, the spark becomes a concrete representation under this new set and new operation; the expansion and diffusion of this representation can then spread across the entire world. This is Badiou’s new materialist dialectic, and also his way of conceiving a future good society. (Notes omitted)

在经过《存在与事件》和《世界的逻辑》的讨论之后，巴迪欧一步步地向我们展现出他的雄心，如果存在着一个未来社会，这个社会不是一种外部，或者像“宗教”那样重返伊甸园，即返回到太一和绝对精神的怀抱，而是在作为例外的事件的冲击下，去创造出一种新的形式，即便这种新的形式是一个空集。但是由于新的形式，是事件之后的类性真理程序，它建构了一个新的结合（类性集合），不断让主体合体到新的集合中，在新的集合的数学形式下道成肉身，具体化为新的对象。我们可以再次回到巴迪欧对毛泽东“星星之火，可以燎原”的理解，星星之火之所以可以燎原，并不是因为它本身代表着超越性的太一，而是它属于在事件之后，由主体形成的新的真理的类性程序，因为符合类性程序，星星之火成为了在这个新集合和新运算下的具体化表象，这种表象的扩展和弥散，便可以遍布整个世界。这是巴迪欧的新唯物辩证法，也是他对未来的美好社会的构想的方式。（注释略）

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