进化就是递归：同一个循环的四个名字

本不该行得通的那件事#

一个细菌每二十分钟分裂一次，而且在某条谱系里，这件事已经做了三十五亿年。这种稳定性的尺度，足以让地质学感到谦卑。与此同时，从那个细菌开始的这条线，产出了眼睛、神经系统、飞行、语言，以及一份关于它自身不完备性的形式证明。这种复杂性的尺度，足以让任何搜索算法感到谦卑。

难题不在于稳定性和复杂性各自存在。难题在于，同一个机制被认为要同时解释这两者。自然选择寻找的是最优解——就结构而言，它是一个爬山过程。爬山者到达山峰，然后就停下来。然而，自然选择一直在其上攀爬的那些生物，并没有停下来。记录显示，没有终点，没有向单一解的收敛，也没有在任何类似最终适应度峰值的地方稳定下来。¹ 稳定性和无界的新颖性，不是同一个过程应该产出的东西。两者之中，总该有一个把另一个压垮。

底下还跑着别的东西。经验层面的迹象是生态位建构​——生物系统性地改造那些作用于它们自己后代的选择环境。² 当一个生物改变的不只是它的局部栖息地，而是它的后代与竞争者被选择的条件时，适应度地形就不再是一片固定的地貌。它变成了一个由行走者一边走一边生成的曲面。这不是爬山。这是某种有着不同形式结构的东西。

什么样的过程，会从同一台引擎里同时产出这个组合——极端的稳定性与无界的新颖性？不是单靠选择。选择在地形上寻找峰值，而“无界”这一半否认了地形是固定的。底下还跑着别的东西。本文要论证的是，那个“别的东西”有一个名字——事实上有四个，由四个研究传统各自独立地指派，而它们并不知道自己命名的是同一样东西。

生物学家不得不承认的事#

海狸是教科书式的案例。在一个群落迁入一条退化的农业溪流十二年之后，每个样方的植物物种丰富度平均上升约 46%，累计记录到的物种数增加 148%。³ 海狸工程造出的池塘，每 1.8 公顷蓄水面积可蓄存约 100 吨沉积物和 16 吨碳。⁴ 海狸不只是生活在它的环境里。它构成了作用于后世海狸的那个选择环境中相当可观的一部分，也构成了作用于那些谱系同样要穿过这片池塘生态系统的昆虫、鱼类和鸟类的选择环境——而且关键在于，它构成了作用于海狸自己后代的选择环境，而这些后代所继承的，不是那条原本的溪流，而是这个群落造出来的、经过工程改造的湿地。

这既不是巧合，也不是边缘案例。这就是生态位建构在生态时间尺度上所采取的形式。

正式定义出自 Laland 和同事 2015 年那篇关于扩展进化综合的论文：生态位建构是“生物的代谢、活动和选择改变或稳定环境状态，并由此影响作用于它们自身以及其他物种的选择的过程”。² 关键的那个从句是“并由此影响作用于它们自身的选择”——建构生态位的那些生物，也正是在这个生态位之内被选择的生物。选择压力并不外在于生物；它有一部分是由生物自身此前的活动构成的。形式化的进化模型确认了这种相互因果关系带来了标准模型预测不到的后果：生态位建构可以把本来有害的等位基因推向固定，可以支撑起本来不该出现的稳定多态，也可以消除本来会持续存在的多态。⁵

大氧化事件是同一个过程在地质尺度上的版本。按照 ASM 微生物学那篇综述的说法，蓝细菌约在 27 亿年前演化出来，随后通过产氧光合作用改造了地球大气，在约 24 亿到 21 亿年前造成了大氧化事件——这次转变，位列地球史上后果最深远的、由生物引发的地球化学转变之一。⁶ 驱动这场事件的那些生物，并没有活着进入它们造出来的富氧世界。但此后每一个需氧生物，都生活在一个其化学组成由先前生物活动所产生的选择环境之中。这些建构者的后代——全部后代——都栖居在一个由它们祖先建造出来的世界里。

这个模式是普遍的。从海狸水坝到产氧光合作用，生物并不只是栖居在它们的环境里——它们构成了自身被选择的条件。标准的进化框架把这当作对模型的一次修正。它不止于此。这种递归不是画面上的一道褶皱。它是这个过程本身的一个结构性特征。

自我情境化，而不是反馈#

反馈回路有固定的规则。恒温器不会去重新设计它正在追踪的那个温度目标——设定点是从回路之外设定的。输出（测得的温度）作为输入被循环回去，但循环的规则——什么算“太冷”、什么触发锅炉——外在于这个回路，也不受它影响。输出修改输入。规则保持固定。

自我情境化的系统则是另一回事。它的输出修改的不只是输入，还有后续输入被处理时所依据的规则​。那些约束、那些边界条件、那些选择压力——都是从这套运作本身涌现出来的，而不是来自某个运作不曾触碰的外部配置。捕捉这一点的形式类别是不动点结构：一个系统在自身的某个描述上运作，产出一个结果，而这个结果随后成为下一次运作的语境。

在形式逻辑中，这个结构的引擎是哥德尔的对角线引理。对任何足够强的形式系统 F 和任何带一个自由变元的公式 A(x)，存在一个语句 D，使得 F ⊢ D ↔ A(⌜D⌝)——D 可证地等价于把公式 A 应用于 D 自己的哥德尔数。⁷ 这个语句包含了它自身的一个描述（被编码为一个数），并且对那个描述断言了某件事。当 A 是“在 F 中不可证”时，得到的 D 就说“我在 F 中不可证”——这就是那个让不完备性结果落地的哥德尔语句。其机制是把一个公式自身的索引代入它自己。系统在自身运作的一个描述上运作，而结果又约束了后续的步骤。

在计算领域，克莱尼第二递归定理陈述：对任何部分递归函数 Q(x,y)，存在一个索引 p，使得 φₚ ≃ λy.Q(p,y)——这个程序的行为，就好像它在以自己的索引作为第一个参数去应用 Q。⁸ 更通俗地说：程序可以携带自身的描述，并在那些描述上行动。lambda 演算中的 Y 组合子把这一点实现为一个不动点：它接受一个泛函 F，返回一个值 x，使得 F(x) = x，从而让非递归的规格说明产生出递归的行为。这就是自我情境化在计算上的实例：一个函数通过找到自己的不动点，生成了自身的运作语境。

这些是关于抽象系统的形式结果——关于可计算动力系统和形式语言。在那个形式模型之内，Hernández-Orozco 等人 2018 年的定理，是那个把论证收口的结果：在可计算动力系统中，展现出强开放式进化——算法复杂度随时间稳定增长——在形式上等价于不可判定性。¹ 可判定的系统在稳定的复杂度增长上面临绝对的上限。一个复杂度无界增长的系统必定是不可判定的。这个结果的适用范围是它所陈述的那个形式模型，而不直接是生物学意义上的进化。它如何关涉生物学，取决于下文 Cárdenas 论证所搭起的那座桥。

同一件事的四个名字#

四个研究传统，用着不同的词汇，在不同的年代，针对不同的问题，其实已经为上一节所锐化的那个东西命过名。没有一个引用另外几个，也没有一个意识到彼此占据的是同一片概念地界。每一个都看着同一头动物，描述了它解剖结构中不同的一块。

Rosen——动力因闭合（关系生物学，1985–1991）

Robert Rosen 在《Life Itself》（1991）中的核心论题，是对“活的”所下的一个形式定义：“一个物质系统是有机体，当且仅当它对动力因是闭合的。”⁹ 用亚里士多德的话说，动力因是那些带来改变的施动者——催化剂、酶，以及维持组织的那些过程。Rosen 的主张是：在一个活的系统里，那些动力因本身就是在系统内部被生产出来的。催化某个反应的酶，是由另一个反应生产的，而那个反应又由第一个反应所维持。其形式结构是 (M,R) 系统：M 指代谢子系统，R 指再生 M 的修复子系统。这个系统是自蕴含的——所有动力因都落在一个非直谓的循环之内。没有任何外部输入来指派催化剂。它们从这个循环本身涌现出来。

这就是关系生物学中的自我情境化结构。运作的条件——催化剂、酶、动力因——是由它们所使能的那个运作生产出来的。Rosen 还提出了一个有争议的附加主张：这种结构无法被任何图灵机模拟。这个主张与上文发展出来的那些形式结果之间形成了张力——而下文的 Cárdenas 论证会化解这个张力。

Von Foerster——本征形式与操作闭合（二阶控制论，1970 年代）

Heinz von Foerster 是从知觉、而不是从生物化学切入这个问题的。他在二阶控制论中工作——他从 1974 年起把它描述为“观察系统的控制论”，即那些把自身观察者也包含在内的系统——并追问：什么是一个稳定的对象？他的回答是：“对象是本征行为的记号。”知觉中的稳定对象，是递归的观察过程的不动点吸引子。一个本征形式，就是使 F(e) = e 成立的那个值 e——一个递归算子被反复施用后所留下的不变量。¹⁰ Louis Kauffman 在 2003 年的一篇论文中把这一点数学化了，他证明：如果 F 是“装进一个盒子里”这个操作，那么在任何初始构型上迭代 F，在极限处会产出一个满足 X = F(X) 的形式——一个自指的稳定形式，由这个操作产生，而这个操作此后又不再改变它。

它与上文所发展的形式词汇之间的结构联系是直接的。F(e) = e 与哥德尔对角线引理、与克莱尼的 Y 组合子，是同一个不动点结构。Von Foerster 在控制论领域为它命名，比 Rosen 的《Life Itself》问世至少早了十年。本征形式这一支，是四次命名中最早的一次。

Maturana 和 Varela——自创生（1980）

Maturana 和 Varela 是从细胞切入的。他们在《Autopoiesis and Cognition》（1980）中对自创生所下的形式定义，把一个活的系统描述为“一个组件生产（转化与销毁）过程的网络，这个网络：（一）通过其组件的相互作用与转化，持续地再生并实现那个生产了它们的过程（关系）网络；（二）通过指定其作为这样一个网络得以实现的拓扑域，把它（这台机器）构成为在其组件所存在的那个空间中的一个具体统一体。”¹¹

那道边界——细胞膜——本身是由它所包围的那个代谢网络生产出来的。网络生产边界，而边界正是界定“内”与“外”、也就是界定什么算作网络一部分的东西。运作的条件（边界、拓扑、网络身份）是由运作本身构成的。这个系统并不占据一个预先给定的域；它在运作的同时生产出这个域。这就是细胞尺度上的自我情境化结构——四次命名中最具体的一次。

Mossio 和 Moreno——约束闭合（2010）

Mossio 和 Moreno 到得最晚——也最锋利。他们 2010 年的论文，以及在《Biological Autonomy》（2015）中的扩展，给出了四次命名中形式上最精确的一次。他们写道，一个系统是组织上闭合的​，“如果它由一组充当约束的结构 C₁…Cₙ 构成，使得对每一个约束 Cᵢ，其维持所需的（至少某些）边界条件，是由另一个约束 Cⱼ 的直接作用所决定的，而 Cⱼ 的维持反过来又依赖于 Cᵢ 作为直接约束。”¹² 每一个约束都依赖于、并维持着这个网络中至少另一个约束。典范实例是酶闭合的细胞代谢：酶催化那些生产其他酶的反应。运作的条件就是这个约束网络；而这个约束网络，又由它所支配的那个运作所维持。

这比单说自创生更严格。Maturana-Varela 说的是系统生产自己的组件；Mossio-Moreno 则明确指出，系统生产的是其组件在其下运作的那些约束​——是支配运作的规则，而不只是实例化这些规则的零件。这是四次命名中最接近上文所发展的形式词汇的一次。

这次趋同

四个名字。四套词汇。四个学科。四个年代。动力因闭合。本征形式。自创生。约束闭合。每一个都独立地抓住了同一个结构属性：系统生产出它自身运作所依据的条件。没有一个引用另外几个，也没有一个意识到彼此占据的是同一片概念地界。这不是牛顿与莱布尼茨各自独立发明微积分那种平行发现——它比那更惊人。牛顿和莱布尼茨是在竞相解决同一个问题。这四个传统不是。它们各自在解决不同的问题，却不约而同地抵达了同一个形式结构。

这次趋同，就是这个结构真实存在的证据——它不是一种被投射到互不相干的现象之上的哲学便利。四个严肃的传统，各自带着形式化的装置，落到了同一个答案上。它们描述的是同一头动物，用的是四种不同的语言，而它们谁也不知道其他几个也在同一个房间里。

Cárdenas 这座桥#

Rosen 的框架带着一个硬主张：对动力因闭合的活系统，无法被任何图灵机模拟。如果他是对的，那么 Hernández-Orozco 关于开放式进化不可判定性的结果——那是一个关于可计算动力系统的定理——对 Rosen 所定义的生命就是不相干的。可计算系统那个结果描述的是一类系统；而 Rosen 把生命放在了那一类之外。本文不能既援引那套形式骨架、又援引那个生物学主张，却不对这个张力表态。

这个张力在文献中是活的。Cárdenas、Letelier、Gutierrez、Cornish-Bowden 和 Soto-Andrade 于 2010 年在《Journal of Theoretical Biology》上发表了对 Rosen 结论的明确挑战。他们的论文论证，Rosen 的不可计算性结论并不能从他自己的 (M,R) 系统形式体系中推出，而且“关于 Rosen 用来达成这种闭合的逻辑，一直存在混淆和误解”。¹³ 他们的关键主张是：以 (M,R) 系统结构所形式化的动力因闭合，是可以用 lambda 演算表达的。而 lambda 演算的可表达性就是图灵等价性——这是 Church 在 1936 年确立的结果——因此，任何能写成 lambda 项的 (M,R) 系统，都落在 Hernández-Orozco 定理所覆盖的那个形式模型之内。如果这一点成立，那么生物学意义上的动力因闭合就与可计算性相容，而那个不可判定性结果就适用于形式模型这一层——而不仅仅是靠类比。

本文采取相容论立场。Cárdenas 这一支，是同行评议文献中已发表的反驳，而且它化解这个张力的方式，保住了本文的形式策略。

有了这座桥，三个层次的主张就可以被明确地陈述出来：

第 1 层——形式上的同一（在可计算系统之内）。 Hernández-Orozco 等人 2018 年的结果是一个形式定理：在可计算动力系统中展现出强开放式进化的系统，必定是不可判定的。¹ 按 Cárdenas 的相容论读法，Rosen 的 (M,R) 系统可以用 lambda 演算表达，因而落在这个结果的适用范围之内。在这一层，主张的是形式上的同一——是同一个数学结构，不是类比。

第 2 层——结构上的类比（生物学意义上的进化）。 真实的生物进化是否严格图灵可计算，仍是一个开放问题——Rosen 与 Cárdenas 之争并未了结。在这一层，本文主张的是结构类比：在生态位建构之下的生物进化，共有着那个在形式系统中生成不可判定性的属性。生物生产出它们自身被选择的条件。生态位建构的文献（Laland 等人 2015、Laland 等人 1999）就是这个结构属性在生物学中确有经验实在性的证据。

第 3 层——家族相似（更大的那一类）。 Von Foerster 的本征形式、侯世达的怪圈、哥德尔对角线、克莱尼的 Y 组合子，共有着自我情境化这个属性，但只是作为一种家族相似——每一个实例都展现出它，却没有哪个形式定理能同时横跨它们全部。这是哲学上的收益，不是形式上的内核。

三层，叠在一起。失败模式就是把它们弄混。用第 1 层的严格性去主张第 2 层的东西，是越界。而在生态位建构的文献确实承担了严肃的经验重量时，还把第 2 层的主张当成只是第 3 层的家族相似，则是虚假的谦虚。所谓纪律，就是把这个分层保持清楚。

侯世达选错了例子#

侯世达的怪圈有一处不对称，已经被两篇形式化的批评揭示出来——而这个不对称一旦被看见，方向就反了。

侯世达用来做怪圈范例的，是哥德尔那个自指语句：形式算术中的一个陈述，它对自己说“我在这个系统中不可证”。这个循环跨越了层次——从算术的对象语言，下到关于可证性的元层主张，再回来——产生出一个真正自指的稳定形式。¹⁴ 侯世达正是把这一点通过类比延伸到意识上：大脑的自我模型本身就实现在大脑的神经基质之中，从而造成一次跨层的回返。怪圈解释了“自我”这种体验。

Andrew Westra 2010 年的批评点出了那处薄弱的关节。侯世达自己写道，哥德尔是“精心配制”出那个自指陈述的。¹⁵ Westra 的论证是：这个形式系统的表征能力——它借助哥德尔编码来编码关于自身的陈述的能力——是怪圈的必要条件，但不是充分条件。充分条件是哥德尔本人那次有意的构造行为。形式系统并没有自动产出那个怪圈。是哥德尔设计了它。于是 Westra 的担忧随之而来：如果形式系统并不自动产出怪圈——如果需要一个非常细心的人才造得出一个——那么侯世达从“形式系统自动产出怪圈”推到“大脑自动产出意识”，可能就建立在一个错误的前提之上。

Nenu 2022 年的批评又加了一层：侯世达的框架“留下了太多分量很重、却未被填上的细节”，而且由于这个类比的表现对侯世达未加处理的元数学选择很敏感，它在结构上是不稳定的，从而损害了其解释力上的收益。¹⁵

这些批评削弱的是侯世达的那一步具体动作。它们并不削弱那个结构属性本身。

而这里就是那个反转。如果形式系统中的怪圈需要外部的有意构造——需要一个哥德尔，精心配制——那么，一个不需要任何外部设计者就展现出同一个结构属性的系统，做的事情就更纯粹。生物进化不是被配制出来的。没有人坐下来把复制机制设计成自指的。复制就是那个递归调用——它就是生物繁殖本身​，而不是它像什么。生物的后代继承的不只是这个生物的基因，还有这个生物参与建构的那个生态位，而这个生态位随后又去选择这些后代。这个递归调用自动运行，运行了三十五亿年，不需要任何外部的构造者。

侯世达选了哥德尔，因为哥德尔既漂亮又精确，而且在 1979 年是现成可用的。他手边没有那个经验案例。生态位建构才是他会想要的案例：三十五亿年的自我情境化组织，不需要任何有意的构造者，而那个递归调用，由从未读过任何证明的细胞每二十分钟做一次。

生物学才是更纯粹的实例。侯世达的怪圈是同一个家族中不那么纯粹的成员——它需要一位天才去人工构造出进化自动完成的东西。这个反转不是对侯世达的否定。他是从形式那一侧指认出了这个结构类别。但那个类别里最干净的经验成员，并不是他所指的那一个。

三个反驳，三个回应#

有三条反对路线值得正面交锋，而不是丢进脚注。

再描述反驳（Scott-Phillips 等人 2014）

针对“生态位建构理论是一次理论推进”这一说法，最有力的反驳是再描述反驳，由 Scott-Phillips、Laland、Shuker、Dickins 和 West 在他们 2014 年发表于《Evolution》的对抗式合作论文中精确陈述。怀疑派的立场是：“怀疑者看不出有什么理由认为，NCT 所导向的任何预测与洞见，无法同样从标准进化理论中推导出来。”¹⁶ 等价地说：生态位建构理论在解释上是冗余的。在进化生物学中，用 NCT 来研究或预测任何东西，在逻辑上都不是必需的；传统框架一向就够用。NCT 添加的是词汇和组织上的侧重，而不是新的预测内容。

本文并不反驳这个反驳的核心。递归这个框架主要是一项概念统合上的贡献。它把此前四次命名收拢到同一个结构刻画之下，并把生物进化呈现为其中一个实例——这是一步哲学动作，而再描述反驳说得对：哲学动作并不自动就是预测动作。

不过，这个框架确实生成了两项承诺，而标准的二元框架要么不作出这些承诺，要么只有经过重新表述才能抵达。第一：演化的重大转变，是递归函数上的类型签名改变——是选择所作用的那个单位在性质上不连续的重组，而不仅仅是渐进的累积。Maynard Smith 和 Szathmáry 通过“生物信息被储存与传递的方式发生改变”以及“新的选择单位层级的形成”来指认这些转变。¹⁷ West 和同事确认了那个两步模式：先是合作性群体的形成，随后通过分工与相互依赖转变为一个整合的实体。¹⁷ Bourrat 和同事（2022）把权衡破除事件指认为这些转变的标记——不是原因，而是那种不连续性的签名。¹⁷ 递归框架把这种不连续性变得可读，读成一次类型签名的改变：追踪适应度的那个单位，不是靠渐进累积而移位，而是靠递归调用的一次性质上的重组而移位。

第二：Banzhaf 和同事把开放式进化系统中的新颖性分为三类——变异（模型之内的新颖性）、创新（改变模型的新颖性）和涌现（改变元模型的新颖性）。¹⁷ 这套分类意味着，一个系统在参数空间中的位置，决定了哪一类新颖性占主导。稳定性区制生成变异型新颖性；复杂性区制生成创新型或涌现型新颖性。这是本文从 Banzhaf 框架推出的推论，而不是 Banzhaf 自己陈述的结论——但它是一个逻辑蕴涵，而递归框架让它变得可见，标准框架则没有。

诚实的立场是：这个框架主要是概念统合性的，并且在这个意义上站得住。上面那两项承诺是真实的，而且是二元框架不作出的承诺。

Williams 不对称（Fromhage & Houston 2022）

对“生物—环境不对称”的当代技术辩护，走的是 Fromhage 和 Houston 2022 年发表于《Evolution》的论文，该文把 Lewontin-Williams（不）对称形式化。他们的主张是：“适应总是不对称的；生物适应它们的环境，反之则从不成立。”即便承认因果影响是双向的——即便承认生物会改造环境——由选择驱动的适应性变化，其方向性仍然是不对称的。¹⁸ 标准的进化模型把这一点编码了进去：dO/dt = f(O,E)（生物因应环境而改变），而 dE/dt = g(E)（环境的改变独立于生物的定向适应）。即便因果影响双向流动，这些方程也不是对称的。

本文的回应遵循 Otsuka 的因果图框架：标准微分方程中的这种不对称，是一个建模假设，而不是一项经验发现。¹⁸ 当性状被归属给类型（基因型）时，基因—环境的独立性就被内建进了数学结构，而不是在自然中被发现的。标准进化理论中的生物—环境二元论，反映的是模型的适用条件，而不是生物学的形而上学结构。于是，生态位建构的批评——生物会改造那些作用于自身后代的选择压力——就不是对标准模型的反驳，而是关于“这个模型的适用条件在哪里收紧”的证据。递归框架并不是在 Williams 不对称自己的地盘上与它作战；它是在指认这个不对称主张得以成立的适用条件，并追问那些条件之外还剩下什么。

经验上审慎的怀疑（Charlesworth、Barton & Charlesworth 2017）

Charlesworth、Barton 和 Charlesworth 2017 年发表在《Proceedings of the Royal Society B》上的达尔文评论，代表了经验上审慎的主流进化生物学立场。他们的判断是：“我们对适应性进化机制的理解，不需要任何激进的修订。”¹⁹ 细致的遗传学研究一再表明，跨物种那些看似令人困惑的结果，与新达尔文主义是相容的。至于“由生态位建构驱动的、能带来范式转移的进化”的经验证据——也就是“生态位建构经常产生标准框架无法解释的重大进化模式”这一点的证据——比 EES 拥护者所声称的要弱。

本文不是一篇 EES 的鼓吹文，这里的承认也是真诚的。递归框架的贡献是结构性的——是关于生物进化属于哪一类——而不是关于生态位建构效应在任何给定种群中有多大量级。Laland 与 Charlesworth 之间关于“NC 在经验上是否驱动了重大进化模式”的争论，与“生物生产出它们自身被选择的条件”这个结构性论点是正交的。即便 NC 在大多数谱系中最终被证明只是一股温和的进化力量，这个结构性主张仍然可以为真。

本文承认再描述反驳的分量，在不对称之争上采纳“建模选择”这一表述，并接受那份经验上的审慎。留下来的，是一个结构性主张——生物进化属于一个被命了名的类别——而这三个反驳，没有一个是冲着它去的。

这个框架买到了什么#

三样东西。

第一样，是一个假二分法的坍塌。Lewontin 在《The Triple Helix》中写道：“正如不可能有没有环境的生物，也不可能有没有生物的环境。”²⁰ 这不是神秘主义。这是站在那个递归调用内部所带来的实际后果。主体——生物——与客体——环境——是同一个运作之内的位置角色，而不是彼此分离的本体论范畴。从循环之外看，只有一个过程：生物改造环境，改造选择压力，改造生物。而从循环之内看——进化生物学实际工作的地方就在循环之内——生物与环境的区分，作为一种建模上的便利，仍然有用。这次坍塌是操作层面的，不是本体论层面的。二元论没有被摧毁；它被重新安置了。

这次重新安置，对如何阅读进化记录有一个实际的后果。Van Valen 的红皇后定律（1973）陈述：任何一组生物的有效环境，都以一个随机的恒定速率恶化——因为竞争物种的进化推进，会系统性地移动彼此的选择地形。²¹ 协同进化的动力学是不终止的：没有稳定的终态会被抵达，因为任何谱系的每一次适应，都会移动所有其他谱系的选择压力。亚麻—锈菌系统在经验尺度上展示了这一点。Antonovics、Thrall、Burdon 和 Laine 对来自六个自然种群的 120 个宿主品系和 60 个病原品系所做的交叉接种研究发现，没有证据表明部分抗性会减慢协同进化的动力学；这场军备竞赛仍在继续，而不是走向收敛。²² 这种不终止，映照着开放式进化那个不停机的结果：协同进化系统相互地、递归地构成着自身的选择环境，因而无法停机。

第二样和第三样收益，是这个框架的两项预测——作为预测而非证明来陈述：

第二，演化的重大转变可以被读作递归函数上类型签名的改变。追踪适应度的那个单位发生不连续的重组——从基因到基因组，从细胞到多细胞生物，从个体到真社会性群落。每一次转变，都标志着自然选择所能作用的那类实体发生了一次性质上的改变。这不是渐进的累积；这是函数签名在变。

第三，稳定性与复杂性之别，是一种参数区制效应。处在稳定性区制中的系统，在它既有的组织之内生成新颖性——同一个主题的变奏。处在复杂性区制中的系统，生成的是重组这个组织本身的新颖性——一个不同的主题。一个系统在参数空间中的位置，决定了它产出哪一种新颖性。两者都是自我情境化过程的形式；它们的区别在于，被更新的是这个递归结构的哪一层。

主体与客体不是世界递给我们的范畴。它们是这个循环所指派的位置。走到循环之外，只有一个过程。走进循环之内，这个区分又回来了，而且重新变得有用。二元论没有被摧毁。它被重新安置了。

延伸阅读#

• Rosen, R. (1991). Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life​. Columbia University Press.——动力因闭合与 (M,R) 系统的第一手来源；本文所交锋的那个完整形式论证。多数读者不曾读过 Rosen；这是推荐的第一站。
• Maturana, H.R. & Varela, F.J. (1980). Autopoiesis and Cognition: The Realization of the Living​. D. Reidel.——自创生的奠基文本。本文所引的形式定义即出自此书；该书还把论证从细胞生物学扩展为一套关于自我生产系统的一般理论。
• Moreno, A. & Mossio, M. (2015). Biological Autonomy: A Philosophical and Theoretical Enquiry​. Springer.——约束闭合的专著级展开；四次命名中形式上最严整、时间上最晚近的一次。专业文献用了十年把它吸收进去；跨学科的读者群还没有。
• Cárdenas, M.L., Letelier, J.C., Gutierrez, C., Cornish-Bowden, A., & Soto-Andrade, J. (2010). Closure to efficient causation, computability and artificial life. Journal of Theoretical Biology​, 263(1), 79–92.——那篇搭桥的论文。Rosen 可计算性之争中已发表的相容论立场；可在 hal.science/hal-00564468v1 开放获取。要理解第 1 层的形式策略，这是必读。
• Hofstadter, D.R. (1979). Gödel, Escher, Bach: An Eternal Golden Braid​. Basic Books.——对于被 GEB 塑造过的读者，这是起点；本文走出了这本书，但对一般读者而言，它仍然是关于怪圈最丰富的一次探索。
• Dawkins, R. (1982). The Extended Phenotype: The Long Reach of the Gene​. Oxford University Press. 以及 Williams, G.C. (1966). Adaptation and Natural Selection​. Princeton University Press.——基因中心视角与生物—环境不对称在历史上的经典表述。本文直接交锋的是当代的技术辩护（Fromhage & Houston 2022），但这两本书才是目标读者更可能读过的、作为文化坐标的版本。

Evolution Is Recursion — Four Names for the Same Loop

The thing that should not work#

A bacterium divides every twenty minutes and has been doing so, in some lineage, for three and a half billion years. That is stability at a scale that humbles geology. At the same time, the line that began with that bacterium produced eyes, nervous systems, flight, language, and a formal proof of its own incompleteness. That is complexity at a scale that humbles any search algorithm.

The puzzle is not that stability and complexity each exist. The puzzle is that the same mechanism is supposed to explain both simultaneously. Natural selection finds optima — it is, structurally, a hill-climbing procedure. Hill-climbers reach peaks and stop. Yet the organisms that natural selection has been climbing on have not stopped. The record shows no terminus, no convergence on a single solution, no stabilization at anything like a final fitness peak.¹ Stability and unbounded novelty are not the expected outputs of the same process. One of them should break the other.

Something else is running underneath. The empirical sign is niche construction — the systematic way organisms modify the selective environments that act on their own descendants.² When an organism alters not just its local habitat but the conditions under which its offspring and competitors are selected, the fitness landscape is no longer a fixed terrain. It becomes a surface the walkers are generating as they walk it. Not hill-climbing. Something with a different formal structure.

What kind of process generates that combination — radical stability and unbounded novelty from the same engine? Not selection alone. Selection finds peaks on landscapes, and the unbounded part denies the landscape is fixed. Something else is running underneath. This article argues that the something else has a name — four of them, in fact, assigned independently by four research traditions that did not know they were naming the same thing.

What biologists were forced to admit#

Beavers are the textbook case. Twelve years after a colony moves into a degraded agricultural stream, mean plant species richness rises by roughly 46% per plot, and the cumulative number of species recorded increases by 148%.³ The pond the beavers engineer stores approximately 100 tonnes of sediment and 16 tonnes of carbon per 1.8 hectares of ponded extent.⁴ The beaver does not merely live in its environment. It constitutes a substantial fraction of the selective environment acting on subsequent generations of beavers, on the insects and fish and birds whose lineages will also pass through the pond ecosystem, and — crucially — on the beavers' own descendants, who will inherit not the original stream but the engineered wetland the colony created.

Not coincidence or edge case. This is the form that niche construction takes at the ecological time scale.

The formal definition, from Laland and colleagues' 2015 Extended Evolutionary Synthesis paper, runs: niche construction is "the process whereby the metabolism, activities and choices of organisms modify or stabilize environmental states, and thereby affect selection acting on themselves and other species."² The critical clause is "thereby affect selection acting on themselves" — the organisms that construct the niche are also the organisms selected within it. The selection pressure is not external to the organism; it is partly constituted by the organism's own prior activity. Formal evolutionary models confirm that this reciprocal causation has consequences the standard model does not predict: niche construction can drive otherwise deleterious alleles to fixation, support stable polymorphisms where none would be expected, and eliminate polymorphisms that would otherwise persist.⁵

The Great Oxidation Event is the same process at geological scale. According to the ASM Microbiology review's characterization, cyanobacteria evolved approximately 2.7 billion years ago and proceeded to transform Earth's atmosphere through oxygenic photosynthesis, producing the GOE around 2.4–2.1 billion years ago — a shift that ranks among the most consequential biologically-induced geochemical transformations in Earth's history.⁶ The organisms that drove the event did not survive into the oxygen-rich world they made. But every aerobic organism since then has lived inside a selective environment whose chemistry was produced by prior biological activity. The constructors' descendants — all of them — inhabit a world their ancestors built.

The pattern is general. From beaver dams to oxygenic photosynthesis, organisms do not merely inhabit their environments — they constitute the conditions of their own selection. The standard evolutionary frame treats this as a correction to the model. It is more than that. The recursion is not a wrinkle in the picture. It is a structural feature of the process itself.

Self-contextualizing, not feedback#

Feedback loops have fixed rules. A thermostat does not redesign the temperature target it is tracking — the setpoint is set from outside the loop. The output (measured temperature) recycles as input, but the rules of recycling — what constitutes "too cold," what triggers the furnace — are external to the loop and unaffected by it. Outputs modify inputs. Rules stay fixed.

A self-contextualizing system is something different. Its outputs modify not just the inputs but the rules under which subsequent inputs are processed. The constraints, the boundary conditions, the selection pressures — these emerge from the operation itself, not from an external configuration that the operation leaves untouched. The formal class that captures this is the fixed-point structure: a system that operates on a description of itself, producing a result that then becomes the context for the next operation.

In formal logic, the engine of this structure is Gödel's diagonal lemma. For any sufficiently strong formal system F and any formula A(x) with one free variable, there exists a sentence D such that F ⊢ D ↔ A(⌜D⌝) — D is provably equivalent to the formula A applied to D's own Gödel number.⁷ The sentence contains a description of itself (encoded as a number), and asserts something about that description. When A is "is not provable in F," the resulting D says "I am not provable in F" — the Gödel sentence, which makes the incompleteness result land. The mechanism is substitution of a formula's own index into itself. The system operates on a description of its own operation, and the result constrains subsequent steps.

In computation, Kleene's second recursion theorem states: for any partial recursive function Q(x,y), there exists an index p such that φₚ ≃ λy.Q(p,y) — a program that behaves as if applying Q with its own index as the first argument.⁸ More informally: programs can carry descriptions of themselves and act on those descriptions. The Y combinator in lambda calculus implements this as a fixed point: it takes a functional F and returns a value x such that F(x) = x, enabling recursive behavior from a non-recursive specification. The computational instance of self-contextualizing: a function that generates its own operating context by finding its own fixed point.

These are formal results about abstract systems — about computable dynamical systems and formal languages. Within that formal model, the Hernández-Orozco et al. 2018 theorem is the result that closes the argument: exhibiting strong open-ended evolution — stable growth of algorithmic complexity over time — is formally equivalent to undecidability in computable dynamical systems.¹ Decidable systems face absolute limits on stable complexity growth. A system whose complexity grows without bound must be undecidable. The scope of this result is the stated formal model, not biological evolution directly. How it bears on biology depends on a bridge built below, in the Cárdenas argument.

Four names for the same thing#

Four research traditions, working in different vocabularies, in different decades, on different problems, have already named what the previous section sharpened. None cited the others as occupying the same conceptual ground. Each looked at the same animal and described a different part of its anatomy.

Rosen — closure to efficient causation (relational biology, 1985–1991)

Robert Rosen's central thesis in Life Itself (1991) is a formal definition of the living: "a material system is an organism if and only if it is closed to efficient causation."⁹ In Aristotelian terms, efficient causes are the agents that bring about change — the catalysts, the enzymes, the processes that maintain organization. Rosen's claim: in a living system, those efficient causes are themselves produced within the system. The enzyme that catalyzes a reaction is produced by another reaction that the first reaction maintains. The formal structure is the (M,R)-system: M designates metabolic subsystems, R designates repair subsystems that regenerate M. The system is self-entailing — all efficient causes fall within an impredicative cycle. No external input assigns the catalysts. They emerge from the cycling itself.

This is the self-contextualizing structure in relational biology. The operating conditions — the catalysts, the enzymes, the efficient causes — are produced by the operation they enable. Rosen made one additional contested claim: this structure cannot be simulated by any Turing machine. That claim sets up a tension with the formal results developed above — a tension the Cárdenas argument resolves below.

Von Foerster — eigenforms and operational closure (second-order cybernetics, 1970s)

Heinz von Foerster approached the problem from perception, not biochemistry. Working in second-order cybernetics — what he described, from 1974, as the "cybernetics of observing systems," systems that include their own observers — he asked: what is a stable object? His answer: "objects are tokens for eigenbehaviors." Stable objects in perception are the fixed-point attractors of recursive processes of observation. An eigenform is the value e such that F(e) = e — the invariant of a recursive operator applied iteratively.¹⁰ Louis Kauffman formalized this mathematically in a 2003 paper, demonstrating that if F is the operation "enclose in a box," iterating F on any initial configuration produces, in the limit, a form that satisfies X = F(X) — a self-referential stable form that the operation produces and that the operation then leaves unchanged.

The structural connection to the formal vocabulary developed above is direct. F(e) = e is the same fixed-point structure as the Gödel diagonal lemma and the Kleene Y combinator. Von Foerster named it in the cybernetics domain at least a decade before Rosen's Life Itself appeared. The eigenform tradition is the earliest of the four namings.

Maturana and Varela — autopoiesis (1980)

Maturana and Varela came at it from the cell. Their formal definition of autopoiesis, from Autopoiesis and Cognition (1980), describes a living system as "a network of processes of production (transformation and destruction) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in the space in which they (the components) exist by specifying the topological domain of its realization as such a network."¹¹

The boundary — the membrane — is itself produced by the metabolic network it encloses. The network produces the boundary, and the boundary is what defines "inside" vs. "outside," i.e., what counts as part of the network. The operating conditions (the boundary, the topology, the network identity) are constituted by the operation itself. The system does not occupy a pre-given domain; it produces the domain as it operates. This is the self-contextualizing structure at the cellular scale — the most concrete of the four namings.

Mossio and Moreno — constraint closure (2010)

Mossio and Moreno arrived last — and sharpest. Their 2010 paper, extended in Biological Autonomy (2015), offers the most formally precise of the four namings. A system, they write, is organisationally closed "if it [is] constituted by a set of structures C₁…Cₙ acting as constraints such that, for each constraint Cᵢ, (at least some of) the boundary conditions required for its maintenance are determined by the immediate action of another constraint Cⱼ, whose maintenance depends in turn on Cᵢ as an immediate constraint."¹² Each constraint depends on, and maintains, at least one other constraint in the network. The canonical instance: enzymatically-closed cellular metabolism, where enzymes catalyze the reactions that produce other enzymes. The operating conditions are the constraint network; the constraint network is maintained by the operation it governs.

This is stricter than autopoiesis alone. Maturana-Varela say the system produces its components; Mossio-Moreno specify that the system produces the constraints under which its components operate — the rules governing the operation, not just the parts that instantiate them. This is the closest of the four namings to the formal vocabulary developed above.

The convergence

Four names. Four vocabularies. Four disciplines. Four decades. Closure to efficient causation. Eigenforms. Autopoiesis. Constraint closure. Each independently captures the same structural property: the system produces the conditions under which it operates. None cited the others as occupying the same conceptual territory. This is not parallel discovery in the way that Newton and Leibniz independently discovered calculus — it is more striking. Newton and Leibniz were racing to solve the same problem. These four traditions were not. They were each solving different problems and arriving, unbidden, at the same formal structure.

That convergence is the evidence that the structure is real — not a philosophical convenience projected onto disparate phenomena. Four serious traditions, each with formal apparatus, landed on the same answer. They were all describing the same animal, in four different languages, and none of them knew the others were in the room.

The Cárdenas bridge#

Rosen's framework comes with a hard claim: living systems closed to efficient causation cannot be simulated by any Turing machine. If he is right, then the Hernández-Orozco OEE undecidability result — which is a theorem about computable dynamical systems — is irrelevant to biology as Rosen defined it. The computable-systems result describes a class of systems; Rosen puts life outside that class. The article cannot invoke both the formal backbone and the biological claim without taking a position on this tension.

The tension is live in the literature. Cárdenas, Letelier, Gutierrez, Cornish-Bowden, and Soto-Andrade published the explicit challenge to Rosen's conclusion in a 2010 paper in the Journal of Theoretical Biology​. Their paper argues that Rosen's non-computability conclusion does not follow from his (M,R)-system formalism itself, and that "there has been confusion and misunderstanding about the logic Rosen used to achieve this closure."¹³ Their key claim: closure to efficient causation, as formalized in the (M,R)-system structure, is expressible in lambda-calculus. Lambda-calculus expressibility is Turing-equivalence — a result Church established in 1936 — so any (M,R)-system that can be written as a lambda-term sits inside the formal model the Hernández-Orozco theorem covers. If that is correct, biological closure to efficient causation is computability-compatible, and the undecidability result applies at the level of the formal model — not merely by analogy.

This article takes the compatibilist position. The Cárdenas line is the published rebuttal in the peer-reviewed literature, and it resolves the tension in a way that preserves the article's formal strategy.

With the bridge in place, three levels of claim can be stated explicitly:

Level 1 — Formal identity (within computable systems). The Hernández-Orozco et al. 2018 result is a formal theorem: systems exhibiting strong open-ended evolution in computable dynamical systems must be undecidable.¹ Rosen's (M,R)-systems, on the Cárdenas compatibilist reading, are expressible in lambda-calculus and fall within the scope of this result. At this level, the claim is formal identity — the same mathematical structure, not analogy.

Level 2 — Structural analogy (biological evolution). Whether actual biological evolution is strictly Turing-computable remains an open question — the Rosen-Cárdenas debate is not settled. At this level, the article claims structural analogy: biological evolution under niche construction shares the property that generates undecidability in formal systems. Organisms produce the conditions of their own selection. The niche construction literature (Laland et al. 2015, Laland et al. 1999) is the evidence that this structural property is empirically real in biology.

Level 3 — Family resemblance (the broader class). Von Foerster's eigenforms, Hofstadter's strange loops, the Gödel diagonal, and the Kleene Y combinator share the self-contextualizing property as a family resemblance — each instance exhibits it, but no formal theorem spans all of them simultaneously. This is the philosophical payoff, not the formal core.

Three levels, stacked. The failure mode is confusing them. Claiming Level 1 rigor for Level 2 claims is overreach. Treating Level 2 claims as merely Level 3 family resemblance is false modesty when the niche construction literature is doing serious empirical lifting. The discipline is holding the stratification clear.

Hofstadter chose the wrong example#

Hofstadter's strange loop has an asymmetry that two formal critiques have surfaced — and the asymmetry, once seen, runs the wrong way.

Hofstadter's paradigm instance of a strange loop is Gödel's self-referential sentence: a statement in formal arithmetic that says, of itself, "I am not provable in this system." The loop crosses levels — from the object-language of arithmetic down to the meta-level claim about provability, and back — producing a genuine self-referential stable form.¹⁴ This is what Hofstadter extends, by analogy, to consciousness: the brain's self-model is itself implemented in the brain's neural substrate, creating a level-crossing return. Strange loops explain the experience of selfhood.

Andrew Westra's 2010 critique identifies the weak joint. Hofstadter himself writes that Gödel "carefully concocted" the self-referential statement.¹⁵ Westra's argument: the representational power of the formal system — its ability to encode statements about itself using Gödel numbering — is a necessary condition for the strange loop but not a sufficient one. The sufficient condition was Gödel's own intentional act of construction. The formal system did not automatically produce the strange loop. Gödel designed it. Westra's worry follows: if formal systems don't produce strange loops automatically — if a very careful person had to produce one — then Hofstadter's inference from "formal systems automatically produce strange loops" to "brains automatically produce consciousness" may rest on a false premise.

Nenu's 2022 critique adds a further layer: Hofstadter's framework "leaves too many weighty details left unfilled" and, because the analogy's behavior is sensitive to meta-mathematical choices Hofstadter does not address, it is structurally unstable in ways that impair the explanatory payoff.¹⁵

These critiques impair Hofstadter's specific move. They do not impair the structural property itself.

Here is the inversion. If strange loops in formal systems require external intentional construction — a Gödel, carefully concocting — then a system that exhibits the same structural property without any external designer is doing something purer. Biological evolution is not concocted. No one sat down and designed the replication mechanism to be self-referential. Replication is the recursive call — it is what biological reproduction is​, not what it resembles​. The organism's descendants inherit not just the organism's genes but the niche the organism helped construct, which then selects those descendants. The recursive call runs automatically, for three and a half billion years, with no external constructor required.

Hofstadter chose Gödel because Gödel was beautiful and precise and available in 1979. He did not have the empirical case in front of him. Niche construction is the case he would have wanted: three and a half billion years of self-contextualizing organization, no intentional constructor required, the recursive call made every twenty minutes by cells that have never read a proof.

Biology is the purer instance. Hofstadter's strange loop is a less pure member of the same family — one that needed a genius to construct artificially what evolution does automatically. The inversion is not a dismissal of Hofstadter. He identified the structural class from the formal side. But the cleanest empirical member of that class was not the one he pointed to.

Three counterarguments, three responses#

Three lines of opposition deserve direct engagement, not footnotes.

The redescription objection (Scott-Phillips et al. 2014)

The strongest objection to niche construction theory as a theoretical advance is the redescription objection, stated with precision by Scott-Phillips, Laland, Shuker, Dickins, and West in their 2014 adversarial collaboration in Evolution​. The skeptics' position: "the skeptics see no reason to think that whatever predictions and insights NCT leads to, the same predictions could not be derived from standard evolutionary theory."¹⁶ Equivalently: niche construction theory is explanatorily redundant. It is not logically necessary to use NCT to study or predict anything in evolutionary biology; the conventional framework was always sufficient. NCT adds vocabulary and organizational emphasis, but no novel predictive content.

The article does not dispute the core of this objection. The recursion frame is primarily a conceptual-unificatory contribution. It gathers four prior namings under a single structural characterization and shows biological evolution as an instance — that is a philosophical move, and the redescription objection is right that philosophical moves are not automatically predictive moves.

The frame does, however, generate two commitments that the standard dualist frame either does not make or reaches only by reframing. First: major evolutionary transitions are type-signature changes in the recursive function — qualitatively discontinuous reorganizations of the unit on which selection acts, not merely gradual accumulation. Maynard Smith and Szathmáry identify transitions by a change in the way biological information is stored and transmitted and the formation of new levels of units of selection.¹⁷ West and colleagues confirm the two-step pattern: cooperative group formation followed by transformation into an integrated entity through division of labor and mutual dependence.¹⁷ Bourrat and colleagues (2022) identify tradeoff-breaking events as a marker of these transitions — not the cause, but the signature of the discontinuity.¹⁷ The recursion frame makes this discontinuity legible as a type-signature change: the fitness-tracking unit shifts not by gradual accumulation but by a qualitative reorganization of the recursive call.

Second: Banzhaf and colleagues classify novelty in open-ended evolving systems into three types — variation (novelty within a model), innovation (novelty that changes the model), and emergence (novelty that changes the meta-model).¹⁷ This taxonomy implies that the position of a system in parameter space determines which type of novelty dominates. A stability regime generates variation-type novelty; a complexity regime generates innovation or emergence-type novelty. This is the article's inference from the Banzhaf framework, not Banzhaf's stated conclusion — but it is a logical implication the recursion frame makes visible where the standard frame does not.

The honest position: the frame is mostly conceptual-unificatory, and defensible on those terms. The two commitments above are genuine, and they are commitments the dualist frame does not make.

The Williams asymmetry (Fromhage & Houston 2022)

The contemporary technical defense of the organism-environment asymmetry runs through Fromhage and Houston's 2022 paper in Evolution​, which formalizes the Lewontin-Williams (a)symmetry. Their claim: "adaptation is always asymmetrical; organisms adapt to their environment, never vice versa." Even granting bidirectional causal influence — granting that organisms modify environments — the directionality of selection-driven adaptive change is asymmetric.¹⁸ The standard evolutionary model encodes this: dO/dt = f(O,E) (organisms change in response to environments), while dE/dt = g(E) (environments change independently of organisms' directed adaptation). The equations are not symmetric, even when causal influence flows both ways.

The article's response follows Otsuka's causal-graph framework: the asymmetry in the standard differential equations is a modeling assumption, not an empirical finding.¹⁸ When traits are ascribed to types (genotypes), the gene-environment independence is built into the mathematical structure, not discovered in nature. The organism-environment dualism in standard evolutionary theory reflects the model's scope conditions, not the metaphysical structure of biology. The niche construction critique — that organisms modify the selection pressures acting on their own descendants — is then not a refutation of the standard model but evidence of where the model's scope conditions bind. The recursion frame is not fighting Williams' asymmetry on its own terms; it is identifying the scope conditions within which the asymmetry claim holds and asking what is left outside them.

The empirically-cautious skepticism (Charlesworth, Barton & Charlesworth 2017)

Charlesworth, Barton, and Charlesworth's 2017 Darwin Review in the Proceedings of the Royal Society B represents the empirically-cautious mainstream evolutionary biology position. Their judgment: "no radical revision of our understanding of the mechanism of adaptive evolution is needed."¹⁹ Careful genetic studies have repeatedly shown that apparently puzzling results across organisms are consistent with neo-Darwinism. The empirical evidence for paradigm-shifting niche-construction-driven evolution — the evidence that niche construction regularly produces major evolutionary patterns not explainable by the standard framework — is weaker than EES advocates claim.

This article is not an EES advocacy piece, and the acknowledgment here is genuine. The recursion frame's contribution is structural — about which class biological evolution belongs to — and not about the magnitude of niche construction effects in any given population. The debate between Laland and Charlesworth about whether NC drives major evolutionary patterns empirically is orthogonal to the structural point that organisms produce the conditions of their own selection. The structural claim can be true even if NC turns out to be a modest evolutionary force in most lineages.

The article concedes the redescription objection's force, defers to the modeling-choice framing for the asymmetry debate, and grants the empirical caution. What survives is a structural claim — that biological evolution belongs to a named class — which none of the three objections targets.

What the frame buys#

Three things.

The first is the collapse of a false dichotomy. Lewontin wrote in The Triple Helix that "just as there can be no organism without an environment, so there can be no environment without an organism."²⁰ This is not mysticism. It is the practical consequence of standing inside the recursive call. Subject — organism — and object — environment — are positional roles within the same operation, not separate ontological categories. From outside the loop there is one process: organisms modifying environments modifying selection pressures modifying organisms. From inside the loop — which is where evolutionary biology actually works — the distinction between organism and environment remains useful as a modeling convenience. The collapse is operational, not ontological. The dualism is not destroyed; it is relocated.

This relocation has a practical consequence for reading the evolutionary record. Van Valen's Red Queen law (1973) states that the effective environment of any group of organisms deteriorates at a stochastic constant rate — because the evolutionary advances of competing species systematically shift each other's selection landscape.²¹ Coevolutionary dynamics are non-terminating: no stable end state is reached, because each adaptation by any lineage shifts the selection pressures for all others. The flax-rust system illustrates this at the empirical scale. Antonovics, Thrall, Burdon, and Laine's cross-inoculation study of 120 host lines and 60 pathogen lines from six natural populations found no evidence that partial resistance slows coevolutionary dynamics; the arms race continues rather than converging.²² The non-termination mirrors the OEE non-halting result: the coevolutionary system, constituting its own selection environment reciprocally and recursively, cannot halt.

The second and third purchases are the frame's two predictions, stated as predictions rather than proofs:

Second, major evolutionary transitions are legible as type-signature changes in the recursive function. The fitness-tracking unit reorganizes discontinuously — from gene to genome, from cell to multicellular organism, from individual to eusocial colony. Each transition marks a qualitative change in the kind of entity natural selection can act upon. This is not gradual accumulation; it is the function signature changing.

Third, stability versus complexity is a parameter-regime effect. A system in the stability regime generates novelty within its existing organization — variations on a theme. A system in the complexity regime generates novelty that reorganizes the organization itself — a different theme. Where in parameter space a system sits determines which kind of novelty it produces. Both are forms of self-contextualizing process; they differ in which tier of the recursive structure is being updated.

Subject and object are not categories the world hands us. They are positions the loop assigns. Step outside the loop and there is one process. Step inside and the distinction returns, useful again. The dualism is not destroyed. It is relocated.

References#

1. Hernández-Orozco, S., Hernández-Quiroz, F., & Zenil, H. (2018). Undecidability and Irreducibility Conditions for Open-Ended Evolution and Emergence. Artificial Life​, 24(1), 56–70. DOI: 10.1162/artl_a_00254. ↩︎ ↩︎ ↩︎

2. Laland, K.N., Uller, T., Feldman, M.W., Sterelny, K., Müller, G.B., Moczek, A., Jablonka, E., & Odling-Smee, J. (2015). The extended evolutionary synthesis: its structure, assumptions and predictions. Proceedings of the Royal Society B: Biological Sciences​, 282(1813), 20151019. DOI: 10.1098/rspb.2015.1019. ↩︎ ↩︎

3. Law, A., Gaywood, M.J., Jones, K.C., Ramsay, P., & Willby, N.J. (2017). Using ecosystem engineers as tools in habitat restoration and rewilding: beaver and wetlands. Science of the Total Environment​, 605–606, 1021–1030. ↩︎

4. Brazier, R.E., Puttock, A., Graham, H.A., Auster, R.E., Davies, K.H., & Brown, C.M.L. (2020). Beaver: Nature's ecosystem engineers. WIREs Water​, 8(1), e1494. DOI: 10.1002/wat2.1494. ↩︎

5. Laland, K.N., Odling-Smee, F.J., & Feldman, M.W. (1999). Evolutionary consequences of niche construction and their implications for ecology. Proceedings of the National Academy of Sciences​, 96(18), 10242–10247. DOI: 10.1073/pnas.96.18.10242. ↩︎

6. ASM Microbiology. (2022). The Great Oxidation Event: How Cyanobacteria Changed Life. ASM.org. https://asm.org/articles/2022/february/the-great-oxidation-event-how-cyanobacteria-change ↩︎

7. Raatikainen, P. (2025). Gödel's Incompleteness Theorems — Supplement: The Diagonalization Lemma. Stanford Encyclopedia of Philosophy​. https://plato.stanford.edu/entries/goedel-incompleteness/sup2.html ↩︎

8. Kleene, S.C. (1952). Introduction to Metamathematics​. North-Holland Publishing. (Theorems first proved 1938.) See also: Kleene's recursion theorem. Wikipedia​. https://en.wikipedia.org/wiki/Kleene%27s_recursion_theorem ↩︎

9. Rosen, R. (1991). Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life​. Columbia University Press. ↩︎

10. Kauffman, L.H. (2003). Eigenforms — Objects as Tokens for Eigenbehaviors. Cybernetics and Human Knowing​, 10(3–4), 73–90. http://homepages.math.uic.edu/~kauffman/Eigen.pdf. See also: von Foerster, H. (1976). Objects: Tokens for (Eigen-)Behaviors. ASC Cybernetics Forum​, 8(3–4), 91–96. Reprinted in von Foerster, H. (2003). Understanding Understanding: Essays on Cybernetics and Cognition​, Springer, pp. 261–271. ↩︎

11. Maturana, H.R. & Varela, F.J. (1980). Autopoiesis and Cognition: The Realization of the Living​. D. Reidel Publishing Company, Dordrecht. [library-only; formal definition confirmed via multiple secondary sources including Springer catalog and independent academic reviews] ↩︎

12. Mossio, M. & Moreno, A. (2010). Organisational closure in biological organisms. History and Philosophy of the Life Sciences​, 32(2–3), 269–288. PMID: 21162371. The quoted definition appears in §3 of the paper; see also Moreno, A. & Mossio, M. (2015). Biological Autonomy: A Philosophical and Theoretical Enquiry​. Springer. ↩︎

13. Cárdenas, M.L., Letelier, J.C., Gutierrez, C., Cornish-Bowden, A., & Soto-Andrade, J. (2010). Closure to efficient causation, computability and artificial life. Journal of Theoretical Biology​, 263(1), 79–92. DOI: 10.1016/j.jtbi.2009.11.010. PubMed: 19962389. ↩︎

14. Hofstadter, D.R. (1979). Gödel, Escher, Bach: An Eternal Golden Braid​. Basic Books. Hofstadter, D.R. (2007). I Am a Strange Loop​. Basic Books. ↩︎

15. Westra, A. (2010). Gödel, Hofstadter, & the Self: A Critical Review of Douglas Hofstadter's I Am a Strange Loop​. Numéro Cinq​, July 1, 2010. https://numerocinqmagazine.com/2010/07/01/godel-hofstadter-the-self-an-essay-by-adam-westra/. Nenu, T. (2022). Douglas Hofstadter's Gödelian Philosophy of Mind. Journal of Artificial Intelligence and Consciousness​, 9(2), 241–266. DOI: 10.1142/S2705078522500011. ↩︎ ↩︎

16. Scott-Phillips, T.C., Laland, K.N., Shuker, D.M., Dickins, T.E., & West, S.A. (2014). The niche construction perspective: a critical appraisal. Evolution​, 68(5), 1231–1243. PMC: 4261998. ↩︎

17. Maynard Smith, J. & Szathmáry, E. (1995). The Major Transitions in Evolution​. Oxford University Press / W.H. Freeman. West, S.A., Fisher, R.M., Gardner, A., & Kiers, E.T. (2015). Major evolutionary transitions in individuality. PNAS​, 112(33), 10112–10119. PMC: 4547252. Bourrat, P., Doulcier, G., Rose, C.J., Rainey, P.B., & Hammerschmidt, K. (2022). Tradeoff breaking as a model of evolutionary transitions in individuality and limits of the fitness-decoupling metaphor. eLife​, 11, e73715. DOI: 10.7554/eLife.73715. Banzhaf, W., et al. (2016). Defining and simulating open-ended novelty: requirements, guidelines, and challenges. Theory in Biosciences​, 135(3), 131–161. PubMed: 27194550. ↩︎ ↩︎ ↩︎ ↩︎

18. Fromhage, L. & Houston, A.I. (2022). Biological adaptation in light of the Lewontin-Williams (a)symmetry. Evolution​, 76(7), 1619–1624. PMC: 9544502. DOI: 10.1111/evo.14502. Otsuka, J. (2019). The Role of Mathematics in Evolutionary Theory​. Cambridge University Press. ↩︎ ↩︎

19. Charlesworth, D., Barton, N.H., & Charlesworth, B. (2017). The sources of adaptive variation. Proceedings of the Royal Society B​, 284, 20162864. PubMed: 28566483. DOI: 10.1098/rspb.2016.2864. ↩︎

20. Lewontin, R.C. (2000). The Triple Helix: Gene, Organism, and Environment​. Harvard University Press. [library-only; near-quote confirmed via PMC1083785 review article and multiple independent secondary sources] ↩︎

21. Van Valen, L. (1973). A new evolutionary law. Evolutionary Theory​, 1(1), 1–30. ↩︎

22. Antonovics, J., Thrall, P.H., Burdon, J.J., & Laine, A.L. (2011). Partial resistance in the Linum–Melampsora host-pathogen system: does partial resistance make the Red Queen run slower? Evolution​, 65(2), 512–522. PMID: 21029078. ↩︎

Further Reading#

• Rosen, R. (1991). Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life​. Columbia University Press. — The primary source for closure to efficient causation and (M,R)-systems; the full formal argument the article engages with. Most readers will not have encountered Rosen; this is the recommended first follow-up.
• Maturana, H.R. & Varela, F.J. (1980). Autopoiesis and Cognition: The Realization of the Living​. D. Reidel. — The foundational autopoiesis text. The formal definition the article quotes derives from this source; the book extends the argument to a general theory of self-producing systems beyond cell biology.
• Moreno, A. & Mossio, M. (2015). Biological Autonomy: A Philosophical and Theoretical Enquiry​. Springer. — The book-length development of constraint closure; the most formal and most recent of the four prior namings. A decade of specialist literature has absorbed it; a cross-disciplinary audience has not.
• Cárdenas, M.L., Letelier, J.C., Gutierrez, C., Cornish-Bowden, A., & Soto-Andrade, J. (2010). Closure to efficient causation, computability and artificial life. Journal of Theoretical Biology​, 263(1), 79–92. — The bridge paper. The published compatibilist position in the Rosen computability debate; available open access at hal.science/hal-00564468v1. Required reading for the formal strategy at Level 1.
• Hofstadter, D.R. (1979). Gödel, Escher, Bach: An Eternal Golden Braid​. Basic Books. — The starting point for the GEB-shaped reader; the article moves beyond this text, but it remains the richest exploration of strange loops for a general audience.
• Dawkins, R. (1982). The Extended Phenotype: The Long Reach of the Gene​. Oxford University Press. Williams, G.C. (1966). Adaptation and Natural Selection​. Princeton University Press. — The historical canonical statement of the gene-centered view and organism-environment asymmetry. The article engages the contemporary technical defense (Fromhage & Houston 2022) directly, but these texts are the cultural-touchstone versions the target audience is likely to have read.