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第128行： − Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of memes). In his book The Blind Watchmaker, Dawkins introduced the term "hierarchical reductionism" to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of hard drives, processors, and memory, but not on the level of logic gates, or on the even simpler level of electrons in a semiconductor medium. − 一些强还原论者认为，行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支（参见理查德·道金斯（Richard Dawkins）的模因概念）。在他的《盲眼钟表匠》一书中，道金斯引入了“层次还原论”来描述这样一种观点，即复杂系统可以用组织的层次来描述，而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例，从硬盘、处理器和内存的角度阐释了层次还原论，而不是基于逻辑门的层次，或者更简单的半导体介质中的电子层次。 + + − Ontological reductionism takes two forms: '''token ontological reductionism''' and '''type ontological reductionism'''.{{Citation needed|date=July 2020}} − 本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。 − Quantum Holonomy theory is a theory of the lowest possible reduction. − 量子整体论是一种最低可能的还原理论。 第149行：
第145行： − Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist Robert Ulanowicz says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) information theory as a framework to study propensities in natural systems. Ulanowicz attributes these criticisms of reductionism to the philosopher Karl Popper and biologist Robert Rosen. − − 其他人认为，不恰当使用还原论限制了我们对复杂系统的理解。特别是，生态学家罗伯特·尤兰维奇（Robert Ulanowicz）说，科学必须发展技术来研究大规模组织影响小规模组织的方式，以及反馈循环在给定层次上创造结构的方式，而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架。乌兰诺维茨（Ulanowicz）把这些还原论的批评归因于哲学家卡尔 · 波普尔（ Karl Popper ）和生物学家罗伯特 · 罗森（Robert Rosen）。 第158行：
第151行： − − Stuart Kauffman has argued that complex systems theory and phenomena such as emergence pose limits to reductionism. Emergence is especially relevant when systems exhibit historicity. Emergence is strongly related to nonlinearity. The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater complexity, including living cells, neural networks, ecosystems, society, and other systems formed from assemblies of large numbers of diverse components linked by multiple feedback loops. − − 斯图尔特 · 考夫曼（Stuart Kauffman）认为复杂系统理论和涌现现象对还原论构成了限制。当系统表现出历史性时，涌现尤为重要。涌现与非线性密切相关。还原论应用的局限性在更复杂的组织层次上尤其明显，包括活细胞、神经网络、生态系统、社会，以及由多个反馈回路连接的大量不同组成部分组成的其他系统。 − 第169行：
第157行： − Nobel laureate Philip Warren Anderson used the idea that symmetry breaking is an example of an emergent phenomenon in his 1972 Science paper "More is different" to make an argument about the limitations of reductionism. One observation he made was that the sciences can be arranged roughly in a linear hierarchy—particle physics, solid state physics, chemistry, molecular biology, cellular biology, physiology, psychology, social sciences—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry." − − 诺贝尔经济学奖获得者菲利普·沃伦·安德森（Philip Warren Anderson）在他1972年发表在《科学》（Science）杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性。他观察到，科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而，这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段，全新的法则、概念和概括都是必要的，需要灵感和创造力，就像前一个阶段一样。心理学不是应用生物学，生物学也不是应用化学。” 第177行：
第162行： − Disciplines such as cybernetics and systems theory imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism. − − 诸如控制论和系统论这样的学科隐含着非还原论，有时达到了用更高层次的现象来解释特定层次上的现象的程度，在某种意义上，这是还原论的对立面。 第188行：
第170行： − In mathematics, reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually axiomatic set theory. Ernst Zermelo was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical axioms by their usefulness in common practice can potentially weaken Zermelo's reductionist claim. − − 在数学中，还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学，而对于现代数学来说，这个基础通常是公理化集合论。策梅洛（Ernst Zermelo）是这种观点的主要倡导者之一，他也对公理化集合论做出了许多发展。有人认为，用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法，可能会削弱泽梅洛的还原论主张。 − − Jouko Väänänen has argued for second-order logic as a foundation for mathematics instead of set theory, whereas others have argued for category theory as a foundation for certain aspects of mathematics. − − Jouko Väänänen认为二阶逻辑是数学的基础，而不是集合论，而其他人则认为范畴论是数学某些方面的基础。 第204行：
第179行： − The incompleteness theorems of Kurt Gödel, published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics. Any such foundation would have to include axioms powerful enough to describe the arithmetic of the natural numbers (a subset of all mathematics). Yet Gödel proved that, for any consistent recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) true propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally undecidable propositions. For example, the continuum hypothesis is undecidable in the Zermelo–Fraenkel set theory as shown by Cohen. − − 1931年发表的库尔特 · 哥德尔（Kurt Gödel）的不完备性定理，引起了对所有数学公理化基础的可达性的怀疑，任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而，哥德尔证明了，对于足以描述自然数算数的任何一致的可递归枚举的公理系统，有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如，在科恩（Cohen）提出的 Zermelo-Fraenkel 集合论中，连续统假设是不可判定的。 第215行：
第187行： − − The role of reduction in computer science can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "theory reductionism". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "hard" to solve as the former. − − 还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确而明确的数学形式化。在一般意义上，一个问题(或集合) ，如果有一个可计算/可行的方法将前者的问题转化为后者，那么，如果一个人知道如何可计算/可行地解决后者的问题，那么他就可以可计算/可行地解决前者。因此，后者至少只能像前者一样“难”解决。 − − Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of [[memes]]). In his book ''[[The Blind Watchmaker]]'', [[Richard Dawkins|Dawkins]] introduced the term "hierarchical reductionism"<ref>Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of [[hard drive]]s, processors, and memory, but not on the level of [[logic gates]], or on the even simpler level of electrons in a [[semiconductor]] medium. − − − − Reduction in theoretical computer science is pervasive in both: the mathematical abstract foundations of computation; and in real-world performance or capability analysis of algorithms. More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in computability (or recursive) theory, where it assumes the form of e.g. Turing reduction, but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it assumes the form of e.g. polynomial-time reduction. − − 理论计算机科学的简化在两个方面都很普遍: 计算的数学抽象基础; 以及在现实世界中算法的性能或能力分析。更具体地说，还原是一个基础的和中心的概念，不仅在数学逻辑和可计算性(或递归)理论的抽象计算领域，在那里它采用的形式是。图灵约简，但也在现实世界的计算领域的时间(或空间)复杂性分析的算法，其中它假设的形式，如。多项式时间图灵归约。 − − Quantum Holonomy theory is a theory of the lowest possible reduction.<ref>{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref>{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref> − Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist [[Robert Ulanowicz]] says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) [[information theory]] as a framework to study [[Propensity probability|propensities]] in natural systems.<ref>R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref> Ulanowicz attributes these criticisms of reductionism to the philosopher [[Karl Popper]] and biologist [[Robert Rosen (theoretical biologist)|Robert Rosen]].<ref>{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref> + + − Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by natural selection. Anthropologists Edward Burnett Tylor and James George Frazer employed some religious reductionist arguments. − 宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是: 宗教可以归结为人类对是非的概念，宗教基本上是控制我们环境的原始尝试，宗教是解释物质世界存在的一种方式，宗教赋予一个群体成员更强的生存能力，自然选择也加强了这种能力。人类学家爱德华·伯内特·泰勒和詹姆斯·弗雷泽使用了一些宗教还原论的观点。+ − [[Stuart Kauffman]] has argued that [[complex systems]] theory and phenomena such as [[emergence]] pose limits to reductionism.<ref>[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref> Emergence is especially relevant when systems exhibit historicity.<ref>{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref> Emergence is strongly related to [[nonlinearity]].<ref>[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater [[complexity]], including living [[Cell (biology)|cells]],<ref name=Huber2013>{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> [[neural networks]], [[ecosystems]], [[society]], and other systems formed from assemblies of large numbers of diverse components linked by multiple [[feedback loop]]s.<ref name="Huber2013" /><ref name=Clayton2006>{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>+ + + − [[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson]] used the idea that [[symmetry breaking]] is an example of an emergent phenomenon in his 1972 ''[[Science (journal)|Science]]'' paper "More is different" to make an argument about the limitations of reductionism.<ref>[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref> One observation he made was that the sciences can be arranged roughly in a linear hierarchy—[[particle physics]], [[solid state physics]], [[chemistry]], [[molecular biology]], [[cellular biology]], [[physiology]], [[psychology]], [[social sciences]]—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry." − Linguistic reductionism is the idea that everything can be described or explained by a language with a limited number of concepts, and combinations of those concepts. An example is the language Toki Pona. − 语言还原论是一种观点，认为一切事物都可以用一种语言来描述或解释，只有有限数量的概念，以及这些概念的组合。一个例子是语言 Toki Pona。+ + + − Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<ref>{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref> + − The concept of downward causation poses an alternative to reductionism within philosophy. This opinion is developed by Peter Bøgh Andersen, Claus Emmeche, Niels Ole Finnemann, and Peder Voetmann Christiansen, among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate. The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as self-organization, natural selection, adaptation, and control.+ − 向下因果关系的概念在哲学中提出了一种还原论的替代方法。这个观点是由 Peter b ø gh Andersen，Claus Emmeche，Niels Ole Finnemann，和 Peder Voetmann Christiansen 等人提出的。这些哲学家探索的方式，其中一个可以谈论的现象，在较大规模的组织水平产生因果影响的较小规模的水平，并发现，一些，但不是所有类型的向下因果关系是与科学兼容的。特别是，他们发现，约束是向下因果关系可以运作的一种方式。因果关系作为约束的概念也被探索作为一种阐明科学概念的方式，例如自我组织、自然选择、适应和控制。+ − + − + + + − + − − Philosophers of the Enlightenment worked to insulate human free will from reductionism. Descartes separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "noumenal" realm that is not governed by the deterministic laws of "phenomenal" nature, where every event is completely determined by chains of causality. The most influential formulation was by Immanuel Kant, who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially Friedrich Schleiermacher and Albrecht Ritschl, used the Romantic method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion. − − 启蒙运动时期的哲学家致力于将人类的自由意志与还原论隔离开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念，这一领域不受“现象”自然界的决定论法则的支配，在这一领域中，每一个事件都完全由一系列因果关系所决定。最有影响力的公式是伊曼努尔 · 康德提出的，他区分了心智强加于世界的因果决定论框架ーー现象领域ーー和现象领域本身存在的世界ーー本体领域，正如他所相信的，这个领域包括自由意志。为了将神学与还原论隔离开来，19世纪后启蒙时代的德国神学家，尤其是弗里德里希·施莱尔马赫和阿尔布雷赫特·立敕尔，使用了浪漫主义的方法，将宗教建立在人类精神的基础之上，因此，一个人对精神事物的感觉或情感构成了宗教。 第276行：
第234行： + − + − Most common philosophical understandings of causation involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts. − − 最常见的哲学上对因果关系的理解包括将它归纳为一些非因果事实的集合。这些简化论观点的反对者认为，所讨论的非因果事实不足以确定因果事实。 − − 第288行：
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第295行： − The development of systems thinking has provided methods that seek to describe issues in a holistic rather than a reductionist way, and many scientists use a holistic paradigm. When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of models or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered. − 系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法，许多科学家使用整体范式。当术语在科学语境中使用时，整体论和还原论主要指的是什么类型的模型或理论提供对自然世界的有效解释; 证伪假设的科学方法，检查经验数据与理论，大体上是不变的，但方法指导哪些理论被考虑。+ − Philosophers of the [[Age of Enlightenment|Enlightenment]] worked to insulate human free will from reductionism. [[Descartes]] separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "[[Noumenon|noumenal]]" realm that is not governed by the deterministic laws of "[[Phenomena (philosophy)|phenomenal]]" nature, where every event is completely determined by chains of causality.<ref>Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref> The most influential formulation was by [[Immanuel Kant]], who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially [[Friedrich Schleiermacher]] and [[Albrecht Ritschl]], used the [[Romanticism|Romantic]] method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.<ref>Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>+ + + − In many cases (such as the kinetic theory of gases), given a good understanding of the components of the system, one can predict all the important properties of the system as a whole. In other systems, especially concerned with life and life's emergent properties (morphogenesis, autopoiesis, and metabolism), emergent properties of the system are said to be almost impossible to predict from knowledge of the parts of the system. Complexity theory studies systems and properties of the latter type.+ − 在许多情况下(例如分子运动论) ，只要对系统的组成部分有很好的了解，就可以预测整个系统的所有重要特性。在其他系统中，特别是关于生命和生命的涌现特性(形态发生、自创生和新陈代谢) ，系统的涌现特性据说几乎不可能从系统各部分的知识中预测。复杂性理论研究系统和后一种类型的性质。+ − === Causation === − Most common philosophical understandings of [[Causality|causation]] involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref> 第412行：
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在宗教中
还原论是一种有关现象之间的联系的哲学观点，认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它基于理智的和哲学的立场，将一个复杂的系统解释为其各部分的总和<ref name=":0" />。
还原论是一种有关现象之间的联系的哲学观点，认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0" />。
本体论还原论否定了本体涌现的观点，认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象，根本上是不存在的<ref name=":5" />。
本体论还原论否定了本体涌现的观点，认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象，根本上是不存在的<ref name=":5" />。
Ontological reductionism takes two forms: '''token ontological reductionism''' and '''type ontological reductionism'''.{{Citation needed|date=July 2020}}
本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。
表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。
表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。
类型本体论还原论的观点是，每一种类型的事物都是事物的总和，每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7" />。
类型本体论还原论的观点是，每一种类型的事物都是事物的总和，每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7" />。
迈克尔·鲁斯（[[Michael Ruse]]）批评本体论还原论是对活力论的一种不恰当的论证。
迈克尔·鲁斯（[[Michael Ruse]]）批评本体论还原论是对活力论的一种不恰当的论证。
=== 方法论还原论 ===
=== 方法论还原论 ===
Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities.<ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref> In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes.<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref> Claim of efficacy is demonstrated that the gene – unit of classical heredity – is the deoxyribonucleic acid (DNA), a macro-molecule.<ref name=":1" />
Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities.<ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref> In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes.<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref> Claim of efficacy is demonstrated that the gene – unit of classical heredity – is the deoxyribonucleic acid (DNA), a macro-molecule.<ref name=":1" />
=== 理论还原论 ===
=== 理论还原论 ===
Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.
Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.
理论还原是一个更一般的而理论吸收一个特殊的理论的过程。例如，开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论，因为前者的所有解释力都包含在后者之中。此外，这种还原被认为是有好处的，因为牛顿力学是一个更普遍的理论——也就是说，它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外，理论归纳通常是一种解释包含另一种解释的过程。
理论还原是一个更一般的而理论吸收一个特殊的理论的过程。例如，开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论，因为前者的所有解释力都包含在后者之中。此外，这种还原被认为是有好处的，因为牛顿力学是一个更普遍的理论——也就是说，它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外，理论归纳通常是一种解释包含另一种解释的过程。
== 在科学中 ==
== 在科学中 ==
{{More citations needed section|date=August 2011}}
{{More citations needed section|date=August 2011}}
Reductionist thinking and methods form the basis for many of the well-developed topics of modern [[science]], including much of [[physics]], [[chemistry]] and [[molecular biology]]. [[Classical mechanics]] in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions.<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> [[Statistical mechanics]] can be considered as a reconciliation of [[macroscopic]] [[thermodynamic laws]] with the reductionist method of explaining macroscopic properties in terms of [[microscopic]] components.
Reductionist thinking and methods form the basis for many of the well-developed topics of modern [[science]], including much of [[physics]], [[chemistry]] and [[molecular biology]]. [[Classical mechanics]] in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions.<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> [[Statistical mechanics]] can be considered as a reconciliation of [[macroscopic]] [[thermodynamic laws]] with the reductionist method of explaining macroscopic properties in terms of [[microscopic]] components.
在科学中，还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理，分子生物学是基于化学，但当一个人思考不那么严格定义的知识领域时，类似的陈述就会变得有争议。例如，人们对声称社会学是以心理学为基础，或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系（例如，大多数人会同意心理学可以影响并影响经济学），但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性，这种特性在组织的某些层次上更为常见。例如，一些人声称复杂的系统从本质上是不可简化的，需要一个整体的方法来理解它们，因而不同意进化心理学和社会生物学的某些观点。
在科学中，还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理，分子生物学是基于化学，但当一个人思考不那么严格定义的知识领域时，类似的陈述就会变得有争议。例如，人们对声称社会学是以心理学为基础，或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系（例如，大多数人会同意心理学可以影响并影响经济学），但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性，这种特性在组织的某些层次上更为常见。例如，一些人声称复杂的系统从本质上是不可简化的，需要一个整体的方法来理解它们，因而不同意进化心理学和社会生物学的某些观点。
Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of [[memes]]). In his book ''[[The Blind Watchmaker]]'', [[Richard Dawkins|Dawkins]] introduced the term "hierarchical reductionism"<ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of [[hard drive]]s, processors, and memory, but not on the level of [[logic gates]], or on the even simpler level of electrons in a [[semiconductor]] medium.
一些强还原论者认为，行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支（参见理查德·道金斯（Richard Dawkins）的模因概念）。在他的《盲眼钟表匠》一书中，道金斯引入了“层次还原论<ref name=":9" /> ”来描述这样一种观点，即复杂系统可以用组织的层次来描述，而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例，从硬盘、处理器和内存的角度阐释了层次还原论，而不是基于逻辑门的层次，或者更简单的半导体介质中的电子层次。
Quantum Holonomy theory is a theory of the lowest possible reduction.<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref>
量子整体论是一种最低可能的还原理论<ref name=":10" /><ref name=":11" />。
Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist [[Robert Ulanowicz]] says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) [[information theory]] as a framework to study [[Propensity probability|propensities]] in natural systems.<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref> Ulanowicz attributes these criticisms of reductionism to the philosopher [[Karl Popper]] and biologist [[Robert Rosen (theoretical biologist)|Robert Rosen]].<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>
其他人认为，不恰当使用还原论限制了我们对复杂系统的理解。特别是，生态学家罗伯特·尤兰维奇（Robert Ulanowicz）说，科学必须发展技术来研究大规模组织影响小规模组织的方式，以及反馈循环在给定层次上创造结构的方式，而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12" /> 。乌兰诺维茨（Ulanowicz）把这些还原论的批评归因于哲学家卡尔 · 波普尔（ Karl Popper ）和生物学家罗伯特 · 罗森（Robert Rosen）<ref name=":13" />。
[[Stuart Kauffman]] has argued that [[complex systems]] theory and phenomena such as [[emergence]] pose limits to reductionism.<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref> Emergence is especially relevant when systems exhibit historicity.<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref> Emergence is strongly related to [[nonlinearity]].<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater [[complexity]], including living [[Cell (biology)|cells]],<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> [[neural networks]], [[ecosystems]], [[society]], and other systems formed from assemblies of large numbers of diverse components linked by multiple [[feedback loop]]s.<ref name="Huber2013" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>
斯图尔特 · 考夫曼（Stuart Kauffman）认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14" />。当系统表现出历史性时，涌现尤为重要<ref name=":15" />。涌现与非线性密切相关<ref name=":16" />。还原论应用的局限性在更复杂的组织层次上尤其明显，包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会，以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013" /><ref name="Clayton2006" />。
[[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson]] used the idea that [[symmetry breaking]] is an example of an emergent phenomenon in his 1972 ''[[Science (journal)|Science]]'' paper "More is different" to make an argument about the limitations of reductionism.<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref> One observation he made was that the sciences can be arranged roughly in a linear hierarchy—[[particle physics]], [[solid state physics]], [[chemistry]], [[molecular biology]], [[cellular biology]], [[physiology]], [[psychology]], [[social sciences]]—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry."
诺贝尔经济学奖获得者菲利普·沃伦·安德森（Philip Warren Anderson）在他1972年发表在《科学》（Science）杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17" /> 。他观察到，科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而，这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段，全新的法则、概念和概括都是必要的，需要灵感和创造力，就像前一个阶段一样。心理学不是应用生物学，生物学也不是应用化学。”
Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>
诸如控制论和系统论这样的学科隐含着非还原论，有时达到了用更高层次的现象来解释特定层次上的现象的程度，在某种意义上，这是还原论的对立面<ref name=":18" />。
== In mathematics ==
== 在数学中 ==
In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref>{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>
In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>
在数学中，还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学，而对于现代数学来说，这个基础通常是公理化集合论。策梅洛（Ernst Zermelo）是这种观点的主要倡导者之一，他也对公理化集合论做出了许多发展。有人认为，用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法，可能会削弱泽梅洛的还原论主张<ref name=":19" />。
Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>
Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref>{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref>{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref>{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>
Jouko Väänänen认为二阶逻辑是数学的基础，而不是集合论<ref name=":20" /> ，而其他人则认为范畴论是数学某些方面的基础<ref name=":21" /><ref name=":22" />。
The [[Gödel's incompleteness theorems|incompleteness theorems]] of [[Kurt Gödel]], published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics. Any such foundation would have to include axioms powerful enough to describe the arithmetic of the natural numbers (a subset of all mathematics). Yet Gödel proved that, for any ''consistent'' recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) ''true'' propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally [[Undecidable problem|undecidable propositions]]. For example, the [[continuum hypothesis]] is undecidable in the [[Zermelo–Fraenkel set theory]] as shown by [[Forcing (mathematics)|Cohen]].
The [[Gödel's incompleteness theorems|incompleteness theorems]] of [[Kurt Gödel]], published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics. Any such foundation would have to include axioms powerful enough to describe the arithmetic of the natural numbers (a subset of all mathematics). Yet Gödel proved that, for any ''consistent'' recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) ''true'' propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally [[Undecidable problem|undecidable propositions]]. For example, the [[continuum hypothesis]] is undecidable in the [[Zermelo–Fraenkel set theory]] as shown by [[Forcing (mathematics)|Cohen]].
1931年发表的库尔特 · 哥德尔（Kurt Gödel）的不完备性定理，引起了对所有数学公理化基础的可达性的怀疑，任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而，哥德尔证明了，对于足以描述自然数算数的任何一致的可递归枚举的公理系统，有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如，在科恩（Cohen）提出的 Zermelo-Fraenkel 集合论中，连续统假设是不可判定的。
=== 在计算机科学中 ===
=== In computer science ===
The role of reduction in [[computer science]] can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "[[#Types|theory reductionism]]". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "[[NP-hardness|hard]]" to solve as the former.
The role of reduction in [[computer science]] can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "[[#Types|theory reductionism]]". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "[[NP-hardness|hard]]" to solve as the former.
还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上，如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合，那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题，那么他就可以可计算/可行地解决前者。因此，后者至少像前者一样“难”解决。
Reduction in [[theoretical computer science]] is pervasive in both: the mathematical abstract foundations of computation; and in real-world [[Analysis of algorithms|performance or capability analysis of algorithms]]. More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in [[Computability theory|computability (or recursive) theory]], where it assumes the form of e.g. [[Turing reduction]], but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it assumes the form of e.g. [[polynomial-time reduction]].
Reduction in [[theoretical computer science]] is pervasive in both: the mathematical abstract foundations of computation; and in real-world [[Analysis of algorithms|performance or capability analysis of algorithms]]. More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in [[Computability theory|computability (or recursive) theory]], where it assumes the form of e.g. [[Turing reduction]], but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it assumes the form of e.g. [[polynomial-time reduction]].
理论计算机科学的还原在两个方面都很普遍：计算的数学抽象基础；以及在现实世界中算法的性能或能力分析。更具体地说，还原是一个基础和核心的概念，不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域（在这些领域里它呈现出图灵还原的形式），而且出现在现实世界的计算领域，比如在时间(或空间)算法复杂性分析中，它呈现出多项式时间还原的形式。
== 在宗教中 ==
== In religion ==
A contrast to reductionism is holism or emergentism. Holism is the idea that, in the whole, items can have properties, known as emergent properties, that are not explainable from the sum of their parts. The principle of holism was summarized concisely by Aristotle in the Metaphysics: "The whole is more than the sum of its parts".
A contrast to reductionism is holism or emergentism. Holism is the idea that, in the whole, items can have properties, known as emergent properties, that are not explainable from the sum of their parts. The principle of holism was summarized concisely by Aristotle in the Metaphysics: "The whole is more than the sum of its parts".
Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by [[natural selection]].<ref>{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref> Anthropologists [[Edward Burnett Tylor]] and [[James George Frazer]] employed some [[Metatheories of religion in the social sciences#Edward Burnett Tylor and James George Frazer|religious reductionist arguments]].<ref>Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>
Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by [[natural selection]].<ref>{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref> Anthropologists [[Edward Burnett Tylor]] and [[James George Frazer]] employed some [[Metatheories of religion in the social sciences#Edward Burnett Tylor and James George Frazer|religious reductionist arguments]].<ref>Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>
宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是: 宗教可以归结为人类对是非的概念，宗教基本上是控制我们环境的原始尝试，宗教是解释物质世界存在的一种方式，宗教赋予一个群体成员更强的生存能力，自然选择也加强了这种能力。人类学家爱德华·伯内特·泰勒和詹姆斯·弗雷泽使用了一些宗教还原论的观点。
The concept of [[downward causation]] poses an alternative to reductionism within philosophy. This opinion is developed by [[Peter Bøgh Andersen]], [[Claus Emmeche]], [[Niels Ole Finnemann]], and [[Peder Voetmann Christiansen]], among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate.<ref>P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref> The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as [[self-organization]], [[natural selection]], [[adaptation]], and control.<ref>{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref>
The concept of [[downward causation]] poses an alternative to reductionism within philosophy. This opinion is developed by [[Peter Bøgh Andersen]], [[Claus Emmeche]], [[Niels Ole Finnemann]], and [[Peder Voetmann Christiansen]], among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate.<ref>P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref> The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as [[self-organization]], [[natural selection]], [[adaptation]], and control.<ref>{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref>
向下因果关系的概念在哲学中提出了一种还原论的替代方法。这个观点是由 Peter b ø gh Andersen，Claus Emmeche，Niels Ole Finnemann，和 Peder Voetmann Christiansen 等人提出的。这些哲学家探索的方式，其中一个可以谈论的现象，在较大规模的组织水平产生因果影响的较小规模的水平，并发现，一些，但不是所有类型的向下因果关系是与科学兼容的。特别是，他们发现，约束是向下因果关系可以运作的一种方式。因果关系作为约束的概念也被探索作为一种阐明科学概念的方式，例如自我组织、自然选择、适应和控制。
=== Free will ===
=== Free will ===
{{Main|Free will}}
{{Main|Free will}}
Philosophers of the [[Age of Enlightenment|Enlightenment]] worked to insulate human free will from reductionism. [[Descartes]] separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "[[Noumenon|noumenal]]" realm that is not governed by the deterministic laws of "[[Phenomena (philosophy)|phenomenal]]" nature, where every event is completely determined by chains of causality.<ref>Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref> The most influential formulation was by [[Immanuel Kant]], who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially [[Friedrich Schleiermacher]] and [[Albrecht Ritschl]], used the [[Romanticism|Romantic]] method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.<ref>Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>
启蒙运动时期的哲学家致力于将人类的自由意志与还原论隔离开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念，这一领域不受“现象”自然界的决定论法则的支配，在这一领域中，每一个事件都完全由一系列因果关系所决定。最有影响力的公式是伊曼努尔 · 康德提出的，他区分了心智强加于世界的因果决定论框架ーー现象领域ーー和现象领域本身存在的世界ーー本体领域，正如他所相信的，这个领域包括自由意志。为了将神学与还原论隔离开来，19世纪后启蒙时代的德国神学家，尤其是弗里德里希·施莱尔马赫和阿尔布雷赫特·立敕尔，使用了浪漫主义的方法，将宗教建立在人类精神的基础之上，因此，一个人对精神事物的感觉或情感构成了宗教。
=== Causation ===
Most common philosophical understandings of [[Causality|causation]] involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>
Most common philosophical understandings of causation involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.
最常见的哲学上对因果关系的理解包括将它归纳为一些非因果事实的集合。这些简化论观点的反对者认为，所讨论的非因果事实不足以确定因果事实。
Alfred North Whitehead's metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.
Alfred North Whitehead's metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.
The development of [[systems thinking]] has provided methods that seek to describe issues in a [[holism|holistic]] rather than a reductionist way, and many scientists use a [[Holism in science|holistic paradigm]].<ref>[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref> When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of [[scientific model|models]] or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.
The development of [[systems thinking]] has provided methods that seek to describe issues in a [[holism|holistic]] rather than a reductionist way, and many scientists use a [[Holism in science|holistic paradigm]].<ref>[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref> When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of [[scientific model|models]] or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.
The development of systems thinking has provided methods that seek to describe issues in a holistic rather than a reductionist way, and many scientists use a holistic paradigm. When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of models or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.
系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法，许多科学家使用整体范式。当术语在科学语境中使用时，整体论和还原论主要指的是什么类型的模型或理论提供对自然世界的有效解释; 证伪假设的科学方法，检查经验数据与理论，大体上是不变的，但方法指导哪些理论被考虑。
In many cases (such as the [[kinetic theory of gases]]), given a good understanding of the components of the system, one can predict all the important properties of the system as a whole. In other systems, especially concerned with life and life's emergent properties ([[morphogenesis]], [[autopoiesis]], and [[metabolism]]), [[emergent properties]] of the system are said to be almost impossible to predict from knowledge of the parts of the system. [[Complex systems|Complexity theory]] studies systems and properties of the latter type.
In many cases (such as the [[kinetic theory of gases]]), given a good understanding of the components of the system, one can predict all the important properties of the system as a whole. In other systems, especially concerned with life and life's emergent properties ([[morphogenesis]], [[autopoiesis]], and [[metabolism]]), [[emergent properties]] of the system are said to be almost impossible to predict from knowledge of the parts of the system. [[Complex systems|Complexity theory]] studies systems and properties of the latter type.
In many cases (such as the kinetic theory of gases), given a good understanding of the components of the system, one can predict all the important properties of the system as a whole. In other systems, especially concerned with life and life's emergent properties (morphogenesis, autopoiesis, and metabolism), emergent properties of the system are said to be almost impossible to predict from knowledge of the parts of the system. Complexity theory studies systems and properties of the latter type.
在许多情况下(例如分子运动论) ，只要对系统的组成部分有很好的了解，就可以预测整个系统的所有重要特性。在其他系统中，特别是关于生命和生命的涌现特性(形态发生、自创生和新陈代谢) ，系统的涌现特性据说几乎不可能从系统各部分的知识中预测。复杂性理论研究系统和后一种类型的性质。
[[Alfred North Whitehead]]'s metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.
[[Alfred North Whitehead]]'s metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.