Reductionism

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"That there is a close connexion between a state of consciousness and the brain we do not dispute. But there is also a close connexion between a coat and the nail on which it hangs, for, if the nail is pulled out, the coat falls to the ground. Shall we say, then, that the shape of the nail gives us the shape of the coat, or in any way corresponds to it ?"--Matter and Memory (1896) by Henri Bergson

"Consciousness is what makes the mind-body problem really intractable. Perhaps that is why current discussions of the problem give it little attention or get it obviously wrong. The recent wave of reductionist euphoria has produced several analyses of mental phenomena and mental concepts designed to explain the possibility of some variety of materialism, psychophysical identification, or reduction. But the problems dealt with are those common to this type of reduction and other types, and what makes the mind-body problem unique, and unlike the water-H2O problem or the Turing machine-IBM machine problem or the lightning-electrical discharge problem or the gene-DNA problem or the oak tree-hydrocarbon problem, is ignored." --"What Is it Like to Be a Bat?"

The Canard Digérateur, or Digesting Duck, was an automaton in the form of duck, created by Jacques de Vaucanson in 1739.

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Reductionism is any of several related philosophical ideas regarding the associations between phenomena, which can be described in terms of other simpler or more fundamental phenomena. It is also described as an intellectual and philosophical position that interprets a complex system as the sum of its parts.

1 In philosophy
- 1.1 Free will
- 1.2 Causation
2 See also

In philosophy

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.

Free will

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.

Causation

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.

 '''Reductionism''' is any of several related [[Philosophy|philosophical]] ideas regarding the associations between [[Phenomenon|phenomena]], which can be described in terms of other simpler or more fundamental phenomena. It is also described as an intellectual and philosophical position that interprets a complex system as the sum of its parts.
-== Definitions ==
+== In philosophy ==
-''[[The Oxford Companion to Philosophy]]'' suggests that reductionism is "one of the most used and abused terms in the philosophical lexicon" and suggests a three part division:<ref name=Ruse>{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</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.
-# '''Ontological reductionism''': a belief that the whole of reality consists of a minimal number of parts.
-# '''Methodological reductionism''': the scientific attempt to provide explanation in terms of ever smaller entities.
-# '''Theory reductionism''': the suggestion that a newer theory does not replace or absorb an older one, but reduces it to more basic terms. Theory reduction itself is divisible into three parts: translation, derivation and explanation.<ref name=Ney />
-Reductionism can be applied to any [[phenomenon]], including [[object (philosophy)|objects]], problems, [[explanation]]s, [[theory|theories]], and meanings.<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism  |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref>For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>
-For the sciences, application of methodological reductionism attempts explanation of entire systems in terms of their individual, constituent parts and their interactions. For example, the temperature of a gas is reduced to nothing beyond the average kinetic energy of its molecules in motion. [[Thomas Nagel]] and others speak of 'psychophysical reductionism' (the attempted reduction of psychological phenomena to physics and chemistry), and 'physico-chemical reductionism' (the attempted reduction of biology to physics and chemistry).<ref name=Nagel /> In a very simplified and sometimes contested form, reductionism is said to imply that a system is nothing but the sum of its parts.<ref name=Polkinghorne /><ref name=GodfreySmith /> However, a more nuanced opinion is that a system is composed entirely of its parts, but the system will have features that none of the parts have (which, in essence is the basis of [[emergentism]]).<ref name=Jones /> "The point of mechanistic explanations is usually showing how the higher level features arise from the parts."<ref name=GodfreySmith />
-Other definitions are used by other authors. For example, what [[John Polkinghorne]] terms 'conceptual' or 'epistemological' reductionism<ref name=Polkinghorne /> is the definition provided by [[Simon Blackburn]]<ref name=Blackburn>{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref> and by [[Jaegwon Kim]]:<ref name=Kim>{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy  |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref> that form of reductionism which concerns a program of replacing the facts or entities involved in one type of discourse with other facts or entities from another type, thereby providing a relationship between them. Richard Jones distinguishes ontological and epistemological reductionism, arguing that many ontological and epistemological reductionists affirm the need for different concepts for different degrees of complexity while affirming a reduction of theories.<ref name=Jones />
-The idea of reductionism can be expressed by "levels" of explanation, with higher levels reducible if need be to lower levels. This use of levels of understanding in part expresses our human limitations in remembering detail. However, "most philosophers would insist that our role in conceptualizing reality [our need for a hierarchy of "levels" of understanding] does not change the fact that different levels of organization in reality do have different 'properties'."<ref name=Jones />
-Reductionism should be distinguished from [[Eliminative materialism|eliminationism]]: reductionists do not deny the existence of phenomena, but explain them in terms of another reality; eliminationists deny the existence of the phenomena themselves. For example, eliminationists deny the existence of life by their explanation in terms of physical and chemical processes.
-Reductionism does not preclude the existence of what might be termed [[Emergence|emergent phenomena]], but it does imply the ability to understand those phenomena completely in terms of the processes from which they are composed. This reductionist understanding is very different from ontological or strong [[emergentism]], which intends that what emerges in "emergence" is more than the sum of the processes from which it emerges, respectively either in the ontological sense or in the epistemological sense.<ref>Axelrod and Cohen "Harnessing Complexity"</ref> Some physicists, however, claim that reductionism and emergentism are complementary: both are needed to explain natural processes.<ref>Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>
-== Types ==
-Most philosophers delineate three types of reductionism and anti-reductionism.<ref name="Ruse" />
-=== Ontological reductionism ===
-Ontological reductionism is the belief that reality is composed of a minimum number of kinds of entities or substances.<ref name=":0" /> This claim is usually [[metaphysics|metaphysical]], and is most commonly a form of [[monism]], in effect claiming that all objects, properties and events are reducible to a single substance. (A [[mind-body dualism|dualist]] who is an ontological reductionist would believe that everything is reducible to two substances—as one possible example, a dualist might claim that reality is composed of "[[matter]]" and "[[spirit]]".)
-Richard Jones divides ontological reductionism into two: the reductionism of substances (e.g., the reduction of mind to matter) and the reduction of the number of structures operating in nature (e.g., the reduction of one physical force to another). This permits scientists and philosophers to affirm the former while being anti-reductionists regarding the latter.<ref>Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>
-[[Nancey Murphy]] has claimed that there are two species of ontological reductionism: one that claims that wholes are nothing more than their parts; and atomist reductionism, claiming that wholes are not "really real". She admits that the phrase "really real" is apparently senseless but she has tried to explicate the supposed difference between the two.<ref>Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>
-Ontological reductionism denies the idea of ontological [[emergence]], and claims that emergence is an [[Epistemology|epistemological]] phenomenon that only exists through analysis or description of a system, and does not exist fundamentally.<ref>[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>
-Ontological reductionism takes two forms: '''token ontological reductionism''' and '''type ontological reductionism'''.{{Citation needed|date=July 2020}}
-Token ontological reductionism is the idea that every item that exists is a sum item. For perceivable items, it affirms that every perceivable item is a sum of items with a lesser degree of complexity. Token ontological reduction of biological things to chemical things is generally accepted.
-Type ontological reductionism is the idea that every type of item is a sum type of item, and that every perceivable type of item is a sum of types of items with a lesser degree of complexity. Type ontological reduction of biological things to chemical things is often rejected.<ref>{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>
-[[Michael Ruse]] has criticized ontological reductionism as an improper argument against [[vitalism]].<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>
-=== Methodological reductionism ===
-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>{{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" />
-=== Theory reductionism ===
-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.
-== In science ==
-{{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>{{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.
-In science, reductionism implies that certain topics of study are based on areas that study smaller spatial scales or organizational units. While it is commonly accepted that the foundations of [[chemistry]] are based in [[physics]], and [[molecular biology]] is based on chemistry, similar statements become controversial when one considers less rigorously defined intellectual pursuits. For example, claims that [[sociology]] is based on [[psychology]], or that [[economics]] is based on [[sociology]] and [[psychology]] would be met with reservations. These claims are difficult to substantiate even though there are obvious associations between these topics (for instance, most would agree that [[psychology]] can affect and inform [[economics]]). The limit of reductionism's usefulness stems from [[Emergence#Emergent properties and processes|emergent properties]] of [[complex systems]], which are more common at certain levels of organization. For example, certain aspects of [[evolutionary psychology]] and [[sociobiology]] are rejected by some who claim that complex systems are inherently irreducible and that a [[holistic]] method is needed to understand them.
-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.
-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>
-[[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."
-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>
-== In mathematics ==
-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>
-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>
-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]].
-=== 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.
-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]].
-== In religion ==
-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>
-== In linguistics ==
-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.<ref>{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref> An example is the language [[Toki Pona]].
-== In philosophy ==
-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>
 === 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. 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.
-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>
 === 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 [[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.
-== Criticism ==
-=== Antireductionism ===
-{{Main|Antireductionism}}
-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 (Aristotle)|Metaphysics]]: "The whole is more than the sum of its parts".
-=== Fragmentalism ===
-An alternative term for ontological reductionism is ''fragmentalism'',<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref> often used in a [[pejorative]] sense.<ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref> [[Anti-realism|Anti-realists]] use the term ''fragmentalism'' in arguments that the world does not exist of separable [[Non-physical entity|entities]], instead consisting of wholes. For example, advocates of this idea claim that:
-<blockquote>
-The linear deterministic approach to nature and technology promoted a fragmented perception of reality, and a loss of the ability to foresee, to adequately evaluate, in all their complexity, global crises in ecology, civilization and education.<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref>
-</blockquote>
-The term ''fragmentalism'' is usually applied to reductionist modes of thought, often with the related pejorative term ''[[scientism]]''. This usage is popular among some ecological activists: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref>{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref></blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin />
-Such opinions also motivate many criticisms of the scientific method:
-<blockquote
->The scientific method only acknowledges monophasic consciousness. The method is a specialized system that emphasizes studying small and distinctive parts in isolation, which results in fragmented knowledge.<ref name=Lumpkin>[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref></blockquote>
-== Alternatives ==
-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.
-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.
-[[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.
-[[Ecologist]] [[Sven Erik Jorgensen]] makes both theoretical and practical arguments for a [[holistic]] method in certain topics of science, especially [[ecology]]. He argues that many systems are so complex that they can ever be described in complete detail. In analogy to the Heisenberg [[uncertainty principle]] in physics, he argues that many interesting ecological phenomena cannot be replicated in laboratory conditions, and so cannot be measured or observed without changing the system in some way. He also indicates the importance of inter-connectedness in biological systems. He believes that science can only progress by outlining questions that are unanswerable and by using models that do not try to explain everything in terms of smaller hierarchical levels of organization, but instead model them on the scale of the system itself, taking into account some (but not all) factors from levels higher and lower in the hierarchy.<ref>S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>
-In [[cognitive psychology]], [[George Kelly (psychologist)|George Kelly]] developed "constructive alternativism" as a form of [[personal construct psychology]] and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful [[mental model]]s of the exterior world, rather than the accumulation of independent "nuggets of truth".<ref>{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref>
 == See also ==

Reductionism

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