The Unity of Science (2024)

The topic of unity in the sciences can be explored through questionssuch as the following: Is unity a feature of reality or of our modesof cognition? Is there one privileged, most basic or fundamentalconcept or kind of thing and, if not, how are the different conceptsor kinds of things in the universe related? Can the various naturalsciences (e.g., physics, astronomy, chemistry, biology) be unifiedinto a single overarching theory, and can theories within a singlescience (e.g., general relativity and quantum theory in physics, ormodels of evolution and development in biology) be unified? How arethe so-called human sciences related to the natural ones? Are theoriesor models the relevant connected units? What other connected orconnecting units are there? Does the unification of these parts ofscience involve only matters of fact or are matters of value involvedas well? What about matters of method, material, institutional,ethical and other aspects of intellectual cooperation? Moreover, whatkinds of unity, not just units, in the sciences are there? And is therelation of unification one of reduction, translation, explanation,logical inference, collaboration or something else? What roles canunification play in scientific practices, their development,application and evaluation? Are those expressions of more generalcognitive activities? How are all these questions to be investigated?Is unification an aim of inquiry or a guiding idea at the service ofulterior aims? Is it a question for philosophy, e.g., for metaphysicsor epistemology? If so, how can examining scientific practices help?Or is philosophy, rather, a resource for understanding science?

1. Historical development in philosophy and science from Greek philosophy to Logical Empiricism in America

1.1 From Greek thought to Western science

Unity has a history as well as a logic. Different formulations anddebates express intellectual and other resources and interests indifferent contexts. Questions about unity belong partly in a traditionof thought that can be traced back to pre-Socratic Greek cosmology, inparticular to the preoccupation with the question of the One and theMany. In what senses is the world and, as a result, our knowledge ofit one? A number of representations of the world in terms of a fewsimple constituents that were considered fundamental emerged:Parmenides’ static substance, Heraclitus’ flux ofbecoming, Empedocles’ four elements, Democritus’ atoms,Pythagoras’ numbers, Plato’s forms, and Aristotle’scategories. The underlying question of the unity of our types ofknowledge was explicitly addressed by Plato in the Sophist asfollows: “Knowledge also is surely one, but each part of it thatcommands a certain field is marked off and given a special name properto itself. Hence language recognizes many arts and many forms ofknowledge” (Sophist, 257c). Aristotle asserted inOn the Heavens that knowledge concerns what is primary, anddifferent “sciences” know different kinds of causes; it ismetaphysics that comes to provide knowledge of the underlyingkind.

With the advent and expansion of Christian monotheism, theorganization of knowledge reflected the idea of a world governed bythe laws dictated by God, its creator and legislator. From thistradition emerged encyclopedic efforts such as theEtymologies, compiled in the sixth century by the AndalusianIsidore, Bishop of Seville, the works of the Catalan Ramon Llull inthe Middle Ages and those of the Frenchman Petrus Ramus in theRenaissance. Llull introduced iconic tree-diagrams andforest-encyclopedias representing the organization of differentdisciplines including law, medicine, theology and logic. He alsointroduced more abstract diagrams—not unlike some found inCabbalistic and esoteric traditions—in an attempt tocombinatorially encode the knowledge of God’s creation in auniversal language of basic symbols. Their combination would beexpected to generate knowledge of the secrets of creation and helparticulate knowledge of universal order (mathesisuniversalis), which would, in turn, facilitate communication withdifferent cultures and their conversion to Christianity. Ramusintroduced diagrams representing dichotomies and gave prominence tothe view that the starting point of all philosophy is theclassification of the arts and sciences. The encyclopedia organizationof knowledge served the project of its preservation andcommunication.

The emergence of a distinctive tradition of scientific thoughtaddressed the question of unity through the designation of aprivileged method, which involved a privileged language and set ofconcepts. Formally, at least, it was modeled after the Euclidean idealof a system of geometry. In the late-sixteenth century, Francis Baconheld that one unity of the sciences was the result of our organizationof records of discovered material facts in the form of a pyramid withdifferent levels of generalities. These could be classified in turnaccording to disciplines linked to human faculties. Concomitantly, thecontrolled interaction with phenomena of study characterized so-calledexperimental philosophy. In accordance with at least threetraditions—the Pythagorean tradition, the Bible’s dictumin the Book of Wisdom and the Italian commercial tradition ofbookkeeping—Galileo proclaimed at the turn of the seventeenthcentury that the Book of Nature had been written by God in thelanguage of mathematical symbols and geometrical truths, and in it,the story of Nature’s laws was told in terms of a reduced set ofobjective, quantitative primary qualities: extension, quantity ofmatter and motion. A persisting rhetorical role for some form oftheological unity of creation should not be neglected when consideringpre-twentieth-century attempts to account for the possibility anddesirability of some form of scientific knowledge. Throughout theseventeenth century, mechanical philosophy and Descartes’ andNewton’s systematization from basic concepts and first laws ofmechanics became the most promising framework for the unification ofnatural philosophy. After the demise of Laplacian molecular physics inthe first half of the nineteenth century, this role was taken over byether mechanics and, unifying forces and matter, energy physics.

1.2 Rationalism and Enlightenment

Descartes and Leibniz gave this tradition a rationalist twist that wascentered on the powers of human reason and the ideal of system ofknowledge founded on rational principles. It became the project of auniversal framework of exact categories and ideas, a mathesisuniversalis (Garber 1992; Gaukroger 2002). Adapting thescholastic image of knowledge, Descartes proposed an image of a treein which metaphysics is depicted by the roots, physics by the trunk,and the branches depict mechanics, medicine and morals. Leibnizproposed a general science in the form of a demonstrativeencyclopedia. This would be based on a “catalogue of simplethoughts” and an algebraic language of symbols,characteristica universalis, which would render all knowledgedemonstrative and allow disputes to be resolved by precisecalculation. Both defended the program of founding much of physics onmetaphysics and ideas from life science (Smith 2011) (Leibniz’sunifying ambitions with symbolic language and physics extended beyondscience, to settle religious and political fractures in Europe). Bycontrast, while sharing a model of a geometric, axiomatic structure ofknowledge, Newton’s project of natural philosophy was meant tobe autonomous from a system of philosophy and, in the new context,still endorsed, for its model of organization and its empiricalreasoning, values of formal synthesis and ontological simplicity (seethe entry onNewton;also Janiak 2008).

Belief in the unity of science or knowledge, along with theuniversality of rationality, was at its strongest during the EuropeanEnlightenment. The most important expression of the encyclopedictradition came in the mid-eighteenth century from Diderot andD’Alembert, editors of the Encyclopédie, oudictionnaire raisonné des sciences, des arts et desmétiers (1751–1772). Following earlierclassifications by Nichols and Bacon, their diagram presenting theclassification of intellectual disciplines was organized in terms of aclassification of human faculties. Diderot stressed in his own entry,“Encyclopaedia”, that the word signifies the unificationof the sciences. The function of the encyclopedia was to exhibit theunity of human knowledge. Diderot and D’Alembert, in contrast toLeibniz, made classification by subject the primary focus, andintroduced cross-references instead of logical connections. TheEnlightenment tradition in Germany culminated in Kant’s criticalphilosophy.

1.3 German tradition since Kant

For Kant, one of the functions of philosophy was to determine theprecise unifying scope and value of each science. For him, the unityof science is not the reflection of a unity found in nature, or, evenless, assumed in a real world behind the apparent phenomena. Rather,it has its foundations in the unifying a priori character or functionof concepts, principles and of Reason itself. Nature is precisely ourexperience of the world under the universal laws that include suchconcepts. And science, as a system of knowledge, is “a whole ofcognition ordered according to principles”, and the principleson which proper science is grounded are a priori (Preface toMetaphysical Foundations of Natural Science). A devoted butnot exclusive follower of Newton’s achievements and insights, hemaintained through most of his life that mathematization and a prioriuniversal laws given by the understanding were preconditions forgenuine scientific character (like Galileo and Descartes earlier, andCarnap later, Kant believed that mathematical exactness constitutedthe main condition for the possibility of objectivity). Here Kantemphasized the role of mathematics coordinating a priori cognition andits determined objects of experience. Thus, he contrasted the methodsemployed by the chemist, a “systematic art” organized byempirical regularities, with those employed by the mathematician orphysicist, which were organized by a priori laws, and he held thatbiology is not reducible to mechanics—as the former involvesexplanations in terms of final causes (see Critique of PureReason, Critique of Judgment and MetaphysicalFoundations of Natural Science). With regards tobiology—insufficiently grounded in the fundamental forces ofmatter—its inclusion requires the introduction of the idea ofpurposiveness (McLaughlin 1991). More generally, for Kant, unity was aregulative principle of reason, namely, an ideal guiding the processof inquiry toward a complete empirical science with its empiricalconcepts and principles grounded in the so-called concepts andprinciples of the understanding that constitute and objectifyempirical phenomena. (On systematicity as a distinctive aspect of thisideal and on its origin in reason, see Kitcher 1986 andHoyningen-Huene 2013).

Kant’s ideas set the frame of reference for discussions of theunification of the sciences in German thought throughout thenineteenth century (Wood and Hahn 2011). He gave philosophicalcurrency to the notion of worldview (Weltanschauung) and,indirectly, world-picture (Weltbild), establishing amongphilosophers and scientists the notion of the unity of science as anintellectual ideal. From Kant, German-speaking Philosophers of Natureadopted the image of Nature in terms of interacting forces or powersand developed it in different ways; this image found its way toBritish natural philosophy. In Great Britain this idealist, unifyingspirit (and other notions of an idealist and romantic turn) wasarticulated in William Whewell’s philosophy of science. Twounifying dimensions are these: his notion of mind-constructedfundamental ideas, which form the basis for organizing axioms andphenomena and classifying sciences, and the argument for the realityof explanatory causes in the form of consilience ofinduction, wherein a single cause is independently arrived atas the hypothesis explaining different kinds of phenomena.

In face of expanding research, the unifying emphasis on organization,classification and foundation led to exploring differences andrationalizing boundaries. The German intellectual current culminatedin the late-nineteenth century in the debates among philosophers suchas Windelband, Rickert and Dilthey. In their views and those ofsimilar thinkers, a worldview often included elements of evaluationand life meaning. Kant had established the basis for the famousdistinction between the natural sciences(Naturwissenschaften) and the cultural, or social, sciences(Geisteswissesnschaften) popularized in theory of science byWilhelm Dilthey and Wilhelm Windelband. Dilthey, Windelband, hisstudent Heinrich Rickert, and Max Weber (although the first twopreferred Kulturwissenschaften, which excluded psychology)debated over how differences in subject matter between the two kindsof sciences forced a distinctive difference between their respectivemethods. Their preoccupation with the historical dimension of thehuman phenomena, along with the Kantian emphasis on the conceptualbasis of knowledge, led to the suggestion that the natural sciencesaimed at generalizations about abstract types and properties, whereasthe human sciences studied concrete individuals and complexes. Thehuman case suggested a different approach based on valuation andpersonal understanding (Weber’s verstehen). ForRickert, individualized concept formation secured knowledge ofhistorical individuals by establishing connections to recognizedvalues (rather than personal valuations). In biology, Ernst Haeckeldefended a monistic worldview (Richards 2008).

The Weltbild tradition influenced the physicists Max Planckand Ernst Mach, who engaged in a heated debate about the precisecharacter of the unified scientific world-picture. Mach’s moreinfluential view was both phenomenological and Darwinian: theunification of knowledge took the form of an analysis of ideas intobiologically embodied elementary sensations (neutral monism) and wasultimately a matter of adaptive economy of thought. Planck adopted arealist view that took science to gradually approach complete truthabout the world, and he fundamentally adopted the thermodynamicalprinciples of energy and entropy (on the Mach-Planck debate seeToulmin 1970). These world-pictures constituted some of thealternatives to a long-standing mechanistic view that, since the riseof mechanistic philosophy with Descartes and Newton, had informedbiology as well as most branches of physics. In the background was theperceived conflict between the so-called mechanical andelectromagnetic worldviews, which resulted throughout the first twodecades of the twentieth century in the work of Albert Einstein(Holton 1998).

In the same German tradition, and amidst the proliferation of work onenergy physics and books on unity of science, the German energeticistWilhelm Ostwald declared the twentieth century the “Monisticcentury”. During the 1904 World’s Fair in St. Louis, theGerman psychologist and Harvard professor Hugo Munsterberg organized acongress under the title “Unity of Knowledge”; invitedspeakers were Ostwald, Ludwig Boltzmann, Ernest Rutherford, EdwardLeamington Nichols, Paul Langevin and Henri Poincaré. In 1911,the International Committee of Monism held its first meeting inHamburg, with Ostwaldpresiding.[1]Two years later it published Ostwald’s monograph, Monism asthe Goal of Civilization. In 1912, Mach, Felix Klein, DavidHilbert, Einstein and others signed a manifesto aiming at thedevelopment of a comprehensive worldview. Unification remained adriving scientific ideal. In the same spirit, Mathieu Leclerc duSablon published his L’Unité de la Science(1919), exploring metaphysical foundations, and Johan Hjorst publishedThe Unity of Science (1921), sketching out a history ofphilosophical systems and unifying scientific hypotheses.

1.4 Positivism and logical empiricism

The German tradition stood in opposition to the prevailing empiricistviews that, since the time of Hume, Comte and Mill, held that themoral or social sciences (even philosophy) relied on conceptual andmethodological analogies with geometry and the natural sciences, notjust astronomy and mechanics, as well as with biology. In the Baconiantradition, Comte emphasized a pyramidal hierarchy of disciplines inhis “encyclopedic law” or order, from the most generalsciences about the simplest phenomena to the most specific sciencesabout the most complex phenomena, each depending on knowledge from itsmore general antecedent: from inorganic physical sciences (arithmetic,geometry, mechanics, astronomy, physics and chemistry) to the organicphysical ones, such as biology and the new “socialphysics”, soon to be renamed sociology (Comte 1830–1842).Mill, instead, pointed to the diversity of methodologies forgenerating, organizing and justifying associated knowledge withdifferent sciences, natural and human, and the challenges to impose asingle standard (Mill 1843, Book VI). He came to view politicaleconomy eventually as an art, a tool for reform more than a system ofknowledge (Snyder 2006).

Different yet connected currents of nineteenth-century positivism,first in European philosophy in the first half of thecentury—Auguste Comte, J.S. Mill and Herbert Spencer—andsubsequently in North American philosophy—John Fiske, ChaunceyWright and William James—arose out of intellectual tensionsbetween metaphysics and the sciences and identified positivism assynthetic and scientific philosophy; accordingly, they were concernedwith the ordering and unification of knowledge through theorganization of the sciences. The synthesis was either of methodsalone—Mill and Wright—or else also ofdoctrines—Comte, Spencer and Fiske. Some used the term“system” especially in relation to a common logic ormethod (Pearce 2015).

In the twentieth century the unity of science became a distinctivetheme of the scientific philosophy of logical empiricism (Cat 2021).The question of unity engaged science and philosophy alike. In theirmanifesto, logical empiricists—known controversially also aslogical positivists—and most notably the founding members of theVienna Circle, adopted the Machian banner of “unity of sciencewithout metaphysics”. This was a normative criterion of unitywith a role in social reform based on the demarcation between scienceand metaphysics: a unity of method and language that included all thesciences, natural and social. A common method did not necessarilyimply a more substantive unity of content involving theories and theirconcepts.

A stronger reductive model within the Vienna Circle was recommended byRudolf Carnap in his The Logical Construction of the World(1928). While embracing the Kantian connotation of the term“constitutive system”, it was inspired by recent formalstandards: Hilbert’s axiomatic approach to formulating theoriesin the exact sciences and Frege’s and Russell’s logicalconstructions in mathematics. It was also predicated on the formalvalues of simplicity, rationality, (philosophical) neutrality andobjectivity associated with scientific knowledge. In particular,Carnap tried to explicate such notions in terms of a rationalreconstruction of science in terms of a method and a structure basedon logical constructions out of (1) basic concepts in axiomaticstructures and (2) rigorous, reductive logical connections betweenconcepts at different levels.

Different constitutive systems or logical constructions would servedifferent (normative) purposes: a theory of science and a theory ofknowledge. Both foundations raised the issue of the nature anduniversality of a physicalist language.

One such system of unified science is the theory of science, in whichthe construction connects concepts and laws of the different sciencesat different levels, with physics and its genuine laws as fundamental,lying at the base of the hierarchy. Because of the emphasis on theformal and structural properties of our representations, objectivity,rationality and unity go hand in hand. Carnap’s formal emphasisdeveloped further in Logical Syntax of Language (1934).Alternatively, all scientific concepts could be constituted orconstructed in a different system in the protocol language out ofclasses of elementary complexes of experiences, scientificallyunderstood, representing experiential concepts. Carnap subsequentlydefended the epistemological and methodological universality ofphysicalist language and physicalist statements. The unity of sciencein this context was an epistemological project (for a survey of theepistemological debates, see Uebel 2007; on different strands of theanti-metaphysical normative project of unity see Frost-Arnold2005).

Whereas Carnap aimed at rational reconstructions, another member ofthe Vienna Circle, Otto Neurath, favored a more naturalistic andpragmatic approach, with a less idealized and reductive model ofunity. His evolving standards of unity were generally motivated by thecomplexity of empirical reality and the application of empiricalknowledge to practical goals. He spoke of an“encyclopedia-model”, opposed to the classic ideal of apyramidal, reductive “system-model”. Theencyclopedia-model took into account the presence within science ofineliminable and imprecise terms from ordinary language and the socialsciences and emphasized a unity of language and the local exchanges ofscientific tools. Specifically, Neurath stressed the material-thinglanguage called “physicalism”, not to be confounded withthe emphasis on the vocabulary of physics. Its motivation was partlyepistemological, and Neurath endorsed anti-foundationalism; no unifiedscience, like a boat at sea, would rest on firm foundations. Thescientific spirit abhorred dogmatism. This weaker model of unityemphasized empiricism and the normative unity of the natural and thehuman sciences.

Like Carnap’s unified reconstructions, Neurath’s hadpragmatic motivations. Unity without reductionism provided a tool forcooperation and it was motivated by the need for successfultreatment—prediction and control—of complex phenomena inthe real world that involved properties studied by different theoriesor sciences (from real forest fires to social policy): unity ofscience at the point of action. It is an argument from holism, thecounterpart of Duhem’s claim that only clusters of hypothesesare confronted with experience. Neurath spoke of a “boat”,a “mosaic”, an “orchestration”, and a“universal jargon”. Following institutions such as theInternational Committee on Monism and the International Council ofScientific Unions, Neurath spearheaded a movement for Unity of Sciencein 1934 that encouraged international cooperation among scientists andlaunched the project of an International Encyclopedia of Unity ofScience. It expressed the internationalism of his socialistconvictions and the international crisis that would lead to the SecondWorld War (Kamminga and Somsen 2016).

At the end of the Eighth International Congress of Philosophy, held inPrague in September of 1934, Neurath proposed a series ofInternational Congresses for the Unity of Science. These took place inParis, 1935; Copenhagen, 1936; Paris, 1937; Cambridge, England, 1938;Cambridge, Massachusetts, 1939; and Chicago, 1941. For theorganization of the congresses and related activities, Neurath foundedthe Unity of Science Institute in 1936 (renamed in 1937 as theInternational Institute for the Unity of Science) alongside theInternational Foundation for Visual Education, founded in 1933. TheInstitute’s executive committee was composed of Neurath, PhilipFrank and Charles Morris.

After the Second World War, a discussion of unity engaged philosophersand scientists in the Inter-Scientific Discussion Group, first as theScience of Science Discussion Group, in Cambridge, Massachusetts,founded in October 1940 primarily by Philip Frank and Carnap(themselves founders of the Vienna Circle), Quine, Feigl, Bridgman,and the psychologists E. Boring and S.S. Stevens. This would laterbecome the Unity of Science Institute. The group was joined byscientists from different disciplines, from quantum mechanics (Kembleand Van Vleck) and cybernetics (Wiener) to economics (Morgenstern), aspart of what was both a self-conscious extension of the Vienna Circleand a reflection of local concerns within a technological cultureincreasingly dominated by the interest in computers and nuclear power.The characteristic feature of the new view of unity was the ideas ofconsensus and, subsequently, especially within the USI,cross-fertilization. These ideas were instantiated in the emphasis onscientific operations (operationalism) and the creation of war-boostedcross-disciplines such as cybernetics, computation, electro-acoustics,psycho-acoustics, neutronics, game theory and biophysics (Galison1998; Hardcastle 2003).

In the late 1960s, Michael Polanyi and Marjorie Grene organized aseries of conferences funded by the Ford Foundation on unity ofscience themes (Grene 1969a, 1969b, 1971). Their general character wasinterdisciplinary and anti-reductionist. The group was originallycalled “Study Group on Foundations of Cultural Unity”, butthis was later changed to “Study Group on the Unity ofKnowledge”. By then, a number of American and internationalinstitutions were already promoting interdisciplinary projects inacademic areas (Klein 1990). For both Neurath and Polanyi, theorganization of knowledge and science, the Republic of Science, wasinseparable from ideals of political organization.

Over the last four decades much historical and philosophicalscholarship has challenged the ideals of monism and reductionism andpursued a growing critical interest in pluralism and interdisciplinarycollaboration (see below). Along the way, the distinction between thehistorical human sciences and ahistorical natural sciences hasreceived much critical and productive attention. One outcome has beenthe application and development of concepts and accounts in philosophyof history in understanding different human and natural sciences ashistorical, with a special focus on the epistemic role of unifyingnarratives and standards and problems in disciplines such asarcheology, geology, cosmology and paleontology (see, for instance,Morgan and Wise 2017; Currie 2019). Another outcome has been a renewedcritique of the autonomy of the social sciences. One concern is, forinstance, the raising social and economic value of the naturalsciences and their influence on the models and methods of the socialsciences; another is the influence on both of certain particularpolitical and economic views. Other related concerns are the role ofthe social sciences in political life and the assumption that humansare unique and superior to animals and emerging technologies (see, forinstance, van Bouwel 2009b; Kincaid and van Bouwel 2023).

2. Varieties of Unity

The historical introductory sections have aimed to show theintellectual centrality, varying formulations, and significance of theconcept of unity. The rest of the entry presents a variety of modernthemes and views. It will be helpful to introduce a number of broadcategories and distinctions that can sort out different kinds ofaccounts and track some relations between them, as well as additionalsignificant philosophical issues. (The categories are not mutuallyexclusive, and they sometimes partly overlap. Therefore, while theyhelp label and characterize different positions, they cannot provide asimple, easy and neatly ordered conceptual map.)

Connective unity is a weaker and more general notion than the specificideal of reductive unity; this requires asymmetric relationsof reduction (see below), which typically rely on assumptions abouthierarchies of levels of description and the primacy—conceptual,ontological, epistemological and so on—of a fundamentalrepresentation. The category of connective unity helps accommodate andbring attention to the diversity of non-reductive accounts.

Another useful distinction is between synchronic anddiachronic unity. Synchronic accounts are ahistorical,assuming no meaningful temporal relations. Diachronic accounts, bycontrast, introduce genealogical hypotheses involving asymmetrictemporal and causal relations between entities or states of thesystems described. Evolutionary models are of this kind; they may bereductive to the extent that the posited original entities are simplerand on a lower level of organization and size. Others simply emphasizeconnection without overall directionality.

In general, it is useful to distinguish between ontologicalunity and epistemological unity, even if many accountsbear both characteristics and fall under both rubrics. In some cases,one kind supports the other salient kind in the model. Ontologicalunity is here broadly understood as involving relations betweendescriptive conceptual elements; in some cases, the concepts willdescribe entities, facts, properties or relations, and descriptivemodels will focus on metaphysical aspects of the unifying connectionssuch as holism, emergence, or downwards causation. Epistemologicalunity applies to epistemic relations or goals such as explanation.Methodological connections and formal (logical, mathematical, etc.)models may belong in this kind. This article does not draw any strictor explicit distinction between epistemological and methodologicaldimensions or modes of unity.

Additional possible categories and distinctions include the following:vertical unity or inter-level unity is unity ofelements attached to levels of analysis, composition or organizationon a hierarchy, whether for a single science or more, whereashorizontal unity or intra-level unity applies to onesingle level and to its corresponding kind of system (Wimsatt 2007).Global unity is unity of any other variety with a universalquantifier of all kinds of elements, aspects or descriptionsassociated with individual sciences as a kind of monism, forinstance, taxonomical monism about natural kinds, while localunity applies to a subset. (Cartwright has distinguished thissame-level global form of reduction, or “imperialism”, inCartwright 1999; see also Mitchell 2003). Obviously, vertical andhorizontal accounts of unity can be either global or local. Finally,the rejection of global unity has been associated with bothisolationism—keeping independent competing alternativerepresentations of the same phenomena or systems—as well as withlocal integration—the local connective unity of thealternative perspectives. A distinction of methodological naturecontrasts internal and external perspectives,according to whether the accounts are based naturalistically on thelocal contingent practices of certain scientific communities at agiven time or based on universal metaphysical assumptions broadlymotivated (Ruphy 2017). (Ruphy has criticized Cartwright andDupré for having adopted external metaphysical positions anddefended the internal perspective, also present in the program of theso-called Minnesota School, i.e., Kellert et al. 2006.)

3. Epistemological unities

3.1 Reduction

The project of unity, as mentioned above, has long guided models ofscientific understanding by privileging descriptions of morefundamental entities and phenomena such as the powers and behaviors ofatoms, molecules and machines. Since at least the 1920s and until the1960s, unity was understood in terms of formal approaches to theories,of semantic relations between vocabularies and of logical relationsbetween linguistic statements in those vocabularies. The ideal ofunity was formulated, accordingly, in terms of reduction relations tomore fundamental terms and statements. Different accounts have sincestood and fallen with any such commitments. Also, note thatidentifying relations of reduction must be distinguished fromthe ideal of reductionism. Reductionism is the adoption ofreduction relations as the global ideal or standard of a properunified structure of scientific knowledge; and distance from thatideal was considered a measure of its unifying progress.

In general, reduction reconciles ontological and epistemologicalconsiderations of identity and difference. Claims such as“mental states are reduceable to neurochemical states”,“chemical differences reduce to differences between atomicstructures” and “optics can be reduced toelectromagnetism” imply the truth of identitystatements—a strong ontological reduction. However, therelations of reduction between entities or properties in such claimsalso get additional epistemic value from the expressed semanticdiversity of conceptual content and the asymmetry of the relationdescribed in such claims between the reducing and the reducedclaims—concepts, laws, theories, etc. (Riel 2014).

Elimination and eliminativism are the extreme forms of reduction andreductionism that commit to aligning the epistemic content with theontological content fixed by the identity statements: since only xexists and claims about x best meet scientific goals, only talk of xmerits scientific consideration and use.

Two formulations of unification in the logical positivist tradition ofthe ideal logical structure of science placed the question of unity atthe core of philosophy of science: Carl Hempel’sdeductive-nomological model of explanation and Ernst Nagel’smodel of reduction. Both are fundamentally epistemological models, andboth are specifically explanatory, at least in the sense thatexplanation serves unification. The emphasis on language and logicalstructure makes explanatory reduction a form of unity of thesynchronic kind. Still, Nagel’s model of reduction is a model ofscientific structure and explanation as well as of scientificprogress. It is based on the problem of relating different theories asdifferent sets of theoretical predicates (Nagel 1961).

Reduction requires two conditions: connectability andderivability. Connectability of laws of different theoriesrequires meaning invariance in the form of extensionalequivalence between descriptions, with bridge principles betweencoextensive but distinct terms in different theories.

Nagel’s account distinguishes two kinds of reductions:homogenous and heterogeneous. When both sets ofterms overlap, the reduction is homogeneous. When the related termsare different, the reduction is heterogeneous. Derivability requires adeductive relation between the laws involved. In the quantitativesciences, the derivation often involves taking a limit. In this sensethe reduced science is considered an approximation to thereducing new one.

Neo-Nagelian accounts have attempted to solve Nagel’s problem ofreduction between putatively incompatible theories. The followingparagraphs list a few.

Nagel’s two-term relation account has been modified by weakerconditions of analogy and a role for conventions, requiring it to besatisfied not necessarily by the two original theories, \(T_1\) and\(T_2\), which are respectively new and old and more and less general,but by the modified theories \(T'_1\) and \(T'_2\). Explanatoryreduction is strictly a four-term relation in which \(T'_1\) is“strongly analogous” to \(T_1\) and corrects, with theinsight that the more fundamental theory can offer, the older theory,\(T_2\), changing it to \(T'_2\). Nagel’s account also requiresthat bridge laws be synthetic identities, in the sense that they befactual, empirically discoverable and testable; in weaker accounts,admissible bridge laws may include elements of convention (Schaffner1967; Sarkar 1998). The difficulty lay especially with the task ofspecifying or giving a non-contextual, transitive account of therelations between \(T\) and \(T'\) (Wimsatt 1976).

An alternative set of semantic and syntactic conditions of reductionbears counterfactual interpretations. For instance, syntacticconditions may take the form of limit relations (e.g., classicalmechanics reduces to relativistic mechanics for the value of the speedof light c 0 and to quantum mechanics for the value of thePlanck constant h 0) and ceteris paribus assumptions(e.g., when optical laws can be identified with results of the theoryof electromagnetism); then, each condition helps explain why thereduced theory works where it does and fails where it does not(Glymour 1969).

A different approach to reductionism acknowledges a commitment toproviding explanation but rejects the value of a focus on the role oflaws. This approach typically draws a distinction between hardsciences such as physics and chemistry and special sciences such asbiology and the social sciences. It claims that laws that are in asense operative in the hard sciences are not available in the specialones, or play a more limited and weaker role, and this on account ofhistorical character, complexity or reduced scope. The rejection ofempirical laws in biology, for instance, has been argued on grounds ofhistorical dependence on contingent initial conditions (Beatty 1995),and as matter of supervenience (see the entry onsupervenience)of spatio-temporally restricted functional claims on lower-levelmolecular ones, and the multiple realization (see the entry onmultiple realizability)of the former by the latter (Rosenberg 1994; Rosenberg’sargument from supervenience to reduction without laws must becontrasted with Fodor’s physicalism about the special sciencesabout laws without reduction (see below and the entry onphysicalism);for a criticism of these views see Sober 1996). This non-Nagelianapproach assumes further that explanation rests on identities betweenpredicates and deductive derivations (reduction and explanation mightbe said to be justified by derivations, but not constituted by them;see Spector 1978). Explanation is provided by lower-level mechanisms;their explanatory role is to replace final why-necessarily questions(functional) with proximate how-possibly questions (molecular).

One suggestion to make sense of the possibility of the superveningfunctional explanations without Nagelian reduction may rely on anontological type of relation of reduction such as the composition ofpowers in explanatory mechanisms (Gillette 2010, 2016). The reductivecommitment to the lower level is based on relations of composition, atplay in epistemological analysis and metaphysical synthesis, but ismerely formal and derivational. We may be able to infer what composesthe higher level, but we cannot simply get all the relevant knowledgeof the higher level from our knowledge of the lower level (see alsoAuyang 1998). This kind of proposal points to epistemicanti-reductionism.

Note that significant proposals of reductive unity rely on ontologicalassumptions about some hierarchy of levels organizing reality andscientific theories of it (more below).

A more general characterization views reductionism as a researchstrategy. On this methodological view reductionism can becharacterized by a set of so-called heuristics (non-algorithmic,efficient, error-based, purpose-oriented, problem-solving tasks)(Wimsatt 2006): heuristics of conceptualization (e.g., descriptivelocalization of properties, system-environment interface determinism,level and entity-dependence), heuristics of model-building and theoryconstruction (e.g., model intra-systemic localization with emphasis ofstructural properties over functional ones, contextual simplificationand external generalization) and heuristics of observation andexperimental design (e.g., focused observation, environmental control,local scope of testing, abstract shared properties, behavioralregularity and context-independence of results).

3.2 Antireductionism

Since the 1930s, the focus was on a syntactic approach, with physicsas the paradigm of science, deductive logical relations as the form ofcognitive or epistemic goals such as explanation and prediction, andtheory and empirical laws as paradigmatic units of scientificknowledge (Suppe 1977; Grünbaum and Salmon 1988). The historicistturn in the 1960s, the semantic turn in philosophy of science in the1970s and a renewed interest in special sciences has changed thisfocus. The very structure of hierarchy of levels has lost itscredibility, even for those who believe in it as a model of autonomyof levels rather than as an image of fundamentalism. The rejection ofsuch models and their emendations have occupied the last four decadesof philosophical discussion about unity in and of the sciences(especially in connection to psychology and biology, and more recentlychemistry). A valuable consequence has been the strengthening ofphilosophical projects and communities devoting more sustained andsophisticated attention to special sciences, different fromphysics.

The first target of antireductionist attacks has been Nagel’sdemand of extensional equivalence. It has been dismissed as aninadequate demand of “meaning invariance” andapproximation, and with it the possibility of deductive connections.Mocking the positivist legacy of progress through unity, empiricismand anti-dogmatism, these constraints have been decried asintellectually dogmatic, conceptually weak and methodologically overlyrestrictive (Feyerabend 1962). The emphasis is placed, instead, on themerits of the new theses of incommensurability and methodologicalpluralism.

A similar criticism of reduction involves a different move: that thedeductive connection be guaranteed provided that the old, reducedtheory was “corrected” beforehand (Shaffner 1967). Theevolution and the structure of scientific knowledge could be neatlycaptured, using Schaffner’s expression, by “layer-cakereduction”. The terms “length” and“mass”—or the symbols \(l\) and \(m\)—forinstance, may be the same in Newtonian and relativistic mechanics, orthe term “electron” the same in classical physics andquantum mechanics, or the term “atom” the same in quantummechanics and in chemistry, or “gene” in Mendeliangenetics and molecular genetics (see, for instance, Kitcher 1984). Butthe corresponding concepts, it is argued, are not. Concepts or wordsare to be understood as getting their content or meaning within aholistic or organic structure, even if the organized wholes are thetheories that include them. From this point of view, different wholes,whether theories or Kuhnian paradigms, manifest degrees of conceptualincommensurability. As a result, the derived, reducing theoriestypically are not the allegedly reduced, older ones; and theirderivation sheds no relevant insight into the relation between theoriginal, older one and the new (Feyerabend 1962; Sklar 1967).

From a historical standpoint, the positivist model collapsed thedistinction between synchronic and diachronic reduction, that is,between reductive models of the structure and the evolution, orsuccession, of scientific theories. By contrast, historicism, asembraced by Kuhn and Feyerabend, drove a wedge between the twodimensions and rejected the linear model of scientific change in termsof accumulation and replacement. For Kuhn, replacement becomes partlycontinuous, partly non-cumulative change in which one world—or,less literally, one world-picture, one paradigm—replaces another(after a revolutionary episode of crisis and proliferation ofalternative contenders) (Kuhn 1962). This image constitutes a form ofpluralism, and, like the reductionism it is meant to replace,it can be either synchronic or diachronic. Here iswhere Kuhn and Feyerabend parted ways. For Kuhn, synchronic pluralismonly describes the situation of crisis and revolution betweenparadigms. For Feyerabend, history is less monistic, and pluralism isand should remain a synchronic and diachronic feature of science andculture (Feyerabend, here, thought science and society inseparable,and followed Mill’s philosophy of liberal individualism anddemocracy).

A different kind of antireductionism addresses a more conceptualdimension, the problem of categorial reduction:Meta-theoretical categories of description and interpretation formathematical formalisms, e.g., criteria of causality, may block fullreduction. Basic interpretative concepts that are not just variablesin a theory or model are not reducible to counterparts in fundamentaldescriptions (Cat 2000; the case of individuality in quantum physicshas been discussed in Healey 1991; Redhead and Teller 1991; Auyang1995; and, in psychology, in Block 2003).

3.3 Epistemic roles: From demarcation to explanation and evidence. Varieties of connective unity. Aesthetic value

Unity has been considered an epistemic virtue and goal, with differentmodes of unification associated with roles such as demarcation,explanation and evidence. It can also be traced to synthetic cognitivetasks of categorization and reasoning—also applied in thesciences—especially through relations of similarity anddifference (Cat 2022b).

Demarcation. Certain models of unity, which we may callcontainer models, attempt to demarcate science from non-science. Thecriteria adopted are typically methodological and normative, notdescriptive. Unlike connective models, they serve a dual function ofdrawing up and policing a boundary that (1) encloses and endorses thesciences and (2) excludes other practices. As noted above, somedemarcation projects have aimed to distinguish between natural andspecial sciences. The more notorious ones, however, have aimed toexclude practices and doctrines dismissed under the labels ofmetaphysics, pseudo-science or popular knowledge. Empirical or not,the applications of standards of epistemic purity are not merelyidentification or labeling exercises for the sake of carving outscientific inquiry as a natural kind or mapping out intellectuallandscapes. The purpose is to establish authority and the stakesinvolve educational, legal and financial interests. Recentcontroversies include not just the teaching of creation science, butalso polemics over the scientific status of, for instance, homeopathy,vaccination and models of plant neurology and climate change.

The most influential demarcation criterion has been Popper’soriginal anti-metaphysics barrier: the condition of empiricalfalsifiability of scientific statements. It required the logicallypossible relation to basic statements, linked to experience, that canprove general hypotheses to be false with certainty. For this purpose,he defended the application of a particular deductive argument, themodus tollens (Popper 1935/1951). Another demarcationcriterion is explanatory unity, empirically grounded. Hempel’sdeductive-nomological model characterizes the scientific explanationof events as a logical argument that expresses their expectability interms of their subsumption under an empirically testablegeneralization. Explanations in the historical sciences too must fitthe model if they are to count as scientific. They could then bebrought into the fold as bona fide scientific explanations even ifthey could qualify only as explanation sketches.

Since their introduction, Hempel’s model and its weaker versionshave been challenged as neither generally applicable nor appropriate.The demarcation criterion of unity is undermined by criteria ofdemarcation between natural and historical sciences. For instance,historical explanations have a genealogical or narrative form, or elsethey require the historian’s engaging problems or issuing aconceptual judgment that brings together meaningfully a set ofhistorical facts (recent versions of such decades-old arguments are inCleland 2002, Koster 2009, Wise 2011). According to more radicalviews, natural sciences such as geology and biology are historical intheir contextual, causal and narrative forms; as well, Hempel’smodel, especially the requirement of empirically testable strictuniversal laws, is satisfied by neither the physical sciences nor thehistorical sciences, including archeology and biology (Ereshefsky1992).

A number of legal decisions have appealed to Popper’s andHempel’s criteria, adding the epistemic role of peer review,publication and consensus around the sound application ofmethodological standards. A more recent criterion has sought adifferent kind of demarcation: it is comparative rather than absolute;it aims to compare science and popular science; it adopts a broadernotion of the German tradition of Wissenschaften, that is,roughly of scholarly fields of research that include formal sciences,natural sciences, human sciences and the humanities; and it emphasizesthe role of systematicity, with an emphasis on different forms ofepistemic connectedness as weak forms of coherence and order(Hoyningen-Huene 2013).

Explanation. Unity has been defended in the wake of authorssuch as Kant and Whewell as an epistemic criterion of explanation orat least fulfilling an explanatory role. In other words, rather thanmodeling unification in terms of explanation, explanation is modeledin terms of unification. A number of proposals introduce anexplanatory measure in terms of the number of independent explanatorylaws or phenomena conjoined in a theoretical structure. On thisrepresentation, unity contributes understanding and confirmation fromthe fewest basic kinds of phenomena, regardless of explanatory powerin terms of derivation or argument patterns (Friedman 1974; Kitcher1981; Kitcher 1989; Wayne 1996; within a probabilistic framework,Myrvold 2003; Sober 2003; Roche and Sober 2017; see below).

A weaker position argues that unification is not explanation on thegrounds that unification is simply systematization of old beliefs andoperates as a criterion of theory-choice (Halonen and Hintikka1999).

The unification account of explanation has been defended within a moredetailed cognitive and pragmatist approach. The key is to think ofexplanations as question–answer episodes involving fourelements: the explanation-seeking question about \(P, P\)?, thecognitive state \(C\) of the questioner/agent for whom \(P\) calls forexplanation, the answer \(A\), and the cognitive state \(C+A\) inwhich the need for explanation of \(P\) has disappeared. A relatedaccount models unity in the cognitive state in terms of thecomparative increase of coherence and elimination of spuriousunity—such as circularity or redundancy (Schurz 1999).Unification is also based on information-theoretic transfer orinference relations. Unification of hypotheses is only a virtue if itunifies data. The last two conditions imply that unification yieldsalso empirical confirmation. Explanations are global increases inunification in the cognitive state of the cognitive agent (Schurz1999; Schurz and Lambert 1994).

The unification–explanation link can be defended on the groundsthat laws make unifying similarity expectable (henceHempel-explanatory), and this similarity becomes the content of a newbelief (Weber and Van Dyck 2002 contra Halonen and Hintikka 1999).Unification is not the mere systematization of old beliefs. ContraSchurz, they argue that scientific explanation is provided by novelunderstanding of facts and the satisfaction of our curiosity (Weberand Van Dyck 2002 contra Schurz 1999). In this sense, causalexplanations, for instance, are genuinely explanatory and do notrequire an increase of unification.

A contextualist and pluralist account argues that understanding is alegitimate aim of science that is pragmatic and not necessarilyformal, or a subjective psychological by-product of explanation (DeRegt and Dieks 2005). In this view explanatory understanding isvariable and can have diverse forms, such as causal-mechanical andunification, without conflict (De Regt and Dieks 2005). In the samespirit, Salmon linked unification to the epistemic virtue or goal ofexplanation and distinguished between unification andcausal-mechanical explanation as forms of scientific explanatoryunderstanding (Salmon 1998).

Explanation may also provide unification of different fields ofresearch through explanatory dependence so that one uses theother’s results to explain one’s own (Kincaid 1997).

The views on scientific explanation have evolved away from the formaland cognitive accounts of the epistemic categories. Accordingly, thesource of understanding provided by scientific explanations has beenmisidentified according to some (Barnes 1992). The genuine source forimportant, but not all, cases lies in causal explanation or causalmechanism (Cartwright 1983; Cartwright 1989; see also Glennan 1996;Craver 2007). Mechanistic models of explanation have become entrenchedin philosophical accounts of the life sciences (Darden 2006; Craven2007). As an epistemic virtue, the role of unification has been tracedto the causal form of the explanation, for instance, in statisticalregularities (Schurz 2015). The challenge extends to the allegedextensional link between explanation on the one hand, and truth anduniversality on the other (Cartwright 1983; Dupré 1993;Woodward 2003). In this sense, explanatory unity, which rests onmetaphysical assumptions about components and their properties, alsoinvolves a form of ontological or metaphysical unity. (For amethodological criticism of external, metaphysical perspectives, seeRuphy 2016.)

Similar criticisms extend to the traditionally formalist arguments inphysics about fundamental levels; there, unification fails to yieldexplanation in the formal scheme based on laws and their symmetries.Unification and explanation conflict on the grounds that in biologyand physics only causal mechanical explanations answeringwhy-questions yield understanding of the connections that contributeto “true unification” (Morrison2000;[2]Morrison’s choice of standard for evaluating the epistemicaccounts of unity and explanation and her focus on systematictheoretical connections without reduction has not been withoutcritics, e.g., Wayne 2002; Plutynski 2005; Karaca2012).[3]

Methodology. Unity has long been understood as amethodological principle, primarily, but not exclusively, inreductionist versions (e.g., for the case of biology, see Wimsatt1976, 2006). This is different from the case of unity throughmethodological prescriptions. One methodological criterion appeals tothe epistemic virtues of simplicity or parsimony, whetherepistemological or ontological (Sober 2003). As a formal probabilisticprinciple of curve-fitting or average predictive accuracy, therelevance of unity is objective. Unity plays the role of an empiricalbackground theory.

The methodological role of unification may track scientific progress.Unlike in the case of the explanatory role of unification presentedabove, this account of progress and interdisciplinarity relies on aunifying role of explanation: as in evo-devo in biology, unificationis a process of advancement in which two fields of research are in theprocess of unification through mutual explanatory relevance, that is,when results in one field are required to pose and address questionsin the other, raising explananda and explanations (Nathan 2017).

Heuristic dependence involves one influencing, accommodating,contributing to and addressing the other’s research questions(for examples relating chemistry and physics see Cat and Best2023).

Evidence. As in the relation of unification to explanation,unification is considered an epistemic criterion of evidence insupport of the unified account (for a non-probabilistic account of therelation between unification and confirmation, see Schurz 1999). Theresulting evidence and demonstration may be called synthetic evidenceand demonstration. Synthetic evidence may be the outcome of syntheticmodes of reasoning that rely on assumptions of similarity anddifference, for instance in cases of robustness, cross-checking andmeta-analysis (Cat 2022b).

Like probabilistic models of explanation, recent formal discussions ofunity and coherence within the framework of Bayesianism place unity inevidentiary reasoning (Forster and Sober 1994, sect. 7; Schurz andLambert 2005 is also a formal model, with an algebraic approach). Moregenerally, the probabilistic framework articulates formalcharacterizations of unity and introduces its role in evaluations ofevidence.

A criterion of unity defended for its epistemic virtue in relation toevidence is simplicity or parsimony (Sober 2013, 2016). Comparativelyspeaking, simpler hypotheses, models or theories present a higherlikelihood of truth, empirical support and accurate prediction. From amethodological standpoint, however, appeals to parsimony might not besufficient. Moreover, the connection between unity as parsimony andlikelihood is not interest-relative, at least in the way that theconnection between unity and explanation is (Sober 2003; Forster andSober 1994; Sober 2013, 2016).

On the Bayesian approach, the rational comparison and acceptance ofprobabilistic beliefs in the light of empirical data is constrained byBayes’ Theorem for conditional probabilities (where \(h\) and\(d\) are the hypothesis and the data respectively):

\[ \P(h \mid d) = \frac{\P(d \mid h) \cdot \P(h)}{P(d)} \]

One explicit Bayesian account of unification as an epistemic,methodological virtue, has introduced the following measure of unity:a hypothesis \(h\) unifies phenomena \(p\) and \(q\) to the degreethat given \(h, p\) is statistically/probabilistically relevant to (orcorrelated with) \(q\) (Myrvold 2003; for a probabilisticallyequivalent measure of unity in Bayesian terms see McGrew 2003; on theequivalence, Schupbach 2005). This measure of unity has beencriticized as neither necessary nor sufficient (Lange 2004;Lange’s criticism assumes the unification–explanationlink; in a rebuttal, Schupbach 2005 rejects this and other assumptionsbehind Lange’s criticism). In a recent development, Myrvoldargues for mutual information unification, i.e., that hypotheses aresaid to be supported by their ability to increase the amount of whathe calls the mutual information of the set of evidence statements (seeMyrvold 2017). The explanatory unification contributed by hypothesesabout common causes is an instance of the information condition.

Evidentiary unification may contribute to the unification of differentfields of research in the form of evidentiary dependence: Evidentiarydependence involves the appeal to the other’s results in theevaluation of one’s own (Kincaid 1997).

Aesthetic value. Finally, epistemic values of unity may relyon subsidiary considerations of aesthetic value. Nevertheless,consideration of beauty, elegance or harmony may also provideautonomous grounds for adopting or pursuing varieties of unificationin terms of simplicity and patterns of order (regularity of specificrelations) (McAllister 1996; Glynn 2010; Orrell 2012). Whetheraesthetic judgments have any epistemic import depends on metaphysical,cognitive or pragmatic assumptions.

Unification without reduction. Reduction is not the solestandard of unity, and models of unification without reduction haveproliferated. In addition, such models introduce new units ofanalysis. An early influential account centers around the notion ofinterfield theories (Darden and Maull 1977; Darden 2006). Theorthodox central place of theories as the unit of scientific knowledgeis replaced by that of fields. Examples of such fields are genetics,biochemistry and cytology. Different levels of organization correspondin this view to different fields: Fields are individuatedintellectually by a focal problem, a domain of facts related to theproblem, explanatory goals, methods and a vocabulary. Fields importand transform terms and concepts from others. The model is based onthe idea that theories and disciplines do not match neat levels oforganization within a hierarchy; rather, many of them in their scopeand development cut across different such levels. Reduction is arelation between theories within a field, not across fields.

Interdependence and hybridity. In general, the higher-leveltheories (for instance, cell physiology) and the lower-level theories(for instance, biochemistry) are ontologically and epistemologicallyinterdependent on matters of informational content and evidentialrelevance; one cannot be developed without the other (Kincaid 1996;Kincaid 1997; Wimsatt 1976; Spector 1977). The interaction betweenfields (through researchers’ judgments and borrowings) mayprovide enabling conditions for subsequent interactions. For instance,Maxwell’s adoption of statistical techniques in color researchenabled the introduction of similar ideas from social statistics inhis research on reductive molecular theories of gases. The reduction,in turn, enabled experimental evidence from chemistry and acoustics;similarly, different chemical and spectroscopic bases for colorsprovided chemical evidence in color research (Cat 2014).

The emergence and development of hybrid disciplines and theories isanother instance of non-reductive cooperation or interaction betweensciences. Noted above is the post-war emergence of interdisciplinaryareas of research: the so-called hyphenated sciences such asneuro-acoustics, radioastronomy, biophysics, etc. (Klein 1990, Galison1997) On a smaller scale, in the domain of, for instance, physics, onecan find semiclassical models in quantum physics or models developedaround phenomena where the limiting reduction relations are singularor catastrophic, such as caustic optics and quantum chaos (Cat 1998;Batterman 2002; Belot 2005). Such semiclassical explanatory modelshave not found successful quantum substitutes and have placedstructural explanations at the heart of the relation between classicaland quantum physics (Bokulich 2008). The general form of pervasivecases of emergence has been characterized with the notion ofcontextual emergence (Bishop and Atmanspacher 2006) whereproperties, behaviors and their laws on a restricted, lower-level,single-scale domain are necessary but not sufficient for theproperties and behaviors of another, e.g., higher-level one, not evenof itself. The latter are also determined by contingent contexts(contingent features of the state space of the relevant system). Theinterstitial formation of more or less stable small-scale synthesesand cross-boundary “alliances” has been common in mostsciences since the early twentieth century. Indeed, it is crucial todevelopment in model building and growing empirical relevance infields ranging anywhere from biochemistry to cell ecology, or fromeconophysics to thermodynamical cosmology. Similar cases can be foundin chemistry and the biomedical sciences.

Conceptual unity. The conceptual dimension of cross-cuttinghas been developed in connection with the possibility of cross-cuttingnatural kinds that challenges taxonomical monism. Categories oftaxonomy and domains of description are interest-relative, as arerationality and objectivity (Khalidi 1998; his view shares positionsand attitudes with Longino 1989; Elgin 1996, 1997). Cross-cuttingtaxonomic systems, then, are not conceptually inconsistent orinapplicable. Both the interest-relativity and hybridity featureprominently in the context of ontological pluralism (see below).

Another, more general, unifying element of this kind is Holton’snotion of themata. Themata are conceptual values that are apriori yet contingent (both individual and social). They are formingand organizing presuppositions that factor centrally in the evolutionof the science and include continuity/discontinuity, harmony,quantification, symmetry, conservation, mechanicism and hierarchy(Holton 1973). Unity of some kind is itself a thematic element. A morecomplex and comprehensive unit of organized scientific practice is thenotion of the various styles of reasoning, such asstatistical, analogical modeling, taxonomical, genetic/genealogical orlaboratory styles; each is a cluster of epistemic standards,questions, tools, ontology, and self-authenticating or stabilizingprotocols (Hacking 1996; see below for the relevance of this accountof a priori elements to claims of global disunity—the accountshares distinctive features of Kuhn’s notion of paradigm).

Another model of non-reductive unification is historical anddiachronic: it emphasizes the genealogical and historical identity ofdisciplines, which has become complex through interaction. Theinteraction extends to relations between specific sciences, philosophyand philosophy of science (Hull 1988). Hull has endorsed an image ofscience as a process, modeling historical unity after aDarwinian-style pattern of evolution (developing an earlier suggestionby Popper). Part of the account is the idea of disciplines asevolutionary historical individuals, which can be revised with thehelp of more recent ideas of biological individuality: hybrid unityas an external model of unity as integration or coordination ofindividual disciplines and disciplinary projects, e.g., characterizedby a form of occurrence, evolution or development whose tracking andidentification involves a conjunction with other disciplines, projectsand domains of resources, from within science or outside science.This diachronic perspective can accommodate models of discovery, inwhich genealogical unity integrates a variety of resources that can beboth theoretical and applied, or scientific and non-scientific (anexample, from physics, the discovery of superconductivity, can befound in Holton, Chang and Jurkowitz 1996). Some models of unity belowprovide further examples.

A generalization of the notion of interfield theories is the idea thatunity is interconnection: Fields are unified theoreticallyand practically (Grantham 2004). This is an extension of the originalmodes of unity or identity that single out individual disciplines.Theoretical unification involves conceptual, ontological andexplanatory relations. Practical unification involves heuristicdependence, confirmational dependence and methodological integration.The social dimension of the epistemology of scientific disciplinesrelies on institutional unity. With regard to disciplines asprofessions, this kind of unity has rested on institutionalarrangements such as professional organizations forself-identification and self-regulation, university mechanisms ofgrowth and reproduction through certification, funding and training,and communication and record through journals.

Many examples of unity without reduction are local rather than global.These are not merely a phase in a global and linear project ortradition of unification (or integration), and they are typicallyfocused on science as a human activity. From that standpoint,unification is typically understood or advocated as a piecemealdescription and strategy of collaboration (see Klein 1990 on thedistinction between global integration and local interdisciplinarity).Cases are restricted to specific models, phenomena or situations.

Material unity. A more recent approach to the connectionbetween different research areas has focused on a material level ofscientific practice, with attention to the use of instruments andother material objects (Galison 1997; Bowker and Star 1999). Forinstance, the material unity of natural philosophy in thesixteenth and seventeenth centuries relied on the circulation,transformation and application of objects in their concrete andabstract representations (Bertoloni-Meli 2006). The latter correspondto the imaginary systems and their representations, which we callmodels. The evolution of objects and images across different theoriesand experiments and their developments in nineteenth-century naturalphilosophy provide a historical model of scientific development, butthe approach is not meant to illustrate reductive materialism, sincethe same objects and models work and are perceived as vehicles forabstract ideas, institutions, cultures, etc., or are prompted by them.On one view, objects are regarded as elements in so-called tradingzones (see below) with shifting meanings in the evolution oftwentieth-century physics, such as with the cloud chamber which wasfirst relevant to meteorology and next to particle physics (Galison1997). Alternatively, material objects have been given the status ofboundary objects, which provide the opportunity for expertsfrom different fields to collaborate through their respectiveunderstandings of the system in question and their respective goals(Bowker and Star 1999).

Graphic unity. At the concrete perceptual level, recentaccounts emphasize the role of visual representations in the sciencesand suggest what may be called graphic unification of thesciences. Their cognitive roles, methodological and rhetorical,include establishing and disseminating facts and their so-calledvirtual witnessing, revealing empirical relations, testing their fitwith available patterns of more abstract theoretical relations(theoretical integration), suggesting new ones, aiding incomputations, serving as aesthetic devices etc. But these uses are nothomogeneous across different sciences and make visible disciplinarydifferences. We may equally speak of graphic pluralism. Therates in the use of diagrams in research publications appear to varyalong the hard–soft axis of pyramidal hierarchy, from physics,chemistry, biology, psychology, economics and sociology, and politicalscience (Smith et al. 2000). The highest use can be found in physics,intuitively identified by the highest degree of hardness understood asconsensus, codification, theoretical integration and factualstability, to the highest interpretive and instability of results.Similarly, the same variation occurs among sub-disciplines within eachdiscipline. The kinds of images and their contents also vary acrossdisciplines and within disciplines, ranging from hand-made images ofparticular specimens to hand-made or mechanically generated images ofparticulars standing in for types, to schematic images of geometricpatterns in space or time, or to abstract diagrams representingquantitative relations. Importantly, graphic tools circulate likeother cognitive tools between areas of research that they in turnconnect (Galison 1997; Daston and Galison 2007; Lopes 2009; see alsoLynch and Woolgar 1990; Baigrie 1996; Jones and Galison 1998; Galison1997; Cat 2014; Kaiser 2005).

Disciplinary unity and collaboration. The relation betweendisciplines or fields of research has often been tracked by relationsbetween their respective theories or epistemic products. Butdisciplines constitute broader and richer units of analysis ofconnections in the sciences characterized, for instance, by theirdomain of inquiry, cognitive tools and social structure (Bechtel1987).

Unification of disciplines, in that sense, has been variouslycategorized, for instance, as interdisciplinary,multidisciplinary, crossdisciplinary ortransdisciplinary (Klein 1990; Graff 2005; Kellert 2008;Repko 2012). It might involve a researcher borrowing from differentdisciplines or the collaboration of different researchers. Neithermodality of connection amounts to a straightforward generalization of,or reduction to, any single discipline, theory, etc. In either case,the strategic development is typically defended for its heuristicproblem-solving or innovative powers, as it is prompted by a problemthat is considered complex in that it does not arise or cannot befully treated within the purview of one specific discipline unified orindividuated around some potentially non-unique set of elements suchas scope of empirical phenomena, rules, standards, techniques,conceptual and material tools, aims, social institutions, etc.Indicators of disciplinary unity may vary (Kuhn 1962; Klein 1990;Kellert 2008). Interdisciplinary research or collaborationcreates a new discipline or project, such as interfield research,often leaving the existence of the original ones intact.Multidisciplinary work involves the juxtaposition of thetreatments and aims of the different disciplines involved inaddressing a common problem. Crossdisciplinary work involvesborrowing resources from one discipline to serve the aims of a projectin another. Transdisciplinary work is a synthetic creationthat encompasses work from different disciplines (Klein 1990; Kellert2008; Brigandt 2010; Hoffmann, Schmidt and Nersessian 2012; Osbeck etal. 2011; Repko 2012). These different modes of synthesis orconnection are not mutually exclusive.

Models of interdisciplinary cooperation and their correspondingoutcomes are often described using metaphors of different kinds:cartographic (domains, boundaries, trading zone, etc.),linguistic (pidgin language, communication, translation,etc.), architectural (building blocks, tiles, etc.),socio-political (imperialism, hierarchy, republic,orchestration, negotiation, coordination, cooperation, etc.) orembodied (cross-training). Each selectively highlights andneglects different aspects of scientific practice and properties ofscientific products. Cartographic and architectural images, forinstance, focus on spatial and static synchronic relations and simplyconnected, compatible elements. Socio-political and embodied imagesemphasize activity and non-propositional elements (Kellert 2008defends the image of cross-training).

In this context, methodological unity often takes the form ofborrowing standards and techniques for the application of formal andempirical methods. They range from calculational techniques and toolsfor theoretical modeling and simulation of phenomena to techniques formodeling of data, using instruments and conducting experiments (e.g.,the culture of field experiments and, more recently, randomizedcontrol trials across natural and social sciences). A key element ofscientific practice, often ignored by philosophical analysis, isexpertise. As part of different forms of methodological unity, it iskey to the acceptance and successful appropriation of techniques.Recent accounts of multidisciplinary collaboration as a human activityhave focused on the dynamics of integrating different kinds ofexpertise around common systems or goals of research (Collins andEvans 2007; Gorman 2002). The same perspective can accommodate therecent interest in so-called mixed methods, e.g., different forms ofintegration of quantitative and qualitative methods and approaches inthe social sciences (but mixed-method approaches do not typicallyinvolve mixed disciplines).

As teamwork and collaboration within and between research units hassteadily increased, so has the degree of specialization (Wutchy et al.2007). Between both trends, new reconfigurations keep forming withdifferent purposes and types of institutional expression and support;for example, STEM, Earth sciences, physical sciences, mind–brainsciences, etc., in addition to hybrid fields mentioned above. Yet,in educational research and funding, disciplinarity has acquirednew normative purchase in opposite directions: while funding agenciesand universities promote interdisciplinarity, universityadministrations encourage both disciplinary competition and moreversatile adisciplinarity (Griffiths 2022). In the face of defenses ofdifferent forms of interdisciplinarity (Graff 2015), there is also arenewed attention to the critical value of autonomy of disciplines, ordisciplinarity, as the key resource in division of labor andcollaboration alike (Jacobs 2013).

The social epistemology of interdisciplinarity is complex. It developsboth top-down from managers and bottom-up from practitioners(Mäki 2016; Mäki and MacLeod 2016), relying on a variety ofkinds of interactions with heuristic and normative dimensions(Boyer-Kassem et al. 2018). More generally, collaborative workarguably provides epistemic, ethical and instrumental advantages,e.g., more comprehensive relevant understanding of complex problems,expanded justice to interests of direct knowledge users and increasedresources (Laursen et al. 2021). Yet, collaboration relies on aplurality of values or norms that may lead to conflicts such as aparalyzing practical incoherence of guiding values and moralincoherence and problematic forms of oppression (Laursen et al.2021; see more on the limits of pluralism below).

Empirical work in sociology and cognitive psychology on scientificcollaboration has led to a broader perspective, including a number ofdimensions of interdisciplinary cooperation involving identificationof conflicts and the setting of sufficient so-called common groundintegrators. These include shared (pre-existing, revised and newlydeveloped) concepts, terminology, standards, techniques, aims,information, tools, expertise, skills (abstract, dialectical, creativeand holistic thinking), cognitive and social ethos (curiosity,tolerance, flexibility, humility, receptivity, reflexivity, honesty,team-play) social interaction, institutional structures andgeography (Cummings and Kiesler 2005; Klein 1990; Kockelmans 1979;Repko 2012). Sociological studies of scientific collaboration can inprinciple place the connective models of unity within the more generalscope of social epistemology, for instance, in relation todistributive cognition (beyond the focus on strategies of consensuswithin communities).

The broad and dynamical approach to processes of interdisciplinaryintegration may effectively be understood to describe the productionof different sorts and degrees of epistemic emergence. The integratedaccounts require shared (old or new) assumptions and may involve acase of ontological integration, for instance in causal models.Suggested kinds of interdisciplinary causal-model integration are thefollowing: sequential causal order in a process or mechanism cuttingacross disciplinary divides; horizontal parallel integration ofdifferent causal models of different elements of a complex phenomenon;horizontal joint causal model of the same effect; and vertical orcross-level causal integration (see emergent or top-down causality,below) (Repko 2012; Kockelmans 1979).

The study of the social epistemology of interdisciplinary andcollaborative research has been carried out and proposed fromdifferent perspectives that illuminate different dimensions andimplications. These include historical typology (Klein 1990), formalmodeling (Boyer-Kassem et al. 2018), ethnography (Nersessian 2022),ethical, scientometrics and multidimensional philosophicalperspectives (Mäki 2016). Other approaches aim to design andoffer tools that facilitate collaboration such as the Toolbox DialogueInitiative (Hubbs et al. 2020). The different forms of plurality andconnection also ultimately inform the organization of science in thesocial and political terms of diversity and democracy (Longino 1998,2001). In terms of cooperation and coordination, unity, in this sense,cannot be reduced to consensus (Rescher 1993; van Bouwel 2009a; Repko2012; Hoffmann, Schmidt and Nersessian 2012.)

A general model of local interconnection, which has acquiredwidespread attention and application in different sciences, is theanthropological model of trading zone, where hybrid languagesand meanings are developed that allow for interaction withoutstraightforward extension of any party’s original language orframework (Galison 1997). Galison has applied this kind ofanthropological analysis to the subcultures of experimentation. Thisstrategy aims to explain the strength, coherence and continuity ofscience in terms of local coordinations of intercalatedlevels of symbolic procedures and meanings, instruments andarguments.

At the experimental level, instruments, as found objects, acquire newmeanings, developments and uses as they bridge over the transitionsbetween theories, observations or theory-laden observations.Instruments and experimental projects in the case of Big Science alsobring together, synchronically and interactively, the skills,standards and other resources from different communities, and theychange each in turn (on interdisciplinary experimentation see alsoOsbeck et al. 2011). Patterns of laboratory research are shared bythe different sciences, including not just instruments but the generalstrategies of reconfiguration of human researchers and the naturalentities researched (Knorr-Cetina 1992). This includes statisticalstandards (e.g., statistical significance) and ideals ofreplication. At the same time, attention has been paid to thedifferent ways in which experimental approaches differ among thesciences (Knorr-Cetina 1992; Guala 2005; Weber 2005) as well as to howthey have been transferred (e.g., field experiments and randomizedcontrol trials) or integrated (e.g., mixed methods combiningquantitative and qualitative techniques).

Interdisciplinary research has been claimed to revolve shared boundaryobjects (Gorman 2002) and to yield evidentiary and heuristicintegration through cooperation (Kincaid 1997). Successfulinterdisciplinary research, however, does not seem to requireintegration, e.g., evolutionary game theory in economics and biology(Grüne-Yanoff 2016). Heuristic cooperation has also led to newstable disciplines through stronger integrative forms of problemsolving. In the life sciences, for instance, computational,mathematical and engineering techniques for modeling and datacollection in molecular biology have led to integrative systemsbiology (MacLeod and Nersessian 2016; Nersessian 2022). Similarly,constraints and resources for problem-solving in physics, chemistryand biology led to the development of quantum chemistry (Gavroglu andSimões 2012; see also the case of nuclear chemistry in Cat andBest 2023).

4. Ontological unities

4.1 Ontological unities and reduction

Since Nagel’s influential model of reduction by derivation, mostdiscussions of the unity of science have been cast in terms ofreductions between concepts and the entities they describe, andbetween theories incorporating the descriptive concepts. Ontologicalunity is expressed by a preferred set of such ontological units. Inthis regard, it should be noted that the selection of units typicallyrelies on assumptions about classification or natural order such ascommitments to natural kinds or a hierarchy of levels.

In terms of concepts featured in preferred descriptions, explanatoryor not, reduction endorses taxonomical monism: a privileged set offundamental kinds of things. These privileged kinds are often known asso-called natural kinds; although, as it has been argued, monism doesnot entail realism (Slater 2005) and the notion admits of multipleinterpretations, ranging from the more conventionalist to the moreessentialist (Tahko 2021; see a critique in Cat 2022a). Naturalkindness has further been debated in terms, for instance, of thecontrast between so-called cluster and causal theories. Connectedly,pluralism does not entail anti-realism (Dupré 1993), nor doesrealism entail monism or essentialism (Khalidi 2021). Withoutadditional metaphysical assumptions, the fundamental units areambiguous with respect to their status as either entity or property.Reduction may determine the fundamental kinds or level through theanalysis of entities.

A distinctive ontological model is as follows. The hierarchy of levelsof reduction is fixed by part-whole relations. The levels ofaggregation of entities run all the way down to atomic particles andfield parts, rendering microphysics the fundamental science (Gillett2016). The focus of recent accounts has been placed on the relationbetween the causal powers at different levels and how lower-levelentities and powers determine higher-level ones. Discussions havecentered on whether the relation is of identity between types ortokens of things (Thalos 2013; Gillette 2016; Wilson 2021; see morebelow) or even if causal powers are the relevant unit of analysis(Thalos 2013).

A classic reference to this compositional type of account is Oppenheimand Putnam’s “The Unity of Science as a WorkingHypothesis” (Oppenheim and Putnam 1958; Oppenheim and Hempel hadworked in the 1930s on taxonomy and typology, a question of broadintellectual, social and political relevance in Germany at the time).Oppenheim and Putnam intended to articulate an idea of science as areductive unity of concepts and laws reduced to those of the mostelementary elements. They also defended it as an empiricalhypothesis—not an a priori ideal, project orprecondition—about science. Moreover, they claimed that itsevolution manifested a trend in that unified direction out of thesmallest entities and lowest levels of aggregation. In an importantsense, the evolution of science recapitulates, in the reverse, theevolution of matter, from aggregates of elementary particles to theformation of complex organisms and species (we find a similarassumption in Weinberg’s downward arrow of explanation). Unity,then, is manifested not just in mereological form, but alsodiachronically, genealogically or historically.

A weaker form of ontological reduction advocated for the biomedicalsciences with the causal notion of partial reductions:explanations of localized scope (focused on parts of higher-levelsystems only) laying out a causal mechanism connecting differentlevels in the hierarchy of composition and organization (Schaffner1993; Schaffner 2006; Scerri has similarly discussed degrees ofreduction in Scerri 1994). An extensional, domain-relative approachintroduces the distinction between “domain preserving” and“domain combining” reductions. Domain-preservingreductions are intra-level reductions and occur between \(T_1\) andits predecessor \(T_2\). In this parlance, however, \(T_2\)“reduces” to \(T_1\). This notion of“reduction” does not refer to any relation of explanation(Nickles 1973).

The claim that reduction, as a relation of explanation, needs to be arelation between theories or even involve any theory has also beenchallenged. One such challenge focuses on “inter-level”explanations in the form of compositional redescription andcausal mechanisms (Wimsatt 1976). The role of biconditionals or evenSchaffner-type identities, as factual relations, is heuristic (Wimsatt1976). The heuristic value extends to the preservation of thehigher-level, reduced concepts, especially for cognitive and pragmaticreasons, including reasons of empirical evidence. This amounts torejecting the structural, formal approach to unity and reductionismfavored by the logical-positivist tradition. Reductionism is anotherexample of the functional, purposive nature of scientific practice.The metaphysical view that follows is a pragmatic and non-eliminativerealism (Wimsatt 2006). As a heuristic, this kind of non-eliminativepragmatic reductionism is a complex stance. It is, across levels,integrative and intransitive, compositional, mechanistic andfunctionally localized, approximative and abstractive. It is bound toadopting false idealizations, focusing on regularities and stablecommon behavior, circumstances and properties. It is also constrainedin its rational calculations and methods, tool-binding andproblem-relative. The heuristic value of eliminative, inter-levelreductions has been defended as well (Poirier 2006).

The appeal to formal laws and deductive relations is dropped for setsof concepts or vocabularies in the replacement analysis(Spector 1978). This approach allows for talk of entity reduction orbranch reduction, and even direct theory replacement, without theoperation of laws, and it circumvents vexing difficulties raised bybridge principles and the deductive derivability condition(self-reduction, infinite regress, etc.). Formal relations onlyguarantee, but do not define, the reduction relation. Replacementfunctions are meta-linguistic statements. As Sellars argued in thecase of explanation, this account distinguishes between reduction andthe testing for reduction, and it highlights the role of derivationsin both. Finally, replacement can be in practice or in theory.Replacement in practice does not advocate elimination of the reducedor replaced entities or concepts (Spector 1978).

As indicated above, reductive models and associated organization ofscientific theories and disciplines assume an epistemic hierarchygrounded on an ontological hierarchy of levels of organization ofentities, properties or phenomena, from societies down to cells,molecules and subatomic elements. Patterns of behavior of entities atlower, more fundamental levels are considered more general, stable andexplanatory.

Levels forming a hierarchy are discrete and stratified so thatentities at level n strongly depend on entities at level \(n-1.\) Thedifferent levels may be distinguished in different ways: bydifferences in scale, by a relation of realization and, especially, bya relation of composition such that entities at level n are consideredcomposed of, or decomposable into, entities at level \(n-1.\)

This assumption has been the target of criticism (Thalos 2013;Potochnik 2017). Neither scales, realization nor decomposition can fixan absolute hierarchy of levels. Critics have noted, for instance,that entities may participate in causal interactions at multiplelevels and across levels in physical models (Thalos 2013) andacross biological and neurobiological models (Haug 2010; Eronen2013).

In addition, the compartmentalization of theories and their conceptsor vocabulary into levels neglects the existence of empiricallymeaningful and causally explanatory relations between entities orproperties at different levels. If they are neglected as theoreticalknowledge and left as only bridge principles, the possibility ofcompleteness of knowledge is jeopardized. Maximizing completeness ofknowledge requires a descriptive unity of all phenomena at all levelsand anything between these levels. Any bounded region or body ofknowledge neglecting such cross-boundary interactions is radicallyincomplete, and not just confirmationally or evidentially so; we mayrefer to this problem as the problem of cross-boundaryincompleteness at either intra-level or horizontalincompleteness and, on a hierarchy, the problem of inter-level orvertical incompleteness (Kincaid 1997; Cat 1998).

If levels cannot track, for instance, same-level causal relations,either their causal explanatory relevance is derivative and contextual(Craver 2007), their role is cognitive and pragmatic as in the role asconceptual coordinate systems or, more radically, altogetherdispensable (Thalos 2013; Potochnik 2017). As a result, they fail tofix a corresponding hierarchy of fields and subfields of scientificresearch defended by reductionist accounts.

The most radical form of reduction as replacement is often calledeliminativism. The position has made a considerable impact inphilosophy of psychology and philosophy of mind (Churchland 1981;Churchland 1986). On this view the vocabulary of the reducing theories(neurobiology) eliminates and replaces that of the reduced ones(psychology), leaving no substantive relation between them (which isonly a replacement rule) (see alsoeliminative materialism).

From a semantic standpoint, one may distinguish different kinds ofreduction in terms of four criteria, two epistemological and twoontological: fundamentalism, approximation, abstract hierarchy andspatial hierarchy. Fundamentalism implies that the featuresof a system can be explained in terms only of factors and rules fromanother realm. Abstract hierarchy is the assumption that therepresentation of a system involves a hierarchy of levels oforganization with the explanatory factors being located at the lowerlevels. Spatial hierarchy is a special case of abstracthierarchy in which the criterion of hierarchical relation is a spatialpart-whole or containment relation. Strong reduction satisfies thethree “substantive” criteria, whereas weak reduction onlysatisfies fundamentalism. Approximate reductions—strong andhierarchical—are those which satisfy the criterion offundamentalism only approximately (Sarkar 1998; the merit ofSarkar’s proposal resides in its systematic attention tohierarchical conditions and, more originally, to different conditionsof approximation; see also Ramsey 1995; Lange 1995).

The semantic turn extends to more recent notion of models that do notfall under the strict semantic or model-theoretic notion ofmathematical structures (Giere 1999; Morgan and Morrison 1999). Thisis a more flexible framework about relevant formal relations and thescope of relevant empirical situations. It is implicitly or explicitlyadopted by most accounts of unity without reduction. One may add theprimacy of temporal representation and temporal parts, temporalhierarchy or temporal compositionality, first emphasizedby Oppenheim and Putnam as a model of genealogical or diachronicunity. This framework applies to processes both of evolution anddevelopment (a more recent version is in McGivern 2008 and in Love andHütteman 2011).

The shift in the accounts of scientific theory from syntactic tosemantic approaches has changed conceptual perspectives and,accordingly, formulations and evaluations of reductive relations andreductionism. However, examples of the semantic approach focusing onmathematical structures and satisfaction of set-theoretic relationshave focused on syntactic features—including the axiomatic formof a theory—in the discussion of reduction (Sarkar 1998; daCosta and French 2003). In this sense, the structuralist approach canbe construed as a neo-Nagelian account, while an alternative line ofresearch has championed the more traditional structuralist semanticapproach (Balzer and Moulines 1996; Moulines 2006; Ruttkamp 2000;Ruttkamp and Heidema 2005).

4.2 Ontological unities and antireductionism

From the opposite direction, arguments concerning new concepts such asmultiple realizability and supervenience, introducedby Putnam, Kim, Fodor and others, have led to talk of higher-levelfunctionalism, a distinction between type-type and token-tokenreductions and the examination of its implications. The concepts ofemergence, supervenience and downward causation are relatedmetaphysical tools for generating and evaluating proposals about unityand reduction in the sciences. This literature has enjoyed its chiefsources and developments in general metaphysics and in philosophy ofmind and psychology (Davidson 1969; Putnam 1975; Fodor 1975; Kim1993).

Supervenience, first introduced by Davidson in discussions ofmental properties, is the notion that a system with properties on onelevel is composed of entities on a lower level and that its propertiesare determined by the properties of the lower-level entities orstates. The relation of determination is that no changes at thehigher-level occur without changes at the lower level. Liketoken-reductionism, supervenience has been adopted by many as the poorman’s reductionism (see the entry onsupervenience).A different case for the autonomy of the macrolevel is based on thenotion of multiple supervenience (Kincaid 1997; Meyering 2000).

The autonomy of the special sciences from physics has been defended interms of a distinction between type-physicalism andtoken-physicalism (Fodor 1974; Fodor countered Oppenheim andPutnam’s hypothesis under the rubric “the disunity ofscience”; see the entry onphysicalism).The key logical assumption is the type-token distinction, wherebytypes are realized by more specific tokens, e.g., the type“animal” is instantiated by different species, the type“tiger” or “electron” can be instantiated bymultiple individual token tigers and electrons. Type-physicalism ischaracterized by a type-type identity between thepredicates/properties in the laws of the special sciences and those ofphysics. By contrast, token-physicalism is based on the token-tokenidentity between the predicates/properties of the special sciences andthose of physics; every event under a special law falls under a law ofphysics and bridge laws express contingent token-identities betweenevents. Token-physicalism operates as a demarcation criterion formaterialism. Fodor argued that the predicates of the special sciencescorrespond to infinite or open-ended disjunctions of physicalpredicates, and these disjunctions do not constitute natural kindsidentified by an associated law. Token-physicalism is the onlyalternative. All special kinds of events are physical, but the specialsciences are not physics (for criticisms based on the presuppositionsin Fodor’s argument, see Sober 1999).

The denial of remedial, weaker forms of reductionism is the basis forthe concept of emergence (Humphreys 1997; Bedau and Humphreys2008; Wilson 2021). Different accounts have attempted to articulatethe idea of a whole being different from or more than the mere sum ofits parts (see the entry onemergent properties).Emergence has been described beyond logical relations, synchronicallyas an ontological property and diachronically as a material process offusion, in which the powers of the separate constituents lose theirseparate existence and effects (Humphreys 1997). This concept has beenwidely applied in discussions of complexity. Unlike theearliest antireductionist models of complexity in terms of holism andcybernetic properties, more recent approaches track the role ofconstituent parts (Simon 1996). Weak emergence has been opposed tonominal and strong forms of emergence. The nominal kind simplyrepresents that some macro-properties cannot be properties ofmicro-constituents. The strong form is based on supervenience andirreducibility, with a role for the occurrence of autonomous downwardscausation upon any constituents (see below). Weak emergence is linkedto processes stemming from the states and powers of constituents, witha reductive notion of downwards causation of the system as a resultantof constituents’ effects (Wilson 2021); however, the connectionis not a matter of Nagelian formal derivation, but of so-calleduniversality classes (Batterman 2002; Thalos 2013), self-organization(Mitchell 2012) and implementation through computational aggregation,compression and iteration. Weak emergence, then, can be defined interms of simulation: a macro-property, state or fact is weaklyemergent if and only if it can be derived from its macro-constituentsonly by simulation (Bedau and Humphreys 2008) The denial of remedial,weaker forms of reductionism is the basis for the concept ofemergence (Humphreys 1997; Bedau 2008); see the entry onsimulations in science).

Computational models of emergence or complexity straddle the boundarybetween formal epistemology and ontology. They are based onsimulations of chaotic dynamical processes such as cellular automata(Wolfram 1984, 2002). Their supposed superiority to combinatorialmodels based on aggregative functions of parts of wholes does not lackdefenders (Crutchfield 1994; Crutchfield and Hanson 1997; Humphreys2004, 2007, 2008; Humphreys and Huneman 2008; Huneman 2008a, 2008b,2010).

Connected to the concept of emergence is top-down ordownward causation, which captures the autonomous and genuinecausal power of higher-level entities or states, especially uponlower-level ones. The most extreme and most controversial versionincludes a violation of laws that regulate the lower level (Meehl andSellars 1956; Campbell 1974). Weaker forms require compatibility withthe microlaws (for a brief survey and discussion see Robinson 2005; ondownward causation without top-down causes, see Craver and Bechtel2007; Bishop 2012). The very concept has become the subject of someinterdisciplinary interest in the sciences (Ellis, Noble andO’Connor 2012).

Another general argument for the autonomy of the macrolevel in theform of non-reductive materialism has been a cognitive type offunctionalism, namely, cognitive pragmatism (Van Gulick 1992). Thisaccount links ontology to epistemology. It discusses four pragmaticdimensions of representations: the nature of the causal interactionbetween theory-user and the theory, the nature of the goals to therealization of which the theory can contribute, the role of indexicalelements in fixing representational content, and differences in theindividuating principles applied by the theory to its types (Wimsattand Spector’s arguments above are of this kind). A moreontologically substantive account of functional reduction isRamsey’s bottom-up construction by reduction:transformation reductions streamline formulations of theories in sucha way that they extend basic theories upwards by engineering theirapplication to specific context or phenomena. As a consequence, theyreveal, by construction, new relations and systems that areantecedently absent from a scientist’s understanding of thetheory—independently of a top or reduced theory (Ramsey 1995). Aweaker framework of ontological unification is categorialunity, wherein abstract categories such as causality,information, etc., are attached to the interpretation of the specificvariables and properties in models of phenomena.

5. Disunity and pluralism

A more radical departure from logical-positivist standards of unity isthe recent criticism of the methodological values of reductionism andunification in the sciences and also its position in culture andsociety. From the descriptive standpoint, many views under therubric of disunity are versions of positions mentioned above. Thedifference is mainly normative and a matter of emphasis, scope andperspective. Such views reject global or universal standards ofunity—including unity of method—by emphasizing disunityand endorsing different forms of epistemological and ontologicalpluralism.

5.1 The Stanford School

An influential picture of disunity comes from related works by membersof the so-called Stanford School such as John Dupré, IanHacking, Peter Galison, Patrick Suppes and Nancy Cartwright. Disunityis, in general terms, a rejection of universalism and uniformity, bothmethodological and metaphysical. Through their work, the rubric ofdisunity has acquired a visibility parallel to the one once acquiredby unity, as an inspiring philosophical rallying cry.

From a methodological point of view, members of the school havedefended, from analysis of actual scientific practice, a model oflocal unity such as the so-called trading-zone, (Galison 1998), aplurality of scientific methods (Suppes 1978), a plurality ofscientific styles with the function of establishing spaces ofepistemic possibility and a plurality of kinds of unities (Hacking1996; Hacking follows the historian A.A. Crombie; for a criticism ofHacking’s historical epistemology see Kusch 2010).

From a metaphysical point of view, the disunity of science can begiven adequate metaphysical foundations that make pluralism compatiblewith realism (Dupré 1993; Cartwright 1983, 1999). Dupréopposes a mechanistic paradigm of unity characterized by determinism,reductionism and essentialism. The paradigm spreads the values andmethods of physics to other sciences that he thinks are scientificallyand socially deleterious. Disunity appears characterized by threepluralistic theses: against essentialism—there is always aplurality of classifications of reality into kinds; againstreductionism—there exists equal reality and causal efficacy ofsystems at different levels of description (that is, the microlevel isnot causally complete, leaving room for downward causation); andagainst epistemological monism—there is no single methodologythat supports a single criterion of scientificity, nor a universaldomain of its applicability, leaving only a plurality of epistemic andnon-epistemic virtues. The unitary concept of science should beunderstood, following the later Wittgenstein, as a family-resemblanceconcept. (For a criticism of Dupré’s ideas, see Mitchell2003; Sklar 2003.)

Against the universalism of explanatory laws, Cartwright has arguedthat laws cannot be both universal and exactly true, as Hempelrequired in his influential account of explanation and demarcation;there exist only patchworks of laws and local cooperation. LikeDupré, Cartwright adopts a kind of scientific realism butdenies that there is a universal order, whether represented by atheory of everything or a corresponding a priori metaphysicalprinciple (Cartwright 1983). Theories apply only locally, where and tothe extent that their interpretive models fit the phenomena studied,ceteris paribus (Cartwright 1999). Cartwright’spluralism is not just opposed to vertical reductionism but alsohorizontal imperialism, or universalism and globalism. She explainstheir more or less general domain of application in terms of causalcapacities and arrangements she calls nomological machines(Cartwright 1989, 1999). The regularities they bring about depend on ashielded environment. As a matter of empiricism, this is the reasonthat it is in the controlled environment of laboratories andexperiments, where causal interference is shielded off, that factualregularities are manifested. The controlled, stable, regular world isan engineered world. Representation rests on intervention (cf. Hacking1983; for criticisms see Winsberg et al. 2000; Hoefer 2003; Sklar2003; Howhy 2003; Teller 2004; McArthur 2006; Ruphy 2016).

Disunity and autonomy of levels have been associated, conversely, withantirealism, meaning instrumentalist or empiricist heuristics. Thisincludes, for Fodor and Rosenberg, higher-level sciences such asbiology and sociology (Fodor 1974; Rosenberg 1994; Huneman 2010). Itis against this picture that Dupré’s andCartwright’s attacks on uniformly global unity and reductionism,above, might seem surprising by including an endorsement, in causalterms, ofrealism.[4]Rohrlich has defended a similar realist position about weaker,conceptual (cognitive) antireductionism, although on the grounds ofthe mathematical success of derivational explanatory reductions(Rohrlich 2001). Ruphy, however, has argued that antireductionismmerely amounts to a general methodological prescription and is tooweak to yield uncontroversial metaphysical lessons; these are in factbased on general metaphysical commitments external to scientificpractice (Ruphy 2005, 2016).

5.2 Pluralism

Unlike more descriptive accounts of plurality, pluralism is anormative endorsement of plurality. The question of the metaphysicalsignificance of disunity and anti-reductionism takes one straight tothe larger issue of the epistemology and metaphysics (and aesthetics,social culture and politics) of pluralism. And here one encounters thefamiliar issues and notions such as conceptual schemes, frameworks andworldviews, incommensurability, relativism, contextualism andperspectivalism about goals and standards of concepts and methods (fora general discussion see Lynch 1998; on perspectivalism aboutscientific models see Giere 1999, 2006; Rueger 2005; Massimi and McCoy2020).

In connection with relativism and instrumentalism, pluralism hastypically been associated with antirealism about taxonomicalpractices. But it has been defended from the standpoint of realism(for instance, Dupré 1993; Chakravartty 2011). Pluralism aboutknowledge of mind-independent facts can be formulated in terms ofdifferent ways to distribute properties (sociability-based pluralism),with more specific commitments about the ontological status of therelated elements and their plural contextual manifestations of powersor dispositions (Chakravartty 2011; Cartwright 2007).

From a more epistemological standpoint, pluralism applies widely toconcepts, explanations, virtues, goals, methods, models and kinds ofrepresentations (see above for graphic pluralism), etc. In this sense,pluralism has been defended as a general framework that rejects theideal of consensus in cognitive, evaluative and practical matters,against pure skepticism (nothing goes) or indifferentism (anythinggoes), including a defense of preferential and contextual rationalitythat notes the role of contextual rational commitments, by analogywith political forms of engagement (Rescher 1993; van Bouwel 2009a;Cat 2012).

Consider at least four distinctions—they are formulatedabout concepts, facts, and descriptions, and they apply also tovalues, virtues, methods, etc.:

  • Vertical vs. horizontal pluralism. Vertical pluralism isinter-level pluralism, the view that there is more than one level offactual description or kind of fact and that each is irreducible,equally fundamental, or ontologically/conceptually autonomous.Horizontal pluralism is intra-level pluralism, the view that there maybe incompatible descriptions or facts on the same level of discourse(Lynch 1998). For instance, the plurality of explanatory causes to bechosen from or integrated in biology or physics has been defended as alesson in pluralism (Sober 1999).
  • Global vs. local pluralism. Global pluralism is pluralismabout every type of fact or description. Global horizontal pluralismis the view that there may be incompatible descriptions of the sametype of fact. Global vertical pluralism is the view that no type offact or description reduces to any other. Local horizontal andvertical pluralism is about one type of fact or description (Lynch1998). It may also concern situated standpoints informed by, amongothers, social differences (Wylie 2015).
  • Difference vs. integrative pluralism. Differencepluralism has been defended in terms of division of labor in the faceof complexity and cognitive limitations (Giere 2006), epistemichumility (Feyerabend 1962 and his final writings in the 1990s; Chang2002), scientific freedom, empirical testability and theory choice(Popper 1935; Feyerabend 1962) and underdetermination.

Underdetermination arguments concern choices from a disjunction ofequivalent types of descriptions (Mitchell 2003, 2009) or ofincompatible partial representations or models of phenomena in thesame intended scope (Longino 2002, 2013). The representationalincompatibility may be traced to competing values or aims, orassumptions in ceteris paribus laws.

Critiques of difference pluralism point to different consequences suchas failure to address complex and boundary phenomena and problemsin, for instance, the life and social sciences (Gorman 2002;Mitchell 2003; 2008); detrimental effects of taxonomic instability(Sullivan 2017) and so-called intraconcept variability (Cunningham2021) in the mind-brain sciences. When the variability characterizeswhat are taken to be the same concepts and terminology, severalcontexts of detrimental effect have been identified: (1) scienceeducation, (2) collaborative research, intra- and cross-disciplinary(e.g., the practical and moral problems of value conflicts mentionedabove), (3) clinical practice, and (4) metascientific research(Cunningham 2021).

Integrative, or connective, types of pluralism are the conjunctive orholistic requirement of different types of descriptions, methods orperspectives (Mitchell 2003, 2009; contrast with the more isolationistposition in Longino 2002 and her essay in Kellert, Longino and Waters2006; Longino 2013).

To a merely syncretistic or tolerant, non-interactive pluralism, arecent body of literature has opposed a dynamic, coordinated,interactive disciplinary kind of pluralism (Chang 2012; Wylie 2015;Sullivan 2017). The former requires only respectful division of labor;the latter may involve either a limited cross-fertilization throughcommunication and assimilation—borrowing or co-optation—ora more robust, integrative epistemic engagement. The latter mayinvolve, for instance, communicative expertise—also known asinteractional expertise—without having contributory expertisein the other practice, exchange and collaboration on the sameproject.

Borrowing and cross-fertilization across divides and over distancesconcern more than theories and change the respective practices,processes and products. They extend to data, concepts, models,methods, evidence, heuristic techniques, technology and otherresources. To mention one distinction, while theoretical integrationconcerns concepts, ontology, explanations, models, etc., practicalintegration concerns methods, heuristics and testing (Grantham 2004).Thus, accounts including different versions of taxonomical pluralismrange from the more conventional and contingent (from Elgin 1997 toastronomical kinds in Ruphy 2016) and the more grounded in contexts ofpractices (categorization work in Bowker and Star 1999; life sciencesand chemistry in Kendig 2016) and the interactive (Hacking’sinteractive kinds in the human sciences) to the more metaphysicallysubstantive. Some methodological prescriptions of pluralism rely onpluralism in metascientific research including history (Chang2012).

Connective varieties of pluralism have been endorsed on grounds oftheir epistemic value. Considerations of empirical adequacy andpredictive power can be traced back to Neurath, the explanatory andmethodological value of cross-fertilization, the epistemic benefits ofa stance of openness to new kinds of facts and ways of inquiry andlearning (Wylie 2015) and evidential value.

From the standpoint of evidence, we find second-order varieties ofmixed evidence patterns—triangulation, security andintegration—that connect different kinds of evidence to provideenhanced evidential value. The relevant plurality or differencerequires independence, a condition to be explicated in different ways(Kuorikoski and Marchionni 2022). Regarding triangulation, enhancedevidence results from multiple theory-laden but theoreticallyindependent lines of evidence in, for instance, microscopy (Hacking1983), archeology (Wylie 1999) and interdisciplinary research in thesocial sciences, for example, neuroeconomics in support of existenceclaims about phenomena and descriptions of phenomena but not to moregeneral theories about them (Kuorikoski and Marchionni 2016).

Connective forms of pluralism have been modeled in terms of relationsbetween disciplines (see above) and defended at the level of socialepistemology by analogy with political models of liberal democracy andas a model of social governance between the extremes of so-calledconsensual mainstreaming and antagonistic exclusivism (van Bouwel2009a). Through dialogue, a plurality of represented perspectivesenables the kind of critical scrutiny of questions and knowledgeclaims that exposes error, bias, unexamined norms of justification andacceptance and the complexity of issues and relevant implications. Asa result, it has been argued, pluralism supports a correspondingstandard of critical objectivity (Longino 2002; Wylie 2015).

  • Internal vs. external pluralism. From a methodologicalstandpoint, an internal perspective is naturalistic in its reliance onthe contingent plurality of scientific practice by any of itsstandards. This has been defended by members of the so-calledMinnesota School (Kellert, Longino and Waters 2006) and Ruphy (2016).The alternative, which Ruphy has attributed to Dupré andCartwright, is the adoption of a metaphysical commitment external toactual scientific practice.

As a matter of actual practice, pluralism has been identified as partof a plurality of projects and perspectives in, for instance,cognitive and mind-brain sciences, where attitudes towards a pluralityof ways of researching and understanding cognition vary (Milkowski andHohol 2021). These attitudes include (1) lamenting the variability ofmeaning and systems of classification (Sullivan 2007; Cunningham2021); (2) embracing complementarity between hierarchical mechanisticand computational approaches—in the face of, for instance,models with propositional declarative and lawlike statements andcomputational models with software codes; (3) seeking integration withmutual consistency and evidential support; (4) seeking reductionprivileging neural models; and (5) seeking grand unification thatvalues simplicity and generality over testability.

5.3 Metapluralism

The preference for one kind of pluralism over another is typicallymotivated by epistemic virtues or constraints. Meta-pluralism, orpluralism about pluralism, is obviously conceivable in similar terms,as it can be found in the formulation of the so-called pluraliststance (Kellert, Longino and Waters 2006). The pluralist stancereplaces metaphysical principles with scientific or empiricalmethodological rules and aims that have been “tested”.Like Dupré’s and Cartwright’s metaphysicalpositions, its metascientific position must be empirically tested.Metascientific conclusions and assumptions cannot be considereduniversal or necessary, but are local, contingent and relative toscientific interests and purposes. Thus, on this view, complexity doesnot always require interdisciplinarity (Kellert 2008), and in somesituations the pluralist stance will defend reductions orspecialization over interdisciplinary integration (Kellert, Longinoand Waters 2006; Cat 2012; Rescher 1993).

6. Conclusion: Why unity? And what difference does it really make?

From Greek philosophy to current debates, justifications for adoptingpositions on matters of unification have varied from the metaphysicaland theological to the epistemic, social and pragmatic. Whether as amatter of truth (Thalos 2013) or consequence, views on matters ofunity and unification make a difference in both science andphilosophy, and, by application, in society as well. In science theyprovide strong heuristic or methodological guidance and evenjustification for hypotheses, projects, and specific goals. In thissense, different rallying cries and idioms such as simplicity, unity,disunity, emergence or interdisciplinarity, have been endowed with anormative value. Their evaluative role extends broadly. They are usedto provide legitimacy, even if rhetorically, in social contexts,especially in situations involving sources of funding and profit. Theyset a standard of what carries the authority and legitimacy of what itis to be scientific. As a result, they make a difference in scientificevaluation, management and application, especially in public domainssuch as healthcare and economic decision-making. For instance,pointing to the complexity of causal structures challenges traditionaldeterministic or simple causal strategies of policy decision-makingwith known risks and unknown effects of known properties (Mitchell2009). Last but not least is the influence that implicit assumptionsabout what unification can do have on science education (Klein1990).

Philosophically, assumptions about unification help choose what sortof philosophical questions to pursue and what target areas to explore.For instance, fundamentalist assumptions typically lead one to addressepistemological and metaphysical issues in terms of only results andinterpretations of fundamental levels of disciplines. Assumptions ofthis sort help define what counts as scientific and shape scientisticor naturalized philosophical projects. In this sense, they determine,or at least strongly suggest, what relevant science carries authorityin philosophical debate.

At the end of the day, one should not lose sight of the larger contextthat sustains problems and projects in most disciplines and practices.We are as free to pursue them as Kant’s dove is free to fly,that is, not without the surrounding air resistance to flap itswings upon and against. Philosophy was once thought to stand for thesystematic unity of the sciences. The foundational character of unitybecame the distinctive project of philosophy, in which conceptualunity played the role of the standard of intelligibility. In addition,the ideal of unity, frequently under the guise of harmony, has longbeen a standard of aesthetic virtue, although this image has beeneloquently challenged by, for instance, John Bailey and Iris Murdoch(Bailey 1976; Murdoch 1992). Unities and unifications help us meetcognitive and practical demands upon our life as well as culturaldemands upon our self-images that are both cosmic and earthly. It isnot surprising that talk of the many meanings and levels ofunity—the fundamental level, unification, system, organization,universality, simplicity, atomism, reduction, harmony, complexity ortotality—can place an urgent grip on our intellectualimagination.

The Unity of Science (2024)

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