## 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 and
debates express intellectual and other resources and interests in
different contexts. Questions about unity belong partly in a tradition
of thought that can be traced back to pre-Socratic Greek cosmology, in
particular to the preoccupation with the question of the One and the
Many. In what senses is the world and, as a result, our knowledge of
it one? A number of representations of the world in terms of a few
simple constituents that were considered fundamental emerged:
Parmenides' static substance, Heraclitus' flux of
becoming, Empedocles' four elements, Democritus' atoms,
Pythagoras' numbers, Plato's forms, and Aristotle's
categories. The underlying question of the unity of our types of
knowledge was explicitly addressed by Plato in the *Sophist* as
follows: "Knowledge also is surely one, but each part of it that
commands a certain field is marked off and given a special name proper
to itself. Hence language recognizes many arts and many forms of
knowledge" (*Sophist*, 257c). Aristotle asserted in
*On the Heavens* that knowledge concerns what is primary, and
different "sciences" know different kinds of causes; it is
metaphysics that comes to provide knowledge of the underlying
kind.



With the advent and expansion of Christian monotheism, the
organization of knowledge reflected the idea of a world governed by
the laws dictated by God, its creator and legislator. From this
tradition emerged encyclopedic efforts such as the
*Etymologies*, compiled in the sixth century by the Andalusian
Isidore, Bishop of Seville, the works of the Catalan Ramon Llull in
the Middle Ages and those of the Frenchman Petrus Ramus in the
Renaissance. Llull introduced iconic tree-diagrams and
forest-encyclopedias representing the organization of different
disciplines including law, medicine, theology and logic. He also
introduced more abstract diagrams--not unlike some found in
Cabbalistic and esoteric traditions--in an attempt to
combinatorially encode the knowledge of God's creation in a
universal language of basic symbols. Their combination would be
expected to generate knowledge of the secrets of creation and help
articulate knowledge of universal order (*mathesis
universalis*), which would, in turn, facilitate communication with
different cultures and their conversion to Christianity. Ramus
introduced diagrams representing dichotomies and gave prominence to
the view that the starting point of all philosophy is the
classification of the arts and sciences. The encyclopedia organization
of knowledge served the project of its preservation and
communication.



The emergence of a distinctive tradition of scientific thought
addressed the question of unity through the designation of a
privileged method, which involved a privileged language and set of
concepts. Formally, at least, it was modeled after the Euclidean ideal
of a system of geometry. In the late-sixteenth century, Francis Bacon
held that one unity of the sciences was the result of our organization
of records of discovered material facts in the form of a pyramid with
different levels of generalities. These could be classified in turn
according to disciplines linked to human faculties. Concomitantly, the
controlled interaction with phenomena of study characterized so-called
experimental philosophy. In accordance with at least three
traditions--the Pythagorean tradition, the Bible's dictum
in the Book of Wisdom and the Italian commercial tradition of
bookkeeping--Galileo proclaimed at the turn of the seventeenth
century that the Book of Nature had been written by God in the
language of mathematical symbols and geometrical truths, and in it,
the story of Nature's laws was told in terms of a reduced set of
objective, quantitative primary qualities: extension, quantity of
matter and motion. A persisting rhetorical role for some form of
theological unity of creation should not be neglected when considering
pre-twentieth-century attempts to account for the possibility and
desirability of some form of scientific knowledge. Throughout the
seventeenth century, mechanical philosophy and Descartes' and
Newton's systematization from basic concepts and first laws of
mechanics became the most promising framework for the unification of
natural philosophy. After the demise of Laplacian molecular physics in
the first half of the nineteenth century, this role was taken over by
ether mechanics and, unifying forces and matter, energy physics.


### 1.2 Rationalism and Enlightenment



Descartes and Leibniz gave this tradition a rationalist twist that was
centered on the powers of human reason and the ideal of system of
knowledge founded on rational principles. It became the project of a
universal framework of exact categories and ideas, a *mathesis
universalis* (Garber 1992; Gaukroger 2002). Adapting the
scholastic image of knowledge, Descartes proposed an image of a tree
in which metaphysics is depicted by the roots, physics by the trunk,
and the branches depict mechanics, medicine and morals. Leibniz
proposed a *general science* in the form of a *demonstrative
encyclopedia*. This would be based on a "catalogue of simple
thoughts" and an algebraic language of symbols,
*characteristica universalis*, which would render all knowledge
demonstrative and allow disputes to be resolved by precise
calculation. Both defended the program of founding much of physics on
metaphysics and ideas from life science (Smith 2011) (Leibniz's
unifying ambitions with symbolic language and physics extended beyond
science, to settle religious and political fractures in Europe). By
contrast, while sharing a model of a geometric, axiomatic structure of
knowledge, Newton's project of natural philosophy was meant to
be autonomous from a system of philosophy and, in the new context,
still endorsed, for its model of organization and its empirical
reasoning, values of formal synthesis and ontological simplicity (see
the entry on
 Newton;
 also Janiak 2008).



Belief in the unity of science or knowledge, along with the
universality of rationality, was at its strongest during the European
Enlightenment. The most important expression of the encyclopedic
tradition came in the mid-eighteenth century from Diderot and
D'Alembert, editors of the *Encyclopedie, ou
dictionnaire raisonne des sciences, des arts et des
metiers* (1751-1772). Following earlier
classifications by Nichols and Bacon, their diagram presenting the
classification of intellectual disciplines was organized in terms of a
classification of human faculties. Diderot stressed in his own entry,
"Encyclopaedia", that the word signifies the unification
of the sciences. The function of the encyclopedia was to exhibit the
unity of human knowledge. Diderot and D'Alembert, in contrast to
Leibniz, made classification by subject the primary focus, and
introduced cross-references instead of logical connections. The
Enlightenment tradition in Germany culminated in Kant's critical
philosophy.


### 1.3 German tradition since Kant



For Kant, one of the functions of philosophy was to determine the
precise unifying scope and value of each science. For him, the unity
of science is not the reflection of a unity found in nature, or, even
less, assumed in a real world behind the apparent phenomena. Rather,
it has its foundations in the unifying a priori character or function
of concepts, principles and of Reason itself. Nature is precisely our
experience of the world under the universal laws that include such
concepts. And science, as a system of knowledge, is "a whole of
cognition ordered according to principles", and the principles
on which proper science is grounded are a priori (Preface to
*Metaphysical Foundations of Natural Science*). A devoted but
not exclusive follower of Newton's achievements and insights, he
maintained through most of his life that mathematization and a priori
universal laws given by the understanding were preconditions for
genuine scientific character (like Galileo and Descartes earlier, and
Carnap later, Kant believed that mathematical exactness constituted
the main condition for the possibility of objectivity). Here Kant
emphasized the role of mathematics coordinating a priori cognition and
its determined objects of experience. Thus, he contrasted the methods
employed by the chemist, a "systematic art" organized by
empirical regularities, with those employed by the mathematician or
physicist, which were organized by a priori laws, and he held that
biology is not reducible to mechanics--as the former involves
explanations in terms of final causes (see *Critique of Pure
Reason*, *Critique of Judgment* and *Metaphysical
Foundations of Natural Science*). With regards to
biology--insufficiently grounded in the fundamental forces of
matter--its inclusion requires the introduction of the idea of
purposiveness (McLaughlin 1991). More generally, for Kant, unity was a
regulative principle of reason, namely, an ideal guiding the process
of inquiry toward a complete empirical science with its empirical
concepts and principles grounded in the so-called concepts and
principles of the understanding that constitute and objectify
empirical phenomena. (On systematicity as a distinctive aspect of this
ideal and on its origin in reason, see Kitcher 1986 and
Hoyningen-Huene 2013).



Kant's ideas set the frame of reference for discussions of the
unification of the sciences in German thought throughout the
nineteenth century (Wood and Hahn 2011). He gave philosophical
currency to the notion of worldview (*Weltanschauung*) and,
indirectly, world-picture (*Weltbild*), establishing among
philosophers and scientists the notion of the unity of science as an
intellectual ideal. From Kant, German-speaking Philosophers of Nature
adopted the image of Nature in terms of interacting forces or powers
and developed it in different ways; this image found its way to
British natural philosophy. In Great Britain this idealist, unifying
spirit (and other notions of an idealist and romantic turn) was
articulated in William Whewell's philosophy of science. Two
unifying dimensions are these: his notion of mind-constructed
fundamental ideas, which form the basis for organizing axioms and
phenomena and classifying sciences, and the argument for the reality
of explanatory causes in the form of *consilience of
induction*, wherein a single cause is independently arrived at
as the hypothesis explaining different kinds of phenomena.



In face of expanding research, the unifying emphasis on organization,
classification and foundation led to exploring differences and
rationalizing boundaries. The German intellectual current culminated
in the late-nineteenth century in the debates among philosophers such
as Windelband, Rickert and Dilthey. In their views and those of
similar thinkers, a worldview often included elements of evaluation
and life meaning. Kant had established the basis for the famous
distinction between the natural sciences
(*Naturwissenschaften*) and the cultural, or social, sciences
(*Geisteswissesnschaften*) popularized in theory of science by
Wilhelm Dilthey and Wilhelm Windelband. Dilthey, Windelband, his
student Heinrich Rickert, and Max Weber (although the first two
preferred *Kulturwissenschaften*, which excluded psychology)
debated over how differences in subject matter between the two kinds
of sciences forced a distinctive difference between their respective
methods. Their preoccupation with the historical dimension of the
human phenomena, along with the Kantian emphasis on the conceptual
basis of knowledge, led to the suggestion that the natural sciences
aimed at generalizations about abstract types and properties, whereas
the human sciences studied concrete individuals and complexes. The
human case suggested a different approach based on valuation and
personal understanding (Weber's *verstehen*). For
Rickert, individualized concept formation secured knowledge of
historical individuals by establishing connections to recognized
values (rather than personal valuations). In biology, Ernst Haeckel
defended a monistic worldview (Richards 2008).



The *Weltbild* tradition influenced the physicists Max Planck
and Ernst Mach, who engaged in a heated debate about the precise
character of the unified scientific world-picture. Mach's more
influential view was both phenomenological and Darwinian: the
unification of knowledge took the form of an analysis of ideas into
biologically embodied elementary sensations (neutral monism) and was
ultimately a matter of adaptive economy of thought. Planck adopted a
realist view that took science to gradually approach complete truth
about the world, and he fundamentally adopted the thermodynamical
principles of energy and entropy (on the Mach-Planck debate see
Toulmin 1970). These world-pictures constituted some of the
alternatives to a long-standing mechanistic view that, since the rise
of mechanistic philosophy with Descartes and Newton, had informed
biology as well as most branches of physics. In the background was the
perceived conflict between the so-called mechanical and
electromagnetic worldviews, which resulted throughout the first two
decades of the twentieth century in the work of Albert Einstein
(Holton 1998).



In the same German tradition, and amidst the proliferation of work on
energy physics and books on unity of science, the German energeticist
Wilhelm Ostwald declared the twentieth century the "Monistic
century". During the 1904 World's Fair in St. Louis, the
German psychologist and Harvard professor Hugo Munsterberg organized a
congress under the title "Unity of Knowledge"; invited
speakers were Ostwald, Ludwig Boltzmann, Ernest Rutherford, Edward
Leamington Nichols, Paul Langevin and Henri Poincare. In 1911,
the International Committee of Monism held its first meeting in
Hamburg, with Ostwald
 presiding.[1]
 Two years later it published Ostwald's monograph, *Monism as
the Goal of Civilization*. In 1912, Mach, Felix Klein, David
Hilbert, Einstein and others signed a manifesto aiming at the
development of a comprehensive worldview. Unification remained a
driving scientific ideal. In the same spirit, Mathieu Leclerc du
Sablon published his *L'Unite de la Science*
(1919), exploring metaphysical foundations, and Johan Hjorst published
*The Unity of Science* (1921), sketching out a history of
philosophical systems and unifying scientific hypotheses.


### 1.4 Positivism and logical empiricism



The German tradition stood in opposition to the prevailing empiricist
views that, since the time of Hume, Comte and Mill, held that the
moral or social sciences (even philosophy) relied on conceptual and
methodological analogies with geometry and the natural sciences, not
just astronomy and mechanics, as well as with biology. In the Baconian
tradition, Comte emphasized a pyramidal hierarchy of disciplines in
his "encyclopedic law" or order, from the most general
sciences about the simplest phenomena to the most specific sciences
about the most complex phenomena, each depending on knowledge from its
more general antecedent: from inorganic physical sciences (arithmetic,
geometry, mechanics, astronomy, physics and chemistry) to the organic
physical ones, such as biology and the new "social
physics", soon to be renamed sociology (Comte 1830-1842).
Mill, instead, pointed to the diversity of methodologies for
generating, organizing and justifying associated knowledge with
different sciences, natural and human, and the challenges to impose a
single standard (Mill 1843, Book VI). He came to view political
economy eventually as an art, a tool for reform more than a system of
knowledge (Snyder 2006).



Different yet connected currents of nineteenth-century positivism,
first in European philosophy in the first half of the
century--Auguste Comte, J.S. Mill and Herbert Spencer--and
subsequently in North American philosophy--John Fiske, Chauncey
Wright and William James--arose out of intellectual tensions
between metaphysics and the sciences and identified positivism as
synthetic and scientific philosophy; accordingly, they were concerned
with the ordering and unification of knowledge through the
organization of the sciences. The synthesis was either of methods
alone--Mill and Wright--or else also of
doctrines--Comte, Spencer and Fiske. Some used the term
"system" especially in relation to a common logic or
method (Pearce 2015).



In the twentieth century the unity of science became a distinctive
theme of the scientific philosophy of logical empiricism (Cat 2021).
The question of unity engaged science and philosophy alike. In their
manifesto, logical empiricists--known controversially also as
logical positivists--and most notably the founding members of the
Vienna Circle, adopted the Machian banner of "unity of science
without metaphysics". This was a normative criterion of unity
with a role in social reform based on the demarcation between science
and metaphysics: a unity of method and language that included all the
sciences, natural and social. A common method did not necessarily
imply a more substantive unity of content involving theories and their
concepts.



A stronger reductive model within the Vienna Circle was recommended by
Rudolf 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 formal
standards: Hilbert's axiomatic approach to formulating theories
in the exact sciences and Frege's and Russell's logical
constructions in mathematics. It was also predicated on the formal
values of simplicity, rationality, (philosophical) neutrality and
objectivity associated with scientific knowledge. In particular,
Carnap tried to explicate such notions in terms of a rational
reconstruction of science in terms of a method and a structure based
on logical constructions out of (1) basic concepts in axiomatic
structures and (2) rigorous, reductive logical connections between
concepts at different levels.



Different constitutive systems or logical constructions would serve
different (normative) purposes: a theory of science and a theory of
knowledge. Both foundations raised the issue of the nature and
universality of a physicalist language.



One such system of unified science is the theory of science, in which
the construction connects concepts and laws of the different sciences
at different levels, with physics and its genuine laws as fundamental,
lying at the base of the hierarchy. Because of the emphasis on the
formal and structural properties of our representations, objectivity,
rationality and unity go hand in hand. Carnap's formal emphasis
developed further in *Logical Syntax of Language* (1934).
Alternatively, all scientific concepts could be constituted or
constructed in a different system in the protocol language out of
classes of elementary complexes of experiences, scientifically
understood, representing experiential concepts. Carnap subsequently
defended the epistemological and methodological universality of
physicalist language and physicalist statements. The unity of science
in this context was an epistemological project (for a survey of the
epistemological debates, see Uebel 2007; on different strands of the
anti-metaphysical normative project of unity see Frost-Arnold
2005).



Whereas Carnap aimed at rational reconstructions, another member of
the Vienna Circle, Otto Neurath, favored a more naturalistic and
pragmatic approach, with a less idealized and reductive model of
unity. His evolving standards of unity were generally motivated by the
complexity of empirical reality and the application of empirical
knowledge to practical goals. He spoke of an
"encyclopedia-model", opposed to the classic ideal of a
pyramidal, reductive "system-model". The
encyclopedia-model took into account the presence within science of
ineliminable and imprecise terms from ordinary language and the social
sciences and emphasized a unity of language and the local exchanges of
scientific tools. Specifically, Neurath stressed the material-thing
language called "physicalism", not to be confounded with
the emphasis on the vocabulary of physics. Its motivation was partly
epistemological, and Neurath endorsed anti-foundationalism; no unified
science, like a boat at sea, would rest on firm foundations. The
scientific spirit abhorred dogmatism. This weaker model of unity
emphasized empiricism and the normative unity of the natural and the
human sciences.



Like Carnap's unified reconstructions, Neurath's had
pragmatic motivations. Unity without reductionism provided a tool for
cooperation and it was motivated by the need for successful
treatment--prediction and control--of complex phenomena in
the real world that involved properties studied by different theories
or sciences (from real forest fires to social policy): unity of
science at the point of action. It is an argument from holism, the
counterpart of Duhem's claim that only clusters of hypotheses
are confronted with experience. Neurath spoke of a "boat",
a "mosaic", an "orchestration", and a
"universal jargon". Following institutions such as the
International Committee on Monism and the International Council of
Scientific Unions, Neurath spearheaded a movement for Unity of Science
in 1934 that encouraged international cooperation among scientists and
launched the project of an International Encyclopedia of Unity of
Science. It expressed the internationalism of his socialist
convictions and the international crisis that would lead to the Second
World War (Kamminga and Somsen 2016).



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



After the Second World War, a discussion of unity engaged philosophers
and scientists in the Inter-Scientific Discussion Group, first as the
Science 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 later
become the Unity of Science Institute. The group was joined by
scientists from different disciplines, from quantum mechanics (Kemble
and Van Vleck) and cybernetics (Wiener) to economics (Morgenstern), as
part of what was both a self-conscious extension of the Vienna Circle
and a reflection of local concerns within a technological culture
increasingly dominated by the interest in computers and nuclear power.
The characteristic feature of the new view of unity was the ideas of
consensus and, subsequently, especially within the USI,
cross-fertilization. These ideas were instantiated in the emphasis on
scientific operations (operationalism) and the creation of war-boosted
cross-disciplines such as cybernetics, computation, electro-acoustics,
psycho-acoustics, neutronics, game theory and biophysics (Galison
1998; Hardcastle 2003).



In the late 1960s, Michael Polanyi and Marjorie Grene organized a
series of conferences funded by the Ford Foundation on unity of
science themes (Grene 1969a, 1969b, 1971). Their general character was
interdisciplinary and anti-reductionist. The group was originally
called "Study Group on Foundations of Cultural Unity", but
this was later changed to "Study Group on the Unity of
Knowledge". By then, a number of American and international
institutions were already promoting interdisciplinary projects in
academic areas (Klein 1990). For both Neurath and Polanyi, the
organization of knowledge and science, the Republic of Science, was
inseparable from ideals of political organization.



Over the last four decades much historical and philosophical
scholarship has challenged the ideals of monism and reductionism and
pursued a growing critical interest in pluralism and interdisciplinary
collaboration (see below). Along the way, the distinction between the
historical human sciences and ahistorical natural sciences has
received much critical and productive attention. One outcome has been
the application and development of concepts and accounts in philosophy
of history in understanding different human and natural sciences as
historical, with a special focus on the epistemic role of unifying
narratives and standards and problems in disciplines such as
archeology, geology, cosmology and paleontology (see, for instance,
Morgan and Wise 2017; Currie 2019). Another outcome has been a renewed
critique of the autonomy of the social sciences. One concern is, for
instance, the raising social and economic value of the natural
sciences and their influence on the models and methods of the social
sciences; another is the influence on both of certain particular
political and economic views. Other related concerns are the role of
the social sciences in political life and the assumption that humans
are unique and superior to animals and emerging technologies (see, for
instance, van Bouwel 2009b; Kincaid and van Bouwel 2023).


## 2. Varieties of Unity



The historical introductory sections have aimed to show the
intellectual centrality, varying formulations, and significance of the
concept of unity. The rest of the entry presents a variety of modern
themes and views. It will be helpful to introduce a number of broad
categories and distinctions that can sort out different kinds of
accounts and track some relations between them, as well as additional
significant philosophical issues. (The categories are not mutually
exclusive, and they sometimes partly overlap. Therefore, while they
help label and characterize different positions, they cannot provide a
simple, easy and neatly ordered conceptual map.)



Connective unity is a weaker and more general notion than the specific
ideal of *reductive unity*; this requires asymmetric relations
of reduction (see below), which typically rely on assumptions about
hierarchies of levels of description and the primacy--conceptual,
ontological, epistemological and so on--of a fundamental
representation. The category of connective unity helps accommodate and
bring attention to the diversity of non-reductive accounts.



Another useful distinction is between *synchronic* and
*diachronic unity*. Synchronic accounts are ahistorical,
assuming no meaningful temporal relations. Diachronic accounts, by
contrast, introduce genealogical hypotheses involving asymmetric
temporal and causal relations between entities or states of the
systems described. Evolutionary models are of this kind; they may be
reductive to the extent that the posited original entities are simpler
and on a lower level of organization and size. Others simply emphasize
connection without overall directionality.



In general, it is useful to distinguish between *ontological
unity* and *epistemological unity*, even if many accounts
bear both characteristics and fall under both rubrics. In some cases,
one kind supports the other salient kind in the model. Ontological
unity is here broadly understood as involving relations between
descriptive conceptual elements; in some cases, the concepts will
describe entities, facts, properties or relations, and descriptive
models will focus on metaphysical aspects of the unifying connections
such as holism, emergence, or downwards causation. Epistemological
unity 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 strict
or explicit distinction between epistemological and methodological
dimensions or modes of unity.



Additional possible categories and distinctions include the following:
*vertical unity* or *inter-level unity* is unity of
elements attached to levels of analysis, composition or organization
on a hierarchy, whether for a single science or more, whereas
*horizontal unity* or *intra-level unity* applies to one
single level and to its corresponding kind of system (Wimsatt 2007).
*Global unity* is unity of any other variety with a universal
quantifier of all kinds of elements, aspects or descriptions
associated with individual sciences as a kind of *monism*, for
instance, taxonomical monism about natural kinds, while *local
unity* applies to a subset. (Cartwright has distinguished this
same-level global form of reduction, or "imperialism", in
Cartwright 1999; see also Mitchell 2003). Obviously, vertical and
horizontal accounts of unity can be either global or local. Finally,
the rejection of global unity has been associated with both
*isolationism*--keeping independent competing alternative
representations of the same phenomena or systems--as well as with
*local integration*--the local connective unity of the
alternative perspectives. A distinction of methodological nature
contrasts *internal* and *external* perspectives,
according to whether the accounts are based naturalistically on the
local contingent practices of certain scientific communities at a
given time or based on universal metaphysical assumptions broadly
motivated (Ruphy 2017). (Ruphy has criticized Cartwright and
Dupre for having adopted external metaphysical positions and
defended the internal perspective, also present in the program of the
so-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 of
scientific understanding by privileging descriptions of more
fundamental entities and phenomena such as the powers and behaviors of
atoms, molecules and machines. Since at least the 1920s and until the
1960s, unity was understood in terms of formal approaches to theories,
of semantic relations between vocabularies and of logical relations
between linguistic statements in those vocabularies. The ideal of
unity was formulated, accordingly, in terms of reduction relations to
more fundamental terms and statements. Different accounts have since
stood and fallen with any such commitments. Also, note that
identifying relations of *reduction* must be distinguished from
the ideal of *reductionism.* Reductionism is the adoption of
reduction relations as the global ideal or standard of a proper
unified structure of scientific knowledge; and distance from that
ideal was considered a measure of its unifying progress.



In general, reduction reconciles ontological and epistemological
considerations of identity and difference. Claims such as
"mental states are reduceable to neurochemical states",
"chemical differences reduce to differences between atomic
structures" and "optics can be reduced to
electromagnetism" imply the truth of identity
statements--a strong ontological reduction. However, the
relations of reduction between entities or properties in such claims
also get additional epistemic value from the expressed semantic
diversity of conceptual content and the asymmetry of the relation
described in such claims between the reducing and the reduced
claims--concepts, laws, theories, etc. (Riel 2014).



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



Two formulations of unification in the logical positivist tradition of
the ideal logical structure of science placed the question of unity at
the core of philosophy of science: Carl Hempel's
deductive-nomological model of explanation and Ernst Nagel's
model of reduction. Both are fundamentally epistemological models, and
both are specifically explanatory, at least in the sense that
explanation serves unification. The emphasis on language and logical
structure makes explanatory reduction a form of unity of the
synchronic kind. Still, Nagel's model of reduction is a model of
scientific structure and explanation as well as of scientific
progress. It is based on the problem of relating different theories as
different sets of theoretical predicates (Nagel 1961).



Reduction requires two conditions: *connectability* and
*derivability*. Connectability of laws of different theories
requires *meaning invariance* in the form of extensional
equivalence between descriptions, with bridge principles between
coextensive but distinct terms in different theories.



Nagel's account distinguishes two kinds of reductions:
*homogenous* and *heterogeneous*. When both sets of
terms overlap, the reduction is homogeneous. When the related terms
are different, the reduction is heterogeneous. Derivability requires a
deductive relation between the laws involved. In the quantitative
sciences, the derivation often involves taking a limit. In this sense
the reduced science is considered an *approximation* to the
reducing new one.



Neo-Nagelian accounts have attempted to solve Nagel's problem of
reduction between putatively incompatible theories. The following
paragraphs list a few.



Nagel's two-term relation account has been modified by weaker
conditions of analogy and a role for conventions, requiring it to be
satisfied 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 \(T'\_2\). Explanatory
reduction is strictly a four-term relation in which \(T'\_1\) is
"strongly analogous" to \(T\_1\) and corrects, with the
insight that the more fundamental theory can offer, the older theory,
\(T\_2\), changing it to \(T'\_2\). Nagel's account also requires
that bridge laws be synthetic identities, in the sense that they be
factual, empirically discoverable and testable; in weaker accounts,
admissible bridge laws may include elements of convention (Schaffner
1967; Sarkar 1998). The difficulty lay especially with the task of
specifying or giving a non-contextual, transitive account of the
relations between \(T\) and \(T'\) (Wimsatt 1976).



An alternative set of semantic and syntactic conditions of reduction
bears counterfactual interpretations. For instance, syntactic
conditions may take the form of limit relations (e.g., classical
mechanics reduces to relativistic mechanics for the value of the speed
of light c[?]  0 and to quantum mechanics for the value of the
Planck constant h[?]  0) and *ceteris paribus* assumptions
(e.g., when optical laws can be identified with results of the theory
of electromagnetism); then, each condition helps explain why the
reduced theory works where it does and fails where it does not
(Glymour 1969).



A different approach to reductionism acknowledges a commitment to
providing explanation but rejects the value of a focus on the role of
laws. This approach typically draws a distinction between hard
sciences such as physics and chemistry and special sciences such as
biology and the social sciences. It claims that laws that are in a
sense operative in the hard sciences are not available in the special
ones, or play a more limited and weaker role, and this on account of
historical character, complexity or reduced scope. The rejection of
empirical laws in biology, for instance, has been argued on grounds of
historical dependence on contingent initial conditions (Beatty 1995),
and as matter of supervenience (see the entry on
 supervenience)
 of spatio-temporally restricted functional claims on lower-level
molecular ones, and the multiple realization (see the entry on
 multiple realizability)
 of the former by the latter (Rosenberg 1994; Rosenberg's
argument from supervenience to reduction without laws must be
contrasted with Fodor's physicalism about the special sciences
about laws without reduction (see below and the entry on
 physicalism);
 for a criticism of these views see Sober 1996). This non-Nagelian
approach assumes further that explanation rests on identities between
predicates and deductive derivations (reduction and explanation might
be 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 supervening
functional explanations without Nagelian reduction may rely on an
ontological type of relation of reduction such as the composition of
powers in explanatory mechanisms (Gillette 2010, 2016). The reductive
commitment to the lower level is based on relations of composition, at
play in epistemological analysis and metaphysical synthesis, but is
merely formal and derivational. We may be able to infer what composes
the higher level, but we cannot simply get all the relevant knowledge
of the higher level from our knowledge of the lower level (see also
Auyang 1998). This kind of proposal points to epistemic
anti-reductionism.



Note that significant proposals of reductive unity rely on ontological
assumptions about some hierarchy of levels organizing reality and
scientific theories of it (more below).



A more general characterization views reductionism as a research
strategy. On this methodological view reductionism can be
characterized by a set of so-called heuristics (non-algorithmic,
efficient, error-based, purpose-oriented, problem-solving tasks)
(Wimsatt 2006): heuristics of conceptualization (e.g., descriptive
localization of properties, system-environment interface determinism,
level and entity-dependence), heuristics of model-building and theory
construction (e.g., model intra-systemic localization with emphasis of
structural properties over functional ones, contextual simplification
and external generalization) and heuristics of observation and
experimental design (e.g., focused observation, environmental control,
local scope of testing, abstract shared properties, behavioral
regularity and context-independence of results).


### 3.2 Antireductionism



Since the 1930s, the focus was on a syntactic approach, with physics
as the paradigm of science, deductive logical relations as the form of
cognitive or epistemic goals such as explanation and prediction, and
theory and empirical laws as paradigmatic units of scientific
knowledge (Suppe 1977; Grunbaum and Salmon 1988). The historicist
turn in the 1960s, the semantic turn in philosophy of science in the
1970s and a renewed interest in special sciences has changed this
focus. The very structure of hierarchy of levels has lost its
credibility, even for those who believe in it as a model of autonomy
of levels rather than as an image of fundamentalism. The rejection of
such models and their emendations have occupied the last four decades
of philosophical discussion about unity in and of the sciences
(especially in connection to psychology and biology, and more recently
chemistry). A valuable consequence has been the strengthening of
philosophical projects and communities devoting more sustained and
sophisticated attention to special sciences, different from
physics.



The first target of antireductionist attacks has been Nagel's
demand of extensional equivalence. It has been dismissed as an
inadequate demand of "meaning invariance" and
approximation, and with it the possibility of deductive connections.
Mocking the positivist legacy of progress through unity, empiricism
and anti-dogmatism, these constraints have been decried as
intellectually dogmatic, conceptually weak and methodologically overly
restrictive (Feyerabend 1962). The emphasis is placed, instead, on the
merits of the new theses of incommensurability and methodological
pluralism.



A similar criticism of reduction involves a different move: that the
deductive connection be guaranteed provided that the old, reduced
theory was "corrected" beforehand (Shaffner 1967). The
evolution and the structure of scientific knowledge could be neatly
captured, using Schaffner's expression, by "layer-cake
reduction". The terms "length" and
"mass"--or the symbols \(l\) and \(m\)--for
instance, may be the same in Newtonian and relativistic mechanics, or
the term "electron" the same in classical physics and
quantum mechanics, or the term "atom" the same in quantum
mechanics and in chemistry, or "gene" in Mendelian
genetics and molecular genetics (see, for instance, Kitcher 1984). But
the corresponding concepts, it is argued, are not. Concepts or words
are to be understood as getting their content or meaning within a
holistic or organic structure, even if the organized wholes are the
theories that include them. From this point of view, different wholes,
whether theories or Kuhnian paradigms, manifest degrees of conceptual
incommensurability. As a result, the derived, reducing theories
typically are not the allegedly reduced, older ones; and their
derivation sheds no relevant insight into the relation between the
original, older one and the new (Feyerabend 1962; Sklar 1967).



From a historical standpoint, the positivist model collapsed the
distinction between synchronic and diachronic reduction, that is,
between reductive models of the structure and the evolution, or
succession, of scientific theories. By contrast, historicism, as
embraced by Kuhn and Feyerabend, drove a wedge between the two
dimensions and rejected the linear model of scientific change in terms
of accumulation and replacement. For Kuhn, replacement becomes partly
continuous, 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 of
alternative contenders) (Kuhn 1962). This image constitutes a form of
*pluralism*, and, like the reductionism it is meant to replace,
it can be either *synchronic* or *diachronic*. Here is
where Kuhn and Feyerabend parted ways. For Kuhn, synchronic pluralism
only describes the situation of crisis and revolution between
paradigms. For Feyerabend, history is less monistic, and pluralism is
and should remain a synchronic and diachronic feature of science and
culture (Feyerabend, here, thought science and society inseparable,
and followed Mill's philosophy of liberal individualism and
democracy).



A different kind of antireductionism addresses a more conceptual
dimension, the problem of *categorial reduction*:
Meta-theoretical categories of description and interpretation for
mathematical formalisms, e.g., criteria of causality, may block full
reduction. Basic interpretative concepts that are not just variables
in a theory or model are not reducible to counterparts in fundamental
descriptions (Cat 2000; the case of individuality in quantum physics
has been discussed in Healey 1991; Redhead and Teller 1991; Auyang
1995; 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 different
modes of unification associated with roles such as demarcation,
explanation and evidence. It can also be traced to synthetic cognitive
tasks of categorization and reasoning--also applied in the
sciences--especially through relations of similarity and
difference (Cat 2022b).



*Demarcation*. Certain models of unity, which we may call
container models, attempt to demarcate science from non-science. The
criteria adopted are typically methodological and normative, not
descriptive. Unlike connective models, they serve a dual function of
drawing up and policing a boundary that (1) encloses and endorses the
sciences and (2) excludes other practices. As noted above, some
demarcation projects have aimed to distinguish between natural and
special sciences. The more notorious ones, however, have aimed to
exclude practices and doctrines dismissed under the labels of
metaphysics, pseudo-science or popular knowledge. Empirical or not,
the applications of standards of epistemic purity are not merely
identification or labeling exercises for the sake of carving out
scientific inquiry as a natural kind or mapping out intellectual
landscapes. The purpose is to establish authority and the stakes
involve educational, legal and financial interests. Recent
controversies include not just the teaching of creation science, but
also 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's
original anti-metaphysics barrier: the condition of empirical
falsifiability of scientific statements. It required the logically
possible relation to basic statements, linked to experience, that can
prove general hypotheses to be false with certainty. For this purpose,
he defended the application of a particular deductive argument, the
*modus tollens* (Popper 1935/1951). Another demarcation
criterion is explanatory unity, empirically grounded. Hempel's
deductive-nomological model characterizes the scientific explanation
of events as a logical argument that expresses their expectability in
terms of their subsumption under an empirically testable
generalization. Explanations in the historical sciences too must fit
the model if they are to count as scientific. They could then be
brought into the fold as bona fide scientific explanations even if
they could qualify only as explanation sketches.



Since their introduction, Hempel's model and its weaker versions
have been challenged as neither generally applicable nor appropriate.
The demarcation criterion of unity is undermined by criteria of
demarcation between natural and historical sciences. For instance,
historical explanations have a genealogical or narrative form, or else
they require the historian's engaging problems or issuing a
conceptual judgment that brings together meaningfully a set of
historical facts (recent versions of such decades-old arguments are in
Cleland 2002, Koster 2009, Wise 2011). According to more radical
views, natural sciences such as geology and biology are historical in
their contextual, causal and narrative forms; as well, Hempel's
model, especially the requirement of empirically testable strict
universal laws, is satisfied by neither the physical sciences nor the
historical sciences, including archeology and biology (Ereshefsky
1992).



A number of legal decisions have appealed to Popper's and
Hempel's criteria, adding the epistemic role of peer review,
publication and consensus around the sound application of
methodological standards. A more recent criterion has sought a
different kind of demarcation: it is comparative rather than absolute;
it aims to compare science and popular science; it adopts a broader
notion 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 emphasizes
the role of systematicity, with an emphasis on different forms of
epistemic connectedness as weak forms of coherence and order
(Hoyningen-Huene 2013).



*Explanation*. Unity has been defended in the wake of authors
such as Kant and Whewell as an epistemic criterion of explanation or
at least fulfilling an explanatory role. In other words, rather than
modeling unification in terms of explanation, explanation is modeled
in terms of unification. A number of proposals introduce an
explanatory measure in terms of the number of independent explanatory
laws or phenomena conjoined in a theoretical structure. On this
representation, unity contributes understanding and confirmation from
the fewest basic kinds of phenomena, regardless of explanatory power
in terms of derivation or argument patterns (Friedman 1974; Kitcher
1981; 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 the
grounds that unification is simply systematization of old beliefs and
operates as a criterion of theory-choice (Halonen and Hintikka
1999).



The unification account of explanation has been defended within a more
detailed cognitive and pragmatist approach. The key is to think of
explanations as question-answer episodes involving four
elements: the explanation-seeking question about \(P, P\)?, the
cognitive state \(C\) of the questioner/agent for whom \(P\) calls for
explanation, the answer \(A\), and the cognitive state \(C+A\) in
which the need for explanation of \(P\) has disappeared. A related
account models unity in the cognitive state in terms of the
comparative increase of coherence and elimination of spurious
unity--such as circularity or redundancy (Schurz 1999).
Unification is also based on information-theoretic transfer or
inference relations. Unification of hypotheses is only a virtue if it
unifies data. The last two conditions imply that unification yields
also empirical confirmation. Explanations are global increases in
unification in the cognitive state of the cognitive agent (Schurz
1999; Schurz and Lambert 1994).



The unification-explanation link can be defended on the grounds
that laws make unifying similarity expectable (hence
Hempel-explanatory), and this similarity becomes the content of a new
belief (Weber and Van Dyck 2002 contra Halonen and Hintikka 1999).
Unification is not the mere systematization of old beliefs. Contra
Schurz, they argue that scientific explanation is provided by novel
understanding of facts and the satisfaction of our curiosity (Weber
and Van Dyck 2002 contra Schurz 1999). In this sense, causal
explanations, for instance, are genuinely explanatory and do not
require an increase of unification.



A contextualist and pluralist account argues that understanding is a
legitimate aim of science that is pragmatic and not necessarily
formal, or a subjective psychological by-product of explanation (De
Regt and Dieks 2005). In this view explanatory understanding is
variable and can have diverse forms, such as causal-mechanical and
unification, without conflict (De Regt and Dieks 2005). In the same
spirit, Salmon linked unification to the epistemic virtue or goal of
explanation and distinguished between unification and
causal-mechanical explanation as forms of scientific explanatory
understanding (Salmon 1998).



Explanation may also provide unification of different fields of
research through explanatory dependence so that one uses the
other's results to explain one's own (Kincaid 1997).



The views on scientific explanation have evolved away from the formal
and cognitive accounts of the epistemic categories. Accordingly, the
source of understanding provided by scientific explanations has been
misidentified according to some (Barnes 1992). The genuine source for
important, but not all, cases lies in causal explanation or causal
mechanism (Cartwright 1983; Cartwright 1989; see also Glennan 1996;
Craver 2007). Mechanistic models of explanation have become entrenched
in philosophical accounts of the life sciences (Darden 2006; Craven
2007). As an epistemic virtue, the role of unification has been traced
to the causal form of the explanation, for instance, in statistical
regularities (Schurz 2015). The challenge extends to the alleged
extensional link between explanation on the one hand, and truth and
universality on the other (Cartwright 1983; Dupre 1993;
Woodward 2003). In this sense, explanatory unity, which rests on
metaphysical assumptions about components and their properties, also
involves a form of ontological or metaphysical unity. (For a
methodological criticism of external, metaphysical perspectives, see
Ruphy 2016.)



Similar criticisms extend to the traditionally formalist arguments in
physics about fundamental levels; there, unification fails to yield
explanation in the formal scheme based on laws and their symmetries.
Unification and explanation conflict on the grounds that in biology
and physics only causal mechanical explanations answering
why-questions yield understanding of the connections that contribute
to "true unification" (Morrison
 2000;[2]
 Morrison's choice of standard for evaluating the epistemic
accounts of unity and explanation and her focus on systematic
theoretical connections without reduction has not been without
critics, e.g., Wayne 2002; Plutynski 2005; Karaca
 2012).[3]



*Methodology*. Unity has long been understood as a
methodological principle, primarily, but not exclusively, in
reductionist versions (e.g., for the case of biology, see Wimsatt
1976, 2006). This is different from the case of unity through
methodological prescriptions. One methodological criterion appeals to
the epistemic virtues of simplicity or parsimony, whether
epistemological or ontological (Sober 2003). As a formal probabilistic
principle of curve-fitting or average predictive accuracy, the
relevance of unity is objective. Unity plays the role of an empirical
background theory.



The methodological role of unification may track scientific progress.
Unlike in the case of the explanatory role of unification presented
above, this account of progress and interdisciplinarity relies on a
unifying role of explanation: as in evo-devo in biology, unification
is a process of advancement in which two fields of research are in the
process of unification through mutual explanatory relevance, that is,
when results in one field are required to pose and address questions
in 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 Best
2023).



*Evidence*. As in the relation of unification to explanation,
unification is considered an epistemic criterion of evidence in
support of the unified account (for a non-probabilistic account of the
relation between unification and confirmation, see Schurz 1999). The
resulting evidence and demonstration may be called synthetic evidence
and demonstration. Synthetic evidence may be the outcome of synthetic
modes of reasoning that rely on assumptions of similarity and
difference, for instance in cases of robustness, cross-checking and
meta-analysis (Cat 2022b).



Like probabilistic models of explanation, recent formal discussions of
unity and coherence within the framework of Bayesianism place unity in
evidentiary reasoning (Forster and Sober 1994, sect. 7; Schurz and
Lambert 2005 is also a formal model, with an algebraic approach). More
generally, the probabilistic framework articulates formal
characterizations of unity and introduces its role in evaluations of
evidence.



A criterion of unity defended for its epistemic virtue in relation to
evidence is simplicity or parsimony (Sober 2013, 2016). Comparatively
speaking, simpler hypotheses, models or theories present a higher
likelihood of truth, empirical support and accurate prediction. From a
methodological standpoint, however, appeals to parsimony might not be
sufficient. Moreover, the connection between unity as parsimony and
likelihood is not interest-relative, at least in the way that the
connection between unity and explanation is (Sober 2003; Forster and
Sober 1994; Sober 2013, 2016).



On the Bayesian approach, the rational comparison and acceptance of
probabilistic beliefs in the light of empirical data is constrained by
Bayes' 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 degree
that given \(h, p\) is statistically/probabilistically relevant to (or
correlated with) \(q\) (Myrvold 2003; for a probabilistically
equivalent measure of unity in Bayesian terms see McGrew 2003; on the
equivalence, Schupbach 2005). This measure of unity has been
criticized as neither necessary nor sufficient (Lange 2004;
Lange's criticism assumes the unification-explanation
link; in a rebuttal, Schupbach 2005 rejects this and other assumptions
behind Lange's criticism). In a recent development, Myrvold
argues for mutual information unification, i.e., that hypotheses are
said to be supported by their ability to increase the amount of what
he calls the mutual information of the set of evidence statements (see
Myrvold 2017). The explanatory unification contributed by hypotheses
about common causes is an instance of the information condition.



Evidentiary unification may contribute to the unification of different
fields of research in the form of evidentiary dependence: Evidentiary
dependence involves the appeal to the other's results in the
evaluation of one's own (Kincaid 1997).



*Aesthetic value*. Finally, epistemic values of unity may rely
on subsidiary considerations of aesthetic value. Nevertheless,
consideration of beauty, elegance or harmony may also provide
autonomous grounds for adopting or pursuing varieties of unification
in terms of simplicity and patterns of order (regularity of specific
relations) (McAllister 1996; Glynn 2010; Orrell 2012). Whether
aesthetic judgments have any epistemic import depends on metaphysical,
cognitive or pragmatic assumptions.



*Unification without reduction*. Reduction is not the sole
standard of unity, and models of unification without reduction have
proliferated. In addition, such models introduce new units of
analysis. An early influential account centers around the notion of
*interfield theories* (Darden and Maull 1977; Darden 2006). The
orthodox central place of theories as the unit of scientific knowledge
is replaced by that of fields. Examples of such fields are genetics,
biochemistry and cytology. Different levels of organization correspond
in this view to different fields: Fields are individuated
intellectually by a focal problem, a domain of facts related to the
problem, explanatory goals, methods and a vocabulary. Fields import
and transform terms and concepts from others. The model is based on
the idea that theories and disciplines do not match neat levels of
organization within a hierarchy; rather, many of them in their scope
and development cut across different such levels. Reduction is a
relation between theories within a field, not across fields.



*Interdependence and hybridity*. In general, the higher-level
theories (for instance, cell physiology) and the lower-level theories
(for instance, biochemistry) are ontologically and epistemologically
interdependent on matters of informational content and evidential
relevance; one cannot be developed without the other (Kincaid 1996;
Kincaid 1997; Wimsatt 1976; Spector 1977). The interaction between
fields (through researchers' judgments and borrowings) may
provide enabling conditions for subsequent interactions. For instance,
Maxwell's adoption of statistical techniques in color research
enabled the introduction of similar ideas from social statistics in
his 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 colors
provided chemical evidence in color research (Cat 2014).



The emergence and development of hybrid disciplines and theories is
another instance of non-reductive cooperation or interaction between
sciences. Noted above is the post-war emergence of interdisciplinary
areas of research: the so-called hyphenated sciences such as
neuro-acoustics, radioastronomy, biophysics, etc. (Klein 1990, Galison
1997) On a smaller scale, in the domain of, for instance, physics, one
can find semiclassical models in quantum physics or models developed
around phenomena where the limiting reduction relations are singular
or catastrophic, such as caustic optics and quantum chaos (Cat 1998;
Batterman 2002; Belot 2005). Such semiclassical explanatory models
have not found successful quantum substitutes and have placed
structural explanations at the heart of the relation between classical
and quantum physics (Bokulich 2008). The general form of pervasive
cases of emergence has been characterized with the notion of
contextual emergence (Bishop and Atmanspacher 2006) where
properties, behaviors and their laws on a restricted, lower-level,
single-scale domain are necessary but not sufficient for the
properties and behaviors of another, e.g., higher-level one, not even
of itself. The latter are also determined by contingent contexts
(contingent features of the state space of the relevant system). The
interstitial formation of more or less stable small-scale syntheses
and cross-boundary "alliances" has been common in most
sciences since the early twentieth century. Indeed, it is crucial to
development in model building and growing empirical relevance in
fields ranging anywhere from biochemistry to cell ecology, or from
econophysics to thermodynamical cosmology. Similar cases can be found
in chemistry and the biomedical sciences.



*Conceptual unity*. The conceptual dimension of cross-cutting
has been developed in connection with the possibility of cross-cutting
natural kinds that challenges taxonomical monism. Categories of
taxonomy and domains of description are interest-relative, as are
rationality and objectivity (Khalidi 1998; his view shares positions
and attitudes with Longino 1989; Elgin 1996, 1997). Cross-cutting
taxonomic systems, then, are not conceptually inconsistent or
inapplicable. Both the interest-relativity and hybridity feature
prominently in the context of ontological pluralism (see below).



Another, more general, unifying element of this kind is Holton's
notion of *themata*. Themata are conceptual values that are a
priori yet contingent (both individual and social). They are forming
and organizing presuppositions that factor centrally in the evolution
of 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 more
complex and comprehensive unit of organized scientific practice is the
notion of the various *styles of reasoning*, such as
statistical, analogical modeling, taxonomical, genetic/genealogical or
laboratory styles; each is a cluster of epistemic standards,
questions, tools, ontology, and self-authenticating or stabilizing
protocols (Hacking 1996; see below for the relevance of this account
of a priori elements to claims of global disunity--the account
shares distinctive features of Kuhn's notion of paradigm).



Another model of non-reductive unification is historical and
diachronic: it emphasizes the genealogical and historical identity of
disciplines, which has become complex through interaction. The
interaction extends to relations between specific sciences, philosophy
and philosophy of science (Hull 1988). Hull has endorsed an image of
science as a process, modeling historical unity after a
Darwinian-style pattern of evolution (developing an earlier suggestion
by Popper). Part of the account is the idea of disciplines as
evolutionary historical individuals, which can be revised with the
help of more recent ideas of biological individuality: hybrid unity
as an external model of unity as integration or coordination of
individual disciplines and disciplinary projects, e.g., characterized
by a form of occurrence, evolution or development whose tracking and
identification involves a conjunction with other disciplines, projects
and domains of resources, from within science or outside science.
This diachronic perspective can accommodate models of discovery, in
which genealogical unity integrates a variety of resources that can be
both theoretical and applied, or scientific and non-scientific (an
example, from physics, the discovery of superconductivity, can be
found in Holton, Chang and Jurkowitz 1996). Some models of unity below
provide further examples.



A generalization of the notion of interfield theories is the idea that
unity is *interconnection*: Fields are unified theoretically
and practically (Grantham 2004). This is an extension of the original
modes of unity or identity that single out individual disciplines.
Theoretical unification involves conceptual, ontological and
explanatory relations. Practical unification involves heuristic
dependence, confirmational dependence and methodological integration.
The social dimension of the epistemology of scientific disciplines
relies on institutional unity. With regard to disciplines as
professions, this kind of unity has rested on institutional
arrangements such as professional organizations for
self-identification and self-regulation, university mechanisms of
growth 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 or
tradition of unification (or integration), and they are typically
focused on science as a human activity. From that standpoint,
unification is typically understood or advocated as a piecemeal
description and strategy of collaboration (see Klein 1990 on the
distinction between global integration and local interdisciplinarity).
Cases are restricted to specific models, phenomena or situations.



*Material unity*. A more recent approach to the connection
between different research areas has focused on a material level of
scientific practice, with attention to the use of instruments and
other material objects (Galison 1997; Bowker and Star 1999). For
instance, the *material unity* of natural philosophy in the
sixteenth and seventeenth centuries relied on the circulation,
transformation and application of objects in their concrete and
abstract representations (Bertoloni-Meli 2006). The latter correspond
to the imaginary systems and their representations, which we call
models. The evolution of objects and images across different theories
and experiments and their developments in nineteenth-century natural
philosophy provide a historical model of scientific development, but
the approach is not meant to illustrate reductive materialism, since
the same objects and models work and are perceived as vehicles for
abstract ideas, institutions, cultures, etc., or are prompted by them.
On one view, objects are regarded as elements in so-called trading
zones (see below) with shifting meanings in the evolution of
twentieth-century physics, such as with the cloud chamber which was
first relevant to meteorology and next to particle physics (Galison
1997). Alternatively, material objects have been given the status of
*boundary objects*, which provide the opportunity for experts
from different fields to collaborate through their respective
understandings of the system in question and their respective goals
(Bowker and Star 1999).



*Graphic unity*. At the concrete perceptual level, recent
accounts emphasize the role of visual representations in the sciences
and suggest what may be called *graphic unification* of the
sciences. Their cognitive roles, methodological and rhetorical,
include establishing and disseminating facts and their so-called
virtual witnessing, revealing empirical relations, testing their fit
with available patterns of more abstract theoretical relations
(theoretical integration), suggesting new ones, aiding in
computations, serving as aesthetic devices etc. But these uses are not
homogeneous across different sciences and make visible disciplinary
differences. We may equally speak of *graphic pluralism*. The
rates in the use of diagrams in research publications appear to vary
along the hard-soft axis of pyramidal hierarchy, from physics,
chemistry, biology, psychology, economics and sociology, and political
science (Smith et al. 2000). The highest use can be found in physics,
intuitively identified by the highest degree of hardness understood as
consensus, codification, theoretical integration and factual
stability, to the highest interpretive and instability of results.
Similarly, the same variation occurs among sub-disciplines within each
discipline. The kinds of images and their contents also vary across
disciplines and within disciplines, ranging from hand-made images of
particular specimens to hand-made or mechanically generated images of
particulars standing in for types, to schematic images of geometric
patterns in space or time, or to abstract diagrams representing
quantitative relations. Importantly, graphic tools circulate like
other cognitive tools between areas of research that they in turn
connect (Galison 1997; Daston and Galison 2007; Lopes 2009; see also
Lynch and Woolgar 1990; Baigrie 1996; Jones and Galison 1998; Galison
1997; Cat 2014; Kaiser 2005).



*Disciplinary unity and collaboration*. The relation between
disciplines or fields of research has often been tracked by relations
between their respective theories or epistemic products. But
disciplines constitute broader and richer units of analysis of
connections in the sciences characterized, for instance, by their
domain of inquiry, cognitive tools and social structure (Bechtel
1987).



Unification of disciplines, in that sense, has been variously
categorized, for instance, as *interdisciplinary*,
*multidisciplinary*, *crossdisciplinary* or
*transdisciplinary* (Klein 1990; Graff 2005; Kellert 2008;
Repko 2012). It might involve a researcher borrowing from different
disciplines or the collaboration of different researchers. Neither
modality 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 heuristic
problem-solving or innovative powers, as it is prompted by a problem
that is considered complex in that it does not arise or cannot be
fully treated within the purview of one specific discipline unified or
individuated around some potentially non-unique set of elements such
as 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 collaboration
creates a new discipline or project, such as interfield research,
often leaving the existence of the original ones intact.
*Multidisciplinary* work involves the juxtaposition of the
treatments and aims of the different disciplines involved in
addressing a common problem. *Crossdisciplinary* work involves
borrowing resources from one discipline to serve the aims of a project
in another. *Transdisciplinary* work is a synthetic creation
that encompasses work from different disciplines (Klein 1990; Kellert
2008; Brigandt 2010; Hoffmann, Schmidt and Nersessian 2012; Osbeck et
al. 2011; Repko 2012). These different modes of synthesis or
connection are not mutually exclusive.



Models of interdisciplinary cooperation and their corresponding
outcomes 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.) or
*embodied* (cross-training). Each selectively highlights and
neglects different aspects of scientific practice and properties of
scientific products. Cartographic and architectural images, for
instance, focus on spatial and static synchronic relations and simply
connected, compatible elements. Socio-political and embodied images
emphasize activity and non-propositional elements (Kellert 2008
defends the image of cross-training).



In this context, methodological unity often takes the form of
borrowing standards and techniques for the application of formal and
empirical methods. They range from calculational techniques and tools
for theoretical modeling and simulation of phenomena to techniques for
modeling of data, using instruments and conducting experiments (e.g.,
the culture of field experiments and, more recently, randomized
control trials across natural and social sciences). A key element of
scientific practice, often ignored by philosophical analysis, is
expertise. As part of different forms of methodological unity, it is
key to the acceptance and successful appropriation of techniques.
Recent accounts of multidisciplinary collaboration as a human activity
have focused on the dynamics of integrating different kinds of
expertise around common systems or goals of research (Collins and
Evans 2007; Gorman 2002). The same perspective can accommodate the
recent interest in so-called mixed methods, e.g., different forms of
integration of quantitative and qualitative methods and approaches in
the social sciences (but mixed-method approaches do not typically
involve mixed disciplines).



As teamwork and collaboration within and between research units has
steadily increased, so has the degree of specialization (Wutchy et al.
2007). Between both trends, new reconfigurations keep forming with
different purposes and types of institutional expression and support;
for example, STEM, Earth sciences, physical sciences, mind-brain
sciences, etc., in addition to hybrid fields mentioned above. Yet,
in educational research and funding, disciplinarity has acquired
new normative purchase in opposite directions: while funding agencies
and universities promote interdisciplinarity, university
administrations encourage both disciplinary competition and more
versatile adisciplinarity (Griffiths 2022). In the face of defenses of
different forms of interdisciplinarity (Graff 2015), there is also a
renewed attention to the critical value of autonomy of disciplines, or
disciplinarity, as the key resource in division of labor and
collaboration alike (Jacobs 2013).



The social epistemology of interdisciplinarity is complex. It develops
both top-down from managers and bottom-up from practitioners
(Maki 2016; Maki and MacLeod 2016), relying on a variety of
kinds of interactions with heuristic and normative dimensions
(Boyer-Kassem et al. 2018). More generally, collaborative work
arguably provides epistemic, ethical and instrumental advantages,
e.g., more comprehensive relevant understanding of complex problems,
expanded justice to interests of direct knowledge users and increased
resources (Laursen et al. 2021). Yet, collaboration relies on a
plurality of values or norms that may lead to conflicts such as a
paralyzing practical incoherence of guiding values and moral
incoherence 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 scientific
collaboration has led to a broader perspective, including a number of
dimensions of interdisciplinary cooperation involving identification
of conflicts and the setting of sufficient so-called common ground
integrators. These include shared (pre-existing, revised and newly
developed) concepts, terminology, standards, techniques, aims,
information, tools, expertise, skills (abstract, dialectical, creative
and holistic thinking), cognitive and social ethos (curiosity,
tolerance, flexibility, humility, receptivity, reflexivity, honesty,
team-play) social interaction, institutional structures and
geography (Cummings and Kiesler 2005; Klein 1990; Kockelmans 1979;
Repko 2012). Sociological studies of scientific collaboration can in
principle place the connective models of unity within the more general
scope of social epistemology, for instance, in relation to
distributive cognition (beyond the focus on strategies of consensus
within communities).



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



The study of the social epistemology of interdisciplinary and
collaborative research has been carried out and proposed from
different perspectives that illuminate different dimensions and
implications. These include historical typology (Klein 1990), formal
modeling (Boyer-Kassem et al. 2018), ethnography (Nersessian 2022),
ethical, scientometrics and multidimensional philosophical
perspectives (Maki 2016). Other approaches aim to design and
offer tools that facilitate collaboration such as the Toolbox Dialogue
Initiative (Hubbs et al. 2020). The different forms of plurality and
connection also ultimately inform the organization of science in the
social 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; Repko
2012; Hoffmann, Schmidt and Nersessian 2012.)



A general model of local interconnection, which has acquired
widespread attention and application in different sciences, is the
anthropological model of *trading zone*, where hybrid languages
and meanings are developed that allow for interaction without
straightforward extension of any party's original language or
framework (Galison 1997). Galison has applied this kind of
anthropological analysis to the subcultures of experimentation. This
strategy aims to explain the strength, coherence and continuity of
science in terms of local *coordinations* of intercalated
levels of symbolic procedures and meanings, instruments and
arguments.



At the experimental level, instruments, as found objects, acquire new
meanings, developments and uses as they bridge over the transitions
between theories, observations or theory-laden observations.
Instruments and experimental projects in the case of Big Science also
bring together, synchronically and interactively, the skills,
standards and other resources from different communities, and they
change each in turn (on interdisciplinary experimentation see also
Osbeck et al. 2011). Patterns of laboratory research are shared by
the different sciences, including not just instruments but the general
strategies of reconfiguration of human researchers and the natural
entities researched (Knorr-Cetina 1992). This includes statistical
standards (e.g., statistical significance) and ideals of
replication. At the same time, attention has been paid to the
different ways in which experimental approaches differ among the
sciences (Knorr-Cetina 1992; Guala 2005; Weber 2005) as well as to how
they have been transferred (e.g., field experiments and randomized
control trials) or integrated (e.g., mixed methods combining
quantitative and qualitative techniques).



Interdisciplinary research has been claimed to revolve shared boundary
objects (Gorman 2002) and to yield evidentiary and heuristic
integration through cooperation (Kincaid 1997). Successful
interdisciplinary research, however, does not seem to require
integration, e.g., evolutionary game theory in economics and biology
(Grune-Yanoff 2016). Heuristic cooperation has also led to new
stable disciplines through stronger integrative forms of problem
solving. In the life sciences, for instance, computational,
mathematical and engineering techniques for modeling and data
collection in molecular biology have led to integrative systems
biology (MacLeod and Nersessian 2016; Nersessian 2022). Similarly,
constraints and resources for problem-solving in physics, chemistry
and biology led to the development of quantum chemistry (Gavroglu and
Simoes 2012; see also the case of nuclear chemistry in Cat and
Best 2023).


## 4. Ontological unities


### 4.1 Ontological unities and reduction



Since Nagel's influential model of reduction by derivation, most
discussions of the unity of science have been cast in terms of
reductions between concepts and the entities they describe, and
between theories incorporating the descriptive concepts. Ontological
unity is expressed by a preferred set of such ontological units. In
this regard, it should be noted that the selection of units typically
relies on assumptions about classification or natural order such as
commitments to natural kinds or a hierarchy of levels.



In terms of concepts featured in preferred descriptions, explanatory
or not, reduction endorses taxonomical monism: a privileged set of
fundamental kinds of things. These privileged kinds are often known as
so-called natural kinds; although, as it has been argued, monism does
not entail realism (Slater 2005) and the notion admits of multiple
interpretations, ranging from the more conventionalist to the more
essentialist (Tahko 2021; see a critique in Cat 2022a). Natural
kindness has further been debated in terms, for instance, of the
contrast between so-called cluster and causal theories. Connectedly,
pluralism does not entail anti-realism (Dupre 1993), nor does
realism entail monism or essentialism (Khalidi 2021). Without
additional metaphysical assumptions, the fundamental units are
ambiguous with respect to their status as either entity or property.
Reduction may determine the fundamental kinds or level through the
analysis of entities.



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



A classic reference to this compositional type of account is Oppenheim
and Putnam's "The Unity of Science as a Working
Hypothesis" (Oppenheim and Putnam 1958; Oppenheim and Hempel had
worked in the 1930s on taxonomy and typology, a question of broad
intellectual, social and political relevance in Germany at the time).
Oppenheim and Putnam intended to articulate an idea of science as a
reductive unity of concepts and laws reduced to those of the most
elementary elements. They also defended it as an empirical
hypothesis--not an a priori ideal, project or
precondition--about science. Moreover, they claimed that its
evolution manifested a trend in that unified direction out of the
smallest entities and lowest levels of aggregation. In an important
sense, the evolution of science recapitulates, in the reverse, the
evolution of matter, from aggregates of elementary particles to the
formation of complex organisms and species (we find a similar
assumption in Weinberg's downward arrow of explanation). Unity,
then, is manifested not just in *mereological* form, but also
diachronically, *genealogically* or *historically*.



A weaker form of ontological reduction advocated for the biomedical
sciences with the causal notion of *partial reductions*:
explanations of localized scope (focused on parts of higher-level
systems only) laying out a causal mechanism connecting different
levels in the hierarchy of composition and organization (Schaffner
1993; Schaffner 2006; Scerri has similarly discussed degrees of
reduction in Scerri 1994). An extensional, domain-relative approach
introduces the distinction between "domain preserving" and
"domain combining" reductions. Domain-preserving
reductions are intra-level reductions and occur between \(T\_1\) and
its 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 a
relation between theories or even involve any theory has also been
challenged. One such challenge focuses on "inter-level"
explanations in the form of *compositional redescription* and
causal mechanisms (Wimsatt 1976). The role of biconditionals or even
Schaffner-type identities, as factual relations, is heuristic (Wimsatt
1976). The heuristic value extends to the preservation of the
higher-level, reduced concepts, especially for cognitive and pragmatic
reasons, including reasons of empirical evidence. This amounts to
rejecting the structural, formal approach to unity and reductionism
favored by the logical-positivist tradition. Reductionism is another
example of the functional, purposive nature of scientific practice.
The metaphysical view that follows is a pragmatic and non-eliminative
realism (Wimsatt 2006). As a heuristic, this kind of non-eliminative
pragmatic reductionism is a complex stance. It is, across levels,
integrative and intransitive, compositional, mechanistic and
functionally localized, approximative and abstractive. It is bound to
adopting false idealizations, focusing on regularities and stable
common behavior, circumstances and properties. It is also constrained
in its rational calculations and methods, tool-binding and
problem-relative. The heuristic value of eliminative, inter-level
reductions has been defended as well (Poirier 2006).



The appeal to formal laws and deductive relations is dropped for sets
of concepts or vocabularies in the *replacement analysis*
(Spector 1978). This approach allows for talk of entity reduction or
branch reduction, and even direct theory replacement, without the
operation of laws, and it circumvents vexing difficulties raised by
bridge principles and the deductive derivability condition
(self-reduction, infinite regress, etc.). Formal relations only
guarantee, but do not define, the reduction relation. Replacement
functions are meta-linguistic statements. As Sellars argued in the
case of explanation, this account distinguishes between reduction and
the testing for reduction, and it highlights the role of derivations
in both. Finally, replacement can be in practice or in theory.
Replacement in practice does not advocate elimination of the reduced
or replaced entities or concepts (Spector 1978).



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



Levels forming a hierarchy are discrete and stratified so that
entities at level n strongly depend on entities at level \(n-1.\) The
different levels may be distinguished in different ways: by
differences in scale, by a relation of realization and, especially, by
a relation of composition such that entities at level n are considered
composed 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 fix
an absolute hierarchy of levels. Critics have noted, for instance,
that entities may participate in causal interactions at multiple
levels and across levels in physical models (Thalos 2013) and
across biological and neurobiological models (Haug 2010; Eronen
2013).



In addition, the compartmentalization of theories and their concepts
or vocabulary into levels neglects the existence of empirically
meaningful and causally explanatory relations between entities or
properties at different levels. If they are neglected as theoretical
knowledge and left as only bridge principles, the possibility of
completeness of knowledge is jeopardized. Maximizing completeness of
knowledge requires a descriptive unity of all phenomena at all levels
and anything between these levels. Any bounded region or body of
knowledge neglecting such cross-boundary interactions is radically
incomplete, and not just confirmationally or evidentially so; we may
refer to this problem as the problem of *cross-boundary
incompleteness* at either intra-level or *horizontal
incompleteness* and, on a hierarchy, the problem of inter-level or
*vertical 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 as
conceptual coordinate systems or, more radically, altogether
dispensable (Thalos 2013; Potochnik 2017). As a result, they fail to
fix a corresponding hierarchy of fields and subfields of scientific
research defended by reductionist accounts.



The most radical form of reduction as replacement is often called
*eliminativism*. The position has made a considerable impact in
philosophy 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 is
only a replacement rule) (see also
 eliminative materialism).



From a semantic standpoint, one may distinguish different kinds of
reduction in terms of four criteria, two epistemological and two
ontological: fundamentalism, approximation, abstract hierarchy and
spatial hierarchy. *Fundamentalism* implies that the features
of a system can be explained in terms only of factors and rules from
another realm. *Abstract hierarchy* is the assumption that the
representation of a system involves a hierarchy of levels of
organization with the explanatory factors being located at the lower
levels. *Spatial hierarchy* is a special case of abstract
hierarchy in which the criterion of hierarchical relation is a spatial
part-whole or containment relation. Strong reduction satisfies the
three "substantive" criteria, whereas weak reduction only
satisfies fundamentalism. Approximate reductions--strong and
hierarchical--are those which satisfy the criterion of
fundamentalism only approximately (Sarkar 1998; the merit of
Sarkar's proposal resides in its systematic attention to
hierarchical conditions and, more originally, to different conditions
of *approximation*; see also Ramsey 1995; Lange 1995).



The semantic turn extends to more recent notion of models that do not
fall under the strict semantic or model-theoretic notion of
mathematical structures (Giere 1999; Morgan and Morrison 1999). This
is a more flexible framework about relevant formal relations and the
scope of relevant empirical situations. It is implicitly or explicitly
adopted by most accounts of unity without reduction. One may add the
primacy of temporal representation and temporal parts, *temporal
hierarchy* or *temporal compositionality*, first emphasized
by Oppenheim and Putnam as a model of genealogical or diachronic
unity. This framework applies to processes both of evolution and
development (a more recent version is in McGivern 2008 and in Love and
Hutteman 2011).



The shift in the accounts of scientific theory from syntactic to
semantic approaches has changed conceptual perspectives and,
accordingly, formulations and evaluations of reductive relations and
reductionism. However, examples of the semantic approach focusing on
mathematical structures and satisfaction of set-theoretic relations
have focused on syntactic features--including the axiomatic form
of a theory--in the discussion of reduction (Sarkar 1998; da
Costa and French 2003). In this sense, the structuralist approach can
be construed as a neo-Nagelian account, while an alternative line of
research has championed the more traditional structuralist semantic
approach (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 as
*multiple realizability* and *supervenience*, introduced
by Putnam, Kim, Fodor and others, have led to talk of higher-level
functionalism, a distinction between type-type and token-token
reductions and the examination of its implications. The concepts of
emergence, supervenience and downward causation are related
metaphysical tools for generating and evaluating proposals about unity
and reduction in the sciences. This literature has enjoyed its chief
sources and developments in general metaphysics and in philosophy of
mind and psychology (Davidson 1969; Putnam 1975; Fodor 1975; Kim
1993).



*Supervenience*, first introduced by Davidson in discussions of
mental properties, is the notion that a system with properties on one
level is composed of entities on a lower level and that its properties
are determined by the properties of the lower-level entities or
states. The relation of determination is that no changes at the
higher-level occur without changes at the lower level. Like
token-reductionism, supervenience has been adopted by many as the poor
man's reductionism (see the entry on
 supervenience).
 A different case for the autonomy of the macrolevel is based on the
notion of multiple supervenience (Kincaid 1997; Meyering 2000).



The autonomy of the special sciences from physics has been defended in
terms of a distinction between *type-physicalism* and
*token-physicalism* (Fodor 1974; Fodor countered Oppenheim and
Putnam's hypothesis under the rubric "the disunity of
science"; see the entry on
 physicalism).
 The key logical assumption is the type-token distinction, whereby
types are realized by more specific tokens, e.g., the type
"animal" is instantiated by different species, the type
"tiger" or "electron" can be instantiated by
multiple individual token tigers and electrons. Type-physicalism is
characterized by a type-type identity between the
predicates/properties in the laws of the special sciences and those of
physics. By contrast, token-physicalism is based on the token-token
identity between the predicates/properties of the special sciences and
those of physics; every event under a special law falls under a law of
physics and bridge laws express contingent token-identities between
events. Token-physicalism operates as a demarcation criterion for
materialism. Fodor argued that the predicates of the special sciences
correspond to infinite or open-ended disjunctions of physical
predicates, and these disjunctions do not constitute natural kinds
identified by an associated law. Token-physicalism is the only
alternative. All special kinds of events are physical, but the special
sciences are not physics (for criticisms based on the presuppositions
in Fodor's argument, see Sober 1999).



The denial of remedial, weaker forms of reductionism is the basis for
the concept of *emergence* (Humphreys 1997; Bedau and Humphreys
2008; Wilson 2021). Different accounts have attempted to articulate
the idea of a whole being different from or more than the mere sum of
its parts (see the entry on
 emergent properties).
 Emergence has been described beyond logical relations, synchronically
as an ontological property and diachronically as a material process of
fusion, in which the powers of the separate constituents lose their
separate existence and effects (Humphreys 1997). This concept has been
widely applied in discussions of *complexity*. Unlike the
earliest antireductionist models of complexity in terms of holism and
cybernetic properties, more recent approaches track the role of
constituent parts (Simon 1996). Weak emergence has been opposed to
nominal and strong forms of emergence. The nominal kind simply
represents that some macro-properties cannot be properties of
micro-constituents. The strong form is based on supervenience and
irreducibility, with a role for the occurrence of autonomous downwards
causation upon any constituents (see below). Weak emergence is linked
to processes stemming from the states and powers of constituents, with
a reductive notion of downwards causation of the system as a resultant
of constituents' effects (Wilson 2021); however, the connection
is not a matter of Nagelian formal derivation, but of so-called
universality classes (Batterman 2002; Thalos 2013), self-organization
(Mitchell 2012) and implementation through computational aggregation,
compression and iteration. Weak emergence, then, can be defined in
terms of simulation: a macro-property, state or fact is weakly
emergent if and only if it can be derived from its macro-constituents
only by simulation (Bedau and Humphreys 2008) The denial of remedial,
weaker forms of reductionism is the basis for the concept of
*emergence* (Humphreys 1997; Bedau 2008); see the entry on
 simulations in science).



Computational models of emergence or complexity straddle the boundary
between formal epistemology and ontology. They are based on
simulations of chaotic dynamical processes such as cellular automata
(Wolfram 1984, 2002). Their supposed superiority to combinatorial
models based on aggregative functions of parts of wholes does not lack
defenders (Crutchfield 1994; Crutchfield and Hanson 1997; Humphreys
2004, 2007, 2008; Humphreys and Huneman 2008; Huneman 2008a, 2008b,
2010).



Connected to the concept of emergence is *top-down* or
*downward causation*, which captures the autonomous and genuine
causal power of higher-level entities or states, especially upon
lower-level ones. The most extreme and most controversial version
includes a violation of laws that regulate the lower level (Meehl and
Sellars 1956; Campbell 1974). Weaker forms require compatibility with
the microlaws (for a brief survey and discussion see Robinson 2005; on
downward causation without top-down causes, see Craver and Bechtel
2007; Bishop 2012). The very concept has become the subject of some
interdisciplinary interest in the sciences (Ellis, Noble and
O'Connor 2012).



Another general argument for the autonomy of the macrolevel in the
form of non-reductive materialism has been a cognitive type of
functionalism, namely, cognitive pragmatism (Van Gulick 1992). This
account links ontology to epistemology. It discusses four pragmatic
dimensions of representations: the nature of the causal interaction
between theory-user and the theory, the nature of the goals to the
realization of which the theory can contribute, the role of indexical
elements in fixing representational content, and differences in the
individuating principles applied by the theory to its types (Wimsatt
and Spector's arguments above are of this kind). A more
ontologically substantive account of functional reduction is
Ramsey's bottom-up *construction by reduction*:
transformation reductions streamline formulations of theories in such
a way that they extend basic theories upwards by engineering their
application to specific context or phenomena. As a consequence, they
reveal, by construction, new relations and systems that are
antecedently absent from a scientist's understanding of the
theory--independently of a top or reduced theory (Ramsey 1995). A
weaker framework of ontological unification is *categorial
unity*, wherein abstract categories such as causality,
information, etc., are attached to the interpretation of the specific
variables and properties in models of phenomena.


## 5. Disunity and pluralism



A more radical departure from logical-positivist standards of unity is
the recent criticism of the methodological values of reductionism and
unification in the sciences and also its position in culture and
society. From the descriptive standpoint, many views under the
rubric of disunity are versions of positions mentioned above. The
difference is mainly normative and a matter of emphasis, scope and
perspective. Such views reject global or universal standards of
unity--including unity of method--by emphasizing disunity
and endorsing different forms of epistemological and ontological
pluralism.


### 5.1 The Stanford School



An influential picture of disunity comes from related works by members
of the so-called Stanford School such as John Dupre, Ian
Hacking, Peter Galison, Patrick Suppes and Nancy Cartwright. Disunity
is, in general terms, a rejection of universalism and uniformity, both
methodological and metaphysical. Through their work, the rubric of
disunity has acquired a visibility parallel to the one once acquired
by unity, as an inspiring philosophical rallying cry.



From a methodological point of view, members of the school have
defended, from analysis of actual scientific practice, a model of
local unity such as the so-called trading-zone, (Galison 1998), a
plurality of scientific methods (Suppes 1978), a plurality of
scientific styles with the function of establishing spaces of
epistemic possibility and a plurality of kinds of unities (Hacking
1996; Hacking follows the historian A.A. Crombie; for a criticism of
Hacking's historical epistemology see Kusch 2010).



From a metaphysical point of view, the disunity of science can be
given adequate metaphysical foundations that make pluralism compatible
with realism (Dupre 1993; Cartwright 1983, 1999). Dupre
opposes a mechanistic paradigm of unity characterized by determinism,
reductionism and essentialism. The paradigm spreads the values and
methods of physics to other sciences that he thinks are scientifically
and socially deleterious. Disunity appears characterized by three
pluralistic theses: against essentialism--there is always a
plurality of classifications of reality into kinds; against
reductionism--there exists equal reality and causal efficacy of
systems at different levels of description (that is, the microlevel is
not causally complete, leaving room for downward causation); and
against epistemological monism--there is no single methodology
that supports a single criterion of scientificity, nor a universal
domain of its applicability, leaving only a plurality of epistemic and
non-epistemic virtues. The unitary concept of science should be
understood, following the later Wittgenstein, as a family-resemblance
concept. (For a criticism of Dupre's ideas, see Mitchell
2003; Sklar 2003.)



Against the universalism of explanatory laws, Cartwright has argued
that laws cannot be both universal and exactly true, as Hempel
required in his influential account of explanation and demarcation;
there exist only patchworks of laws and local cooperation. Like
Dupre, Cartwright adopts a kind of scientific realism but
denies that there is a universal order, whether represented by a
theory of everything or a corresponding a priori metaphysical
principle (Cartwright 1983). Theories apply only locally, where and to
the extent that their interpretive models fit the phenomena studied,
*ceteris paribus* (Cartwright 1999). Cartwright's
pluralism is not just opposed to vertical reductionism but also
horizontal imperialism, or universalism and globalism. She explains
their more or less general domain of application in terms of causal
capacities and arrangements she calls *nomological machines*
(Cartwright 1989, 1999). The regularities they bring about depend on a
shielded environment. As a matter of empiricism, this is the reason
that it is in the controlled environment of laboratories and
experiments, where causal interference is shielded off, that factual
regularities are manifested. The controlled, stable, regular world is
an engineered world. Representation rests on intervention (cf. Hacking
1983; for criticisms see Winsberg et al. 2000; Hoefer 2003; Sklar
2003; Howhy 2003; Teller 2004; McArthur 2006; Ruphy 2016).



Disunity and autonomy of levels have been associated, conversely, with
antirealism, meaning instrumentalist or empiricist heuristics. This
includes, for Fodor and Rosenberg, higher-level sciences such as
biology and sociology (Fodor 1974; Rosenberg 1994; Huneman 2010). It
is against this picture that Dupre's and
Cartwright's attacks on uniformly global unity and reductionism,
above, might seem surprising by including an endorsement, in causal
terms, of
 realism.[4]
 Rohrlich has defended a similar realist position about weaker,
conceptual (cognitive) antireductionism, although on the grounds of
the mathematical success of derivational explanatory reductions
(Rohrlich 2001). Ruphy, however, has argued that antireductionism
merely amounts to a general methodological prescription and is too
weak to yield uncontroversial metaphysical lessons; these are in fact
based on general metaphysical commitments external to scientific
practice (Ruphy 2005, 2016).


### 5.2 Pluralism



Unlike more descriptive accounts of plurality, pluralism is a
normative endorsement of plurality. The question of the metaphysical
significance of disunity and anti-reductionism takes one straight to
the larger issue of the epistemology and metaphysics (and aesthetics,
social culture and politics) of pluralism. And here one encounters the
familiar issues and notions such as conceptual schemes, frameworks and
worldviews, incommensurability, relativism, contextualism and
perspectivalism about goals and standards of concepts and methods (for
a general discussion see Lynch 1998; on perspectivalism about
scientific models see Giere 1999, 2006; Rueger 2005; Massimi and McCoy
2020).



In connection with relativism and instrumentalism, pluralism has
typically been associated with antirealism about taxonomical
practices. But it has been defended from the standpoint of realism
(for instance, Dupre 1993; Chakravartty 2011). Pluralism about
knowledge of mind-independent facts can be formulated in terms of
different ways to distribute properties (sociability-based pluralism),
with more specific commitments about the ontological status of the
related elements and their plural contextual manifestations of powers
or dispositions (Chakravartty 2011; Cartwright 2007).



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



Consider at least four distinctions--they are formulated
about concepts, facts, and descriptions, and they apply also to
values, virtues, methods, etc.:


* *Vertical vs. horizontal pluralism*. Vertical pluralism is
inter-level pluralism, the view that there is more than one level of
factual 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 may
be incompatible descriptions or facts on the same level of discourse
(Lynch 1998). For instance, the plurality of explanatory causes to be
chosen from or integrated in biology or physics has been defended as a
lesson in pluralism (Sober 1999).
* *Global vs. local pluralism*. Global pluralism is pluralism
about every type of fact or description. Global horizontal pluralism
is the view that there may be incompatible descriptions of the same
type of fact. Global vertical pluralism is the view that no type of
fact or description reduces to any other. Local horizontal and
vertical pluralism is about one type of fact or description (Lynch
1998). It may also concern situated standpoints informed by, among
others, social differences (Wylie 2015).
* *Difference vs. integrative pluralism*. Difference
pluralism has been defended in terms of division of labor in the face
of complexity and cognitive limitations (Giere 2006), epistemic
humility (Feyerabend 1962 and his final writings in the 1990s; Chang
2002), scientific freedom, empirical testability and theory choice
(Popper 1935; Feyerabend 1962) and underdetermination.



Underdetermination arguments concern choices from a disjunction of
equivalent types of descriptions (Mitchell 2003, 2009) or of
incompatible partial representations or models of phenomena in the
same intended scope (Longino 2002, 2013). The representational
incompatibility may be traced to competing values or aims, or
assumptions in *ceteris paribus* laws.



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



Integrative, or connective, types of pluralism are the conjunctive or
holistic requirement of different types of descriptions, methods or
perspectives (Mitchell 2003, 2009; contrast with the more isolationist
position in Longino 2002 and her essay in Kellert, Longino and Waters
2006; Longino 2013).



To a merely syncretistic or tolerant, non-interactive pluralism, a
recent 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 through
communication and assimilation--borrowing or co-optation--or
a more robust, integrative epistemic engagement. The latter may
involve, for instance, communicative expertise--also known as
interactional expertise--without having contributory expertise
in the other practice, exchange and collaboration on the same
project.



Borrowing and cross-fertilization across divides and over distances
concern more than theories and change the respective practices,
processes and products. They extend to data, concepts, models,
methods, evidence, heuristic techniques, technology and other
resources. To mention one distinction, while theoretical integration
concerns concepts, ontology, explanations, models, etc., practical
integration concerns methods, heuristics and testing (Grantham 2004).
Thus, accounts including different versions of taxonomical pluralism
range from the more conventional and contingent (from Elgin 1997 to
astronomical kinds in Ruphy 2016) and the more grounded in contexts of
practices (categorization work in Bowker and Star 1999; life sciences
and chemistry in Kendig 2016) and the interactive (Hacking's
interactive kinds in the human sciences) to the more metaphysically
substantive. Some methodological prescriptions of pluralism rely on
pluralism in metascientific research including history (Chang
2012).



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



From the standpoint of evidence, we find second-order varieties of
mixed evidence patterns--triangulation, security and
integration--that connect different kinds of evidence to provide
enhanced evidential value. The relevant plurality or difference
requires independence, a condition to be explicated in different ways
(Kuorikoski and Marchionni 2022). Regarding triangulation, enhanced
evidence results from multiple theory-laden but theoretically
independent lines of evidence in, for instance, microscopy (Hacking
1983), archeology (Wylie 1999) and interdisciplinary research in the
social sciences, for example, neuroeconomics in support of existence
claims about phenomena and descriptions of phenomena but not to more
general theories about them (Kuorikoski and Marchionni 2016).



Connective forms of pluralism have been modeled in terms of relations
between disciplines (see above) and defended at the level of social
epistemology by analogy with political models of liberal democracy and
as a model of social governance between the extremes of so-called
consensual mainstreaming and antagonistic exclusivism (van Bouwel
2009a). Through dialogue, a plurality of represented perspectives
enables the kind of critical scrutiny of questions and knowledge
claims that exposes error, bias, unexamined norms of justification and
acceptance and the complexity of issues and relevant implications. As
a result, it has been argued, pluralism supports a corresponding
standard of critical objectivity (Longino 2002; Wylie 2015).


* *Internal vs. external pluralism*. From a methodological
standpoint, an internal perspective is naturalistic in its reliance on
the contingent plurality of scientific practice by any of its
standards. This has been defended by members of the so-called
Minnesota School (Kellert, Longino and Waters 2006) and Ruphy (2016).
The alternative, which Ruphy has attributed to Dupre and
Cartwright, is the adoption of a metaphysical commitment external to
actual scientific practice.



As a matter of actual practice, pluralism has been identified as part
of a plurality of projects and perspectives in, for instance,
cognitive and mind-brain sciences, where attitudes towards a plurality
of ways of researching and understanding cognition vary (Milkowski and
Hohol 2021). These attitudes include (1) lamenting the variability of
meaning and systems of classification (Sullivan 2007; Cunningham
2021); (2) embracing complementarity between hierarchical mechanistic
and computational approaches--in the face of, for instance,
models with propositional declarative and lawlike statements and
computational models with software codes; (3) seeking integration with
mutual consistency and evidential support; (4) seeking reduction
privileging neural models; and (5) seeking grand unification that
values simplicity and generality over testability.


### 5.3 Metapluralism



The preference for one kind of pluralism over another is typically
motivated by epistemic virtues or constraints. Meta-pluralism, or
pluralism about pluralism, is obviously conceivable in similar terms,
as it can be found in the formulation of the so-called pluralist
stance (Kellert, Longino and Waters 2006). The pluralist stance
replaces metaphysical principles with scientific or empirical
methodological rules and aims that have been "tested".
Like Dupre's and Cartwright's metaphysical
positions, its metascientific position must be empirically tested.
Metascientific conclusions and assumptions cannot be considered
universal or necessary, but are local, contingent and relative to
scientific interests and purposes. Thus, on this view, complexity does
not always require interdisciplinarity (Kellert 2008), and in some
situations the pluralist stance will defend reductions or
specialization over interdisciplinary integration (Kellert, Longino
and 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 adopting
positions on matters of unification have varied from the metaphysical
and theological to the epistemic, social and pragmatic. Whether as a
matter of truth (Thalos 2013) or consequence, views on matters of
unity and unification make a difference in both science and
philosophy, and, by application, in society as well. In science they
provide strong heuristic or methodological guidance and even
justification for hypotheses, projects, and specific goals. In this
sense, different rallying cries and idioms such as simplicity, unity,
disunity, emergence or interdisciplinarity, have been endowed with a
normative value. Their evaluative role extends broadly. They are used
to provide legitimacy, even if rhetorically, in social contexts,
especially in situations involving sources of funding and profit. They
set a standard of what carries the authority and legitimacy of what it
is to be scientific. As a result, they make a difference in scientific
evaluation, management and application, especially in public domains
such as healthcare and economic decision-making. For instance,
pointing to the complexity of causal structures challenges traditional
deterministic or simple causal strategies of policy decision-making
with known risks and unknown effects of known properties (Mitchell
2009). Last but not least is the influence that implicit assumptions
about what unification can do have on science education (Klein
1990).



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



At the end of the day, one should not lose sight of the larger context
that 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 its
wings upon and against. Philosophy was once thought to stand for the
systematic unity of the sciences. The foundational character of unity
became the distinctive project of philosophy, in which conceptual
unity played the role of the standard of intelligibility. In addition,
the ideal of unity, frequently under the guise of harmony, has long
been a standard of aesthetic virtue, although this image has been
eloquently challenged by, for instance, John Bailey and Iris Murdoch
(Bailey 1976; Murdoch 1992). Unities and unifications help us meet
cognitive and practical demands upon our life as well as cultural
demands upon our self-images that are both cosmic and earthly. It is
not surprising that talk of the many meanings and levels of
unity--the fundamental level, unification, system, organization,
universality, simplicity, atomism, reduction, harmony, complexity or
totality--can place an urgent grip on our intellectual
imagination.