## 1. Introduction



In the influential *The Structure of Scientific Revolutions*
(1962), Kuhn made the dramatic claim that history of science reveals
proponents of competing paradigms failing to make complete contact
with each other's views, so that they are always talking at
least slightly at cross-purposes. Kuhn characterized the collective
reasons for these limits to communication as the incommensurability of
pre- and post-revolutionary scientific traditions, claiming that the
Newtonian paradigm is incommensurable with its Cartesian and
Aristotelian predecessors in the history of physics, just as
Lavoisier's paradigm is incommensurable with that of
Priestley's in chemistry (Kuhn 1962, 147-150; cf.
Caamano 2009 and Hoyningen-Huene 2008). These competing
paradigms lack a common measure because they use different concepts
and methods to address different problems, limiting communication
across the revolutionary divide. Kuhn initially used
incommensurability predominately to challenge *cumulative*
characterizations of scientific advance, according to which scientific
progress is an improving approximation to the truth, and to challenge
the idea that there are unchanging, neutral methodological standards
for comparing theories throughout the development of the natural
sciences. Like in evolution, the process does not change
*toward* some fixed goal according to some fixed rules, methods
or standards, but rather it changes *away* from the pressures
exerted by anomalies on the reigning theory (Kuhn 1962,
170-173). The process of scientific change is eliminative and
permissive rather than instructive. In the process of confronting
anomalies, certain alternatives are excluded, but nature does not
guide us to some uniquely correct theory.



Kuhn developed and refined his initial idea over the following
decades, repeatedly emphasizing that incommensurability neither means
nor implies incomparability; nor does it make science irrational (e.g.
Kuhn 2000 [1970], 155ff.). He focused increasingly on conceptual
incompatibility as manifest in the structural differences used to
classify the kinds whose relations are stated in laws and theories,
such as chemical elements and biological species (Kuhn 2000, see
especially chs. 3, 4, 5, 10 & 11). He used incommensurability to
attack the idea, prominent among logical positivists and logical
empiricists, that comparing theories requires translating their
consequences into a neutral observation language (cf. Hoyningen-Huene
1993, 213-214). In the late 1990s, he explicated
incommensurability in terms of *ineffability*, emphasizing that
it became possible for scientists to make and understand certain new
statements *only after* a particular theory had been introduced
(in the older vocabulary the new sentences are nonsensical), just as
it only becomes possible for historians to understand certain older
statements by setting aside current conceptions that otherwise cause
distortions (Kuhn 2000 [1989], 58-59; 2000 [1993], 244). Such
'*taxonomic incommensurability*' results in
translation failure between local subsets of inter-defined terms due
to the cross-classification of objects into mutually exclusive
taxonomies. This can be distinguished from '*methodological
incommensurability*', according to which there is no common
measure between successive scientific theories, in the sense that
theory comparison is sometimes a matter of weighing historically
developing values, not following fixed, definitive rules (Sankey and
Hoyningen-Huene 2001, vii-xv). This makes room for rational
disagreement in theory comparison, as scientists may apply different
values (such as scope, simplicity, fruitfulness, accuracy) in
evaluating and comparing particular theories, so that theory choice is
not unequivocally determined throughout the scientific community.



Paul Feyerabend first used the term incommensurable in 1962 in
"Explanation, Reduction and Empiricism" to describe the
lack of logical relations between the concepts of fundamental theories
in his critique of logical empiricists models of explanation and
reduction. He argued that in the course of scientific advance, when
fundamental theories change, meanings change, which can result in a
new conception of the nature of reality. By calling two fundamental
theories incommensurable, Feyerabend meant that they were conceptually
incompatible: The main concepts of one could neither be defined on the
basis of the primitive descriptive terms of the other, nor related to
them via a correct empirical statement (Feyerabend 1962, 74, 90). For
example, Feyerabend claimed that the concepts of temperature and
entropy in kinetic theory are incommensurable with those of
phenomenological thermodynamics (1962, 78); whereas the Newtonian
concepts of mass, length and time are incommensurable with those of
relativistic mechanics (1962, 80). Feyerabend repeatedly used the idea
of incommensurability to challenge a wide range of forms of conceptual
conservativism, arguing that they unjustifiably favor successful,
entrenched concepts over potential improvements, and overlook the
possibility of developing incommensurable alternatives (Oberheim 2005,
2006).



The entry is organized around the 1962 popularisations of the concept
of incommensurability by Kuhn and Feyerabend and the basic ideas that
influenced their developments of this concept. First, Kuhn's
notion of incommensurability as it was initially developed is
characterized, as is its cause and its purported consequences. That is
followed by an examination of Kuhn's route to the idea, and then
his subsequent development after 1962. The sections on
Feyerabend's notion of incommensurability mirror the same basic
structure. They are followed by a brief comparison of Kuhn and
Feyerabend's views on incommensurability, especially its
relation to theory comparison.


## 2. Revolutionary paradigms: Thomas Kuhn on incommensurability



Kuhn's notion of incommensurability in *The Structure of
Scientific Revolutions* misleadingly appeared to imply that
science was somehow irrational, and consequently it faced many
challenges and caused many confusions. This led to many
clarifications, and eventually to a substantial redevelopment of a
more precise and restricted version of it over the following decades.
Kuhn initially used the term holistically to capture methodological,
observational and conceptual disparities between successive scientific
paradigms that he had encountered in his historical investigations
into the development of the natural sciences (Kuhn 1962,
148-150). Later, he refined the idea arguing that
incommensurability is due to differences in the taxonomic structures
of successive scientific theories and neighbouring contemporaneous
sub-disciplines. Kuhn's developing notion of incommensurability
has received much attention, and it continues to provoke plenty of
controversy (cf. Bird 2007, Demir 2008, Moreno 2009, Psillos 2008, and
Soler, Sankey and Hoyningen-Huene 2008).


### 2.1 *The Structure of Scientific Revolutions*



In *The Structure of Scientific Revolutions* (1962), Thomas
Kuhn used the term 'incommensurable' to characterize the
holistic nature of the changes that take place in a scientific
revolution. His investigations into the history of science revealed a
phenomena often now called 'Kuhn loss': Problems whose
solution was vitally important to the older tradition may temporarily
disappear, become obsolete or even unscientific. On the other hand,
problems that had not even existed, or whose solution had been
considered trivial, may gain extraordinary significance in the new
tradition. Kuhn concluded that proponents of incommensurable theories
have different conceptions of their discipline and different views
about what counts as good science; and that these differences arise
because of changes in the list of problems that a theory must resolve
and a corresponding change in the standards for the admissibility of
proposed solutions (cf. Stillwaggon Swan and Bruce 2011). So for
example, Newton's theory was initially widely rejected because
it did not explain the attractive forces between matter, something
required of any mechanics from the perspective of the proponents of
Aristotle and Descartes' theories (Kuhn 1962, 148). According to
Kuhn, with the acceptance of Newton's theory, this question was
banished from science as illegitimate, only to re-emerge with the
solution offered by general relativity. He concluded that scientific
revolutions alter the very definition of science itself.



Changes in problems and standards come with corresponding conceptual
changes, so that after a revolution, many (though not all) of the
older concepts are still used, but in a slightly modified way. Such
conceptual changes have both intensional and extensional aspects,
which is to say that the same terms take on different meanings and are
used to refer to different things when used by proponents of competing
incommensurable theories. The changes in the intensional aspects of
concepts result because the terms used to express a theory are
inter-defined and their meanings depend on the theories to which they
belong. For example, the meanings of the terms
'temperature', 'mass', 'chemical
element' and 'chemical compound' depend on which
theories are used to interpret them. Conceptual changes also result in
the exclusion of some old elements of the extension of a concept,
while new elements come to be subsumed by it, so that the same term
comes to refer to different things. For example, the term
'Planet' referred to the sun but not the earth in the
Ptolemaic theory, whereas it refers to the earth and not the sun in
the Copernican theory. Incommensurable theories use some of the same
terms, but with different meanings, to refer to different sets of
things. Two scientists who perceive the same situation differently,
but nevertheless use the same vocabulary to describe it, speak from
incommensurable viewpoints (Kuhn 1970, 201).



One of the most controversial claims to emerge from Kuhn's
assertions about the incommensurability of scientific theories is that
the proponents of different paradigms work in different worlds (Kuhn
1962, 150; cf. Hoyningen-Huene 1990; 1993). Drawing on experiments in
the psychology of perception, Kuhn argued that the rigorous training
required for admittance to a paradigm conditions scientist's
reactions, expectations and beliefs (Kuhn 1962, 128; 2000 [1989],
66-71), so that learning how to apply the concepts of a theory
to solve exemplary problems determines scientists' experiences.
So for example, where a proponent of the Newtonian theory sees a
pendulum, an Aristotelian saw constrained free fall; where Priestley
saw dephlogisticated air, Lavoisier saw oxygen; where Berthollet saw a
compound that could vary in proportion, Proust saw only a physical
mixture. Kuhn (and Feyerabend) used the analogy of a Gestalt switch to
illustrate this point. In this way, one main source of the notion of
incommensurability of scientific theories has been the development of
Gestalt psychology.



According to Kuhn, these three interrelated aspects of
incommensurability (changes in problems and standards that define a
discipline, changes in the concepts used to state and solve those
problems, and world change) jointly constrain the interpretation of
scientific advance as cumulative. Scientific progress, Kuhn argued, is
not simply the continual discovery of new facts duly explained.
Instead, revolutions change what counts as the facts in the first
place. When reigning theories are replaced by incommensurable
challengers, the purported facts are re-described according to new and
incompatible theoretical principles. The main goal of Kuhn's
*Structure* was to challenge the idea of scientific progress as
cumulative, according to which what is corrected or discarded in the
course of scientific advance is that which was never really scientific
in the first place, and Kuhn used incommensurability as the basis of
his challenge. Instead of understanding scientific progress as a
process of change toward some fixed truth, Kuhn compared his
suggestion to that of Darwin's: scientific progress is like
evolution in that its development should be understood without
reference to a fixed, permanent goal (1962, 173).


### 2.2 Kuhn's route to incommensurability


#### 2.2.1 Kuhn's discovery of incommensurability



According to Kuhn, he discovered incommensurability as a graduate
student in the mid to late 1940s while struggling with what appeared
to be nonsensical passages in Aristotelian physics (Kuhn 2000 [1989],
59-60). He could not believe that someone as extraordinary as
Aristotle could have written them. Eventually patterns in the
disconcerting passages began to emerge, and then all at once, the text
made sense to him: a Gestalt switch that resulted when he changed the
meanings of some of the central terms. He saw this process of meaning
changing as a method of historical recovery. He realized that in his
earlier encounters, he had been projecting contemporary meanings back
into his historical sources (Whiggish history), and that he would need
to peel them away in order to remove the distortion and understand the
Aristotelian system in its own right (hermeneutic history). For
instance, when he encountered the word "motion" in
Aristotle (the standard translation of the Greek *kinesis*), he
was thinking in terms of the change of position of objects in space
(as we do today). But to get more closely at Aristotle's
original usage, he had to expand the meaning of motion to cover a much
broader range of phenomena that include various other sorts of change,
such as growth and diminution, alternation, and generation and
corruption, making an objects motion in space (displacement or
'locomotion') just a special case of motion. Kuhn realized
that these sorts of conceptual differences indicated breaks between
different modes of thought, and he suspected that such breaks must be
significant both for the nature of knowledge, and for the sense in
which the development of knowledge can be said to make progress.
Having made this discovery, Kuhn changed his career plans, leaving
theoretical physics to pursue this strange phenomenon. Some fifteen
years later the term 'incommensurable' first appears in
his classic *The Structure of Scientific Revolutions*
(1962).


#### 2.2.2 Conceptual replacement and theory-ladenness of observation: Ludwik Fleck



Of all the sources influencing Kuhn on incommensurability, at least
one deserves special attention. In the foreword of *The Structure
of Scientific Revolutions*, Kuhn acknowledged a deep debt to
Ludwik Fleck, a bacteriologist who developed the first explicit
sociology of natural science, and anticipated many contemporary views
about the social construction of knowledge. Around 1950, Kuhn was
enticed by the potential relevance to his experience of
incommensurability of Fleck's paradoxical title: *Entstehung
und Entwicklung einer wissenschaftlichen Tatsache: Einfuhrung in
die Lehre von Denkstil und Denkkollektiv* (1935)*(Genesis and
Development of a Scientific Fact*, 1979). There and in other
earlier works, Fleck had already used 'inkommensurabel' to
describe different styles of thinking within the natural sciences as
well as to discuss the ramifications of radical conceptual change in
the history of science. For example, Fleck used the term
'inkommensurabel' to describe the differences between
'medical thinking' and 'scientific thinking'.
The former addresses irregular, temporally dynamic phenomena such as
an illness, while the later addresses uniform phenomena (Fleck 1986
[1927], 44-45). Fleck also used the term
'inkommensurabel' to describe conceptual replacements in
theoretical transitions within what he considered the most vital of
the natural sciences, the medical sciences. For example, he claimed
that an old concept of disease became incommensurable with a newer
concept that was not a completely adequate substitute for it (Fleck
1979 [1935], 62). While Fleck's program of comparative
epistemology anticipates Kuhn's ideas in many significant
respects, it is also strikingly different (Harwood 1986; Oberheim
2005; Peine 2011). The most pervasive differences concerning
incommensurability are that Fleck treats meaning and meaning change as
a function of how concepts are received and developed by the
collective, while for Kuhn it is individuals who develop and apply the
concepts that advance science. Moreover, for Fleck meaning change is a
continuous feature of scientific development, whereas Kuhn
distinguishes normal scientific development that does not change
meanings from revolutionary developments that do.



Even so, Fleck emphasized all three of the interrelated aspects of the
shifts that Kuhn called revolutions and tried to capture by calling
theories 'incommensurable' (changes in problems and
standards (1979 [1935], 75-76; 1979 [1936], 89), conceptual
change (e.g. 1979 [1935]; 1979 [1936], 72, 83) and world change (e.g.
1986 [1936], 112). Fleck argued that science does not approach the
truth because successive thought-styles raise new problems and discard
older forms of knowledge (Fleck 1986 [1936], 111-112; 1979
[1935], 19, 51, 137-139; cf. Harwood 1986, 177). Fleck
emphasized that scientific terms acquire their meanings through their
application within a particular theoretical context and that those
meanings change when theories change in the course of advance, even
offering the example of 'chemical elements' and
'compounds' repeated by Kuhn (Fleck 1979 [1935], 25, 39,
40, 53-54). Fleck emphasized the theory-ladenness of observation
with explicit reference to Gestalt switches; stressing that a
'thought-style' determines not only the meanings of the
concepts it uses, but also the perception of phenomena to be
explained, developing examples from the history of anatomical
representation (1979 [1935], 66; 1986 [1947]). Fleck (like Kuhn,
Feyerabend and Wittgenstein) acknowledged Wolfgang Kohler's
work in psychology of perception in this regard. Fleck concluded that
scientific advance is not cumulative, that conceptual differences
between members of different scientific communities cause
communication difficulties between them (1979 [1936], 109), and later
for historians trying to understand older ideas (1979 [1936],
83-85, 89). Fleck even emphasized that meaning change in the
course of scientific advance causes translation failure between
theories, anticipating a central aspect of Kuhn's later notion
of taxonomic incommensurability (e.g. 1986 [1936], 83).


#### 2.2.3 Gestalt psychology and organized perception



Another major source of Kuhn's idea of the incommensurability of
scientific theories is Gestalt psychology (Kuhn 1962, vi). Wolfgang
Kohler, for example, had emphasized the active role of
organization in perception and argued that in psychology one begins
with *Gestalten* (organized, segregated wholes such as the
objects of human perception or identifiable human behaviours) and then
proceeds to discover their natural parts (and not vice versa, like in
particle physics). In the opening sentences of the condensed English
version of Kohler's investigation of the relationship
between the mental concepts of psychology and the material concepts of
physics, Kohler wrote: "In order to orient itself in the
company of natural sciences, psychology must discover connections
wherever it can between its own phenomena and those of other
disciplines. If this search fails, then psychology must recognize that
its categories and those of natural science are incommensurable"
(1938 [1920], 17).


#### 2.2.4 The image of art and the image of science



In a preliminary draft "The Structure of Scientific Revolutions,
Chapter 1, What are Scientific Revolutions?" (dated 1958-1960,
likely composed in late 1958) of the first chapter of his projected
book, Kuhn initially used the idea of incommensurability to
characterize stages of development in the arts in contrast to the
traditional image of scientific progress as cumulative that he set out
to challenge (see Pinto de Oliveira, 2017). Although, this draft
chapter was entirely rewritten as the introduction of Kuhn (1962), and
was explicitly intended only to provoke exploratory discussion and not
for publication, it strongly suggests that, at that time, Kuhn began
to develop the idea of the incommensurability in science in reaction
to the traditional (e.g. Sarton, Conant) contrast between development
in the arts and cumulative progress in the sciences (see Pinto de
Oliveira, 2017). In the draft, Kuhn announced his project as an
attempt to reshape the image of science so as to make it closer to the
image of art (see Pinto de Oliveira, 2017). He wanted to challenge the
cumulative conception of scientific progress promoted by the old
historiography of science, according to which "science appears
to advance by accretion" and science is "an ever-growing
edifice to which each scientist strives to add a few stones or a bit
of mortar" (Kuhn 1958, 2, as cited in Pinto de Oliveira 2017,
748) in contrast to the image of art according to which "the
transition between one stage of artistic development and the next is a
transition between incommensurables" (Kuhn 1958, 3, as cited in
Pinto de Oliveira 2017, 749).



A few pages later, Kuhn proceeds to apply the idea of
incommensurability to science for the very first time, again while
comparing scientific revolutions to the non-cumulative nature of
progress in the arts: "Often a decision to embrace a new theory
turns out to involve an implicit redefinition of the corresponding
science. Old problems may be relegated to another science or may be
declared entirely 'unscientific'. Problems that, on the old
theory, were non-existent or trivial may, with a new theory, become
the very archetypes of significant scientific achievement. And, as the
problems change, so, often, does the standard that distinguishes a
real scientific solution from a mere metaphysical speculation, word
game, or mathematical play. It follows that, to a significant extent,
the science that emerges from a scientific revolution is not only
incompatible, but often actually incommensurable, with that which has
gone before. Only as this is realized, can we grasp the full sense in
which scientific revolutions are like those in the arts" (Kuhn
1958, 17-18 as cited in Pinto de Oliveira 2017, 756). Kuhn
concludes that "If we are to preserve any part of the metaphor
which makes inventions and discoveries new bricks for the scientific
edifice, and if we are simultaneously to give resistance and
controversy an essential place in the development of science, then we
may have to recognize that the addition of new bricks demands at least
partial demolition of the existing structure, and that the new edifice
erected to include the new brick is not just the old one plus, but a
new building. We may, that is, be forced to recognize that new
discoveries and new theories do not simply add to the stock of
pre-existing scientific knowledge. They change it." (Kuhn 1958,
7, as cited in Pinto de Oliveira 2017, 756).


### 2.3 Kuhn's subsequent development of incommensurability



Kuhn continued to struggle with, develop, and then refine his
understanding of incommensurability until his death in 1996. Although
his development of incommensurability went through several stages (cf.
Hoyningen-Huene 1993, 206-222), he claimed to have made a
"series of significant breakthroughs" beginning in 1987
(Kuhn 2000 [1993], 228). They are described in a number of essays and
published lectures that were collected in (Kuhn 2000, cf. chs. 3, 4,
5, 10 & 11), and a last as yet unpublished book by Kuhn on
incommensurability is still pending (Conant and Haugeland 2000, 2).
The nature of these developments is controversial. Some commentators
claim that Kuhn's incommensurability thesis underwent a
'major transformation' (Sankey 1993), while others
(including Kuhn himself) see only a more specific characterization of
the original core insight (Hoyningen-Huene 1993, 212; Kuhn 2000,
[1983], 33ff.; Chen 1997). Kuhn's original holistic
characterization of incommensurability has been distinguished into two
separate theses. 'Taxonomic incommensurability' involves
conceptual change in contrast to 'methodological
incommensurability', which involves the epistemic values used to
evaluate theories (Sankey 1991; Sankey and Hoyningen-Huene 2001; see
Section 2.3.2 below).


#### 2.3.1 Taxonomic incommensurability



Kuhn continued to emphasize the difference between normal, cumulative
growth that does not change existing concepts; such as the discovery
of Boyle's law, which left the concepts of gas, pressure and
volume and the instruments used to measure them unchanged, from
revolutionary discoveries that could not have been made on the basis
of antecedently available concepts; such as the discovery of
Newton's theory (Kuhn 2000 [1981], 14). Such developments
require *replacing* existing concepts with new concepts that
are *incompatible* with the older ideas. To help explain the
nature of this conceptual incompatibility, Kuhn adopted the notion of
a 'lexical taxonomy' or 'lexicon' from
linguistics (2000 [1989]). A lexical taxonomy stores and structures
the vocabulary used to state laws and theories; or more specifically,
the kinds of things that they describe. It is the "mental
module" in which members of a speech community store the kind
terms prerequisite to generalization and description (2000 [1991],
92-97; 2000 [1993], 229, 233, 238-239, 242, 244). To
communicate, the terms that speakers use do not have to have the same
meanings, nor do speakers need to use the same criteria for
identifying something as a member of a particular kind (one
ornithologist might identify ducks by their beaks, another by their
tails) (cf. Hoyningen-Huene 1993, 99). Speakers need only share
homologous lexical structures; that is, vocabularies incorporating the
same system of taxonomic classification. This suffices to ensure that
they refer to the same objects with the same kind terms. If two
theories do not share the same taxonomic lexical structure, then they
are incommensurable (2000 [1989], 63; 2000 [1991]; cf. Sankey 1997 and
Wolf 2007).



To help explicate incommensurability in terms of taxonomic
classification, Kuhn developed the *no-overlap principl*e. The
no-overlap principle precludes cross-classification of objects into
different kinds within a theory's taxonomy. According to the
no-overlap principle, no two kind terms may overlap in their referents
unless they are related as species to genus. For example, there are no
dogs that are also cats; no gold that is also silver, and that is what
makes the terms 'dogs', 'cats',
'silver', and 'gold' kind terms (Kuhn 2000
[1991], 92). Such kind terms are used to state laws and theories and
must be learned *together* through experience (2000 [1993],
230; cf. Barker et al. 2003, 214 ff.). There are two possibilities.
Most kind terms must be learned as members of one or another contrast
set. For example to learn the term 'liquid', one must also
master the terms 'solid' and 'gas'. Other
types of kind terms are not learned through contrast sets, but
together with closely related terms through their joint application to
situations that exemplify natural laws. For example, the term
'force' must be learned together with terms like
'mass' and 'weight' through an application of
Hooke's law and either Newton's three laws of motion or
else the first and third laws together with the law of gravity (2000
[1993], 231). According to Kuhn, scientific revolutions change the
structural relations between pre-existing kind terms, breaking the
no-overlap principle (2000 [1991], 92-96]. This is to say that
theories separated by a revolution cross-classify the same things into
mutually exclusive sets of kinds. A kind from one taxonomy is mutually
exclusive with another if it cannot simply be introduced into it
because the objects to which it refers would be subject to different
sets of natural laws. This would result in conflicting expectations
about the same objects, loss of logical relations between statements
made with those concepts, and ultimately incoherence and
miscommunication (Kuhn 2000 [1993], 232, 238). For example,
Ptolemy's theory classifies the sun as a planet, where planets
orbit the earth, while Copernicus' theory classifies the sun as
a star, where planets orbit stars like the sun. A correct statement
according to Copernican theory, such as "Planets orbit the
sun" is incoherent in Ptolemaic vocabulary (2000 [1991], 94).
Moreover, the Copernican claim that the planets orbit the sun could
not even have been made without abandoning the Ptolemaic concepts and
developing new ones to *replace* (and not supplement) them.



Furthermore, Kuhn (in a move toward Feyerabend's view) now
claims that the same types of difficulties in communication that arise
due to incommensurability between members of different scientific
communities separated by the passage of time *also* occur
between members of different contemporaneous sub-disciplines that
result from scientific revolutions (Kuhn 2000 [1993], 238). This
represents a significant change to his original phase-model of
scientific advance, and a corresponding shift in his application of
the notion of incommensurability. Kuhn no longer represents scientific
advance as a *linear* progression from pre-normal science to
normal science, through crisis to revolution *that results in a new
phase of normal science*. Instead, scientific revolutions are
compared to the process of speciation in biology, in that they result
in *branching* into sub-disciplines that resemble a
phylogenetic tree. The application of the relation of
incommensurability is no longer restricted to diachronic episodes of
scientific advance in which two theories are separated by a
revolution. The contemporaneous sub-disciplines that result from a
scientific revolution can also be incommensurable with each other. The
incommensurability derives from different training required to master
the incompatible kind terms used to state their laws and theories.
These shared kind terms cross-classify the same set of objects into
different sets of kinds, resulting in mutually exclusive lexical
taxonomies that break the no-overlap principle. Moreover, now not only
are both processes (scientific progress and biological evolution)
similar in that they are not fixed in advance on some set goal (i.e.
truth), but driven from behind (i.e. away from anomalies that play an
analogous role to selection pressure), but also the incommensurability
of scientific theories is presented as analogous to the isolating
mechanisms required for speciation (Kuhn 2000 [1991],
94-99).



Kuhn compared the function of such lexical taxonomies to Kant's
*a priori* when taken in a relativized sense. Each lexicon
makes a corresponding form of life possible within which the truth or
falsity of propositions may be both claimed and rationally justified.
For example, with the Aristotelian lexicon, one can speak of the truth
or falsity of Aristotelian assertions, but these truth values have no
bearing on the truth of apparently similar assertions made with the
Newtonian lexicon (Kuhn 2000 [1993], 244). A lexicon is thus
*constitutive* of the objects of knowledge (Kuhn 2000 [1993],
245); and consequently, Kuhn rejected characterizations of scientific
progress according to which science zeros in on the truth:
"*no shared metric* is available to compare our
assertions ... and thus to provide a basis for a claim that our
(or, for that matter, his) are closer to the truth" (2000
[1993], 244). Instead, the logical status of a lexical structure, like
that of word-meanings in general, is that of convention, and the
justification of a lexicon or of lexical change can only be pragmatic
(2000 [1993], 244). Kuhn thus reaffirmed his earlier claim that the
notion of a match or correspondence between the ontology of a theory
and its real counterpart in nature is illusive in principle (1970,
206; 2000 [1993], 244). The implications that incommensurability has
for scientific realism have been widely discussed and continue to be
controversial (cf. Devitt 2001, Oberheim and Hoyningen-Huene 1997,
Sankey 2009).



A lexicon is not only prerequisite to making meaningful statements, it
also sets limits on what can be meaningfully said within the community
of speakers that share it: "There is, for example, no way, even
in an enriched Newtonian vocabulary, to convey the Aristotelian
propositions regularly misconstrued as asserting the proportionality
of force and motion or the impossibility of a void. Using our
conceptual lexicon, these Aristotelian propositions cannot be
expressed -- they are simply ineffable -- and we are barred
by the no-overlap principle from access to the concepts required to
express them " (Kuhn 2000 [1993], 244; cf. 2000 [1989], 76). In
this way, Kuhn's later notion of the incommensurability of
scientific theories is based on *effability*. The structure of
the lexicon shared by a particular community determines how the world
can be described by its members, as well as how they will
misunderstand the history of their own discipline; that is, unless
they learn to understand older terms according to the structure of the
older lexicon. Where Kuhn had earlier likened the process by which
historians come to understand antiquated science as a special type of
translation, he retracted these claims, insisting that the process is
one of language learning, not translation (2000 [1993], 238, 244).
Kuhn often claimed that incommensurable theories are untranslatable
(e.g. Kuhn 2000 [1991], 94). However, he also emphasized that
translation is neither needed in the comparison of incommensurable
theories, nor in the hermeneutic historical method necessary to
understand antiquated sciences (Kuhn 2000 [1993], 237, 238, 244). To
overcome the barriers posed by incommensurability to understanding
antiquated sciences, and to understanding the special technical
vocabulary used by contemporaneous, phylogenetically related
sub-disciplines, it is neither necessary not possible to translate
between them. Rather, one must become *bilingual*, learning to
use (and keep separate) the incongruently structured lexical
taxonomies underwriting different laws and theories.


#### 2.3.2 Methodological incommensurability



As Kuhn refined his notion of incommensurability as a special type of
conceptual incompatibility, some commentators began to distinguish it
from 'methodological incommensurability'. Methodological
incommensurability is the idea that there are no shared, objective
standards of scientific theory appraisal, so that there are no
external or neutral standards that univocally determine the
comparative evaluation of competing theories (Sankey and
Hoyningen-Huene 2001, xiii). This idea has also been recently
discussed in detail under the rubric
"Kuhn-underdetermination" (Carrier 2008, 278). The basic
idea was developed out of Kuhn and Feyerabend's rejections of
the traditional view that a distinguishing feature of science is a
uniform, invariant scientific method, that remains fixed throughout
its development (Kuhn 1962, 94, 103; Feyerabend 1975, 23-32; cf.
Farrell 2003). Feyerabend famously argued that every proposed
methodological rule has been fruitfully violated at some point in the
course of scientific advance, and that only by breaking such rules
could scientists have made the progressive steps for which they are
praised (1975). He concluded that the idea of a fixed, historically
invariant scientific method is a myth. There are no universally
applicable methodological rules. The only methodological rule that is
universally applicable is 'anything goes', which buys its
universality at the cost of being completely empty (1970a, 105). Kuhn
challenged the traditional view of scientific method as a set of
rules, claiming that the standards of theory appraisal, such as
simplicity, accuracy, consistency, scope and fruitfulness (1977, 322),
depend on and vary with the currently dominant paradigm. He is often
cited for having pointed out that as in political revolutions, so in
choice of paradigm, there is no standard higher than the assent of the
relevant community (1962, 94), and as having argued that there is
"no neutral algorithm for theory choice, no systematic decision
procedure which, properly applied, must lead each individual in the
group to the same decision" (1970, 200). Kuhn developed the idea
that such epistemic standards do not function as rules that determine
rational theory choice, but as values that merely guide it (1977,
331). Different scientists apply these values differently, and they
may even pull in different directions, so that there may be rational
disagreement between scientists from incommensurable paradigms, who
support different theories due to their weighing the same values
differently.


## 3. Combating conceptual conservativism: Paul Feyerabend on incommensurability



An examination of Feyerabend's use and development of the idea
of incommensurability of scientific theories reveals just how
widespread it was prior to 1962. It also reveals the veiled common
core of Feyerabend's philosophy of science, which otherwise
appears to be a series of critical papers on unrelated topics
(Oberheim 2005, 2006). That common core is the use of the idea of
incommensurability to challenge many different forms of conceptual
conservativism in science and philosophy. Conceptual conservativism
unjustly favors existing ideas over potential improvements offered by
incommensurable alternatives. Feyerabend used the notion of
incommensurability to attack the following forms of conceptual
conservativism: Heisenberg's idea of closed theories (1951),
attempts to distinguish philosophical accounts of ontology from
physics (1954), the foundational role of the stability thesis in
logical positivism (1951, 1958a), Bohr's principle of
complementarity (1958b, 1961, 1962, 1965b, 1970a), and the logical
empiricists' models of explanation and reduction (1962, 1963a).
He also used the idea of incommensurability to attack forms of
conceptual conservativism implicit in the models of theory testing
promoted by classical empiricists, the logical positivists, the
logical empiricists, Popper, and Kuhn (1958a, 1962, 1963a, 1965b,
1970a), Kantian transcendental necessities (1962, 1965b, 1965c),
traditional philosophical conundrums like the problem of the existence
of the external world, the problem of the existence of other minds,
and especially the mind-body problem (1962, 1965b, 1967, 1969a),
certain aspects of Wittgenstein's later philosophy, as well as
the linguistic philosophical movement that takes the utility of
everyday concepts as given and merely attempts to analyze them,
without changing their meanings (or 'arguments from
synonymy') (1962, 1963a, 1965b, 1969b, 1970a), Popper's
conception of verisimilitude (1970b), and scientific realist
characterizations of scientific knowledge and scientific advance
(1970b). Feyerabend argued that all of these views cannot accommodate
the fact that the history of science reveals revolutionary
developments in which incommensurable alternatives replaced existing
ideas in the course of progress.


### 3.1 'Explanation, Reduction and Empiricism' (1962)



In his landmark 1962 "Explanation, Reduction and
Empiricism", Paul Feyerabend initially introduced the term
'incommensurable' as part of a criticism of the
*conceptual conservativism* that he found in Nagel's
theory of reduction and the Hempel-Oppenheim theory of explanation. He
argued that formal accounts of reduction and explanation are
impossible for general theories because they cannot accommodate the
development of incommensurable concepts in the course of scientific
advance. Feyerabend used the notion of incommensurability to
characterize the relation between two successive fundamental,
universal scientific theories interpreted realistically; i.e. as
purported descriptions of reality. By limiting incommensurability to
universal theories, Feyerabend meant only those that apply to all
objects in the universe. By limiting incommensurability to fundamental
theories, Feyerabend meant those that have ontological implications;
i.e., those that have implications about the very nature of reality.
Universal, fundamental scientific theories can be incommensurable only
if they are interpreted realistically, according to Feyerabend,
because otherwise they cannot compete as the one true theory, and are
thus not mutually exclusive. By calling two such theories
incommensurable, Feyerabend meant that they were conceptually
incompatible: The main concepts of one could neither be defined on the
basis of the primitive descriptive terms of the other, nor related to
them via a correct empirical statement (1962, 74, 90). As a
consequence, it is impossible to reduce incommensurable theories
formally.



In 1962, Feyerabend illustrated the incommensurability of scientific
theories with a comparison of six pairs of central concepts drawn from
three episodes of fundamental theory change in the course of
scientific advance: (1) The dynamical characterization of impetus in
the impetus theory of motion and the concept of force in the
conceptual apparatus of Newtonian mechanics, (2 & 3) the concepts
of temperature and entropy in the transition from phenomenological
thermodynamics to kinetic theory, and (4, 5 & 6) the concepts
mass, length and time in the transition from Newtonian to relativistic
mechanics. Feyerabend subsequently added the example of geometrical
optics and wave optics (1965b, 227). In 1962, Feyerabend also claimed
that incommensurability occurs between traditional, fundamental
theories in philosophy, and consequently arises in the discussions of
the mind-body problem, the problem of the reality of the external
world, and the problem of other minds (1962, 31, 90). Feyerabend
argued that such age-old philosophical problems have not been solved
because the disputants resist the kind of meaning change necessary for
their dissolution. Concepts are incommensurable, according to
Feyerabend, because they belong to mutually exclusive theoretical
perspectives. These perspectives are mutually exclusive because they
give incompatible accounts of the nature of reality. Feyerabend argued
that because the meanings of their terms are provided by the theories
to which they belong, when there is theoretical change, there are
meaning changes (1962, 68, 94). Feyerabend argued that these changes
in meaning affect our theoretical and observational terms, as well as
our conception of the nature of reality. When this occurs, there is
incommensurability; or as Feyerabend later characterized his view:
"a theory is incommensurable with another if its ontological
consequences are incompatible with the ontological consequences of the
latter" (1981a, xi). The idea is intended to capture conceptual
incompatibility due to changes of meaning that occur in theoretical
transitions that affect our ontological beliefs. Two fundamental
theories are incommensurable because the meanings of their terms are
determined by the theoretical principles that govern their use, and
these principles are qualitatively incompatible (1962, 58).



Feyerabend used the idea of incommensurability to attempt to expose a
dogmatic element that contemporary empiricists share with school
philosophies such as Platonism and Cartesianism (from whom empiricists
had tried to distance themselves by insisting on an empirical
foundation for scientific knowledge). The dogmatic element is due to
the assumption that the meanings of empirical terms remain stable
through theoretical transitions; or what Feyerabend called the
principle of meaning invariance (1962, 30). Feyerabend argued that
this principle is inconsistent with the existence of incommensurable
concepts. Feyerabend drew two main consequences from the insight that
some pairs of successive scientific theories are incommensurable.
First, successive scientific theories that are incommensurable have no
logical relations: "The order introduced into our experiences by
Newton's theory is retained and improved by relativity. This
means that the concepts of relativity theory are sufficiently rich to
allow us to state all the facts which were stated before with the help
of Newtonian physics. Yet these two sets of categories are completely
different *and bear no logical relation to each other*"
(1962, 88-89). Because their concepts have different meanings,
they cannot be brought into formal logical relations. Second, a
revision in the logical empiricist conception of scientific advance is
required. Older theories, and the concepts used to state them, are not
corrected and absorbed, and thereby legitimised. Rather, they are
rejected and replaced, having been falsified. In this way, the logical
empiricists' conceptually conservative (or retentive) accounts
of reduction and explanation are undermined. They cannot accommodate
the development of incommensurable concepts in the course of
scientific advance.



In 1965, Feyerabend attempted to clarify his notion, claiming that two
theories are incommensurable when the meanings of their main
descriptive terms depend on mutually inconsistent principles (1965c,
227; 1975, 269-270, 276). He also claimed that two theories are
incommensurable if a new theory entails that all the concepts of the
preceding theory have zero extension or if it introduces rules that
change the system of classes itself (1965a, 268). On this account, in
order for there to be incommensurability, the "situation must be
rigged in such a way that the conditions of concept formation in one
theory forbid the formation of the basic concepts of the other"
(Feyerabend 1978, 68; cf. 1975, 269; 1981b, 154). Still later, he
claimed that with the term "incommensurability" he always
meant "deductive disjointedness, and nothing else" (1977,
365). These subsequent formulations were all intended to capture the
same idea.


### 3.2 Feyerabend's route to incommensurability



Although Feyerabend first used the term 'incommensurable'
to describe successive scientific theories in 1962, he had been
developing his conception of incommensurability for about a decade
prior to meeting Kuhn in the late 1950s. According to Feyerabend, he
first discussed his notion of incommensurable concepts with the Kraft
Circle from 1949-1951, while working toward his doctoral thesis
on protocol statements (Feyerabend 1951). The Kraft Circle was a
student group named after Feyerabend's Ph.D. supervisor Viktor
Kraft, which was modeled after the Vienna Circle of which Kraft had
been a member. Prominent guests such as Elizabeth Anscombe and Ludwig
Wittgenstein attended some meetings (Feyerabend 1978, 108ff.,
115-116; 1993, 259-260; 1995, 92). Feyerabend traced the
origins of his conception of incommensurability to those ideas as
represented by 'thesis I' in "An attempt at a
realistic interpretation of experience" (1958a), which is a
condensed version of his 1951 doctoral thesis.



In his (1958a), Feyerabend criticized two conceptions of meaning. He
argued against the logical positivist idea that the meaning of an
observational term is determined by immediate experiences, as well as
against the Wittgensteinian idea that the meaning of an observational
term is determined by its use. Instead, Feyerabend argued that the
meaning of a term, even an observation term, is determined by its
theoretical context, or more precisely, by the theoretical principles
that govern its correct use according to our best theories. For
example, according to Feyerabend, the correct meaning of the term
'temperature' is not determined by its everyday use, but
by the principles of statistical thermodynamics. On the basis of such
a conception, Feyerabend developed 'thesis I', according
to which the interpretation of an observation language is determined
by the theories that we use to explain what we observe, and it changes
as soon as those theories change (1958a, 163). Feyerabend proceeded to
argue that when older theories are replaced, the meanings of the
observational terms used to test those theories change. Just as in
(1962), the result is incommensurability: The idea that successive
scientific theories are conceptually incompatible and consequently
logically disjoint due to differences in the meanings of the
observation statements used to test them. Feyerabend's
'thesis I' is thus an early version of his
incommensurability thesis. In his (1958a), with this notion of
incommensurability, Feyerabend challenged an implicit conceptual
conservativism in logical positivism: The assumptions that theoretical
terms derive their meaning solely through their connection with
experience and that experience itself is a stable (or unchanging)
foundation on which theoretical meaning can be based. Instead of such
a bottom-up version of the relation of experience and theoretical
knowledge, according to which experience determines the meanings of
our theoretical terms, Feyerabend argued for a top-down version,
according to which our best theories determine the meanings that we
attach to our experiences. According to Feyerabend, experience cannot
be taken for granted as some kind of fixed, neutral basis for
comparing theories. Rather, it takes on its particular character in
light of the theories we bring to it. 



At the time Feyerabend was developing these views, he was working very
closely with Karl Popper. There has been much controversy concerning
Feyerabend's evolving relationship to Popper, especially given
its tumultuous trajectory, the revisions Feyerabend made concerning
his debts to Popper in the reprints of his original papers (see
Preston 1997), informal accusations of plagiarism by Popperians (see
Collodel 2016), and Feyerabend's subsequent increasingly vocal
denials of his debts to Popper (Oberheim 2006, Ch. 3.4). It has
however always been clear that Feyerabend developed his views on
incommensurability while working as a vocal proponent of Karl
Popper's critical rationalist philosophy (Preston 1997, Oberheim
2006, Collodel 2016), and that there are many different
interpretations of the relationships between their ideas. Bschir
(2015) recently emphasizes just how Popperian Feyerabend's
philosophy was at that time, and casts Feyerabend's idea of
incommensurability as a positive extension of many of Popper's
views. Oberheim (2006) argues that incommensurability is exactly the
point at which Feyerabend breaks the Popperian framework. Many
(including Popper) seem to interpret Feyerabend's conception of
incommensurability as a rather misguided development (or even
misunderstanding) of Karl Popper's views (see Bschir 2015,
Collodel 2016), which Feyerabend often repeated, sometimes seemingly
as if they were his own. In any case, incommensurability marks the
point after which Feyerabend and Popper's philosophies
dramatically part ways, as they lead to very different conceptions of
progress (see Tambolo 2017). 



Feyerabend's route to the idea of the incommensurability of
scientific theories was heavily influenced by a number of prominent
individuals who had been discussing a wide range of related topics. An
investigation of the source of these ideas reveals some of the
founding fathers of the notion of incommensurability in the
contemporary history and philosophy of science.


#### 3.2.1 Progress through meaning change: Pierre Duhem



Feyerabend drew heavily from Duhem's *The Aim and Structure
of Physical Theory* (1954 [1906]) in his development of the notion
of incommensurability of scientific theories. Many of the main points
Feyerabend emphasized by calling scientific theories incommensurable
had been developed already by Duhem, who had argued that logic is
insufficient for determining the outcome of theoretical disputes in
the natural sciences, and who documented the difficulties historians
have in understanding the development of the natural sciences due to
meaning change. Duhem also already highlighted the communication
difficulties between proponents of competing scientific theories
because of these differences in meaning. For example, Duhem had
claimed that what a physicist states as the result of an experiment is
not simply the recital of some observed facts. Rather, it is the
interpretation of these facts on the basis of the theories the
scientist regards as true (1954 [1906], 159). It follows, according to
Duhem, that in order to understand the meanings that scientists
ascribe to their own statements, it is necessary to understand the
theories that they use in order to interpret what they observe. Thus,
Duhem had stated an early version of Feyerabend's
incommensurability thesis. Moreover, Duhem explicitly limited his
discussion to non-instantial, physical theories, as opposed to mere
experimental laws. This is very similar to the criteria that marks the
most significant difference between Kuhn and Feyerabend's
development of the idea of incommensurability (see Section 4), and
that also delimits Einstein's use of
'incommensurable' while discussing the problems of theory
comparison (see Section 3.2.3).



After explaining that the meaning of a term depends on the theory to
which it belongs, and that a consequence of theoretical advance is
meaning change, Duhem continued: "If the theories admitted by
this physicist are those we accept, and if we agree to follow the same
rules in the interpretation of the same phenomena, we speak the same
language and can understand each other. But that is not always the
case. It is not so when we discuss the experiments of a physicist who
does not belong to our school; and it is especially not so when we
discuss the experiments of a physicist separated from us by fifty
years, a century, or two centuries" (1954 [1906], 159). Duhem
continued: "How many scientific discussions there are in which
each of the contenders claims to have crushed his adversary under the
overwhelming testimony of the facts! ... How many propositions
are regarded as monstrous errors in the writings of those who have
preceded us! We should perhaps commemorate them as great truths if we
really wished to enquire into the theories which gave their
propositions their true meaning" (Duhem 1954 [1906],
160-161). These passages make the same basic points that both
Feyerabend and Kuhn made with their claims about incommensurability of
scientific theories: Because older ideas are misunderstood, as a
result of taking them out of their theoretical context, proponents of
incommensurable scientific theories misunderstand each other, both
claiming to have the facts on their side. Kuhn and Feyerabend both
claimed that in such a situation, even empirical arguments can become
circular (Feyerabend 1965b, 152; Kuhn 1962, 94).


#### 3.2.2 The square root of 2 and complementarity: Niels Bohr



In his autobiography, Feyerabend acknowledged Niels Bohr's
direct influence on the development of his notion of
incommensurability in the 1950s. Feyerabend recalled a conversation in
which Bohr had talked about the discovery that the square root of two
cannot be an integer or a fraction. According to Feyerabend, Bohr
presented the event as having led to the extension of a concept of
number that retained some properties of integers and fractions, but
changed others; and claimed that the transition from classical to
quantum mechanics was carried out in accordance with precisely this
principle (1995, 78). Feyerabend also used the notion of
incommensurability in a publication on Bohr's complementarity
thesis, where Feyerabend argued that Bohr's complementarity
thesis is an example of an unjustified conceptual conservativism,
taking issue with Bohr's contention that all quantum mechanical
evidence will always necessarily be expressed in classical terms
(Feyerabend 1958b). He presented Bohr's defence of the principle
of complementarity as based on the conviction that every experience
must necessarily make its appearance within the frame of our customary
points of view, which is currently that of classical physics. However,
according to Feyerabend, even though classical concepts have been
successful in the past, and even though at the moment it may be
difficult, or even impossible, for us to imagine how to replace them,
it does not follow that the classical framework could not one day be
superseded by an incommensurable rival. Consequently, it does not
follow that all our future microscopic theories will have to take the
notion of complementarity as fundamental. Instead, according to
Feyerabend, a theory may be found whose conceptual apparatus, when
applied to the domain of validity of classical physics, would be just
as comprehensive and useful as the classical apparatus, without
coinciding with it. He claimed that such a situation is by no means
uncommon, and he used the transition from Newtonian to relativistic
physics to bolster his point. According to Feyerabend, while the
concepts of relativity theory are sufficiently rich to state all of
the facts captured by Newtonian physics, the two sets of concepts are
"completely different" and bear "no logical
relations" to each other (1958b, 83; 1961, 388; 1962,
88-89). This is clearly an early version of his
incommensurability thesis. On Feyerabend's fallibilist view of
empirical knowledge, no element of our knowledge can be held to be
necessary or absolutely certain. In our search for satisfactory
explanations, we are at liberty to change any parts of our existing
knowledge, however fundamental they may seem, including the concepts
of classical physics.


#### 3.2.3 'Kant on wheels' and universal theories: Albert Einstein



Albert Einstein used the term 'incommensurable' to apply
specifically to difficulties selecting and evaluating scientific
theories before Kuhn and Feyerabend, and there are strong reasons to
believe that Feyerabend's development of incommensurability was
directly inspired by Einstein's use of the term (Oberheim 2016).
In his 'Autobiographical notes' (1949), Einstein attempted
to explain that assessing the relative merits of universal physical
theories involves making difficult judgments about their
'naturalness' that requires making judgments based on the
reciprocal weighing of incommensurable qualities: "The second
point of view is not concerned with the relation to the material
observation but with the premises of the theory itself, with what may
briefly but vaguely be characterized as the 'naturalness'
or 'logical simplicity' of the premises (of the basic
concepts and of the relations between these which are taken as a
basis). This point of view, an exact formulation of which meets with
great difficulties, has played an important role in the selection and
evaluation of theories since time immemorial. The problem here is not
simply one of a kind of enumeration of the logically independent
premises (if anything like this were at all unequivocally possible),
but that of a kind of reciprocal weighing of incommensurable
qualities" (1949a, 23).



There are good reasons to believe that these admittedly cryptic
remarks directly inspired Feyerabend's use and development of
the idea of incommensurability. Although Feyerabend did not cite from
Einstein (1949) in his (1962), he does cite from Bohr's paper in
that very same edited volume (Schilpp 1949). Moreover, there are
striking similarities between Feyerabend and Einstein's uses of
the term. First, both make a distinction between universal theories
and theories that do not apply to the totality of all physical
appearances, and then use this distinction to limit the application of
incommensurability in the same way; i.e., the problem of weighing
incommensurable qualities in selecting and evaluating theories is
explicitly only meant to apply to such *universal* physical
theories, and not just any pair of scientific theories (cf. Feyerabend
1962a, 28 and Einstein 1949a, 23). Second, Einstein's
theoretical attitude is explicitly a form of neo-Kantianism very much
like that of Feyerabend and Kuhn's. According to Einstein, his
theoretical attitude "is distinct from that of Kant only by the
fact that we do not conceive of the 'categories' as
unalterable (conditioned by the nature of the understanding) but as
(in the logical sense) free conventions. They appear to be *a
priori* only insofar as thinking without the positing of
categories and of concepts in general would be as impossible as is
breathing in a vacuum" (Einstein 1949b, 374). This is the same
basic perspective that both Kuhn and Feyerabend delineated when they
developed their ideas of incommensurability. For example, Kuhn says,
"I go around explaining my own position saying I am a Kantian
with moveable categories" (Kuhn 2000 [1995], 264), an idea
developed in detail by Hoyningen-Huene (1993). As for Feyerabend, he
set out such a 'Kant on wheels' approach - to use
Peter Lipton's apt expression (Lipton 2001) - at the
beginning of 'Explanation, Reduction and Empiricism'
(1962a). Feyerabend overtly adopted such a neo-Kantian metaphysical
perspective with changing categories in order to pursue the question:
If universal theories determine all of our experiences of the world,
how can experience be used to test such theories? Third, the main
example Feyerabend used to illustrate that and how incommensurable
theories can indeed be compared on the basis of a 'crucial
experiment' was Einstein's quantitative prediction, and
Perrin's subsequent confirmation, of Brownian motion, which
served as a crucial experiment between classical and statistical
thermodynamics - one of only three examples of incommensurable
scientific theories in Feyerabend (1962a) (cf. Oberheim 2006, 253ff.;
Sirtes and Oberheim 2006). Feyerabend argued that although Brownian
motion was already a well-known phenomenon, it became
*evidence* for statistical thermodynamics and against classical
thermodynamics *only after* the development of the kinetic
theory, which was needed to interpret it as such. Even though there
was a crucial experiment between these two universal theories, the
theories have no *common* measure as the observations of
Brownian motion that confirmed statistical thermodynamics were not
couched in a *neutral* observation language. The observations
only became evidence after they were interpreted according to
statistical theory. Einstein discussed exactly this episode at length
in his 'Autobiographical notes', where he used the term
'incommensurable' to apply to difficulties in judging the
merits of universal physical theories. Fourth, later Feyerabend often
defended his view that there is no *fixed* scientific method
(e.g. 1975, 10-11) by citing Einstein: "The external
conditions which are set for [the scientist] by the facts of
experience do not permit him to let himself be too much restricted, in
the construction of his conceptual world, by the adherence to an
epistemological system. He therefore must appear to the systematic
epistemologist as a type of unscrupulous opportunist"
(Einstein1949b, 683ff.). Although Feyerabend's development of
the idea of incommensurability of scientific theories was received by
the philosophic and scientific communities as propagating radical,
irrationalist ideas about science, he was actually trying to develop
something he found in Einstein. In the preface to the German version
of *Against Method*, Feyerabend wrote, "I want to
emphasize yet again that the views in this book are not new -
for physicist like Mach, Boltzmann, Einstein and Bohr they were a
triviality. But the ideas of these great thinkers have been distorted
[by positivist philosophers] beyond recognition" (1983, 12, our
translation).


#### 3.2.4 The mental and the material



Feyerabend, like Kuhn, explicitly drew from Wolfgang
Kohler's work in Gestalt psychology in the development of
his notion of incommensurability. Moreover, Kohler had already
applied the notion of incommensurability to scientific theories (see
Section 2.2.2). Kohler's use applies to different areas
within natural science, not to successive scientific theories such as
in early Kuhn (1962). Kohler's use of the term
'incommensurable' to describe the relationship between the
concepts of psychology and physics was a main source of
Feyerabend's development of the idea of the incommensurability
(Oberheim 2005). Feyerabend's discussion of incommensurability
in the formulation of the mind-body problem derives directly from
Kohler's claims (Oberheim 2005). However,
Feyerabend's (Wittgensteinian) strategy for overcoming the
incommensurability in the dissolution of philosophical conundrums is
not Kohler's (Oberheim 2006, 43-45). Feyerabend
suggested that the insolubility is due to the unwillingness of
philosophers of different persuasions to change the deeply entrenched
meanings of their terms, and that in this case, the mental should be
reinterpreted so that it is compatible with materialism (Feyerabend
1963b).


### 3.3 Feyerabend's later notion of incommensurability



While Feyerabend's notion of the incommensurability did not
significantly change throughout his early writings in the philosophy
of science, in his later more general philosophy, Feyerabend extended
the application of the term beyond universal scientific theories. For
example, he used it to characterize the transition from the Greek
archaic, aggregate worldview of Homer to the substance world-view of
the Pre-Socratics (1975, 261-269), and thereafter in a very broad
sense, discussing incommensurable frameworks of thought and action
(1975, 271), incommensurability in the domain of perceptions (1975,
225, 271), incommensurable discoveries and attitudes (1975, 269) and
incommensurable paradigms (1981b [1970], 131-161), where such
incommensurability involves the suspension of some of the universal
principles of the received view. Feyerabend characterized this wider
notion of incommensurability as a historical, anthropological thesis
(1975, 271), but also applied it to different stages of the
development of thought and perception in the individual (1975, 274).
He also further developed his notion of incommensurability, claiming
that it involves major conceptual changes of both 'overt'
and 'covert classifications' (in Whorff's sense), so
that incommensurability is difficult to explicitly define, and can
only be shown (1975, 224-225). Still later, Feyerabend argued
that 'potentially every culture is all cultures',
apparently retracting a wider, cultural notion of incommensurability
(Feyerabend 1994).


## 4. A comparison of Kuhn and Feyerabend on incommensurability



Initially, Feyerabend had a more concrete characterization of the
nature and origins of incommensurability than Kuhn. On
Feyerabend's view, because the nature of objects depends on the
most advanced theories about them, and because the meaning of
observation statements depends on the nature of those objects, the
interpretation of an observation language is determined by the
theories we use to explain what we observe. Kuhn, by contrast, was
initially much less sure about the exact meaning of his notion of
incommensurability, especially regarding world change, which he saw as
the most fundamental aspect of incommensurability. Kuhn frankly
confessed to have been at a loss: "In a sense that I am unable
to explicate further, the proponents of competing paradigms practice
their trades in different worlds" (1962, 150). He suggested that
"we must learn to make sense of statements that at least
resemble these" (1962, 121), and then spent a great deal of
effort attempting to do so.



Furthermore, Feyerabend's concept of incommensurability of
scientific theories was much more restricted than Kuhn's. For
Kuhn, incommensurability had three *prima facie* heterogeneous
domains, holistically bound: a change of problems and standards, a
change of concepts used to state and solve them, and a change of
world-view in which they arise. Feyerabend's focus, on the other
hand, was initially exclusively on concepts occurring in universal or
fundamental theories, together with their ontological implications.
Ironically, however, in developments after 1962, both authors move in
opposite directions. Kuhn gradually eliminated everything from his
notion of incommensurability that does not concern scientific
concepts, and ended more or less where Feyerabend began (see Carrier
2001; Chen 1997; Hoyningen-Huene 1990, 487-488; Hoyningen-Huene 1993,
212-218; Hoyningen-Huene 2004, Sankey 1993; Sankey 1994, 16-30; Sankey
1997). Feyerabend, by contrast, increasingly emphasized aspects of
perceptual change (1975, 225-229, 273-274; 1978, 68; 1988,
172-176), and also changes to the set of legitimate problems a
discipline should handle (1975, 274-275), and his later
philosophy emphasizes one of Kuhn's original points; the role of
non-binding, epistemic values in theory choice (cf. Farrell 2003).



With respect to the range of theories that are subject to
incommensurability, Feyerabend's concept is again much more
restricted than Kuhn's. For Feyerabend, only *universal*,
*fundamental*, *non-instantial* theories that are
*interpreted realistically* can be incommensurable (Feyerabend
1962, 44; 1965b, 216; 1975, 114, 271, 284; 1975, 221-222; 1987,
272). Feyerabend was interested in fundamental, universal theories
that apply to everything, because he believed that only "such
comprehensive structures of thought" have ontological
implications that are capable of sustaining entire worldviews
(Feyerabend 1962, 28; cf. Feyerabend 1954 and Oberheim 2006, 157ff.).
He restricted incommensurability to non-instantial theories, which he
distinguished from empirical generalizations, on the basis of the
differences in their test procedures. Generalizations of the form
'All *A*s are *B*s' (regardless of whether the
*A*s or *B*s are observable) are tested by inspecting
instances. So for example, Kepler's first law makes claims about
the planets, which can be tested directly by inspecting their motion.
In order to test non-instantial theories, such as Newton's
theory of gravitation, first empirical generalizations must be derived
from them with the help of auxiliary hypothesis, and only thereafter
can they be tested by inspection (Feyerabend 1962, 28). Due to these
restrictions (only universal, fundamental, non-instantial theories),
for Feyerabend, incommensurability of scientific theories occurs
comparatively rarely (1987, 272). Kuhn included a wider range of
theories as candidates for incommensurability. For him, even smaller
episodes, like unexpected discoveries, might be incommensurable with
the earlier tradition (cf. Hoyningen-Huene 1993, 197-201). This
difference in the range of incommensurability between Kuhn and
Feyerabend's versions finds its most striking expression in the
way they regard the transition from the Ptolemaic to the Copernican
theory. For Kuhn, the differences between these two theories comprise
an exemplary illustration of incommensurability. For Feyerabend,
however, because planetary theory lacks the quality of universality,
there is no incommensurability (1975, 114). Furthermore, in his later
writings Kuhn insisted that the version of incommensurability he
championed had always been "local incommensurability," a
notion that restricts conceptual change to a few, typically
interconnected concepts (cf. Hoyningen-Huene 1993, 213, 219). Thus,
there may be empirical consequences of incommensurable theory pairs
that can be immediately compared. For instance, the geocentric and
heliocentric planetary theories are incommensurable in Kuhn's
sense, while predictions of the planetary positions of both theories
are fully commensurable, and can be immediately compared regarding
their empirical accuracy. By contrast, Feyerabend always thought of
his concept more globally, as affecting *all* statements
derivable from two fundamental theories (1962, 93; 1965c, 117; 1965b,
216; 1975, 275-276; 1981a, xi). 



Both Kuhn and Feyerabend have often been misread as advancing the view
that incommensurability implies incomparability (cf. Hoyningen-Huene
1993, 218ff.; Oberheim 2006, 235). In response to this misreading,
Kuhn repeatedly emphasized that incommensurability does not imply
incomparability (cf. Hoyningen-Huene 1993, 236ff.). Theory comparison
is merely more complicated than imagined by some philosophers of
science. In particular, it cannot fully be made
'point-by-point'. It is not an algorithmic procedure (cf.
Hoyningen-Huene 1993, 147-154; Feyerabend 1975, 114; 1981a, 238), nor
one that requires translation into a neutral observation language.
Different epistemic values, such as universality, accuracy,
simplicity, fruitfulness may pull in different directions (cf.
Hoyningen-Huene 1992, 492-496; 1993, 150-154; Feyerabend
1981a, 16; 1981c, 238) allowing for the possibility of rational
disagreement. But even if a full point-by-point comparison of
incommensurable theories is impossible, and even if theory comparison
does not have the status of a proof, a comparative evaluation of
incommensurable theories is still possible (cf. Hoyningen-Huene 1993,
236-258; Carrier 2001) and rational in a means/ends or instrumental
sense. For example, according to Kuhn it is rational to choose
theories that are better problem-solvers because they better serve the
ends of science. This property of theory choice makes the overall
process of science both rational and progressive. With the notion of
incommensurability, Kuhn was not so much challenging the rationality
of theory choice, as trying to make room for the possibility of
rational disagreement between proponents of competing paradigms. In
fact, according to Kuhn, "incommensurability is far from being
the threat to rational evaluation of truth claims that it has
frequently seemed. Rather, it's what is needed, within a
developmental perspective, to restore some badly needed bite to the
whole notion of cognitive evaluation. It is needed, that is, to defend
notions like truth and knowledge from, for example, the excesses of
post-modernist movements like the strong program" (2000 [1991],
91).



The extent of the misreading of incommensurability as implying
incomparability is even more dramatic in Feyerabend's case. A
far cry from claiming that incommensurable theories cannot be
compared, Feyerabend explicitly and repeatedly argued that
incommensurable alternatives actually offer a *better* means of
comparing the merits of theories than the mere development of
commensurable alternatives (Feyerabend 1962, 66; cf. Oberheim 2006,
235ff.). He illustrated this point with an example of a *crucial
experiment* between incommensurable theories. He argued that even
though the central concepts of statistical and classical
phenomenological thermodynamics are incommensurable, it was still
possible indirectly to stage a crucial experiment between them
(Perrin's confirmation of Einstein's quantitative
predictions of Brownian motion). This was the centre piece of
Feyerabend's argument for pluralism. The argument turns on the
claim that this refutation of classical phenomenological
thermodynamics could not have been conducted without the development
of statistical thermodynamics, which is an incommensurable
alternative. Feyerabend concluded that some observations can
*only* be interpreted as refutations of an existing theory
after an incommensurable alternative has been developed with which to
interpret them (cf. Oberheim 2006, 240-245). His unorthodox
image of scientific progress is delineated as an increase in a set of
incommensurable alternatives, each forcing the others into greater
articulation (Feyerabend 1965c, 107; 1975, 30; cf. Oberheim 2005;
Oberheim 2006, 260ff.).



The source of the misunderstanding concerning incomparability appears
to be Feyerabend's onetime suggestion that
"incommensurable theories may not possess any comparable
consequences" (1962, 94). However, here Feyerabend was arguing
that although the same experimental set-up might produce a numerical
result that can be used to *confirm* both of two
incommensurable theories (e.g. measuring the time of a freefalling
stone to test predictions by both Newtonian mechanics and Relativity
theory), in order to use the result to confirm a theory, it must be
interpreted by that theory. Given that the two incommensurable
theories will use *qualitatively* incompatible concepts to
interpret *quantitatively* identical results, they will
interpret the same quantitative sentences as different qualitative
statements. Feyerabend concluded directly thereafter: "Hence,
there may not exist any possibility of finding a
*characterization* of the observations which are supposed to
confirm two incommensurable theories" (1962, 94, italics
inserted). This does rule out the possibility of using a
*neutral* observation language to compare the empirical
consequences of two incommensurable theories. Yet Feyerabend did not
conclude that this inhibits their comparison, but rather that there is
no need for a *neutral* observation language in order to
compare them. Feyerabend also mentions other possibilities of
comparing incommensurable theories (Feyerabend 1965b, 217; 1970, 228;
1975, 284; 1978, 68; 1981a, 16). Some of these involve making
subjective judgments about how to weigh different values that may pull
in different directions (methodological incommensurability).



Finally, there is one central, substantive point of agreement between
Kuhn and Feyerabend. Both see incommensurability as precluding the
possibility of interpreting scientific development as an approximation
to truth (or as an "increase of verisimilitude")
(Feyerabend, 1965c, 107; 1970, 220, 222, 227-228; 1975, 30, 284;
1978, 68; Kuhn 1970, 206; 2000 [1991], 95; 2000 [1993], 243ff.; cf.
Oberheim 2006, 180ff.; Hoyningen-Huene 1993, 262-264). They reject
such characterizations of scientific progress because they recognize
and emphasize that scientific revolutions result in changes in
ontology. Such changes are not just refinements of, or additions to,
the older ontology, such that these developments could be seen as
cumulative additions to already established theoretical views. Rather,
the new ontology *replaces* its predecessor. Consequently,
neither Kuhn nor Feyerabend can correctly be characterized as
scientific realists who believe that science makes progress toward the
truth.